Mercurial > hg > truffle
changeset 16390:ae8f4016792a
HSAIL: added support for several missing java.lang.Math routines
Contributed-by: Tom Deneau <tom.deneau@amd.com>
Contributed-by: Gustav Trede <gustav.trede@gmail.com>
line wrap: on
line diff
--- a/graal/com.oracle.graal.asm.hsail/src/com/oracle/graal/asm/hsail/HSAILAssembler.java Wed Jul 02 13:40:10 2014 -0700 +++ b/graal/com.oracle.graal.asm.hsail/src/com/oracle/graal/asm/hsail/HSAILAssembler.java Wed Jul 02 23:40:19 2014 +0200 @@ -98,12 +98,7 @@ } private void emitAddrOp(String instr, Value reg, HSAILAddress addr) { - String storeValue = null; - if (reg instanceof RegisterValue) { - storeValue = HSAIL.mapRegister(reg); - } else if (reg instanceof Constant) { - storeValue = ((Constant) reg).toValueString(); - } + String storeValue = mapRegOrConstToString(reg); emitString(instr + " " + storeValue + ", " + mapAddress(addr) + ";"); } @@ -163,11 +158,11 @@ } public final void emitStoreImmediate(float src, HSAILAddress addr) { - storeImmediateImpl("f32", Float.toString(src), addr); + storeImmediateImpl("f32", floatToString(src), addr); } public final void emitStoreImmediate(double src, HSAILAddress addr) { - storeImmediateImpl("f64", Double.toString(src), addr); + storeImmediateImpl("f64", doubleToString(src), addr); } public final void emitSpillLoad(Kind kind, Value dest, Value src) { @@ -302,7 +297,12 @@ } public void emitConvert(Value dest, Value src, String destType, String srcType) { - String prefix = (destType.equals("f32") && srcType.equals("f64")) ? "cvt_near_" : "cvt_"; + String prefix = "cvt_"; + if (destType.equals("f32") && srcType.equals("f64")) { + prefix = "cvt_near_"; + } else if (srcType.startsWith("f") && (destType.startsWith("s") || destType.startsWith("u"))) { + prefix = "cvt_zeroi_sat_"; + } emitString(prefix + destType + "_" + srcType + " " + HSAIL.mapRegister(dest) + ", " + HSAIL.mapRegister(src) + ";"); } @@ -327,6 +327,26 @@ return "[$d" + addr.getBase().encoding() + " + " + addr.getDisplacement() + "]"; } + private static String doubleToString(double dval) { + long lval = Double.doubleToRawLongBits(dval); + long lvalIgnoreSign = lval & 0x7fffffffffffffffL; + if (lvalIgnoreSign >= 0x7ff0000000000000L) { + return "0D" + String.format("%16x", lval); + } else { + return Double.toString(dval); + } + } + + private static String floatToString(float fval) { + int ival = Float.floatToRawIntBits(fval); + int ivalIgnoreSign = ival & 0x7fffffff; + if (ivalIgnoreSign >= 0x7f800000) { + return "0F" + String.format("%8x", ival); + } else { + return Float.toString(fval) + "f"; + } + } + private static String mapRegOrConstToString(Value src) { if (!isConstant(src)) { return HSAIL.mapRegister(src); @@ -337,9 +357,9 @@ case Int: return Integer.toString(consrc.asInt()); case Float: - return Float.toString(consrc.asFloat()) + "f"; + return floatToString(consrc.asFloat()); case Double: - return Double.toString(consrc.asDouble()); + return doubleToString(consrc.asDouble()); case Long: return "0x" + Long.toHexString(consrc.asLong()); case Object:
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleAcosTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#acos(double)}. + */ +public class DoubleAcosTest extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.acos(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleAsinTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#asin(double)}. + */ +public class DoubleAsinTest extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.asin(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleAtan2Test.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,51 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#atan2(double, double)}. + */ +public class DoubleAtan2Test extends DoubleTwoInputMathBase { + + // for atan2 ULPs can be off by 2 ulps. + @Override + protected int ulpsDelta() { + return 2; + } + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size * size, (gid) -> { + bigOutArray[gid] = Math.atan2(inArray1[gid], inArray2[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleAtanTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#atan(double)}. + */ +public class DoubleAtanTest extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.atan(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleCbrtTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,52 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#cbrt(double)}. + */ +public class DoubleCbrtTest extends DoubleMathBase { + + /** + * Dispatches the HSAIL kernel for this test case. + */ + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.cbrt(inArray[gid]); + }); + } + + /** + * Tests the HSAIL code generated for this unit test by comparing the result of executing this + * code with the result of executing a sequential Java version of this unit test. + */ + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleCosTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#cos(double)}. + */ +public class DoubleCosTest extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.cos(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleCoshTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#cosh(double)}. + */ +public class DoubleCoshTest extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.cosh(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleExpTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#exp(double)}. + */ +public class DoubleExpTest extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.exp(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleExpm1Test.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#expm1(double)}. + */ +public class DoubleExpm1Test extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.expm1(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleGetExponentTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,47 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#getExponent(double)}. + */ +public class DoubleGetExponentTest extends DoubleMathLargeBase { + + @Result int[] outIntArray = new int[size]; + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outIntArray[gid] = Math.getExponent(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleHypotTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#hypot(double, double)}. + */ +public class DoubleHypotTest extends DoubleTwoInputMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size * size, (gid) -> { + bigOutArray[gid] = Math.hypot(inArray1[gid], inArray2[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleIeeeRemainderTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,53 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#IEEEremainder(double, double)}. + */ +public class DoubleIeeeRemainderTest extends DoubleTwoInputMathBase { + + @Override + public void runTest() { + setupArrays(); + // for debugging + inArray1[0] = inArray1[258]; + inArray2[0] = inArray2[258]; + + dispatchLambdaKernel(size * size, (gid) -> { + bigOutArray[gid] = Math.IEEEremainder(inArray1[gid], inArray2[gid]); + }); + + for (int i = 0; i < 300; i++) { + System.out.println(i + "| " + inArray1[i] + ", " + inArray2[i] + " -> " + bigOutArray[i]); + } + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleLog10Test.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#log10(double)}. + */ +public class DoubleLog10Test extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.log10(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleLogTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#log(double)}. + */ +public class DoubleLogTest extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.log(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleMathBase.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,57 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +public abstract class DoubleMathBase extends MathTestBase { + + static final int size = 256; + @Result double[] outArray = new double[size]; + double[] inArray = new double[size]; + + @Override + String getInputString(int idx) { + return Double.toString(inArray[idx]); + } + + double largestValue() { + return Math.PI; + } + + /** + * Initializes the input and output arrays + */ + void setupArrays() { + for (int i = 0; i < size / 2; i++) { + // Include positive and negative values as well as corner cases. + double val = (largestValue() / (size / 2)) * i; + inArray[i] = val; + inArray[i + size / 2] = -val; + } + // special values filled at end + inArray[size - 1] = Double.NaN; + inArray[size - 2] = Double.NEGATIVE_INFINITY; + inArray[size - 3] = Double.POSITIVE_INFINITY; + } + +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleMathLargeBase.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,41 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +public abstract class DoubleMathLargeBase extends DoubleMathBase { + + @Override + void setupArrays() { + for (int i = 0; i < size / 2; i++) { + // Include positive and negative values as well as corner cases. + double val = (i == 0 ? 0 : Math.pow(1.99, i)); + inArray[i] = val; + inArray[i + size / 2] = -val; + } + // special values filled at end + inArray[size - 1] = Double.NaN; + inArray[size - 2] = Double.NEGATIVE_INFINITY; + inArray[size - 3] = Double.POSITIVE_INFINITY; + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleNextAfterTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,46 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#nextAfter(double, double)}. + */ +public class DoubleNextAfterTest extends DoubleMathLargeBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + double direction = (gid & 1) == 0 ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY; + outArray[gid] = Math.nextAfter(inArray[gid], direction); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleNextUpTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#nextUp(double)}. + */ +public class DoubleNextUpTest extends DoubleMathLargeBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.nextUp(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoublePowTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#pow(double, double)}. + */ +public class DoublePowTest extends DoubleTwoInputMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size * size, (gid) -> { + bigOutArray[gid] = Math.pow(inArray1[gid], inArray2[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleRoundTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,49 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#round(double)}. + */ +public class DoubleRoundTest extends DoubleMathLargeBase { + + @Result long[] outLongArray = new long[size]; + + @Override + public void runTest() { + setupArrays(); + // for testing + inArray[0] = inArray[66]; + dispatchLambdaKernel(size, (gid) -> { + outLongArray[gid] = Math.round(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleScalbTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#scalb(double, int)}. + */ +public class DoubleScalbTest extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.scalb(inArray[gid], 64 - (gid % 128)); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleSignumTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#signum(double)}. + */ +public class DoubleSignumTest extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.signum(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleSinTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#sin(double)}. + */ +public class DoubleSinTest extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.sin(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleSinhTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#sinh(double)}. + */ +public class DoubleSinhTest extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.sinh(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleTanTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#tan(double)}. + */ +public class DoubleTanTest extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.tan(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleTanhTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#tanh(double)}. + */ +public class DoubleTanhTest extends DoubleMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.tanh(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleToLongTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,49 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#round(double)}. + */ +public class DoubleToLongTest extends DoubleMathLargeBase { + + @Result long[] outLongArray = new long[size]; + + @Override + public void runTest() { + setupArrays(); + // for testing + // inArray[0] = inArray[66]; + dispatchLambdaKernel(size, (gid) -> { + outLongArray[gid] = (long) inArray[gid]; + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleTwoInputMathBase.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,54 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +public abstract class DoubleTwoInputMathBase extends DoubleMathBase { + + double[] inArray1 = new double[size * size]; + double[] inArray2 = new double[size * size]; + @Result double[] bigOutArray = new double[size * size]; + + @Override + String getInputString(int idx) { + return "(" + inArray1[idx] + ", " + inArray2[idx] + ")"; + } + + /** + * Initializes the input and output arrays + */ + @Override + void setupArrays() { + super.setupArrays(); + // make combinations of the input array + for (int i = 0; i < size; i++) { + for (int j = 0; j < size; j++) { + int idx = i * size + j; + inArray1[idx] = inArray[i]; + inArray2[idx] = inArray[j]; + bigOutArray[idx] = 0; + } + } + } + +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DoubleUlpTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#ulp(double)}. + */ +public class DoubleUlpTest extends DoubleMathLargeBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.ulp(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/DremTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,49 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests the DREM bytecode instruction + */ +public class DremTest extends DoubleTwoInputMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size * size, (gid) -> { + double f1 = inArray1[gid]; + double f2 = inArray2[gid]; + bigOutArray[gid] = f1 % f2; + }); + } + + // ignoring until we implement support for DREM bytecode + @Ignore + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatAcosTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#acos(double)} with float arg. + */ +public class FloatAcosTest extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = (float) Math.acos(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatAsinTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#asin(double)} with float arg. + */ +public class FloatAsinTest extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = (float) Math.asin(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatAtan2Test.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,51 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#atan2(double, double)}. + */ +public class FloatAtan2Test extends FloatTwoInputMathBase { + + // for atan2 ULPs can be off by 2 ulps. + @Override + protected int ulpsDelta() { + return 2; + } + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size * size, (gid) -> { + bigOutArray[gid] = (float) Math.atan2(inArray1[gid], inArray2[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatAtanTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#atan(double)} with float arg. + */ +public class FloatAtanTest extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = (float) Math.atan(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatCbrtTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#cbrt(double)} with float arg. + */ +public class FloatCbrtTest extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = (float) Math.cbrt(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatCosTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#cos(double)} with float arg. + */ +public class FloatCosTest extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = (float) Math.cos(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatCoshTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#cosh(double)} with float arg. + */ +public class FloatCoshTest extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = (float) Math.cosh(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatExpTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#exp(double)} with float arg. + */ +public class FloatExpTest extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = (float) Math.exp(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatExpm1Test.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#expm1(double)} with float arg. + */ +public class FloatExpm1Test extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = (float) Math.expm1(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatGetExponentTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,47 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#getExponent(double)} with float arg. + */ +public class FloatGetExponentTest extends FloatMathLargeBase { + + @Result int[] outIntArray = new int[size]; + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outIntArray[gid] = Math.getExponent(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatIeeeRemainderTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#IEEEremainder(double, double)}. + */ +public class FloatIeeeRemainderTest extends FloatTwoInputMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size * size, (gid) -> { + bigOutArray[gid] = (float) Math.IEEEremainder(inArray1[gid], inArray2[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatLog10Test.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#log10(double)} with float arg. + */ +public class FloatLog10Test extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = (float) Math.log10(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatLogTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#log(double)} with float arg. + */ +public class FloatLogTest extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = (float) Math.log(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatMathBase.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,55 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +public abstract class FloatMathBase extends MathTestBase { + + static final int size = 256; + @Result float[] outArray = new float[size]; + float[] inArray = new float[size]; + + @Override + String getInputString(int idx) { + return Float.toString(inArray[idx]); + } + + /** + * Initializes the input and output arrays + */ + void setupArrays() { + for (int i = 0; i < size / 2; i++) { + // Include positive and negative values as well as corner cases. + float val = (float) (i * Math.PI / (size / 2)); + inArray[i] = val; + inArray[i + size / 2] = -val; + outArray[i] = 999.0f; + outArray[i + size / 2] = 999.0f; + } + // special values filled at end + inArray[size - 1] = Float.NaN; + inArray[size - 2] = Float.NEGATIVE_INFINITY; + inArray[size - 3] = Float.POSITIVE_INFINITY; + } + +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatMathLargeBase.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,41 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +public abstract class FloatMathLargeBase extends FloatMathBase { + + @Override + void setupArrays() { + for (int i = 0; i < size / 2; i++) { + // Include positive and negative values as well as corner cases. + float val = (float) (i == 0 ? 0 : Math.pow(1.99, (i % 100))); + inArray[i] = val; + inArray[i + size / 2] = -val; + } + // special values filled at end + inArray[size - 1] = Float.NaN; + inArray[size - 2] = Float.NEGATIVE_INFINITY; + inArray[size - 3] = Float.POSITIVE_INFINITY; + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatNextAfterTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,46 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#nextAfter(float, double)}. + */ +public class FloatNextAfterTest extends FloatMathLargeBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + float direction = (gid & 1) == 0 ? Float.POSITIVE_INFINITY : Float.NEGATIVE_INFINITY; + outArray[gid] = Math.nextAfter(inArray[gid], direction); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatNextUpTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#nextUp(float)} with float arg. + */ +public class FloatNextUpTest extends FloatMathLargeBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.nextUp(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatPowTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#pow(double, double)}. + */ +public class FloatPowTest extends FloatTwoInputMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size * size, (gid) -> { + bigOutArray[gid] = (float) Math.pow(inArray1[gid], inArray2[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatRoundTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,47 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#round(float)}. + */ +public class FloatRoundTest extends FloatMathLargeBase { + + @Result int[] outIntArray = new int[size]; + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outIntArray[gid] = Math.round(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatScalbTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#scalb(float, int)}. + */ +public class FloatScalbTest extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.scalb(inArray[gid], 64 - (gid % 128)); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatSignumTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#signum(float)}. + */ +public class FloatSignumTest extends FloatMathLargeBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.signum(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatSinTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#sin(double)} with float arg. + */ +public class FloatSinTest extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = (float) Math.sin(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatSinhTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#sinh(double)} with float arg. + */ +public class FloatSinhTest extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = (float) Math.sinh(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatTanTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#tan(double)} with float arg. + */ +public class FloatTanTest extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = (float) Math.tan(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatTanhTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#tanh(double)} with float arg. + */ +public class FloatTanhTest extends FloatMathBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = (float) Math.tanh(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatTwoInputMathBase.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,54 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +public abstract class FloatTwoInputMathBase extends FloatMathBase { + + float[] inArray1 = new float[size * size]; + float[] inArray2 = new float[size * size]; + @Result float[] bigOutArray = new float[size * size]; + + @Override + String getInputString(int idx) { + return "(" + inArray1[idx] + ", " + inArray2[idx] + ")"; + } + + /** + * Initializes the input and output arrays + */ + @Override + void setupArrays() { + super.setupArrays(); + // make combinations of the input array + for (int i = 0; i < size; i++) { + for (int j = 0; j < size; j++) { + int idx = i * size + j; + inArray1[idx] = inArray[i]; + inArray2[idx] = inArray[j]; + bigOutArray[idx] = 0; + } + } + } + +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/FloatUlpTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,45 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +/** + * Tests call to {@link Math#ulp(float)}. + */ +public class FloatUlpTest extends FloatMathLargeBase { + + @Override + public void runTest() { + setupArrays(); + dispatchLambdaKernel(size, (gid) -> { + outArray[gid] = Math.ulp(inArray[gid]); + }); + } + + @Test + public void testUsingLambdaMethod() { + testGeneratedHsailUsingLambdaMethod(); + } +}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.compiler.hsail.test/src/com/oracle/graal/compiler/hsail/test/lambda/MathTestBase.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,95 @@ +/* + * Copyright (c) 2009, 2013, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.compiler.hsail.test.lambda; + +import org.junit.*; + +import com.oracle.graal.debug.*; +import com.oracle.graal.debug.Debug.Scope; + +import com.oracle.graal.compiler.hsail.test.infra.*; + +/** + * Tests call to Math.tan(double) + */ +public abstract class MathTestBase extends GraalKernelTester { + + abstract String getInputString(int idx); + + // standard ulps requirement for these tests is one ULP + @Override + protected int ulpsDelta() { + return 1; + } + + // if logging of DeepEquals is set, override assertDeepEquals to just log all input and output + // with ulps errors if any + @Override + protected void assertDeepEquals(String message, Object expected, Object actual, int ulpsDelta) { + try (Scope s = Debug.scope("DeepEquals")) { + if (Debug.isLogEnabled()) { + if (expected != null && actual != null) { + Class<?> expectedClass = expected.getClass(); + Class<?> actualClass = actual.getClass(); + Assert.assertEquals(message, expectedClass, actualClass); + if (expectedClass.isArray()) { + if (expected instanceof double[]) { + double[] ae = (double[]) expected; + double[] aa = (double[]) actual; + for (int i = 0; i < ae.length; i++) { + double de = ae[i]; + double da = aa[i]; + String ulpsStr = ""; + if (!Double.isNaN(de) && Double.isFinite(de)) { + double absdiff = Math.abs(de - da); + double absdiffUlps = absdiff / Math.ulp(de); + ulpsStr = ", absDiffUlps=" + absdiffUlps; + } + Debug.log(i + "| input=" + getInputString(i) + ", expected=" + de + ", actual=" + da + ulpsStr); + } + return; + } else if (expected instanceof float[]) { + float[] ae = (float[]) expected; + float[] aa = (float[]) actual; + for (int i = 0; i < ae.length; i++) { + float fe = ae[i]; + float fa = aa[i]; + String ulpsStr = ""; + if (!Float.isNaN(fe) && Float.isFinite(fe)) { + float absdiff = Math.abs(fe - fa); + float absdiffUlps = absdiff / Math.ulp(fe); + ulpsStr = ", absDiffUlps=" + absdiffUlps; + } + Debug.log(i + "| input=" + getInputString(i) + ", expected=" + fe + ", actual=" + fa + ulpsStr); + } + return; + } + } + } + } + } + super.assertDeepEquals(message, expected, actual, ulpsDelta); + } + +}
--- a/graal/com.oracle.graal.compiler.hsail/src/com/oracle/graal/compiler/hsail/HSAILLIRGenerator.java Wed Jul 02 13:40:10 2014 -0700 +++ b/graal/com.oracle.graal.compiler.hsail/src/com/oracle/graal/compiler/hsail/HSAILLIRGenerator.java Wed Jul 02 23:40:19 2014 +0200 @@ -212,7 +212,14 @@ public void emitIntegerTestBranch(Value left, Value right, LabelRef trueDestination, LabelRef falseDestination, double trueDestinationProbability) { Variable result = emitAnd(left, right); Variable dummyResult = newVariable(left.getLIRKind()); - append(new CompareBranchOp(mapKindToCompareOp(left.getKind()), Condition.EQ, result, Constant.forInt(0), dummyResult, dummyResult, trueDestination, falseDestination, false)); + append(new CompareBranchOp(mapKindToCompareOp(result.getKind()), Condition.EQ, result, Constant.forInt(0), dummyResult, dummyResult, trueDestination, falseDestination, false)); + } + + @Override + public Variable emitIntegerTestMove(Value left, Value right, Value trueValue, Value falseValue) { + Variable result = emitAnd(left, right); + append(new CondMoveOp(mapKindToCompareOp(result.getKind()), result, Constant.forInt(0), result, Condition.EQ, load(trueValue), load(falseValue))); + return result; } @Override @@ -236,11 +243,6 @@ return result; } - @Override - public Variable emitIntegerTestMove(Value left, Value right, Value trueValue, Value falseValue) { - throw GraalInternalError.unimplemented(); - } - /** * Generates the LIR instruction for a negation operation. *
--- a/graal/com.oracle.graal.lir.hsail/src/com/oracle/graal/lir/hsail/HSAILControlFlow.java Wed Jul 02 13:40:10 2014 -0700 +++ b/graal/com.oracle.graal.lir.hsail/src/com/oracle/graal/lir/hsail/HSAILControlFlow.java Wed Jul 02 23:40:19 2014 +0200 @@ -301,7 +301,7 @@ @Use({REG, CONST}) protected Value right; protected final Condition condition; - public CondMoveOp(HSAILCompare opcode, Variable left, Variable right, Variable result, Condition condition, Value trueValue, Value falseValue) { + public CondMoveOp(HSAILCompare opcode, Variable left, Value right, Variable result, Condition condition, Value trueValue, Value falseValue) { this.opcode = opcode; this.result = result; this.left = left;
--- a/graal/com.oracle.graal.replacements.hsail/src/com/oracle/graal/replacements/hsail/HSAILMathSubstitutions.java Wed Jul 02 13:40:10 2014 -0700 +++ b/graal/com.oracle.graal.replacements.hsail/src/com/oracle/graal/replacements/hsail/HSAILMathSubstitutions.java Wed Jul 02 23:40:19 2014 +0200 @@ -34,7 +34,7 @@ /** * Substitution for {@link Math#abs(int)}. - * + * * @param x the input * @return the result of the computation */ @@ -45,7 +45,7 @@ /** * Substitution for {@link Math#abs(long)}. - * + * * @param x the input * @return the result of the computation */ @@ -56,7 +56,7 @@ /** * Substitution for {@link Math#abs(float)}. - * + * * @param x the input * @return the result of the computation */ @@ -67,7 +67,7 @@ /** * Substitution for {@link Math#abs(double)}. - * + * * @param x the input * @return the result of the computation */ @@ -78,7 +78,7 @@ /** * Substitution for Math.ceil(double). - * + * * @param x the input * @return the result of the computation */ @@ -89,7 +89,7 @@ /** * Substitution for {@link Math#floor(double)}. - * + * * @param x the input * @return the result of the computation */ @@ -100,7 +100,7 @@ /** * Substitution for {@link Math#rint(double)}. - * + * * @param x the input * @return the result of the computation */ @@ -111,7 +111,7 @@ /** * Substitution for {@link Math#sqrt(double)}. - * + * * @param x the input * @return the result of the computation */ @@ -119,4 +119,100 @@ public static double sqrt(double x) { return HSAILMathIntrinsicsNode.compute(x, HSAILArithmetic.SQRT); } + + /** + * Methods below this point are more complicated transcendentals and such and use + * {@link JStrictMath} for method substitution. + */ + + @MethodSubstitution + public static double sin(double x) { + return JStrictMath.sin(x); + } + + @MethodSubstitution + public static double cos(double x) { + return JStrictMath.cos(x); + } + + @MethodSubstitution + public static double tan(double x) { + return JStrictMath.tan(x); + } + + @MethodSubstitution + public static double exp(double x) { + return JStrictMath.exp(x); + } + + @MethodSubstitution + public static double expm1(double x) { + return JStrictMath.expm1(x); + } + + @MethodSubstitution + public static double log(double x) { + return JStrictMath.log(x); + } + + @MethodSubstitution + public static double log10(double x) { + return JStrictMath.log10(x); + } + + @MethodSubstitution + public static double cbrt(double x) { + return JStrictMath.cbrt(x); + } + + @MethodSubstitution + public static double asin(double x) { + return JStrictMath.asin(x); + } + + @MethodSubstitution + public static double acos(double x) { + return JStrictMath.acos(x); + } + + @MethodSubstitution + public static double atan(double x) { + return JStrictMath.atan(x); + } + + @MethodSubstitution + public static double atan2(double x, double y) { + return JStrictMath.atan2(x, y); + } + + @MethodSubstitution + public static double pow(double x, double y) { + return JStrictMath.pow(x, y); + } + + @MethodSubstitution + public static double IEEEremainder(double x, double y) { + return JStrictMath.IEEEremainder(x, y); + } + + @MethodSubstitution + public static double sinh(double x) { + return JStrictMath.sinh(x); + } + + @MethodSubstitution + public static double cosh(double x) { + return JStrictMath.cosh(x); + } + + @MethodSubstitution + public static double tanh(double x) { + return JStrictMath.tanh(x); + } + + @MethodSubstitution + public static double hypot(double x, double y) { + return JStrictMath.hypot(x, y); + } + }
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/graal/com.oracle.graal.replacements.hsail/src/com/oracle/graal/replacements/hsail/JStrictMath.java Wed Jul 02 23:40:19 2014 +0200 @@ -0,0 +1,3391 @@ +/* + * Copyright (c) 2014, Oracle and/or its affiliates. All rights reserved. + * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. + * + * This code is free software; you can redistribute it and/or modify it + * under the terms of the GNU General Public License version 2 only, as + * published by the Free Software Foundation. + * + * This code is distributed in the hope that it will be useful, but WITHOUT + * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or + * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License + * version 2 for more details (a copy is included in the LICENSE file that + * accompanied this code). + * + * You should have received a copy of the GNU General Public License version + * 2 along with this work; if not, write to the Free Software Foundation, + * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. + * + * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA + * or visit www.oracle.com if you need additional information or have any + * questions. + */ + +package com.oracle.graal.replacements.hsail; + +import java.util.Random; + +import com.oracle.graal.api.replacements.*; + +import sun.misc.FpUtils; +import sun.misc.DoubleConsts; + +/** + * This class contains methods for performing basic numeric operations such as the elementary + * exponential, logarithm, square root, and trigonometric functions. It is a Java port of the native + * methods in {@link StrictMath} and can thus be used by Graal backends to provide + * {@link MethodSubstitution}s for the native methods. + * + * <p> + * To help ensure portability of Java programs, the definitions of some of the numeric functions in + * this package require that they produce the same results as certain published algorithms. These + * algorithms are available from the well-known network library {@code netlib} as the package + * "Freely Distributable Math Library," <a href="ftp://ftp.netlib.org/fdlibm.tar">{@code fdlibm} + * </a>. These algorithms, which were originally written in the C programming language, are then to + * be understood as executed with all floating-point operations following the rules of Java + * floating-point arithmetic. + * + * <p> + * The Java math library is defined with respect to {@code fdlibm} version 5.3. Where {@code fdlibm} + * provides more than one definition for a function (such as {@code acos}), use the + * "IEEE 754 core function" version (residing in a file whose name begins with the letter {@code e} + * ). The methods which require {@code fdlibm} semantics are {@link #sin}, {@link #cos}, + * {@link #tan}, {@link #asin}, {@link #acos}, {@link #atan}, {@link #exp}, {@link #log}, + * {@link #log10}, {@link #cbrt}, {@link #atan2}, {@link #pow}, {@link #sinh}, {@link #cosh}, + * {@link #tanh}, {@link #hypot}, {@link #expm1}, and {@link #log1p}. + * + * @author Gustav Trede (port to Java) + */ +public final class JStrictMath { + + /** + * Don't let anyone instantiate this class. + */ + private JStrictMath() { + } + + /** + * The {@code double} value that is closer than any other to <i>e</i>, the base of the natural + * logarithms. + */ + public static final double E = 2.7182818284590452354; + /** + * The {@code double} value that is closer than any other to <i>pi</i>, the ratio of the + * circumference of a circle to its diameter. + */ + public static final double PI = 3.14159265358979323846; + + /** + * Returns the trigonometric sine of an angle. Special cases: + * <ul> + * <li>If the argument is NaN or an infinity, then the result is NaN. + * <li>If the argument is zero, then the result is a zero with the same sign as the argument. + * </ul> + * + * @param a an angle, in radians. + * @return the sine of the argument. + */ + @SuppressWarnings("javadoc") + public static double sin(double x) { + int hx = (int) (Double.doubleToRawLongBits(x) >> 32); + int ix = hx & 0x7fffffff; + if (ix >= 0x7ff00000) { + // x is inf or NaN + return Double.NaN; + } + return ix <= 0x3fe921fb ? __kernel_sin_(x, ix) : __ieee754_rem_pio2_(x, hx, sintype); + } + + /** + * Returns the trigonometric cosine of an angle. Special cases: + * <ul> + * <li>If the argument is NaN or an infinity, then the result is NaN. + * </ul> + * + * @param x an angle, in radians. + * @return the cosine of the argument. + */ + public static double cos(double x) { + int hx = (int) (Double.doubleToRawLongBits(x) >> 32); + int ix = hx & 0x7fffffff; + if (ix >= 0x7ff00000) { + // x is inf or NaN + return Double.NaN; + } + return ix <= 0x3fe921fb ? __kernel_cos_(x, 0, ix) : __ieee754_rem_pio2_(x, hx, costype); + } + + /** + * Returns the trigonometric tangent of an angle. Special cases: + * <ul> + * <li>If the argument is NaN or an infinity, then the result is NaN. + * <li>If the argument is zero, then the result is a zero with the same sign as the argument. + * </ul> + * + * @param x an angle, in radians. + * @return the tangent of the argument. + */ + public static double tan(double x) { + final int hx = (int) (Double.doubleToRawLongBits(x) >> 32); + int ix = hx & 0x7fffffff; + if (ix >= 0x7ff00000) { + // x is inf or NaN + return Double.NaN; + } + return ix <= 0x3fe921fb ? __kernel_tan(x, 0d, 1, hx) : __ieee754_rem_pio2_(x, hx, tantype); + } + + /** + * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * + * Algorithm 1. Since tan(-x) = -tan(x), we need only to consider positive x. 2. if x < 2^-28 + * (hx<0x3e300000 0), return x with inexact if x!=0. 3. tan(x) is approximated by a odd + * polynomial of degree 27 on [0,0.67434] 3 27 tan(x) ~ x + T1*x + ... + T13*x where + * + * |tan(x) 2 4 26 | -59.2 |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 | x | + * + * Note: tan(x+y) = tan(x) + tan'(x)*y ~ tan(x) + (1+x*x)*y Therefore, for better accuracy in + * computing tan(x+y), let 3 2 2 2 2 r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) then 3 2 + * tan(x+y) = x + (T1*x + (x *(r+y)+y)) + * + * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then tan(x) = tan(pi/4-y) = + * (1-tan(y))/(1+tan(y)) = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) + * + * @param xx is assumed to be bounded by ~pi/4 in magnitude. + * @param yy is the tail of x + * @param k indicates whether tan (if k=1) or -1/tan (if k= -1) is returned. + * @param hx high bits of x + * @return + */ + @SuppressWarnings("javadoc") + private static double __kernel_tan(double xx, double yy, int k, int hx) { + double w, r; + double x = xx; + double y = yy; + final int ix = hx & 0x7fffffff; + if (ix < 0x3e300000 && (int) x == 0) { // |x| < 2**-28 + if (k == 1) { + return x; + } + if ((ix | hx) == 0) { + return one / abs(x); // generate inexact + } + // compute -1 / (x+y) carefully + r = y; + w = x + y; + } else { + if (ix >= 0x3FE59428) { // |x|>=0.67434 + if (hx < 0) { + x = 0.0d - x; + y = 0.0d - y; + } + x = (pio4 - x) + (pio4lo - y); + y = 0.0; + } + final double z = x * x; + w = z * z; + + /* + * Break x^5*(T[1]+x^2*T[2]+...) into x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + + * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) + */ + + final double s = z * x; + double v = z * (T2 + w * (T4 + w * (T6 + w * (T8 + w * (T10 + w * T12))))); + r = (y + z * (s * ((T1 + w * (T3 + w * (T5 + w * (T7 + w * (T9 + w * T11))))) + v) + y)) + T0 * s; + w = x + r; + if (ix >= 0x3FE59428) { + v = k; + return (1 - ((hx >> 30) & 2)) * (v - 2.0d * (x - (((w * w) / (w + v)) - r))); + } + if (k == 1) { + return w; + } + // if allow error up to 2 ulp, simply return -1.0/(x+r) here + } + // compute -1.0/(x+r) accurately + final double a = negone / w; + final double t = clearLow32bits(a); + final double z = clearLow32bits(w); + return t + a * ((1.0d + t * z) + t * (r - (z - x))); + } + + private static final double S1 = -1.66666666666666324348e-01, S2 = 8.33333333332248946124e-03, /* + * 0x3F811111 + * , + * 0x1110F8A6 + */ + S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ + S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ + S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ + S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ + + /** + * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 Input x is assumed to be bounded by ~pi/4 + * in magnitude. Input y is the tail of x. Input iy indicates whether y is 0. (if iy=0, y assume + * to be 0). + * + * Algorithm 1. Since sin(-x) = -sin(x), we need only to consider positive x. 2. if x < 2^-27 + * (hx<0x3e400000 0), return x with inexact if x!=0. 3. sin(x) is approximated by a polynomial + * of degree 13 on [0,pi/4] 3 13 sin(x) ~ x + S1*x + ... + S6*x where + * + * |sin(x) 2 4 6 8 10 12 | -58 |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 | x | + * + * 4. sin(x+y) = sin(x) + sin'(x')*y ~ sin(x) + (1-x*x/2)*y For better accuracy, let 3 2 2 2 2 r + * = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) then 3 2 sin(x) = x + (S1*x + (x *(r-y/2)+y)) + * + * @param x + * @param y + * @return + */ + @SuppressWarnings("javadoc") + private static double __kernel_sin(double x, double y, int ix) { + if (ix < 0x3e400000 && (int) x == 0) { + return x; // |x| < 2**-27 generate inexact + } + final double z = x * x; + final double v = z * x; + final double r = v * (S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)))); + return x - ((z * (half * y - r) - y) - v * S1); + } + + private static double __kernel_sin_(double x, int ix) { + if (ix < 0x3e400000 && (int) x == 0) { + return x; // |x| < 2**-27 generate inexact + } + final double z = x * x; + return x + (z * x) * (S1 + z * (S2 + z * (S3 + z * (S4 + z * (S5 + z * S6))))); + } + + private static final double two = 2.0d, one = Double.longBitsToDouble(0x3ff0000000000000L), negone = -one, C1 = 4.16666666666666019037e-02, C2 = -1.38888888888741095749e-03, + C3 = 2.48015872894767294178e-05, C4 = -2.75573143513906633035e-07, C5 = 2.08757232129817482790e-09, C6 = -1.13596475577881948265e-11; + + /** + * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 Input x is assumed to be bounded by + * ~pi/4 in magnitude. Input y is the tail of x. + * + * Algorithm 1. Since cos(-x) = cos(x), we need only to consider positive x. 2. if x < 2^-27 + * (hx<0x3e400000 0), return 1 with inexact if x!=0. 3. cos(x) is approximated by a polynomial + * of degree 14 on [0,pi/4] 4 14 cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x where the remez error is + * + * | 2 4 6 8 10 12 14 | -58 |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 | | + * + * 4 6 8 10 12 14 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then cos(x) = 1 - x*x/2 + r + * since cos(x+y) ~ cos(x) - sin(x)*y ~ cos(x) - x*y, a correction term is necessary in cos(x) + * and hence cos(x+y) = 1 - (x*x/2 - (r - x*y)) For better accuracy when x > 0.3, let qx = |x|/4 + * with the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. Then cos(x+y) = (1-qx) + * - ((x*x/2-qx) - (r-x*y)). Note that 1-qx and (x*x/2-qx) is EXACT here, and the magnitude of + * the latter is at least a quarter of x*x/2, thus, reducing the rounding error in the + * subtraction. + * + * @param x + * @param y + * @param ix + * @return + */ + @SuppressWarnings("javadoc") + private static double __kernel_cos_(double x, double y, int ix) { + if (ix < 0x3e400000 && ((int) x) == 0) { + return one; // x < 2**27 generate inexact + } + final double z = x * x; + double r = z * (z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))))) - x * y; + if (ix < 0x3FD33333) { // |x| < 0.3 + return one - (0.5 * z - r); + } + final double qx = ix > 0x3fe90000 ? 0.28125 : // x > 0.78125 + Double.longBitsToDouble((long) (ix - 0x00200000) << 32); // x/4 + return (one - qx) - ((0.5 * z - qx) - r); + } + + private static final int sintype = 0; + private static final int costype = 1; + private static final int tantype = 3; + + /** + * Returns final values for tan , cos and sin. + * + * @param trigtype + * @param NN + * @param y0 + * @param y1 + * @author gustav trede + * @return + */ + @SuppressWarnings("javadoc") + private static double getTrigres(int trigtype, int NN, double y0, double y1) { + int N = NN; + int hx = ((int) (Double.doubleToRawLongBits(y0) >> 32)); + if (trigtype == tantype) { + return __kernel_tan(y0, y1, 1 - ((N & 1) << 1), hx); + } + hx &= 0x7fffffff; + N = (N & 3) - trigtype; + double v = (N == 0 || N == 2) ? __kernel_sin(y0, y1, hx) : __kernel_cos_(y0, y1, hx); + + if (N == 0 || N == 1) { + return trigtype == 0 ? v : 0.0d - v; + } + return trigtype == 0 ? 0.0d - v : v; + } + + private static final double pio4 = 7.85398163397448278999e-01, pio4lo = 3.06161699786838301793e-17, T0 = 3.33333333333334091986e-01, T1 = 1.33333333333201242699e-01, + T2 = 5.39682539762260521377e-02, T3 = 2.18694882948595424599e-02, T4 = 8.86323982359930005737e-03, T5 = 3.59207910759131235356e-03, T6 = 1.45620945432529025516e-03, + T7 = 5.88041240820264096874e-04, T8 = 2.46463134818469906812e-04, T9 = 7.81794442939557092300e-05, T10 = 7.14072491382608190305e-05, T11 = -1.85586374855275456654e-05, + T12 = 2.59073051863633712884e-05; + + /* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ + private static final int[] two_over_pi = {0xa2f983, 0x6e4e44, 0x1529fc, 0x2757d1, 0xf534dd, 0xc0db62, 0x95993c, 0x439041, 0xfe5163, 0xabdebb, 0xc561b7, 0x246e3a, 0x424dd2, 0xe00649, 0x2eea09, + 0xd1921c, 0xfe1deb, 0x1cb129, 0xa73ee8, 0x8235f5, 0x2ebb44, 0x84e99c, 0x7026b4, 0x5f7e41, 0x3991d6, 0x398353, 0x39f49c, 0x845f8b, 0xbdf928, 0x3b1ff8, 0x97ffde, 0x05980f, 0xef2f11, + 0x8b5a0a, 0x6d1f6d, 0x367ecf, 0x27cb09, 0xb74f46, 0x3f669e, 0x5fea2d, 0x7527ba, 0xc7ebe5, 0xf17b3d, 0x0739f7, 0x8a5292, 0xea6bfb, 0x5fb11f, 0x8d5d08, 0x560330, 0x46fc7b, 0x6babf0, + 0xcfbc20, 0x9af436, 0x1da9e3, 0x91615e, 0xe61b08, 0x659985, 0x5f14a0, 0x68408d, 0xffd880, 0x4d7327, 0x310606, 0x1556ca, 0x73a8c9, 0x60e27b, 0xc08c6b}; + + private static final int[] npio2_hw = {0x3ff921fb, 0x400921fb, 0x4012d97c, 0x401921fb, 0x401f6a7a, 0x4022d97c, 0x4025fdbb, 0x402921fb, 0x402c463a, 0x402f6a7a, 0x4031475c, 0x4032d97c, 0x40346b9c, + 0x4035fdbb, 0x40378fdb, 0x403921fb, 0x403ab41b, 0x403c463a, 0x403dd85a, 0x403f6a7a, 0x40407e4c, 0x4041475c, 0x4042106c, 0x4042d97c, 0x4043a28c, 0x40446b9c, 0x404534ac, 0x4045fdbb, + 0x4046c6cb, 0x40478fdb, 0x404858eb, 0x404921fb}; + + private static final double zero = 0.00000000000000000000e+00, half = 5.00000000000000000000e-01, + /* 1.67772160000000000000e+07 */ + two24 = Double.longBitsToDouble(0x4170000000000000L), + /* 6.36619772367581382433e-01 53 bits of 2/pi */ + invpio2 = Double.longBitsToDouble(0x3fe45f306dc9c883L), + /* 1.57079632673412561417e+00 first 33 bit of pi/2 */ + pio2_1 = Double.longBitsToDouble(0x3ff921fb54400000L), + /* 6.07710050650619224932e-11 pi/2 - pio2_1 */ + pio2_1t = Double.longBitsToDouble(0x3dd0b4611a626331L), + /* 6.07710050630396597660e-11 second 33 bit of pi/2 */ + pio2_2 = Double.longBitsToDouble(0x3dd0b4611a600000L), + /* 2.02226624879595063154e-21 pi/2 - (pio2_1+pio2_2) */ + pio2_2t = Double.longBitsToDouble(0x3ba3198a2e037073L), + /* 2.02226624871116645580e-21 third 33 bit of pi/2 */ + pio2_3 = Double.longBitsToDouble(0x3ba3198a2e000000L), + /* 8.47842766036889956997e-32 pi/2 - (pio2_1+pio2_2+pio2_3) */ + pio2_3t = Double.longBitsToDouble(0x397b839a252049c1L); + + private static double __ieee754_rem_pio2_(double xx, int hx, int trigtype) { + double x = xx; + int ix = hx & 0x7fffffff; + if (ix <= 0x413921fb) { // |x| ~<= 2^19*(pi/2) + double y0, y1; + int n; + if (ix < 0x4002d97c) { // |x| < 3pi/4, special case with n=+-1 + if (hx > 0) { + x -= pio2_1; + if (ix != 0x3ff921fb) { // 33+53 bit pi is good enough + y0 = x - pio2_1t; + y1 = (x - y0) - pio2_1t; + } else { // near pi/2, use 33+33+53 bit pi + x -= pio2_2; + y0 = x - pio2_2t; + y1 = (x - y0) - pio2_2t; + } + n = 1; + } else { // negative x + x += pio2_1; + if (ix != 0x3ff921fb) { // 33+53 bit pi is good enough + y0 = x + pio2_1t; + y1 = (x - y0) + pio2_1t; + } else { // near pi/2, use 33+33+53 bit pi + x += pio2_2; + y0 = x + pio2_2t; + y1 = (x - y0) + pio2_2t; + } + n = -1; + } + } else { + double t = abs(x); + n = (int) (t * invpio2 + half); + final double fn = n; + double w = fn * pio2_1t; // 1st round good to 85 bit + double r = t - fn * pio2_1; + y0 = r - w; + // quick check no cancellation + if (n >= 32 || ix == npio2_hw[n - 1]) { + int i = ix - (((int) (Double.doubleToRawLongBits(y0) >> 32)) & (0x7ff << 20)); + if (i > (16 << 20)) { // 2nd iteration needed, good to 118 + w = fn * pio2_2; + t = r; + r -= w; + w = fn * pio2_2t - ((t - r) - w); + y0 = r - w; + i = ix - (((int) (Double.doubleToRawLongBits(y0) >> 32)) & (0x7ff << 20)); + if (i > (49 << 20)) {// 3rd iteration need, 151 bits acc + w = fn * pio2_3; + t = r; + r -= w; + w = fn * pio2_3t - ((t - r) - w); + y0 = r - w; + } + } + } + y1 = (r - y0) - w; + if (hx < 0) { + y1 = 0.0d - y1; + y0 = 0.0d - y0; + n = -n; + } + } + return getTrigres(trigtype, n, y0, y1); + } + + return ix >= 0x7ff00000 ? x - x : // x is inf or NaN + __kernel_rem_pio2(x, hx, trigtype); + } + + private static final double[] PIo2 = {1.57079625129699707031e+00, 7.54978941586159635335e-08, 5.39030252995776476554e-15, 3.28200341580791294123e-22, 1.27065575308067607349e-29, + 1.22933308981111328932e-36, 2.73370053816464559624e-44, 2.16741683877804819444e-51}; + + private static final double twon24 = 5.96046447753906250000e-08; + + /** + * Used for tlocal storage to save __kernel_rem_pio2 from major mem allocs. + * + * @author gustav trede + */ + private static class Rempiostruct { + final double[] f = new double[20]; + final double[] q = new double[20]; + final double[] fq = new double[20]; + final double[] x = new double[3]; + final int[] iq = new int[20]; + } + + /******* + * private static final ThreadLocal<Rempiostruct> rempstruct = new ThreadLocal<Rempiostruct>() { + * + * @Override protected Rempiostruct initialValue() { return new Rempiostruct(); } }; + *******/ + + private static class RempStructAcccessor { + Rempiostruct get() { + return new Rempiostruct(); + } + } + + static RempStructAcccessor rempstruct; + + /** + * + * __kernel_rem_pio2 return the last three digits of N with y = x - N*pi/2 so that |y| < pi/2. + * + * The method is to compute the integer (mod 8) and fraction parts of (2/pi)*x without doing the + * full multiplication. In general we skip the part of the product that are known to be a huge + * integer (more accurately, = 0 mod 8 ). Thus the number of operations are independent of the + * exponent of the input. + * + * (2/pi) is represented by an array of 24-bit integers in two_over_pi[]. + * + * Input parameters: x[] The input value (must be positive) is broken into nx pieces of 24-bit + * integers in double precision format. x[i] will be the i-th 24 bit of x. The scaled exponent + * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 match x's up to 24 bits. + * + * Example of breaking a double positive z into x[0]+x[1]+x[2]: e0 = ilogb(z)-23 z = + * scalbn(z,-e0) for i = 0,1,2 x[i] = floor(z) z = (z-x[i])*2**24 + * + * + * y[] ouput result in an array of double precision numbers. The dimension of y[] is: 24-bit + * precision 1 53-bit precision 2 64-bit precision 2 113-bit precision 3 The actual value is the + * sum of them. Thus for 113-bit precison, one may have to do something like: + * + * long double t,w,r_head, r_tail; t = (long double)y[2] + (long double)y[1]; w = (long + * double)y[0]; r_head = t+w; r_tail = w - (r_head - t); + * + * e0 The exponent of x[0] + * + * nx dimension of x[] + * + * prec an integer indicating the precision: 0 24 bits (single) 1 53 bits (double) 2 64 bits + * (extended) 3 113 bits (quad) + * + * two_over_pi[] integer array, contains the (24*i)-th to (24*i+23)-th bit of 2/pi after binary + * point. The corresponding floating value is + * + * two_over_pi[i] * 2^(-24(i+1)). + * + * External function: double scalbn(), floor(); + * + * + * Here is the description of some local variables: + * + * jk jk+1 is the initial number of terms of two_over_pi[] needed in the computation. The + * recommended value is 2,3,4, 6 for single, double, extended,and quad. + * + * jz local integer variable indicating the number of terms of two_over_pi[] used. + * + * jx nx - 1 + * + * jv index for pointing to the suitable two_over_pi[] for the computation. In general, we want + * ( 2^e0*x[0] * two_over_pi[jv-1]*2^(-24jv) )/8 is an integer. Thus e0-3-24*jv >= 0 or + * (e0-3)/24 >= jv Hence jv = max(0,(e0-3)/24). + * + * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. + * + * q[] double array with integral value, representing the 24-bits chunk of the product of x and + * 2/pi. + * + * q0 the corresponding exponent of q[0]. Note that the exponent for q[i] would be q0-24*i. + * + * PIo2[] double precision array, obtained by cutting pi/2 into 24 bits chunks. + * + * f[] two_over_pi[] in floating point + * + * iq[] integer array by breaking up q[] in 24-bits chunk. + * + * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] + * + * ih integer. If >0 it indicates q[] is >= 0.5, hence it also indicates the *sign* of the + * result. + * + * @param xv + * @param hx + * @param trig trigtype + * @return + */ + @SuppressWarnings("javadoc") + private static double __kernel_rem_pio2(double xv, int hx, final int trig) { + Rempiostruct rmp = rempstruct.get(); + double[] x = rmp.x; + double[] f = rmp.f; + double[] q = rmp.q; + double[] fq = rmp.fq; + int[] iq = rmp.iq; + + /* set z = scalbn(|x|,ilogb(x)-23) */ + long lx = Double.doubleToRawLongBits(xv); + long exp = ((lx & 0x7ff0000000000000L) >> 52) - 1046; + lx = (lx - (exp << 52)) & 0x7fffffffffffffffL; + double zz = Double.longBitsToDouble(lx); + for (int i = 0; i < 2; i++) { + x[i] = (int) zz; + zz = (zz - x[i]) * two24; + } + x[2] = zz; + int nx = 3; + while (x[nx - 1] == zero) { /* skip zero term */ + nx--; + } + double z, fw; + int ih, n; + int jk = 4; + int jp = jk; + /* determine jx,jv,q0, note that 3>q0 */ + int jx = nx - 1; + int e0 = (int) exp; + int jv = (e0 - 3) / 24; + if (jv < 0) { + jv = 0; + } + int q0 = e0 - (24 * (jv + 1)); + /* set up f[0] to f[jx+jk] where f[jx+jk] = two_over_pi[jv+jk] */ + int j = jv - jx; + int m = jx + jk; + for (int i = 0; i <= m; i++, j++) { + f[i] = ((j < 0) ? zero : two_over_pi[j]); + } + + /* compute q[0],q[1],...q[jk] */ + for (int i = 0; i <= jk; i++) { + for (j = 0, fw = 0.0; j <= jx; j++) { + fw += (x[j] * f[(jx + i) - j]); + } + q[i] = fw; + } + int jz = jk; + while (true) { // recompute: + /* distill q[] into iq[] reversingly */ + j = jz; + z = q[jz]; + for (int i = 0; j > 0; i++, j--) { + fw = ((int) (twon24 * z)); + iq[i] = (int) (z - (two24 * fw)); + z = q[j - 1] + fw; + } + /* compute n */ + z = scalb(z, q0); /* actual value of z */ + z -= (8.0 * floor(z * 0.125)); /* trim off integer >= 8 */ + n = (int) z; + z -= n; + ih = 0; + if (q0 > 0) { /* need iq[jz-1] to determine n */ + int i = (iq[jz - 1] >> (24 - q0)); + n += i; + iq[jz - 1] -= (i << (24 - q0)); + ih = iq[jz - 1] >> (23 - q0); + } else if (q0 == 0) { + ih = iq[jz - 1] >> 23; + } else if (z >= 0.5) { + ih = 2; + } + if (ih > 0) { /* q > 0.5 */ + n += 1; + int carry = 0; + for (int i = 0; i < jz; i++) { /* compute 1-q */ + j = iq[i]; + if (carry == 0) { + if (j != 0) { + carry = 1; + iq[i] = 0x1000000 - j; + } + } else { + iq[i] = 0xffffff - j; + } + } + /* rare case: chance is 1 in 12 */ + if (q0 == 1) { + iq[jz - 1] &= 0x7fffff; + } else if (q0 == 2) { + iq[jz - 1] &= 0x3fffff; + } + if (ih == 2) { + z = one - z; + if (carry != 0) { + z -= scalb(one, q0); + } + } + } + /* check if recomputation is needed */ + if (z == zero) { + j = 0; + for (int i = jz - 1; i >= jk; i--) { + j |= iq[i]; + } + if (j == 0) { /* need recomputation */ + int k = 1; + for (; iq[jk - k] == 0; k++) { + }/* k = no. of terms needed */ + for (int i = jz + 1; i <= (jz + k); i++) { + // add q[jz+1] to q[jz+k] + f[jx + i] = two_over_pi[jv + i]; + for (j = 0, fw = 0.0; j <= jx; j++) { + fw += (x[j] * f[(jx + i) - j]); + } + q[i] = fw; + } + jz += k; + continue; + } + } + break; + } + /* chop off zero terms */ + if (z == 0.0d) { + jz--; + q0 -= 24; + while (iq[jz] == 0) { + jz--; + q0 -= 24; + } + } else { /* break z into 24-bit if necessary */ + z = scalb(z, -q0); + if (z >= two24) { + fw = (int) (twon24 * z); + iq[jz] = (int) (z - (two24 * fw)); + jz++; + q0 += 24; + iq[jz] = (int) fw; + } else { + iq[jz] = (int) z; + } + } + /* convert integer "bit" chunk to floating-point value */ + fw = scalb(one, q0); + for (int i = jz; i >= 0; i--) { + q[i] = fw * iq[i]; + fw *= twon24; + } + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for (int i = jz; i >= 0; i--) { + int k = 0; + for (fw = 0.0; (k <= jp) && (k <= (jz - i)); k++) { + fw += PIo2[k] * q[i + k]; + } + fq[jz - i] = fw; + } + /* compress fq[] into y[] */ + fw = 0.0d; + for (int i = jz; i >= 0; i--) { + fw += fq[i]; + } + double y0 = (ih == 0) ? fw : (0.0d - fw); + fw = fq[0] - fw; + for (int i = 1; i <= jz; i++) { + fw += fq[i]; + } + double y1 = ((ih == 0) ? fw : (0.0d - fw)); + n &= 7; + if (hx < 0) { + y0 = 0.0d - y0; + y1 = 0.0d - y1; + n = -n; + } + return getTrigres(trig, n, y0, y1); + } + + private static final double pio2_hi = 1.57079632679489655800e+00; + private static final double pio2_lo = 6.12323399573676603587e-17; + private static final double pio4_hi = 7.85398163397448278999e-01; + private static final double PIret = PI + 2.0 * pio2_lo; + + /* coefficient for R(x^2) */ + private static final double pS0 = 1.66666666666666657415e-01; + private static final double pS1 = -3.25565818622400915405e-01; + private static final double pS2 = 2.01212532134862925881e-01; + private static final double pS3 = -4.00555345006794114027e-02; + private static final double pS4 = 7.91534994289814532176e-04; + private static final double pS5 = 3.47933107596021167570e-05; + private static final double qS1 = -2.40339491173441421878e+00; + private static final double qS2 = 2.02094576023350569471e+00; + private static final double qS3 = -6.88283971605453293030e-01; + private static final double qS4 = 7.70381505559019352791e-02; + + /** + * Returns the arc sine of a value; the returned angle is in the range -<i>pi</i>/2 through + * <i>pi</i>/2. Special cases: + * <ul> + * <li>If the argument is NaN or its absolute value is greater than 1, then the result is NaN. + * <li>If the argument is zero, then the result is a zero with the same sign as the argument. + * </ul> + * + * @param a the value whose arc sine is to be returned. + * @return the arc sine of the argument. + */ + public static double asin(double a) { + /* + * asin(x) Method : Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... we approximate + * asin(x) on [0,0.5] by asin(x) = x + x*x^2*R(x^2) where R(x^2) is a rational approximation + * of (asin(x)-x)/x^3 and its remez error is bounded by |(asin(x)-x)/x^3 - R(x^2)| < + * 2^(-58.75) + * + * For x in [0.5,1] asin(x) = pi/2-2*asin(sqrt((1-x)/2)) Let y = (1-x), z = y/2, s := + * sqrt(z),and pio2_hi+pio2_lo=pi/2; then for x>0.98 asin(x) = pi/2 - 2*(s+s*z*R(z)) = + * pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) For x<=0.98, let pio4_hi = pio2_hi/2, then f = hi + * part of s; c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) and asin(x) = pi/2 - + * 2*(s+s*z*R(z)) = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) = + * pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: if x is NaN, return x itself; if |x|>1, return NaN with invalid signal. + */ + int hx = __HI(a); + int ix = hx & 0x7fffffff; + if (ix >= 0x3ff00000) { /* |x|>= 1 */ + return ((ix - 0x3ff00000) | __LO(a)) == 0 ? a * pio2_hi + a * pio2_lo : // asin(1)=+-pi/2 + // with inexact + (a - a) / (a - a); // asin(|x|>1) is NaN + } + if (ix < 0x3fe00000) { /* |x|<0.5 */ + if (ix < 0x3e400000) { /* if |x| < 2**-27 */ + if (huge + a > one) + return a; /* return x with inexact if x!=0 */ + } else + return a + (a * getPdivQ(a * a)); + } + // 1> |x|>= 0.5 + double t = (one - abs(a)) * 0.5; + double pdivq = getPdivQ(t); + double s = java.lang.Math.sqrt(t); + if (ix >= 0x3FEF3333) { /* if |x| > 0.975 */ + t = pio2_hi - (2.0 * (s + s * pdivq) - pio2_lo); + } else { + double w = clearLow32bits(s); + double p = 2.0d * s * pdivq - (pio2_lo - 2.0d * ((t - (w * w)) / (s + w))); + t = pio4_hi - (p - (pio4_hi - 2.0d * w)); + } + return hx > 0 ? t : -t; + } + + /** + * Returns the arc cosine of a value; the returned angle is in the range 0.0 through <i>pi</i>. + * Special case: + * <ul> + * <li>If the argument is NaN or its absolute value is greater than 1, then the result is NaN. + * </ul> + * + * @param a the value whose arc cosine is to be returned. + * @return the arc cosine of the argument. + */ + public static double acos(double a) { + /* + * Method : acos(x) = pi/2 - asin(x) acos(-x) = pi/2 + asin(x) For |x|<=0.5 acos(x) = pi/2 - + * (x + x*x^2*R(x^2)) (see asin.c) For x>0.5 acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) + * = 2asin(sqrt((1-x)/2)) = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) = 2f + (2c + 2s*z*R(z)) + * where f=hi part of s, and c= (z-f*f)/(s+f) is the correction term for f so that f+c ~ + * sqrt(z). For x<-0.5 acos(x) = pi - 2asin(sqrt((1-|x|)/2)) = pi - 0.5*(s+s*z*R(z)), where + * z=(1-|x|)/2,s=sqrt(z) + * + * Special cases: if x is NaN, return x itself; if |x|>1, return NaN with invalid signal. + */ + + final int hx = __HI(a); + final int ix = hx & 0x7fffffff; + if (ix >= 0x3ff00000) { // |x| >= 1 + if (((ix - 0x3ff00000) | __LO(a)) == 0) { // |x|==1 + return a > 0 ? 0.0 : PIret; + } + return (a - a) / (a - a); // acos(|x|>1) is NaN + } + + if (ix < 0x3fe00000) { // |x| < 0.5 + return ix <= 0x3c600000 ? pio2_hi + pio2_lo : // |x|<2**-57 + pio2_hi - (a - (pio2_lo - a * getPdivQ(a * a))); + } + + final double z = 0.5 * ((hx < 0) ? (one + a) : (one - a)); + final double s = java.lang.Math.sqrt(z); + final double pdivq = s * getPdivQ(z); + + if (hx < 0) { // x < -0.5 + return PI - 2.0 * (s + (pdivq - pio2_lo)); + } + // x > 0.5 + final double df = clearLow32bits(s); + return 2.0 * (df + (pdivq + (z - df * df) / (s + df))); + } + + private static double getPdivQ(double z) { + return (z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))))) / (one + z * (qS1 + z * (qS2 + (z * (qS3 + (z * qS4)))))); + } + + private static final double atanhi[] = {4.63647609000806093515e-01, // atan(0.5)hi + 7.85398163397448278999e-01, // atan(1.0)hi + 9.82793723247329054082e-01, // atan(1.5)hi + 1.57079632679489655800e+00};// atan(inf)hi + + private static final double atanlo[] = {2.26987774529616870924e-17, // atan(0.5)lo + 3.06161699786838301793e-17, // atan(1.0)lo + 1.39033110312309984516e-17, // atan(1.5)lo + 6.12323399573676603587e-17};// atan(inf)lo) + + private static final double ln2_hi = 6.93147180369123816490e-01, ln2_lo = 1.90821492927058770002e-10, Lg1 = 6.666666666666735130e-01, Lg2 = 3.999999999940941908e-01, + Lg3 = 2.857142874366239149e-01, Lg4 = 2.222219843214978396e-01, Lg5 = 1.818357216161805012e-01, Lg6 = 1.531383769920937332e-01, Lg7 = 1.479819860511658591e-01, + two54 = 1.80143985094819840000e+16, aT0 = 3.33333333333329318027e-01, aT1 = -1.99999999998764832476e-01, aT2 = 1.42857142725034663711e-01, aT3 = -1.11111104054623557880e-01, + aT4 = 9.09088713343650656196e-02, aT5 = -7.69187620504482999495e-02, aT6 = 6.66107313738753120669e-02, aT7 = -5.83357013379057348645e-02, aT8 = 4.97687799461593236017e-02, + aT9 = -3.65315727442169155270e-02, aT10 = 1.62858201153657823623e-02, atanhi3PLUSatanlo3 = atanhi[3] + atanlo[3], negatanhi3MINUSatanlo3 = -atanhi[3] - atanlo[3], + pi_o_4 = 7.8539816339744827900e-01, pi_o_2 = 1.5707963267948965580e+00, pi_lo = 1.2246467991473531772e-16, huge = 1.0e+300, tiny = 1.0e-300; + + /** + * Returns the arc tangent of a value; the returned angle is in the range -<i>pi</i>/2 through + * <i>pi</i>/2. Special cases: + * <ul> + * <li>If the argument is NaN, then the result is NaN. + * <li>If the argument is zero, then the result is a zero with the same sign as the argument. + * </ul> + * + * @param aa the value whose arc tangent is to be returned. + * @return the arc tangent of the argument. + */ + public static double atan(double aa) { + /* + * Method 1. Reduce x to positive by atan(x) = -atan(-x). 2. According to the integer + * k=4t+0.25 chopped, t=x, the argument is further reduced to one of the following intervals + * and the arctangent of t is evaluated by the corresponding formula: + * + * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) [7/16,11/16] atan(x) = + * atan(1/2) + atan( (t-0.5)/(1+t/2) ) [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) + * ) [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) [39/16,INF] atan(x) = + * atan(INF) + atan( -1/t ) + */ + + double a = aa; + int hx = __HI(a); + int ix = hx & 0x7fffffff; + if (ix >= 0x44100000) { /* if |x| >= 2^66 */ + if ((ix > 0x7ff00000) || (ix == 0x7ff00000 && __LO(a) != 0)) { + return a + a; /* NaN */ + } + return hx > 0 ? atanhi3PLUSatanlo3 : negatanhi3MINUSatanlo3; + } + int id; + if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ + if (ix < 0x3e200000 && /* |x| < 2^-29 */ + (huge + a > one)) { + return a; /* raise inexact */ + } + id = -1; + } else { + a = abs(a); + if (ix < 0x3ff30000) { /* |x| < 1.1875 */ + if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ + id = 0; + a = (2.0d * a - one) / (2.0d + a); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; + a = (a - one) / (a + one); + } + } else { + if (ix < 0x40038000) { /* |x| < 2.4375 */ + id = 2; + a = (a - 1.5d) / (one + 1.5d * a); + } else { /* 2.4375 <= |x| < 2^66 */ + id = 3; + a = negone / a; + } + } + } + + /* end of argument reduction */ + double z = a * a; + double w = z * z; + + /* break sum from i=0 to 10 aTi z**(i+1) into odd and even poly */ + double ss = a * (z * (aT0 + w * (aT2 + w * (aT4 + w * (aT6 + w * (aT8 + w * aT10))))) + w * (aT1 + w * (aT3 + w * (aT5 + w * (aT7 + w * aT9))))); + if (id < 0) { + return a - ss; + } + z = atanhi[id] - ((ss - atanlo[id]) - a); + return hx < 0 ? 0.0d - z : z; + } + + /** + * Converts an angle measured in degrees to an approximately equivalent angle measured in + * radians. The conversion from degrees to radians is generally inexact. + * + * @param angdeg an angle, in degrees + * @return the measurement of the angle {@code angdeg} in radians. + */ + public static strictfp double toRadians(double angdeg) { + return angdeg / 180.0 * PI; + } + + /** + * Converts an angle measured in radians to an approximately equivalent angle measured in + * degrees. The conversion from radians to degrees is generally inexact; users should <i>not</i> + * expect {@code cos(toRadians(90.0))} to exactly equal {@code 0.0}. + * + * @param angrad an angle, in radians + * @return the measurement of the angle {@code angrad} in degrees. + */ + public static strictfp double toDegrees(double angrad) { + return angrad * 180.0 / PI; + } + + private static final double ivln10 = 4.34294481903251816668e-01, log10_2hi = 3.01029995663611771306e-01, log10_2lo = 3.69423907715893078616e-13, halF[] = {0.5, -0.5}, + twom1000 = 9.33263618503218878990e-302,// 2**-1000=0x01700000,0 + o_threshold = 7.09782712893383973096e+02, u_threshold = -7.45133219101941108420e+02, ln2HI[] = {6.93147180369123816490e-01, -6.93147180369123816490e-01,}, ln2LO[] = { + 1.90821492927058770002e-10, -1.90821492927058770002e-10,}, invln2 = 1.44269504088896338700e+00, ln2HI0 = ln2HI[0], ln2LO0 = ln2LO[0]; + + /** + * Returns Euler's number <i>e</i> raised to the power of a {@code double} value. Special cases: + * <ul> + * <li>If the argument is NaN, the result is NaN. + * <li>If the argument is positive infinity, then the result is positive infinity. + * <li>If the argument is negative infinity, then the result is positive zero. + * </ul> + * + * @param aa the exponent to raise <i>e</i> to. + * @return the value <i>e</i><sup>{@code a}</sup>, where <i>e</i> is the base of the natural + * logarithms. + */ + public static double exp(double aa) { + /* + * exp(x) Returns the exponential of x. + * + * Method 1. Argument reduction: Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. Given x, + * find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2. + * + * Here r will be represented as r = hi-lo for better accuracy. + * + * 2. Approximation of exp(r) by a special rational function on the interval [0,0.34658]: + * Write R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... We use a special + * Reme algorithm on [0,0.34658] to generate a polynomial of degree 5 to approximate R. The + * maximum error of this polynomial approximation is bounded by 2**-59. In other words, R(z) + * ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 (where z=r*r, and the values of P1 + * to P5 are listed below) and | 5 | -59 | 2.0+P1*z+...+P5*z - R(z) | <= 2 | | The + * computation of exp(r) thus becomes 2*r exp(r) = 1 + ------- R - r r*R1(r) = 1 + r + + * ----------- (for better accuracy) 2 - R1(r) where 2 4 10 R1(r) = r - (P1*r + P2*r + ... + + * P5*r ). + * + * 3. Scale back to obtain exp(x): From step 1, we have exp(x) = 2^k * exp(r) + * + * Special cases: exp(INF) is INF, exp(NaN) is NaN; exp(-INF) is 0, and for finite argument, + * only exp(0)=1 is exact. + * + * Accuracy: according to an error analysis, the error is always less than 1 ulp (unit in + * the last place). + * + * Misc. info. For IEEE double if x > 7.09782712893383973096e+02 then exp(x) overflow if x < + * -7.45133219101941108420e+02 then exp(x) underflow + */ + double a = aa; + int hx = __HI(a); /* high word of x */ + final int xsb = (hx >>> 31) & 1; /* sign bit of x */ + final boolean xsb0 = xsb == 0; + hx &= 0x7fffffff; /* high word of |x| */ + // preliminary check for Nan or Infinity + if (hx >= 0x7ff00000) { + // aa is inf or NaN + if (xsb0) { // aa == Double.NaN || aa == Double.POSITIVE_INFINITY) + return aa; + } else { + // negative infinity? + return 0.0; + } + } + + /* filter out non-finite argument */ + if (hx >= 0x40862E42) { /* if |x|>=709.78... */ + if (hx >= 0x7ff00000) { + if (((hx & 0xfffff) | __LO(a)) != 0) { + return a + a; /* NaN */ + } + return xsb0 ? a : 0.0d; /* exp(+-inf)={inf,0} */ + } + if (a > o_threshold) { + return huge * huge; /* overflow */ + } + if (a < u_threshold) { + return twom1000 * twom1000; /* underflow */ + } + } + + double hi = 0; + double lo = 0; + int k = 0; + /* argument reduction */ + if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + hi = a - ln2HI[xsb]; + lo = ln2LO[xsb]; + k = 1 - xsb - xsb; + } else { + k = (int) (invln2 * a + halF[xsb]); + double t = k; + hi = a - t * ln2HI0; /* t*ln2HI is exact here */ + lo = t * ln2LO0; + } + a = hi - lo; + } else if (hx < 0x3e300000) { /* when |x|<2**-28 */ + if (huge + a > one) { + return one + a; /* trigger inexact */ + } + } + + /* x is now in primary range */ + final double t = a * a; + final double c = a - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5)))); + if (k == 0) { + return one - (((a * c) / (c - 2.0)) - a); + } + final long ybits = Double.doubleToRawLongBits(one - ((lo - ((a * c) / (2.0 - c))) - hi)); + return (k >= -1021) ? addToHighBits(ybits, k << 20) : addToHighBits(ybits, (k + 1000) << 20) * twom1000; + } + + /** + * Returns the natural logarithm (base <i>e</i>) of a {@code double} value. Special cases: + * <ul> + * <li>If the argument is NaN or less than zero, then the result is NaN. + * <li>If the argument is positive infinity, then the result is positive infinity. + * <li>If the argument is positive zero or negative zero, then the result is negative infinity. + * </ul> + * + * @param xx a value + * @return the value ln {@code a}, the natural logarithm of {@code a}. + */ + public static double log(double xx) { + /* + * __ieee754_log(x) Return the logrithm of x + * + * Method : 1. Argument Reduction: find k and f such that x = 2^k * (1+f), where sqrt(2)/2 < + * 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) = + * 2s + 2/3 s**3 + 2/5 s**5 + ....., = 2s + s*R We use a special Reme algorithm on + * [0,0.1716] to generate a polynomial of degree 14 to approximate R The maximum error of + * this polynomial approximation is bounded by 2**-58.45. In other words, 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s (the values of Lg1 to Lg7 are + * listed in the program) and | 2 14 | -58.45 | Lg1*s +...+Lg7*s - R(z) | <= 2 | | Note that + * 2s = f - s*f = f -hfsq + s*hfsq, where hfsq = f*f/2. In order to guarantee error in log + * below 1ulp, we compute log by log(1+f) = f - s*(f - R) (if f is not too large) log(1+f) = + * f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) =k*ln2 + log(1+f). =k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) Here ln2 + * is split into two floating point number: ln2_hi + ln2_lo, where n*ln2_hi is always exact + * for |n| < 2000. + * + * Special cases: log(x) is NaN with signal if x < 0 (including -INF) ; log(+INF) is +INF; + * log(0) is -INF with signal; log(NaN) is that NaN with no signal. + * + * Accuracy: according to an error analysis, the error is always less than 1 ulp (unit in + * the last place). + */ + double x = xx; + int hx = (int) (Double.doubleToRawLongBits(x) >> 32); + int k = 0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx & 0x7fffffff) | (__LO(x) & 0xFFFFFFFF)) == 0) { + return Double.NEGATIVE_INFINITY; // -two54 / zero; /* log(+-0)=-inf */ + } + if (hx < 0) { + return Double.NaN; // (x - x) / zero; /* log(-#) = NaN */ + } + k = -54; + x *= two54; /* subnormal number, scale up x */ + hx = __HI(x); /* high word of x */ + } + if (hx >= 0x7ff00000) { + return x + x; + } + k += (hx >> 20) - 1023; + hx &= 0x000fffff; + final int i = (hx + 0x95f64) & 0x100000; + k += i >> 20; + /* normalize x or x/2 */ + final double dkln2hi = k * ln2_hi; + final double dkln2lo = k * ln2_lo; + final boolean KisZero = k == 0; + final double f = setHigh32bits(x, hx | (i ^ 0x3ff00000)) - 1.0; + if ((0x000fffff & (2 + hx)) < 3) { /* |f| < 2**-20 */ + if (f == zero) { + return KisZero ? zero : dkln2hi + dkln2lo; + } + double R = f * f * (0.5 - (0.33333333333333333 * f)); + return KisZero ? f - R : dkln2hi - ((R - dkln2lo) - f); + } + double s = f / (2.0 + f); + final double z = s * s; + final double w = z * z; + final double R = w * (Lg2 + w * (Lg4 + w * Lg6)) + z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7))); + if (((hx - 0x6147a) | (0x6b851 - hx)) > 0) { + double hfsq = 0.5 * f * f; + s *= hfsq + R; + return KisZero ? f - (hfsq - s) : dkln2hi - ((hfsq - (s + dkln2lo)) - f); + } + s *= f - R; + return KisZero ? f - s : dkln2hi - ((s - dkln2lo) - f); + } + + /** + * Returns the base 10 logarithm of a {@code double} value. Special cases: + * + * <ul> + * <li>If the argument is NaN or less than zero, then the result is NaN. + * <li>If the argument is positive infinity, then the result is positive infinity. + * <li>If the argument is positive zero or negative zero, then the result is negative infinity. + * <li>If the argument is equal to 10<sup><i>n</i></sup> for integer <i>n</i>, then the result + * is <i>n</i>. + * </ul> + * + * @param aa a value + * @return the base 10 logarithm of {@code a}. + * @since 1.5 + */ + public static double log10(double aa) { + /* + * __ieee754_log10(x) Return the base 10 logarithm of x + * + * Method : Let log10_2hi = leading 40 bits of log10(2) and log10_2lo = log10(2) - + * log10_2hi, ivln10 = 1/log(10) rounded. Then n = ilogb(x), if(n<0) n = n+1; x = + * scalbn(x,-n); log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) + * + * Note 1: To guarantee log10(10**n)=n, where 10**n is normal, the rounding mode must set to + * Round-to-Nearest. Note 2: [1/log(10)] rounded to 53 bits has error .198 ulps; log10 is + * monotonic at all binary break points. + * + * Special cases: log10(x) is NaN with signal if x < 0; log10(+INF) is +INF with no signal; + * log10(0) is -INF with signal; log10(NaN) is that NaN with no signal; log10(10**N) = N for + * N=0,1,...,22. + */ + double a = aa; + int hx = (int) (Double.doubleToRawLongBits(a) >> 32); + int k = 0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + // unsigned low bits + if (((hx & 0x7fffffff) | (__LO(a) & 0xFFFFFFFF)) == 0) { + return Double.NEGATIVE_INFINITY; // -two54 / zero; /* log(+-0)=-inf */ + } + if (hx < 0) { + return Double.NaN; // (x - x) / zero; /* log(-#) = NaN */ + } + k = -54; + a *= two54; /* subnormal number, scale up x */ + hx = __HI(a); /* high word of x */ + } + if (hx >= 0x7ff00000) { + return a + a; + } + k += (hx >> 20) - 1023; + // i = ((unsigned)k&0x80000000)>>31; + final int i = (k & 0x80000000) >>> 31; + hx = (hx & 0x000fffff) | ((0x3ff - i) << 20); + final double y = k + i; + return (y * log10_2lo + ivln10 * log(setHigh32bits(a, hx))) + y * log10_2hi; + } + + /** + * Returns the correctly rounded positive square root of a {@code double} value. Special cases: + * <ul> + * <li>If the argument is NaN or less than zero, then the result is NaN. + * <li>If the argument is positive infinity, then the result is positive infinity. + * <li>If the argument is positive zero or negative zero, then the result is the same as the + * argument. + * </ul> + * Otherwise, the result is the {@code double} value closest to the true mathematical square + * root of the argument value. + * + * @param a a value. + * @return the positive square root of {@code a}. + */ + public static native double sqrt(double a); + + private static final int B1 = 715094163;// B1 = (682-0.03306235651)*2**20 + private static final long B2highbits = 696219795L << 32;// (664-0.03306235651)*2**20 << 32 + + private static final double C_ = 5.42857142857142815906e-01, // 19/35 = 0x3FE15F15, 0xF15F15F1 + D_ = -7.05306122448979611050e-01,// -864/1225= 0xBFE691DE, 0x2532C834 + E_ = 1.41428571428571436819e+00, // 99/70 = 0x3FF6A0EA, 0x0EA0EA0F + F_ = 1.60714285714285720630e+00, // 45/28 = 0x3FF9B6DB, 0x6DB6DB6E + G_ = 3.57142857142857150787e-01, // 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 + TWOpow54 = Double.longBitsToDouble(0x43500000L << 32); + + /** + * Returns the cube root of a {@code double} value. For positive finite {@code x}, + * {@code cbrt(-x) == + * -cbrt(x)}; that is, the cube root of a negative value is the negative of the cube root of + * that value's magnitude. Special cases: + * + * <ul> + * + * <li>If the argument is NaN, then the result is NaN. + * + * <li>If the argument is infinite, then the result is an infinity with the same sign as the + * argument. + * + * <li>If the argument is zero, then the result is a zero with the same sign as the argument. + * + * </ul> + * + * @param xx x value. + * @return the cube root of {@code xx}. + * @since 1.5 + */ + public static double cbrt(double xx) { + double x = xx; + long xb = Double.doubleToRawLongBits(x); + long hx = xb >> 32; // todo check if faster to not store sign + final long sign = hx & 0x80000000;// unsigned in c /* sign= sign(x) */ + hx ^= sign; + if (hx >= 0x7ff00000L) { + return x + x; /* cbrt(NaN,INF) is itself */ + } + if ((hx | (xb & 0x00000000FFFFFFFFL)) == 0) { + return x; /* cbrt(0) is itself */ + } + + x = setHigh32bits(xb, hx); /* x <- |x| */ + /* rough cbrt to 5 bits */ + if (hx < 0x00100000L) { /* subnormal number */ + // HI(t)=0x43500000; /* set t= 2**54 */ + // t*=x; __HI(t)=__HI(t)/3+B2; + long tb = Double.doubleToRawLongBits(TWOpow54 * x); + hx = (tb & 0x00000000FFFFFFFFL) | (tb / 3 + B2highbits); + } else { + hx = (hx / 3 + B1) << 32; + } + double t = Double.longBitsToDouble(hx); + + /* new cbrt to 23 bits, may be implemented in single precision */ + final double s = C_ + (t * t / x) * t; + t *= G_ + F_ / (s + E_ + D_ / s); + + /* chopped to 20 bits and make it larger than cbrt(x) */ + // __LO(t)=0; __HI(t)+=0x00000001; + t = Double.longBitsToDouble(((Double.doubleToRawLongBits(t) >> 32) + 0x00000001) << 32); + // one step newton iteration to 53 bits with error less than 0.667 ulps + final double r = x / (t * t); /* t*t is exact */ + t += t * ((r - t) / ((t + t) + r)); /* r-s is exact */ + /* retore the sign bit */ + return Double.longBitsToDouble(Double.doubleToRawLongBits(t) | (sign << 32)); + } + + /** + * Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard. The + * remainder value is mathematically equal to <code>f1 - f2</code> + * × <i>n</i>, where <i>n</i> is the mathematical integer closest to the exact + * mathematical value of the quotient {@code f1/f2}, and if two mathematical integers are + * equally close to {@code f1/f2}, then <i>n</i> is the integer that is even. If the remainder + * is zero, its sign is the same as the sign of the first argument. Special cases: + * <ul> + * <li>If either argument is NaN, or the first argument is infinite, or the second argument is + * positive zero or negative zero, then the result is NaN. + * <li>If the first argument is finite and the second argument is infinite, then the result is + * the same as the first argument. + * </ul> + * + * @param f1in the dividend. + * @param f2in the divisor. + * @return the remainder when {@code f1} is divided by {@code f2}. + */ + public static double IEEEremainder(double f1in, double f2in) { + /* + * __ieee754_remainder(x,p) Return : returns x REM p = x - [x/p]*p as if in infinite precise + * arithmetic, where [x/p] is the (infinite bit) integer nearest x/p (in half way case + * choose the even one). Method : Based on fmod() return x-[x/p]chopped*p exactlp. + */ + double f1 = f1in; + double f2 = f2in; + // todo need to verify that this implementation works. + long t = Double.doubleToRawLongBits(f1); + int hx = (int) (t >> 32); + final long sx = (long) (hx & 0x80000000) << 32; // unsigned in c + hx &= 0x7fffffff; + + int lx = (int) t; // unsigned in c + t = Double.doubleToRawLongBits(f2); + int hp = (int) (t >> 32) & 0x7fffffff; + int lp = (int) t; // unsigned in c + + /* purge off exception values */ + if (((hp | lp) == 0) || /* p = 0 */ + (hx >= 0x7ff00000) || /* x not finite */ + ((hp >= 0x7ff00000) && /* p is NaN */ + (((hp - 0x7ff00000) | lp) != 0))) { + return (f1 * f2) / (f1 * f2); + } + + if (hp <= 0x7fdfffff) { + // f1 = __ieee754_fmod(f1,f2+f2); /* now x < 2p */ + // f1 = f1 % (f2 + f2); /* now x < 2p */ + // until we get the DREM bytecode working, call fmod here + f1 = fmod(f1, f2 + f2); /* now x < 2p */ + } + + if (((hx - hp) | (lx - lp)) == 0) { + return zero * f1; + } + + f1 = abs(f1); + f2 = abs(f2); + if (hp < 0x00200000) { + if ((f1 + f1) > f2) { + f1 -= f2; + if ((f1 + f1) >= f2) { + f1 -= f2; + } + } + } else { + final double p_half = 0.5 * f2; + if (f1 > p_half) { + f1 -= f2; + if (f1 >= p_half) { + f1 -= f2; + } + } + } + return setHigh32bitsXOR(f1, sx); + } + + /** + * Returns the smallest (closest to negative infinity) {@code double} value that is greater than + * or equal to the argument and is equal to a mathematical integer. Special cases: + * <ul> + * <li>If the argument value is already equal to a mathematical integer, then the result is the + * same as the argument. + * <li>If the argument is NaN or an infinity or positive zero or negative zero, then the result + * is the same as the argument. + * <li>If the argument value is less than zero but greater than -1.0, then the result is + * negative zero. + * </ul> + * Note that the value of {@code JStrictMath.ceil(x)} is exactly the value of + * {@code -JStrictMath.floor(-x)}. + * + * @param a a value. + * @return the smallest (closest to negative infinity) floating-point value that is greater than + * or equal to the argument and is equal to a mathematical integer. + */ + public static double ceil(double a) { + return Math.ceil(a); + // return floorOrCeil(a, false); + } + + /** + * Returns the largest (closest to positive infinity) {@code double} value that is less than or + * equal to the argument and is equal to a mathematical integer. Special cases: + * <ul> + * <li>If the argument value is already equal to a mathematical integer, then the result is the + * same as the argument. + * <li>If the argument is NaN or an infinity or positive zero or negative zero, then the result + * is the same as the argument. + * </ul> + * + * @param a a value. + * @return the largest (closest to positive infinity) floating-point value that less than or + * equal to the argument and is equal to a mathematical integer. + */ + public static double floor(double a) { + return Math.floor(a); + // return floorOrCeil(a, true); + } + + /** + * FDLIBM 5.3 s_ceil.c and s_floor.c combined in one method. + * + * @param x value to perform floor or ceil on. + * @param isfloor true if floor operation, false if ceil + * @author gustav trede + * @return + */ + @SuppressWarnings("javadoc") + private static double floorOrCeil(double x, boolean isfloor) { + long xb = Double.doubleToRawLongBits(x); + long i0 = xb >> 32; + long i1 = (int) xb; + final int j0 = (int) (((i0 >> 20) & 0x7ff) - 0x3ff); + if (j0 < 20) { + if (j0 < 0) { /* raise inexact if x != 0 */ + if (huge + x > 0.0d) {/* return 0*sign(x) if |x|<1 */ + if (isfloor) { // floor version + if (i0 >= 0) { + i0 = i1 = 0; + } else if (((i0 & 0x7fffffff) | i1) != 0) { + i0 = 0xbff00000; + i1 = 0; + } + } else { // ceil version + if (i0 < 0) { + i0 = 0x80000000; + i1 = 0; + } else if ((i0 | i1) != 0) { + i0 = 0x3ff00000; + i1 = 0; + } + } + } + } else { + int i = (0x000fffff) >>> j0; // unsigned declared in c + if (((i0 & i) | i1) == 0) { + return x; /* x is integral */ + } + if (huge + x > 0.0d) { /* raise inexact flag */ + if (isfloor && i0 < 0 || !isfloor && i0 > 0) { + i0 += (0x00100000) >> j0; + } + i0 &= (~i); + i1 = 0; + } + } + } else if (j0 > 51) { + return j0 == 0x400 ? x + x : x; /* inf or NaN , integral */ + } else { + // i = ((unsigned)(0xffffffff))>>(j0-20); + int i = 0xffffffff >>> (j0 - 20); // unsigned declared in c + if ((i1 & i) == 0) { + return x; /* x is integral */ + } + if (huge + x > 0.0d) { /* raise inexact flag */ + if (isfloor && i0 < 0 || !isfloor && i0 > 0) { + if (j0 == 20) { + i0 += 1; + } else { + // unsigned j = i1+(1<<(52-j0)); + // if(j<i1) + long j = i1 + (1L << (52 - j0)); + if ((j & 0x7fffffffffffffffL) < (i1 & 0x7fffffffffffffffL)) { + i0 += 1; /* got a carry */ + } + i1 = j; + } + } + i1 &= ~i; + } + } + return Double.longBitsToDouble((i0 << 32) | (i1 & 0x00000000FFFFFFFFL)); + } + + /** + * Returns the {@code double} value that is closest in value to the argument and is equal to a + * mathematical integer. If two {@code double} values that are mathematical integers are equally + * close to the value of the argument, the result is the integer value that is even. Special + * cases: + * <ul> + * <li>If the argument value is already equal to a mathematical integer, then the result is the + * same as the argument. + * <li>If the argument is NaN or an infinity or positive zero or negative zero, then the result + * is the same as the argument. + * </ul> + * + * @param aa a value. + * @return the closest floating-point value to {@code a} that is equal to a mathematical + * integer. + * @author Joseph D. Darcy + */ + @SuppressWarnings("deprecation") + public static double rint(double aa) { + /* + * If the absolute value of a is not less than 2^52, it is either a finite integer (the + * double format does not have enough significand bits for a number that large to have any + * fractional portion), an infinity, or a NaN. In any of these cases, rint of the argument + * is the argument. + * + * Otherwise, the sum (twoToThe52 + a ) will properly round away any fractional portion of a + * since ulp(twoToThe52) == 1.0; subtracting out twoToThe52 from this sum will then be exact + * and leave the rounded integer portion of a. + * + * This method does *not* need to be declared strictfp to get fully reproducible results. + * Whether or not a method is declared strictfp can only make a difference in the returned + * result if some operation would overflow or underflow with strictfp semantics. The + * operation (twoToThe52 + a ) cannot overflow since large values of a are screened out; the + * add cannot underflow since twoToThe52 is too large. The subtraction ((twoToThe52 + a ) - + * twoToThe52) will be exact as discussed above and thus cannot overflow or meaningfully + * underflow. Finally, the last multiply in the return statement is by plus or minus 1.0, + * which is exact too. + */ + double a = aa; + double twoToThe52 = 1L << 52; // 2^52 + double sign = FpUtils.rawCopySign(1.0, a); // preserve sign info + a = Math.abs(a); + + if (a < twoToThe52) { // E_min <= ilogb(a) <= 51 + a = ((twoToThe52 + a) - twoToThe52); + } + + return sign * a; // restore original sign + } + + /** + * Returns the angle <i>theta</i> from the conversion of rectangular coordinates ({@code x} + * , {@code y}) to polar coordinates (r, <i>theta</i>). This method computes the phase + * <i>theta</i> by computing an arc tangent of {@code y/x} in the range of -<i>pi</i> to + * <i>pi</i>. Special cases: + * <ul> + * <li>If either argument is NaN, then the result is NaN. + * <li>If the first argument is positive zero and the second argument is positive, or the first + * argument is positive and finite and the second argument is positive infinity, then the result + * is positive zero. + * <li>If the first argument is negative zero and the second argument is positive, or the first + * argument is negative and finite and the second argument is positive infinity, then the result + * is negative zero. + * <li>If the first argument is positive zero and the second argument is negative, or the first + * argument is positive and finite and the second argument is negative infinity, then the result + * is the {@code double} value closest to <i>pi</i>. + * <li>If the first argument is negative zero and the second argument is negative, or the first + * argument is negative and finite and the second argument is negative infinity, then the result + * is the {@code double} value closest to -<i>pi</i>. + * <li>If the first argument is positive and the second argument is positive zero or negative + * zero, or the first argument is positive infinity and the second argument is finite, then the + * result is the {@code double} value closest to <i>pi</i>/2. + * <li>If the first argument is negative and the second argument is positive zero or negative + * zero, or the first argument is negative infinity and the second argument is finite, then the + * result is the {@code double} value closest to -<i>pi</i>/2. + * <li>If both arguments are positive infinity, then the result is the {@code double} value + * closest to <i>pi</i>/4. + * <li>If the first argument is positive infinity and the second argument is negative infinity, + * then the result is the {@code double} value closest to 3*<i>pi</i>/4. + * <li>If the first argument is negative infinity and the second argument is positive infinity, + * then the result is the {@code double} value closest to -<i>pi</i>/4. + * <li>If both arguments are negative infinity, then the result is the {@code double} value + * closest to -3*<i>pi</i>/4. + * </ul> + * + * @param y the ordinate coordinate + * @param x the abscissa coordinate + * @return the <i>theta</i> component of the point (<i>r</i>, <i>theta</i>) in polar + * coordinates that corresponds to the point (<i>x</i>, <i>y</i>) in Cartesian + * coordinates. + */ + public static double atan2(double y, double x) { + /* + * __ieee754_atan2(y,x) Method : 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). 2. + * Reduce x to positive by (if x and y are unexceptional): ARG (x+iy) = arctan(y/x) ... if x + * > 0, ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * + * Special cases: + * + * ATAN2((anything), NaN ) is NaN; ATAN2(NAN , (anything) ) is NaN; ATAN2(+-0, +(anything + * but NaN)) is +-0 ; ATAN2(+-0, -(anything but NaN)) is +-pi ; ATAN2(+-(anything but 0 and + * NaN), 0) is +-pi/2; ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; ATAN2(+-(anything + * but INF and NaN), -INF) is +-pi; ATAN2(+-INF,+INF ) is +-pi/4 ; ATAN2(+-INF,-INF ) is + * +-3pi/4; ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; + */ + long t = Double.doubleToRawLongBits(x); + int hx = (int) (t >> 32); + int lx = (int) t; + int ix = hx & 0x7fffffff; + t = Double.doubleToRawLongBits(y); + int hy = (int) (t >> 32); + int ly = (int) t; + int iy = hy & 0x7fffffff; + if (((ix | ((lx | -lx) >>> 31)) > 0x7ff00000) || ((iy | ((ly | -ly) >>> 31)) > 0x7ff00000)) {/* + * x + * or + * y + * is + * NaN + */ + return x + y; + } + if (((hx - 0x3ff00000) | lx) == 0) { + return atan(y); /* x=1.0 */ + } + int m = ((hy >> 31) & 1) | ((hx >> 30) & 2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if ((iy | ly) == 0) { + switch (m) { + case 0: + case 1: + return y; /* atan(+-0,+anything)=+-0 */ + case 2: + return PI + tiny; /* atan(+0,-anything) = pi */ + case 3: + return -PI - tiny; /* atan(-0,-anything) =-pi */ + } + } + + /* when x = 0 */ + if ((ix | lx) == 0) { + return hy < 0 ? -pi_o_2 - tiny : pi_o_2 + tiny; + } + + /* when x is INF */ + if (ix == 0x7ff00000) { + if (iy == 0x7ff00000) { + switch (m) { + case 0: + return pi_o_4 + tiny; /* atan(+INF,+INF) */ + case 1: + return -pi_o_4 - tiny; /* atan(-INF,+INF) */ + case 2: + return (3.0 * pi_o_4) + tiny; /* atan(+INF,-INF) */ + case 3: + return (-3.0 * pi_o_4) - tiny; /* atan(-INF,-INF) */ + } + } else { + switch (m) { + case 0: + return zero; /* atan(+...,+INF) */ + case 1: + return -zero; /* atan(-...,+INF) */ + case 2: + return PI + tiny; /* atan(+...,-INF) */ + case 3: + return -PI - tiny; /* atan(-...,-INF) */ + } + } + } + + /* when y is INF */ + if (iy == 0x7ff00000) { + return hy < 0 ? -pi_o_2 - tiny : pi_o_2 + tiny; + } + + /* compute y/x */ + double z; + int k = (iy - ix) >> 20; + if (k > 60) { /* |y/x| > 2**60 */ + z = pi_o_2 + (0.5 * pi_lo); + } else if ((hx < 0) && (k < -60)) { + z = 0.0; /* |y|/x < -2**60 */ + } else { + z = atan(abs(y / x)); /* safe to do y/x */ + } + + switch (m) { + case 0: + return z; /* atan(+,+) */ + case 1: + return setHigh32bitsXOR(z, (0x80000000L << 32));// atan(-,+) + case 2: + return PI - (z - pi_lo); /* atan(+,-) */ + default: + return (z - pi_lo) - PI; /* atan(-,-) */ + } + } + + private static final double bp[] = {1.0, 1.5,}, dp_h[] = {0.0, 5.84962487220764160156e-01,}, dp_l[] = {0.0, 1.35003920212974897128e-08,}, two53 = 9007199254740992.0, + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ + L1 = 5.99999999999994648725e-01, L2 = 4.28571428578550184252e-01, L3 = 3.33333329818377432918e-01, L4 = 2.72728123808534006489e-01, L5 = 2.30660745775561754067e-01, + L6 = 2.06975017800338417784e-01, P1 = 1.66666666666666019037e-01, P2 = -2.77777777770155933842e-03, P3 = 6.61375632143793436117e-05, P4 = -1.65339022054652515390e-06, + P5 = 4.13813679705723846039e-08, lg2 = 6.93147180559945286227e-01, lg2_h = 6.93147182464599609375e-01, lg2_l = -1.90465429995776804525e-09, ovt = 8.0085662595372944372e-0017,// -(1024-log2(ovfl+.5ulp)) + cp = 9.61796693925975554329e-01, // =2/(3ln2) + cp_h = 9.61796700954437255859e-01, // =(float)cp + cp_l = -7.02846165095275826516e-09,// =tail of cp_h + ivln2 = 1.44269504088896338700e+00, // =1/ln2 + ivln2_h = 1.44269502162933349609e+00,// =24b 1/ln2 + ivln2_l = 1.92596299112661746887e-08;// =1/ln2 tail + + /** + * Returns the value of the first argument raised to the power of the second argument. Special + * cases: + * + * <ul> + * <li>If the second argument is positive or negative zero, then the result is 1.0. + * <li>If the second argument is 1.0, then the result is the same as the first argument. + * <li>If the second argument is NaN, then the result is NaN. + * <li>If the first argument is NaN and the second argument is nonzero, then the result is NaN. + * + * <li>If + * <ul> + * <li>the absolute value of the first argument is greater than 1 and the second argument is + * positive infinity, or + * <li>the absolute value of the first argument is less than 1 and the second argument is + * negative infinity, + * </ul> + * then the result is positive infinity. + * + * <li>If + * <ul> + * <li>the absolute value of the first argument is greater than 1 and the second argument is + * negative infinity, or + * <li>the absolute value of the first argument is less than 1 and the second argument is + * positive infinity, + * </ul> + * then the result is positive zero. + * + * <li>If the absolute value of the first argument equals 1 and the second argument is infinite, + * then the result is NaN. + * + * <li>If + * <ul> + * <li>the first argument is positive zero and the second argument is greater than zero, or + * <li>the first argument is positive infinity and the second argument is less than zero, + * </ul> + * then the result is positive zero. + * + * <li>If + * <ul> + * <li>the first argument is positive zero and the second argument is less than zero, or + * <li>the first argument is positive infinity and the second argument is greater than zero, + * </ul> + * then the result is positive infinity. + * + * <li>If + * <ul> + * <li>the first argument is negative zero and the second argument is greater than zero but not + * a finite odd integer, or + * <li>the first argument is negative infinity and the second argument is less than zero but not + * a finite odd integer, + * </ul> + * then the result is positive zero. + * + * <li>If + * <ul> + * <li>the first argument is negative zero and the second argument is a positive finite odd + * integer, or + * <li>the first argument is negative infinity and the second argument is a negative finite odd + * integer, + * </ul> + * then the result is negative zero. + * + * <li>If + * <ul> + * <li>the first argument is negative zero and the second argument is less than zero but not a + * finite odd integer, or + * <li>the first argument is negative infinity and the second argument is greater than zero but + * not a finite odd integer, + * </ul> + * then the result is positive infinity. + * + * <li>If + * <ul> + * <li>the first argument is negative zero and the second argument is a negative finite odd + * integer, or + * <li>the first argument is negative infinity and the second argument is a positive finite odd + * integer, + * </ul> + * then the result is negative infinity. + * + * <li>If the first argument is finite and less than zero + * <ul> + * <li>if the second argument is a finite even integer, the result is equal to the result of + * raising the absolute value of the first argument to the power of the second argument + * + * <li>if the second argument is a finite odd integer, the result is equal to the negative of + * the result of raising the absolute value of the first argument to the power of the second + * argument + * + * <li>if the second argument is finite and not an integer, then the result is NaN. + * </ul> + * + * <li>If both arguments are integers, then the result is exactly equal to the mathematical + * result of raising the first argument to the power of the second argument if that result can + * in fact be represented exactly as a {@code double} value. + * </ul> + * + * <p> + * (In the foregoing descriptions, a floating-point value is considered to be an integer if and + * only if it is finite and a fixed point of the method {@link #ceil ceil} or, equivalently, a + * fixed point of the method {@link #floor floor}. A value is a fixed point of a one-argument + * method if and only if the result of applying the method to the value is equal to the value.) + * + * @param x base. + * @param y the exponent. + * @return the value {@code a}<sup>{@code b}</sup>. + */ + public static double pow(double x, double y) { + /* + * __ieee754_pow(x,y) return x**y + * + * n Method: Let x = 2 * (1+f) 1. Compute and return log2(x) in two pieces: log2(x) = w1 + + * w2, where w1 has 53-24 = 29 bit trailing zeros. 2. Perform y*log2(x) = n+y' by simulating + * muti-precision arithmetic, where |y'|<=0.5. 3. Return x**y = 2**n*exp(y'*log2) + * + * Special cases: 1. (anything) ** 0 is 1 2. (anything) ** 1 is itself 3. (anything) ** NAN + * is NAN 4. NAN ** (anything except 0) is NAN 5. +-(|x| > 1) ** +INF is +INF 6. +-(|x| > 1) + * ** -INF is +0 7. +-(|x| < 1) ** +INF is +0 8. +-(|x| < 1) ** -INF is +INF 9. +-1 ** +-INF + * is NAN 10. +0 ** (+anything except 0, NAN) is +0 11. -0 ** (+anything except 0, NAN, odd + * integer) is +0 12. +0 ** (-anything except 0, NAN) is +INF 13. -0 ** (-anything except 0, + * NAN, odd integer) is +INF 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) 15. +INF ** + * (+anything except 0,NAN) is +INF 16. +INF ** (-anything except 0,NAN) is +0 17. -INF ** + * (anything) = -0 ** (-anything) 18. (-anything) ** (integer) is + * (-1)**(integer)*(+anything**integer) 19. (-anything except 0 and inf) ** (non-integer) is + * NAN + * + * Accuracy: pow(x,y) returns x**y nearly rounded. In particular pow(integer,integer) always + * returns the correct integer provided it is representable. + */ + + // i0 = ((*(int*)&one)>>29)^1; i1=1-i0; + + long xb = Double.doubleToRawLongBits(x); + int hx = (int) (xb >> 32); + int lx = (int) xb & 0x7fffffff; // unsigned + int ix = hx & 0x7fffffff; + xb = Double.doubleToRawLongBits(y); + int hy = (int) (xb >> 32); + int ly = (int) xb & 0x7fffffff; // unsigned + int iy = hy & 0x7fffffff; + + /* y==zero: x**0 = 1 */ + if ((iy | ly) == 0) + return one; + + /* +-NaN return x+y */ + if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) || iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0))) + return x + y; + + /* + * determine if y is an odd int when x < 0 yisint = 0 ... y is not an integer yisint = 1 ... + * y is an odd int yisint = 2 ... y is an even int + */ + int yisint = 0; + if (hx < 0) { + if (iy >= 0x43400000) + yisint = 2; /* even integer y */ + else if (iy >= 0x3ff00000) { + int k = (iy >> 20) - 0x3ff; /* exponent */ + if (k > 20) { + int j = ly >> (52 - k); + if ((j << (52 - k)) == ly) + yisint = 2 - (j & 1); + } else if (ly == 0) { + int j = iy >> (20 - k); + if ((j << (20 - k)) == iy) + yisint = 2 - (j & 1); + } + } + } + + /* special value of y */ + if (ly == 0) { + if (iy == 0x7ff00000) { /* y is +-inf */ + if (((ix - 0x3ff00000) | lx) == 0) + return y - y; /* inf**+-1 is NaN */ + return (ix >= 0x3ff00000) ? /* (|x|>1)**+-inf = inf,0 */ + (hy >= 0) ? y : zero : /* (|x|<1)**-,+inf = inf,0 */ + (hy < 0) ? -y : zero; + } + if (iy == 0x3ff00000) { /* y is +-1 */ + return (hy < 0) ? one / x : x; + } + if (hy == 0x40000000) + return x * x; /* y is 2 */ + if (hy == 0x3fe00000) { /* y is 0.5 */ + if (hx >= 0) /* x >= +0 */ + return Math.sqrt(x); + } + } + + double ax = abs(x); + /* special value of x */ + if (lx == 0) { + if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) { + double z = ax; /* x is +-0,+-inf,+-1 */ + if (hy < 0) + z = one / z; /* z = (1/|x|) */ + if (hx < 0) { + if (((ix - 0x3ff00000) | yisint) == 0) { + z = (z - z) / (z - z); /* (-1)**non-int is NaN */ + } else if (yisint == 1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + } + + int n = (hx >> 31) + 1; + + /* (x<0)**(non-int) is NaN */ + if ((n | yisint) == 0) + return (x - x) / (x - x); + + double s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if ((n | (yisint - 1)) == 0) + s = -one;/* (-ve)**(odd int) */ + + double t1, t2; + /* |y| is huge */ + if (iy > 0x41e00000) { /* if |y| > 2**31 */ + if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */ + if (ix <= 0x3fefffff) + return (hy < 0) ? huge * huge : tiny * tiny; + if (ix >= 0x3ff00000) + return (hy > 0) ? huge * huge : tiny * tiny; + } + /* over/underflow if x is not close to one */ + if (ix < 0x3fefffff) + return (hy < 0) ? s * huge * huge : s * tiny * tiny; + if (ix > 0x3ff00000) + return (hy > 0) ? s * huge * huge : s * tiny * tiny; + /* + * now |1-x| is tiny <= 2**-20, suffice to compute log(x) by x-x^2/2+x^3/3-x^4/4 + */ + double t = ax - one; /* t has 20 trailing zeros */ + double w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25)); + double u = ivln2_h * t; /* ivln2_h has 21 sig. bits */ + double v = t * ivln2_l - w * ivln2; + t1 = clearLow32bits(u + v); + t2 = v - (t1 - u); + } else { + n = 0; + /* take care subnormal number */ + if (ix < 0x00100000) { + ax *= two53; + n -= 53; + ix = __HI(ax); + } + n += ((ix) >> 20) - 0x3ff; + int j = ix & 0x000fffff; + /* determine interval */ + ix = j | 0x3ff00000; /* normalize ix */ + int k = 0; + if (j <= 0x3988E) + k = 0; /* |x|<sqrt(3/2) */ + else if (j < 0xBB67A) + k = 1; /* |x|<sqrt(3) */ + else { + n += 1; + ix -= 0x00100000; + } + + ax = setHigh32bits(ax, ix); // __HI(ax) = ix; + + /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ + double u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ + double v = one / (ax + bp[k]); + double ss = u * v; + double s_h = clearLow32bits(ss); + /* t_h=ax+bp[k] High */ + // __HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18); + double t_h = setHigh32bitsDontMask(zerobitshigh, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18)); + double s_l = v * ((u - s_h * t_h) - s_h * (ax - (t_h - bp[k]))); + /* compute log(ax) */ + double s2 = ss * ss; + double r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6))))) + s_l * (s_h + ss); + s2 = s_h * s_h; + t_h = clearLow32bits(3.0 + s2 + r); + /* u+v = ss*(1+...) */ + u = s_h * t_h; + v = s_l * t_h + (r - ((t_h - 3.0) - s2)) * ss; + /* 2/(3log2)*(ss+...) */ + double p_h = clearLow32bits(u + v); // __LO(p_h) = 0; + double z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */ + double z_l = cp_l * p_h + (v - (p_h - u)) * cp + dp_l[k]; + /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + double t = n; + t1 = clearLow32bits((((z_h + z_l) + dp_h[k]) + t)); // __LO(t1) = 0; + t2 = z_l - (((t1 - t) - dp_h[k]) - z_h); + } + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + double y1 = clearLow32bits(y); // __LO(y1) = 0; + double p_l = (y - y1) * t1 + y * t2; + double p_h = y1 * t1; + double z = p_l + p_h; + long zb = Double.doubleToRawLongBits(z); + int j = (int) (zb >> 32); + if (j >= 0x40900000) { /* z >= 1024 */ + if (((j - 0x40900000) | ((int) zb)) != 0) /* if z > 1024 */ + return s * huge * huge; /* overflow */ + else { + if (p_l + ovt > z - p_h) + return s * huge * huge; /* overflow */ + } + } else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */ + if (((j - 0xc090cc00) | ((int) zb)) != 0) /* z < -1075 */ + return s * tiny * tiny; /* underflow */ + else { + if (p_l <= z - p_h) + return s * tiny * tiny; /* underflow */ + } + } + /* + * compute 2**(p_h+p_l) + */ + int i = j & 0x7fffffff; + n = 0; + if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j + (0x00100000 >> ((i >> 20) - 0x3ff + 1)); + final int k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */ + double t = setHigh32bitsDontMask(zerobitshigh, (n & ~(0x000fffff >> k))); + n = ((n & 0x000fffff) | 0x00100000) >> (20 - k); + if (j < 0) + n = -n; + p_h -= t; + } + double t = clearLow32bits(p_l + p_h);// __LO(t) = 0; + double u = t * lg2_h; + double v = (p_l - (t - p_h)) * lg2 + t * lg2_l; + z = u + v; + double w = v - (z - u); + t = z * z; + t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5)))); + z = one - (((z * t1) / (t1 - two) - (w + z * w)) - z); + j = __HI(z) + (n << 20); + return s * ((j >> 20) <= 0 ? scalb(z, n) : /* subnormal output */ + addToHighBits(z, (long) n << (20)));// __HI(z) += (n<<20); + } + + /** + * Returns the closest {@code int} to the argument. The result is rounded to an integer by + * adding 1/2, taking the floor of the result, and casting the result to type {@code int}. In + * other words, the result is equal to the value of the expression: + * <p> + * {@code (int)Math.floor(a + 0.5f)} + * + * <p> + * Special cases: + * <ul> + * <li>If the argument is NaN, the result is 0. + * <li>If the argument is negative infinity or any value less than or equal to the value of + * {@code Integer.MIN_VALUE}, the result is equal to the value of {@code Integer.MIN_VALUE}. + * <li>If the argument is positive infinity or any value greater than or equal to the value of + * {@code Integer.MAX_VALUE}, the result is equal to the value of {@code Integer.MAX_VALUE}. + * </ul> + * + * @param a a floating-point value to be rounded to an integer. + * @return the value of the argument rounded to the nearest {@code int} value. + * @see java.lang.Integer#MAX_VALUE + * @see java.lang.Integer#MIN_VALUE + */ + public static int round(float a) { + return (int) floor(a + 0.5f); + } + + /** + * Returns the closest {@code long} to the argument. The result is rounded to an integer by + * adding 1/2, taking the floor of the result, and casting the result to type {@code long}. In + * other words, the result is equal to the value of the expression: + * <p> + * {@code (long)Math.floor(a + 0.5d)} + * + * <p> + * Special cases: + * <ul> + * <li>If the argument is NaN, the result is 0. + * <li>If the argument is negative infinity or any value less than or equal to the value of + * {@code Long.MIN_VALUE}, the result is equal to the value of {@code Long.MIN_VALUE}. + * <li>If the argument is positive infinity or any value greater than or equal to the value of + * {@code Long.MAX_VALUE}, the result is equal to the value of {@code Long.MAX_VALUE}. + * </ul> + * + * @param a a floating-point value to be rounded to a {@code long}. + * @return the value of the argument rounded to the nearest {@code long} value. + * @see java.lang.Long#MAX_VALUE + * @see java.lang.Long#MIN_VALUE + */ + public static long round(double a) { + return (long) floor(a + 0.5d); + } + + private static Random randomNumberGenerator; + + private static synchronized void initRNG() { + if (randomNumberGenerator == null) { + randomNumberGenerator = new Random(); + } + } + + /** + * Returns a {@code double} value with a positive sign, greater than or equal to {@code 0.0} and + * less than {@code 1.0}. Returned values are chosen pseudorandomly with (approximately) uniform + * distribution from that range. + * + * <p> + * When this method is first called, it creates a single new pseudorandom-number generator, + * exactly as if by the expression <blockquote>{@code new java.util.Random}</blockquote> This + * new pseudorandom-number generator is used thereafter for all calls to this method and is used + * nowhere else. + * + * <p> + * This method is properly synchronized to allow correct use by more than one thread. However, + * if many threads need to generate pseudorandom numbers at a great rate, it may reduce + * contention for each thread to have its own pseudorandom number generator. + * + * @return a pseudorandom {@code double} greater than or equal to {@code 0.0} and less than + * {@code 1.0}. + * @see java.util.Random#nextDouble() + */ + public static double random() { + if (randomNumberGenerator == null) { + initRNG(); + } + return randomNumberGenerator.nextDouble(); + } + + /** + * Returns the absolute value of an {@code int} value.. If the argument is not negative, the + * argument is returned. If the argument is negative, the negation of the argument is returned. + * + * <p> + * Note that if the argument is equal to the value of {@link Integer#MIN_VALUE}, the most + * negative representable {@code int} value, the result is that same value, which is negative. + * + * @param a the argument whose absolute value is to be determined. + * @return the absolute value of the argument. + */ + public static int abs(int a) { + return Math.abs(a); + // return (a < 0) ? -a : a; + } + + /** + * Returns the absolute value of a {@code long} value. If the argument is not negative, the + * argument is returned. If the argument is negative, the negation of the argument is returned. + * + * <p> + * Note that if the argument is equal to the value of {@link Long#MIN_VALUE}, the most negative + * representable {@code long} value, the result is that same value, which is negative. + * + * @param a the argument whose absolute value is to be determined. + * @return the absolute value of the argument. + */ + public static long abs(long a) { + return Math.abs(a); + // return (a < 0) ? -a : a; + } + + /** + * Returns the absolute value of a {@code float} value. If the argument is not negative, the + * argument is returned. If the argument is negative, the negation of the argument is returned. + * Special cases: + * <ul> + * <li>If the argument is positive zero or negative zero, the result is positive zero. + * <li>If the argument is infinite, the result is positive infinity. + * <li>If the argument is NaN, the result is NaN. + * </ul> + * In other words, the result is the same as the value of the expression: + * <p> + * {@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))} + * + * @param a the argument whose absolute value is to be determined + * @return the absolute value of the argument. + */ + public static float abs(float a) { + return Math.abs(a); + // return (a <= 0.0F) ? 0.0F - a : a; + } + + /** + * Returns the absolute value of a {@code double} value. If the argument is not negative, the + * argument is returned. If the argument is negative, the negation of the argument is returned. + * Special cases: + * <ul> + * <li>If the argument is positive zero or negative zero, the result is positive zero. + * <li>If the argument is infinite, the result is positive infinity. + * <li>If the argument is NaN, the result is NaN. + * </ul> + * In other words, the result is the same as the value of the expression: + * <p> + * {@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)} + * + * @param a the argument whose absolute value is to be determined + * @return the absolute value of the argument. + */ + public static double abs(double a) { + return Math.abs(a); + // return (a <= 0.0D) ? 0.0D - a : a; + } + + /** + * Returns the greater of two {@code int} values. That is, the result is the argument closer to + * the value of {@link Integer#MAX_VALUE}. If the arguments have the same value, the result is + * that same value. + * + * @param a an argument. + * @param b another argument. + * @return the larger of {@code a} and {@code b}. + */ + public static int max(int a, int b) { + return Math.max(a, b); + // return (a >= b) ? a : b; + } + + /** + * Returns the greater of two {@code long} values. That is, the result is the argument closer to + * the value of {@link Long#MAX_VALUE}. If the arguments have the same value, the result is that + * same value. + * + * @param a an argument. + * @param b another argument. + * @return the larger of {@code a} and {@code b}. + */ + public static long max(long a, long b) { + return Math.max(a, b); + // return (a >= b) ? a : b; + } + + private final static long negativeZeroFloatBits = Float.floatToIntBits(-0.0f), negativeZeroDoubleBits = Double.doubleToLongBits(-0.0d); + + /** + * Returns the greater of two {@code float} values. That is, the result is the argument closer + * to positive infinity. If the arguments have the same value, the result is that same value. If + * either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this + * method considers negative zero to be strictly smaller than positive zero. If one argument is + * positive zero and the other negative zero, the result is positive zero. + * + * @param a an argument. + * @param b another argument. + * @return the larger of {@code a} and {@code b}. + */ + public static float max(float a, float b) { + return Math.max(a, b); + /***** + * if (a != a) { return a; // a is NaN } if ((a == 0.0f) && (b == 0.0f) && + * (Float.floatToIntBits(a) == negativeZeroFloatBits)) { return b; } return (a >= b) ? a : + * b; + *****/ + } + + /** + * Returns the greater of two {@code double} values. That is, the result is the argument closer + * to positive infinity. If the arguments have the same value, the result is that same value. If + * either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this + * method considers negative zero to be strictly smaller than positive zero. If one argument is + * positive zero and the other negative zero, the result is positive zero. + * + * @param a an argument. + * @param b another argument. + * @return the larger of {@code a} and {@code b}. + */ + public static double max(double a, double b) { + return Math.max(a, b); + /****** + * if (a != a) { return a; // a is NaN } if ((a == 0.0d) && (b == 0.0d) && + * (Double.doubleToLongBits(a) == negativeZeroDoubleBits)) { return b; } return (a >= b) ? a + * : b; + ******/ + } + + /** + * Returns the smaller of two {@code int} values. That is, the result the argument closer to the + * value of {@link Integer#MIN_VALUE}. If the arguments have the same value, the result is that + * same value. + * + * @param a an argument. + * @param b another argument. + * @return the smaller of {@code a} and {@code b}. + */ + public static int min(int a, int b) { + return Math.min(a, b); + // return (a <= b) ? a : b; + } + + /** + * Returns the smaller of two {@code long} values. That is, the result is the argument closer to + * the value of {@link Long#MIN_VALUE}. If the arguments have the same value, the result is that + * same value. + * + * @param a an argument. + * @param b another argument. + * @return the smaller of {@code a} and {@code b}. + */ + public static long min(long a, long b) { + return Math.min(a, b); + // return (a <= b) ? a : b; + } + + /** + * Returns the smaller of two {@code float} values. That is, the result is the value closer to + * negative infinity. If the arguments have the same value, the result is that same value. If + * either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this + * method considers negative zero to be strictly smaller than positive zero. If one argument is + * positive zero and the other is negative zero, the result is negative zero. + * + * @param a an argument. + * @param b another argument. + * @return the smaller of {@code a} and {@code b.} + */ + public static float min(float a, float b) { + return Math.min(a, b); + /******* + * if (a != a) { return a; // a is NaN } if ((a == 0.0f) && (b == 0.0f) && + * (Float.floatToIntBits(b) == negativeZeroFloatBits)) { return b; } return (a <= b) ? a : + * b; + *****/ + } + + /** + * Returns the smaller of two {@code double} values. That is, the result is the value closer to + * negative infinity. If the arguments have the same value, the result is that same value. If + * either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this + * method considers negative zero to be strictly smaller than positive zero. If one argument is + * positive zero and the other is negative zero, the result is negative zero. + * + * @param a an argument. + * @param b another argument. + * @return the smaller of {@code a} and {@code b}. + */ + public static double min(double a, double b) { + return Math.min(a, b); + /********* + * if (a != a) { return a; // a is NaN } if ((a == 0.0d) && (b == 0.0d) && + * (Double.doubleToLongBits(b) == negativeZeroDoubleBits)) { return b; } return (a <= b) ? a + * : b; + *******/ + } + + /** + * Returns the size of an ulp of the argument. An ulp of a {@code double} value is the positive + * distance between this floating-point value and the {@code double} value next larger in + * magnitude. Note that for non-NaN <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>. + * + * <p> + * Special Cases: + * <ul> + * <li>If the argument is NaN, then the result is NaN. + * <li>If the argument is positive or negative infinity, then the result is positive infinity. + * <li>If the argument is positive or negative zero, then the result is {@code Double.MIN_VALUE}. + * <li>If the argument is ±{@code Double.MAX_VALUE}, then the result is equal to + * 2<sup>971</sup>. + * </ul> + * + * @param d the floating-point value whose ulp is to be returned + * @return the size of an ulp of the argument + * @author Joseph D. Darcy + * @since 1.5 + */ + @SuppressWarnings("deprecation") + public static double ulp(double d) { + return sun.misc.FpUtils.ulp(d); + } + + /** + * Returns the size of an ulp of the argument. An ulp of a {@code float} value is the positive + * distance between this floating-point value and the {@code float} value next larger in + * magnitude. Note that for non-NaN <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>. + * + * <p> + * Special Cases: + * <ul> + * <li>If the argument is NaN, then the result is NaN. + * <li>If the argument is positive or negative infinity, then the result is positive infinity. + * <li>If the argument is positive or negative zero, then the result is {@code Float.MIN_VALUE}. + * <li>If the argument is ±{@code Float.MAX_VALUE}, then the result is equal to + * 2<sup>104</sup>. + * </ul> + * + * @param f the floating-point value whose ulp is to be returned + * @return the size of an ulp of the argument + * @author Joseph D. Darcy + * @since 1.5 + */ + @SuppressWarnings("deprecation") + public static float ulp(float f) { + return sun.misc.FpUtils.ulp(f); + } + + /** + * Returns the signum function of the argument; zero if the argument is zero, 1.0 if the + * argument is greater than zero, -1.0 if the argument is less than zero. + * + * <p> + * Special Cases: + * <ul> + * <li>If the argument is NaN, then the result is NaN. + * <li>If the argument is positive zero or negative zero, then the result is the same as the + * argument. + * </ul> + * + * @param d the floating-point value whose signum is to be returned + * @return the signum function of the argument + * @author Joseph D. Darcy + * @since 1.5 + */ + @SuppressWarnings("deprecation") + public static double signum(double d) { + return sun.misc.FpUtils.signum(d); + } + + /** + * Returns the signum function of the argument; zero if the argument is zero, 1.0f if the + * argument is greater than zero, -1.0f if the argument is less than zero. + * + * <p> + * Special Cases: + * <ul> + * <li>If the argument is NaN, then the result is NaN. + * <li>If the argument is positive zero or negative zero, then the result is the same as the + * argument. + * </ul> + * + * @param f the floating-point value whose signum is to be returned + * @return the signum function of the argument + * @author Joseph D. Darcy + * @since 1.5 + */ + @SuppressWarnings("deprecation") + public static float signum(float f) { + return sun.misc.FpUtils.signum(f); + } + + private static final double shuge = 1.0e307; + + /** + * Returns the hyperbolic sine of a {@code double} value. The hyperbolic sine of <i>x</i> is + * defined to be (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2 where <i>e</i> is + * {@linkplain Math#E Euler's number}. + * + * <p> + * Special cases: + * <ul> + * + * <li>If the argument is NaN, then the result is NaN. + * + * <li>If the argument is infinite, then the result is an infinity with the same sign as the + * argument. + * + * <li>If the argument is zero, then the result is a zero with the same sign as the argument. + * + * </ul> + * + * @param x The number whose hyperbolic sine is to be returned. + * @return The hyperbolic sine of {@code x}. + * @since 1.5 + */ + public static double sinh(double x) { + /* + * __ieee754_sinh(x) Method : mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 1. + * Replace x by |x| (sinh(-x) = -sinh(x)). 2. E + E/(E+1) 0 <= x <= 22 : sinh(x) := + * --------------, E=expm1(x) 2 + * + * 22 <= x <= lnovft : sinh(x) := exp(x)/2 lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * + * exp(x/2) ln2ovft < x : sinh(x) := x*shuge (overflow) + * + * Special cases: sinh(x) is |x| if x is +INF, -INF, or NaN. only sinh(0)=0 is exact for + * finite x. + */ + + final long xb = Double.doubleToLongBits(x); + final double h = (xb >> 32) < 0 ? -0.5 : 0.5; + final int ix = (int) ((xb >> 32) & 0x7fffffff); + + if (ix >= 0x7ff00000) { /* x is INF or NaN */ + return x + x; + } + + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix < 0x3e300000) /* |x|<2**-28 */ + if (shuge + x > one) { + return x;/* sinh(tiny) = tiny with inexact */ + } + final double t = expm1(abs(x)); + return (ix < 0x3ff00000) ? h * (2.0 * t - t * t / (t + one)) : h * (t + t / (t + one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x40862E42) + return h * exp(abs(x)); + + // |x| in [log(Double.MAX_VALUE), overflowthreshold] + if (ix < 0x408633ce || (ix == 0x408633ce && (xb & 0x00000000ffffffffL) <= 0x8fb9f87dL)) { + final double w = exp(0.5 * abs(x)); + return (h * w) * w; + } + /* |x| > overflowthresold, sinh(x) overflow */ + return x * shuge; + + } + + /** + * Returns the hyperbolic cosine of a {@code double} value. The hyperbolic cosine of <i>x</i> is + * defined to be (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2 where <i>e</i> is + * {@linkplain Math#E Euler's number}. + * + * <p> + * Special cases: + * <ul> + * + * <li>If the argument is NaN, then the result is NaN. + * + * <li>If the argument is infinite, then the result is positive infinity. + * + * <li>If the argument is zero, then the result is {@code 1.0}. + * + * </ul> + * + * @param x The number whose hyperbolic cosine is to be returned. + * @return The hyperbolic cosine of {@code x}. + * @since 1.5 + */ + public static double cosh(double x) { + /* + * __ieee754_cosh(x) Method : mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 1. + * Replace x by |x| (cosh(x) = cosh(-x)). 2. [ exp(x) - 1 ]^2 0 <= x <= ln2/2 : cosh(x) := 1 + * + ------------------- 2*exp(x) + * + * exp(x) + 1/exp(x) ln2/2 <= x <= 22 : cosh(x) := ------------------- 2 22 <= x <= lnovft : + * cosh(x) := exp(x)/2 lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) ln2ovft < x + * : cosh(x) := huge*huge (overflow) + * + * Special cases: cosh(x) is |x| if x is +INF, -INF, or NaN. only cosh(0)=1 is exact for + * finite x. + */ + + final long xb = Double.doubleToRawLongBits(x); + final int ix = ((int) (xb >> 32)) & 0x7fffffff; + + /* x is INF or NaN */ + if (ix >= 0x7ff00000) { + return x * x; + } + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if (ix < 0x3fd62e43) { + final double t = expm1(abs(x)); + final double w = one + t; + // for tiny arguments return 1. + return (ix < 0x3c800000) ? w : one + (t * t) / (w + w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x40360000) { + final double t = exp(abs(x)); + return half * t + half / t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x40862e42) { + return half * exp(abs(x)); + } + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix < 0x408633ce || (ix == 0x408633ce && (xb & 0x00000000ffffffffL) <= 0x8fb9f87dL)) { + final double w = exp(half * abs(x)); + return (half * w) * w; + } + /* |x| > overflowthresold, cosh(x) overflow */ + return huge * huge; + } + + /** + * Returns the hyperbolic tangent of a {@code double} value. The hyperbolic tangent of <i>x</i> + * is defined to be + * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> +  + * ;e<sup>-x</sup></i>), in other words, {@linkplain Math#sinh sinh(<i>x</i>)}/ + * {@linkplain Math#cosh cosh(<i>x</i>)}. Note that the absolute value of the exact tanh is + * always less than 1. + * + * <p> + * Special cases: + * <ul> + * + * <li>If the argument is NaN, then the result is NaN. + * + * <li>If the argument is zero, then the result is a zero with the same sign as the argument. + * + * <li>If the argument is positive infinity, then the result is {@code +1.0}. + * + * <li>If the argument is negative infinity, then the result is {@code -1.0}. + * + * </ul> + * + * @param xx The number whose hyperbolic tangent is to be returned. + * @return The hyperbolic tangent of {@code x}. + * @since 1.5 + */ + public static double tanh(double xx) { + /* + * Tanh(x) Return the Hyperbolic Tangent of x + * + * Method : x -x e - e 0. tanh(x) is defined to be ----------- x -x e + e 1. reduce x to + * non-negative by tanh(-x) = -tanh(x). 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) -t 2**-55 + * < x <= 1 : tanh(x) := -----; t = expm1(-2x) t + 2 2 1 <= x <= 22.0 : tanh(x) := 1- ----- + * ; t=expm1(2x) t + 2 22.0 < x <= INF : tanh(x) := 1. + * + * Special cases: tanh(NaN) is NaN; only tanh(0)=0 is exact for finite argument. + */ + + double x = xx; + /* High word of |x|. */ + final int hx = (int) (Double.doubleToRawLongBits(x) >> 32); + final int ix = hx & 0x7fffffff; + + /* x is INF or NaN */ + if (ix >= 0x7ff00000) { + return hx >= 0 ? one / x + one : /* tanh(+-inf)=+-1 */ + one / x - one; /* tanh(NaN) = NaN */ + } + + double z; + /* |x| < 22 */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix < 0x3c800000) { /* |x|<2**-55 */ + return x * (one + x); /* tanh(small) = small */ + } + x = abs(x); + if (ix >= 0x3ff00000) { /* |x|>=1 */ + z = one - two / (expm1(2.0d * x) + two); + } else { + double t = expm1(-two * x); + z = -t / (t + two); + } + /* |x| > 22, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return hx >= 0 ? z : 0.0d - z; + } + + private static final double TWOpow1022 = setHigh32bits(0x7fd00000); + private static final long onebits = Double.doubleToLongBits(one), clearHighmask = 0x00000000FFFFFFFFL, onebitshigh = onebits & clearHighmask, zerobitshigh = Double.doubleToLongBits(zero) & + clearHighmask; + + /** + * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>) without intermediate overflow + * or underflow. + * + * <p> + * Special cases: + * <ul> + * + * <li>If either argument is infinite, then the result is positive infinity. + * + * <li>If either argument is NaN and neither argument is infinite, then the result is NaN. + * + * </ul> + * + * @param aa a value + * @param bb a value + * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>) without intermediate overflow + * or underflow + * @since 1.5 + */ + public static double hypot(double aa, double bb) { + /* + * __ieee754_hypot(x,y) + * + * Method : If (assume round-to-nearest) z=x*x+y*y has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x+y*y) with some care as follows to get the error below 1 ulp: + * + * Assume x>y>0; (if possible, set rounding to round-to-nearest) 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y where x1 = x with lower 32 bits cleared, x2 = x-x1; + * else 2. if x <= 2y use t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) where t1 = 2x with lower 32 bits + * cleared, t2 = 2x-t1, y1= y with lower 32 bits chopped, y2 = y-y1. + * + * NOTE: scaling may be necessary if some argument is too large or too tiny + * + * Special cases: hypot(x,y) is INF if x or y is +INF or -INF; else hypot(x,y) is NAN if x + * or y is NAN. + * + * Accuracy: hypot(x,y) returns sqrt(x^2+y^2) with error less than 1 ulps (units in the last + * place) + */ + + double a = aa; + double b = bb; + long hx = (Double.doubleToRawLongBits(a) >>> 32) & 0x7fffffff; + long hy = (Double.doubleToRawLongBits(b) >>> 32) & 0x7fffffff; + if (hy > hx) { + double at = a; + a = b; + b = at; + long j = hx; + hx = hy; + hy = j; + } + + a = abs(a); + b = abs(b); + + // a = setHigh32bits(a,hx); + // b = setHigh32bits(b,hy); + + // System.err.println("a1 "); + if (hx - hy > 0x3c00000) { + return a + b; + } /* x/y > 2**60 */ + // System.err.println("a2"); + int k = 0; + if (hx > 0x5f300000) { /* a>2**500 */ + // System.err.println("b1 "+hx +" >= "+ 0x7ff00000); + if (hx >= 0x7ff00000) { /* Inf or NaN */ + // System.err.println("b2"); + return Double.isInfinite(a) || Double.isInfinite(b) ? Double.POSITIVE_INFINITY : Double.NaN; + } + /* scale a and b by 2**-600 */ + k = 600; + a = setHigh32bits(a, hx -= 0x25800000); + b = setHigh32bits(b, hy -= 0x25800000); + } + if (hy < 0x20b00000) { /* b < 2**-500 */ + if (hy <= 0x000fffff) { /* subnormal b or 0 */ + // if ((hy | (bbits&clearHighmask)) == 0) { + if ((hy | __LO(b)) == 0) { + return a; + } + b *= TWOpow1022; + a *= TWOpow1022; + k -= 1022; + } else { /* scale a and b by 2^600 */ + k -= 600; + a = setHigh32bits(a, hx += 0x25800000); /* a *= 2^600 */ + b = setHigh32bits(b, hy += 0x25800000); /* b *= 2^600 */ + } + } + + /* medium size a and b */ + double w = a - b; + if (w > b) { + final double t1 = Double.longBitsToDouble(hx << 32); + w = t1 * t1 - (b * -b - (a - t1) * (a + t1)); + } else { + final double y1 = Double.longBitsToDouble(hy << 32); + final double t1 = Double.longBitsToDouble((hx + 0x00100000) << 32); + w = t1 * y1 - (w * -w - (t1 * (b - y1) + b * ((a + a) - t1))); + } + w = java.lang.Math.sqrt(w); + return k != 0 ? w * setHhighbitsAddSome(onebits, (long) k << (20 + 32)) : w; + } + + /* scaled coefficients related to expm1 */ + private static final double Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */ + Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ + Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ + Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ + Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ + + /** + * Returns <i>e</i><sup>x</sup> -1. Note that for values of <i>x</i> near 0, the exact sum + * of {@code expm1(x)} + 1 is much closer to the true result of <i>e</i><sup>x</sup> + * than {@code exp(x)}. + * + * <p> + * Special cases: + * <ul> + * <li>If the argument is NaN, the result is NaN. + * + * <li>If the argument is positive infinity, then the result is positive infinity. + * + * <li>If the argument is negative infinity, then the result is -1.0. + * + * <li>If the argument is zero, then the result is a zero with the same sign as the argument. + * + * </ul> + * + * @param xx the exponent to raise <i>e</i> to in the computation of <i>e</i><sup>{@code x} + * </sup> -1. + * @return the value <i>e</i><sup>{@code x}</sup> - 1. + * @since 1.5 + */ + public static double expm1(double xx) { + /* + * expm1(x) Returns exp(x)-1, the exponential of x minus 1. + * + * Method 1. Argument reduction: Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 + * + * Here a correction term c will be computed to compensate the error in r when rounded to a + * floating-point number. + * + * 2. Approximating expm1(r) by a special rational function on the interval [0,0.34658]: + * Since r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ... we define R1(r*r) by + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r) That is, R1(r**2) = 6/r + * *((exp(r)+1)/(exp(r)-1) - 2/r) = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r)) = 1 - r^2/60 + + * r^4/2520 - r^6/100800 + ... We use a special Reme algorithm on [0,0.347] to generate a + * polynomial of degree 5 in r*r to approximate R1. The maximum error of this polynomial + * approximation is bounded by 2**-61. In other words, R1(z) ~ 1.0 + Q1*z + Q2*z**2 + + * Q3*z**3 + Q4*z**4 + Q5*z**5 where Q1 = -1.6666666666666567384E-2, Q2 = + * 3.9682539681370365873E-4, Q3 = -9.9206344733435987357E-6, Q4 = 2.5051361420808517002E-7, + * Q5 = -6.2843505682382617102E-9; (where z=r*r, and the values of Q1 to Q5 are listed + * below) with error bounded by | 5 | -61 | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 | | + * + * expm1(r) = exp(r)-1 is then computed by the following specific way which minimize the + * accumulation rounding error: 2 3 r r [ 3 - (R1 + R1*r/2) ] expm1(r) = r + --- + --- * + * [--------------------] 2 2 [ 6 - r*(3 - R1*r/2) ] + * + * To compensate the error in the argument reduction, we use expm1(r+c) = expm1(r) + c + + * expm1(r)*c ~ expm1(r) + c + r*c Thus c+r*c will be added in as the correction terms for + * expm1(r+c). Now rearrange the term to avoid optimization screw up: ( 2 2 ) ({ ( r [ R1 - + * (3 - R1*r/2) ] ) } r ) expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) ({ + * ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) ( ) + * + * = r - E 3. Scale back to obtain expm1(x): From step 1, we have expm1(x) = either + * 2^k*[expm1(r)+1] - 1 = or 2^k*[expm1(r) + (1-2^-k)] 4. Implementation notes: (A). To save + * one multiplication, we scale the coefficient Qi to Qi*2^i, and replace z by (x^2)/2. (B). + * To achieve maximum accuracy, we compute expm1(x) by (i) if x < -56*ln2, return -1.0, + * (raise inexact if x!=inf) (ii) if k=0, return r-E (iii) if k=-1, return 0.5*(r-E)-0.5 + * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E) else return 1.0+2.0*(r-E); (v) if + * (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1) (vi) if k <= 20, return + * 2^k((1-2^-k)-(E-r)), else (vii) return 2^k(1-((E+2^-k)-r)) + * + * Special cases: expm1(INF) is INF, expm1(NaN) is NaN; expm1(-INF) is -1, and for finite + * argument, only expm1(0)=0 is exact. + * + * Accuracy: according to an error analysis, the error is always less than 1 ulp (unit in + * the last place). + * + * Misc. info. For IEEE double if x > 7.09782712893383973096e+02 then expm1(x) overflow + * + * Constants: The hexadecimal values are the intended ones for the following constants. The + * decimal values may be used, provided that the compiler will convert from decimal to + * binary accurately enough to produce the hexadecimal values shown. + */ + + double x = xx; + long xb = Double.doubleToRawLongBits(x); + int hx = (int) (xb >> 32); /* high word of x UNSIGNED */ + final boolean xsbzero = (hx & 0x80000000) == 0; /* sign bit of x */ + // double y = xsbzero ? x : 0.0d - x; /* y = |x| */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out huge and non-finite argument */ + if (hx >= 0x4043687A) { /* if |x|>=56*ln2 */ + if (hx >= 0x40862E42) { /* if |x|>=709.78... */ + if (hx >= 0x7ff00000) { + return (((hx & 0xfffff) | (int) xb) != 0) ? x + x : /* NaN */ + xsbzero ? x : -1.0; /* exp(+-inf)={inf,-1} */ + } + if (x > o_threshold) { + return huge * huge; /* overflow */ + } + } + /* x < -56*ln2, return -1.0 with inexact */ + if (!xsbzero && (x + tiny < 0.0)) { /* raise inexact */ + return tiny - one; /* return -1 */ + } + } + + double hi, lo, c = 0; + int k = 0; + /* argument reduction */ + if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + if (xsbzero) { + hi = x - ln2_hi; + lo = ln2_lo; + k = 1; + } else { + hi = x + ln2_hi; + lo = -ln2_lo; + k = -1; + } + } else { + // loss of precision here ?: + k = (int) (invln2 * x + (xsbzero ? 0.5 : -0.5)); + hi = x - k * ln2_hi; /* t*ln2_hi is exact here */ + lo = k * ln2_lo; + } + x = hi - lo; + c = (hi - x) - lo; + } else if (hx < 0x3c900000) { /* when |x|<2**-54, return x */ + /* return x with inexact flags when x!=0 */ + return x - ((huge + x) - (huge + x)); + } + + /* x is now in primary range */ + final double hfx = 0.5 * x; + final double hxs = x * hfx; + final double r1 = one + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5)))); + final double t = 3.0 - r1 * hfx; + double e = hxs * ((r1 - t) / (6.0 - x * t)); + if (k == 0) { + return x - (x * e - hxs); /* c is 0 */ + } + e = (x * (e - c) - c) - hxs; + if (k == -1) { + return 0.5 * (x - e) - 0.5; + } + if (k == 1) { + return x < -0.25 ? -2.0 * (e - (x + 0.5)) : one + 2.0 * (x - e); + } + if (k <= -2 || k > 56) { /* suffice to return exp(x)-1 */ + /* add k to y's exponent */ + return setHhighbitsAddSome(one - (e - x), (long) k << (20 + 32)) - one; + } + final double y = k < 20 ? /* 1-2^-k */ + setHigh32bitsDontMask(onebitshigh, 0x3ff00000 - (0x200000 >> k)) - (e - x) : (x - (e + setHigh32bitsDontMask(onebitshigh, (0x3ff - k) << 20))) + one;// 2^-k + /* add k to y's exponent */ + return setHhighbitsAddSome(y, (long) k << (20 + 32)); + } + + private static final double Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ + Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ + Lp3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ + Lp4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ + Lp5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ + Lp6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ + Lp7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + + /** + * Returns the natural logarithm of the sum of the argument and 1. Note that for small values + * {@code x}, the result of {@code log1p(x)} is much closer to the true result of ln(1 + + * {@code x}) than the floating-point evaluation of {@code log(1.0+x)}. + * + * <p> + * Special cases: + * <ul> + * + * <li>If the argument is NaN or less than -1, then the result is NaN. + * + * <li>If the argument is positive infinity, then the result is positive infinity. + * + * <li>If the argument is negative one, then the result is negative infinity. + * + * <li>If the argument is zero, then the result is a zero with the same sign as the argument. + * + * </ul> + * + * @param x a value + * @return the value ln({@code x} + 1), the natural log of {@code x} + 1 + * @since 1.5 + */ + @SuppressWarnings("cast") + public static double log1p(double x) { + /* + * double log1p(double x) + * + * Method : 1. Argument Reduction: find k and f such that 1+x = 2^k * (1+f), where sqrt(2)/2 + * < 1+f < sqrt(2) . + * + * Note. If k=0, then f=x is exact. However, if k!=0, then f may not be representable + * exactly. In that case, a correction term is need. Let u=1+x rounded. Let c = (1+x)-u, + * then log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u), and add back the + * correction term c/u. (Note: when x > 2**53, one can simply return log(x)) + * + * 2. Approximation of log1p(f). Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) = + * 2s + 2/3 s**3 + 2/5 s**5 + ....., = 2s + s*R We use a special Reme algorithm on + * [0,0.1716] to generate a polynomial of degree 14 to approximate R The maximum error of + * this polynomial approximation is bounded by 2**-58.45. In other words, 2 4 6 8 10 12 14 + * R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s (the values of Lp1 to Lp7 are + * listed in the program) and | 2 14 | -58.45 | Lp1*s +...+Lp7*s - R(z) | <= 2 | | Note that + * 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. In order to guarantee error in log + * below 1ulp, we compute log by log1p(f) = f - (hfsq - s*(hfsq+R)). + * + * 3. Finally, log1p(x) = k*ln2 + log1p(f). = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) Here + * ln2 is split into two floating point number: ln2_hi + ln2_lo, where n*ln2_hi is always + * exact for |n| < 2000. + * + * Special cases: log1p(x) is NaN with signal if x < -1 (including -INF) ; log1p(+INF) is + * +INF; log1p(-1) is -INF with signal; log1p(NaN) is that NaN with no signal. + * + * Accuracy: according to an error analysis, the error is always less than 1 ulp (unit in + * the last place). + * + * Constants: The hexadecimal values are the intended ones for the following constants. The + * decimal values may be used, provided that the compiler will convert from decimal to + * binary accurately enough to produce the hexadecimal values shown. + * + * Note: Assuming log() return accurate answer, the following algorithm can be used to + * compute log1p(x) to within a few ULP: + * + * u = 1+x; if(u==1.0) return x ; else return log(u)*(x/(u-1.0)); + * + * See HP-15C Advanced Functions Handbook, p.193. + */ + double f = 0; + int k = 1, hu = 0; + final int hx = __HI(x); /* high word of x */ + final int ax = hx & 0x7fffffff; + if (hx < 0x3FDA827A) { /* x < 0.41422 */ + if (ax >= 0x3ff00000) { /* x <= -1.0 */ + return x == -1.0d ? -two54 / zero : /* log1p(-1)=-inf */ + (x - x) / (x - x); /* log1p(x<-1)=NaN */ + } + if (ax < 0x3e200000) { /* |x| < 2**-29 */ + if (two54 + x > zero /* raise inexact */ + && ax < 0x3c900000) /* |x| < 2**-54 */{ + return x; + } + return x - x * x * 0.5; + } + if (hx > 0 || hx <= ((int) 0xbfd2bec3)) { /* -0.2929<x<0.41422 */ + k = 0; + f = x; + hu = 1; + } + } + + if (hx >= 0x7ff00000) { + return x + x; + } + double c; + if (k != 0) { + final double u = hx < 0x43400000 ? 1.0 + x : x; + long ub = Double.doubleToRawLongBits(u); + hu = (int) (ub >> 32); /* high word of u */ + k = (hu >> 20) - 1023; + c = hx < 0x43400000 ? (k > 0 ? 1.0 - (u - x) : x - (u - 1.0)) / u : 0; + int newhu; + if ((hu &= 0x000fffff) < 0x6a09e) { + newhu = hu | 0x3ff00000; /* normalize u */ + } else { + k += 1; + newhu = hu | 0x3fe00000; /* normalize u/2 */ + hu = (0x00100000 - hu) >> 2; + } + f = setHigh32bits(ub, newhu) - 1.0; + } else + c = 0; + + double hfsq = 0.5 * f * f; + if (hu == 0) { /* |f| < 2**-20 */ + if (f == zero) { + return k == 0 ? zero : k * ln2_hi + (c + k * ln2_lo); + } + final double R = hfsq * (1.0 - 0.66666666666666666 * f); + return k == 0 ? f - R : k * ln2_hi - ((R - (k * ln2_lo + c)) - f); + } + final double s = f / (2.0 + f); + final double z = s * s; + final double R = s * (hfsq + z * (Lp1 + z * (Lp2 + z * (Lp3 + z * (Lp4 + z * (Lp5 + z * (Lp6 + z * Lp7))))))); + return k == 0 ? f - (hfsq - R) : k * ln2_hi - ((hfsq - (R + (k * ln2_lo + c))) - f); + } + + /** + * Returns the first floating-point argument with the sign of the second floating-point + * argument. For this method, a NaN {@code sign} argument is always treated as if it were + * positive. + * + * @param magnitude the parameter providing the magnitude of the result + * @param sign the parameter providing the sign of the result + * @return a value with the magnitude of {@code magnitude} and the sign of {@code sign}. + * @since 1.6 + */ + @SuppressWarnings("deprecation") + public static double copySign(double magnitude, double sign) { + return sun.misc.FpUtils.copySign(magnitude, sign); + } + + /** + * Returns the first floating-point argument with the sign of the second floating-point + * argument. For this method, a NaN {@code sign} argument is always treated as if it were + * positive. + * + * @param magnitude the parameter providing the magnitude of the result + * @param sign the parameter providing the sign of the result + * @return a value with the magnitude of {@code magnitude} and the sign of {@code sign}. + * @since 1.6 + */ + @SuppressWarnings("deprecation") + public static float copySign(float magnitude, float sign) { + return sun.misc.FpUtils.copySign(magnitude, sign); + } + + /** + * Returns the unbiased exponent used in the representation of a {@code float}. Special cases: + * + * <ul> + * <li>If the argument is NaN or infinite, then the result is {@link Float#MAX_EXPONENT} + 1. + * <li>If the argument is zero or subnormal, then the result is {@link Float#MIN_EXPONENT} -1. + * </ul> + * + * @param f a {@code float} value + * @since 1.6 + */ + @SuppressWarnings("deprecation") + public static int getExponent(float f) { + return sun.misc.FpUtils.getExponent(f); + } + + /** + * Returns the unbiased exponent used in the representation of a {@code double}. Special cases: + * + * <ul> + * <li>If the argument is NaN or infinite, then the result is {@link Double#MAX_EXPONENT} + 1. + * <li>If the argument is zero or subnormal, then the result is {@link Double#MIN_EXPONENT} -1. + * </ul> + * + * @param d a {@code double} value + * @since 1.6 + */ + @SuppressWarnings("deprecation") + public static int getExponent(double d) { + return sun.misc.FpUtils.getExponent(d); + } + + /** + * Returns the floating-point number adjacent to the first argument in the direction of the + * second argument. If both arguments compare as equal the second argument is returned. + * + * <p> + * Special cases: + * <ul> + * <li>If either argument is a NaN, then NaN is returned. + * + * <li>If both arguments are signed zeros, {@code direction} is returned unchanged (as implied + * by the requirement of returning the second argument if the arguments compare as equal). + * + * <li>If {@code start} is ±{@link Double#MIN_VALUE} and {@code direction} has a value + * such that the result should have a smaller magnitude, then a zero with the same sign as + * {@code start} is returned. + * + * <li>If {@code start} is infinite and {@code direction} has a value such that the result + * should have a smaller magnitude, {@link Double#MAX_VALUE} with the same sign as {@code start} + * is returned. + * + * <li>If {@code start} is equal to ± {@link Double#MAX_VALUE} and {@code direction} has + * a value such that the result should have a larger magnitude, an infinity with same sign as + * {@code start} is returned. + * </ul> + * + * @param start starting floating-point value + * @param direction value indicating which of {@code start}'s neighbors or {@code start} should + * be returned + * @return The floating-point number adjacent to {@code start} in the direction of + * {@code direction}. + * @since 1.6 + */ + @SuppressWarnings("deprecation") + public static double nextAfter(double start, double direction) { + return sun.misc.FpUtils.nextAfter(start, direction); + } + + /** + * Returns the floating-point number adjacent to the first argument in the direction of the + * second argument. If both arguments compare as equal a value equivalent to the second argument + * is returned. + * + * <p> + * Special cases: + * <ul> + * <li>If either argument is a NaN, then NaN is returned. + * + * <li>If both arguments are signed zeros, a value equivalent to {@code direction} is returned. + * + * <li>If {@code start} is ±{@link Float#MIN_VALUE} and {@code direction} has a value + * such that the result should have a smaller magnitude, then a zero with the same sign as + * {@code start} is returned. + * + * <li>If {@code start} is infinite and {@code direction} has a value such that the result + * should have a smaller magnitude, {@link Float#MAX_VALUE} with the same sign as {@code start} + * is returned. + * + * <li>If {@code start} is equal to ± {@link Float#MAX_VALUE} and {@code direction} has a + * value such that the result should have a larger magnitude, an infinity with same sign as + * {@code start} is returned. + * </ul> + * + * @param start starting floating-point value + * @param direction value indicating which of {@code start}'s neighbors or {@code start} should + * be returned + * @return The floating-point number adjacent to {@code start} in the direction of + * {@code direction}. + * @since 1.6 + */ + @SuppressWarnings("deprecation") + public static float nextAfter(float start, double direction) { + return sun.misc.FpUtils.nextAfter(start, direction); + } + + /** + * Returns the floating-point value adjacent to {@code d} in the direction of positive infinity. + * This method is semantically equivalent to {@code nextAfter(d, + * Double.POSITIVE_INFINITY)}; however, a {@code nextUp} implementation may run faster than its + * equivalent {@code nextAfter} call. + * + * <p> + * Special Cases: + * <ul> + * <li>If the argument is NaN, the result is NaN. + * + * <li>If the argument is positive infinity, the result is positive infinity. + * + * <li>If the argument is zero, the result is {@link Double#MIN_VALUE} + * + * </ul> + * + * @param d starting floating-point value + * @return The adjacent floating-point value closer to positive infinity. + * @since 1.6 + */ + @SuppressWarnings("deprecation") + public static double nextUp(double d) { + return sun.misc.FpUtils.nextUp(d); + } + + /** + * Returns the floating-point value adjacent to {@code f} in the direction of positive infinity. + * This method is semantically equivalent to {@code nextAfter(f, + * Float.POSITIVE_INFINITY)}; however, a {@code nextUp} implementation may run faster than its + * equivalent {@code nextAfter} call. + * + * <p> + * Special Cases: + * <ul> + * <li>If the argument is NaN, the result is NaN. + * + * <li>If the argument is positive infinity, the result is positive infinity. + * + * <li>If the argument is zero, the result is {@link Float#MIN_VALUE} + * + * </ul> + * + * @param f starting floating-point value + * @return The adjacent floating-point value closer to positive infinity. + * @since 1.6 + */ + @SuppressWarnings("deprecation") + public static float nextUp(float f) { + return sun.misc.FpUtils.nextUp(f); + } + + /** + * Return {@code d} × 2<sup>{@code scaleFactor}</sup> rounded as if performed by a single + * correctly rounded floating-point multiply to a member of the double value set. See the Java + * Language Specification for a discussion of floating-point value sets. If the exponent of the + * result is between {@link Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the answer is + * calculated exactly. If the exponent of the result would be larger than + * {@code Double.MAX_EXPONENT}, an infinity is returned. Note that if the result is subnormal, + * precision may be lost; that is, when {@code scalb(x, n)} is subnormal, + * {@code scalb(scalb(x, n), -n)} may not equal <i>x</i>. When the result is non-NaN, the result + * has the same sign as {@code d}. + * + * <p> + * Special cases: + * <ul> + * <li>If the first argument is NaN, NaN is returned. + * <li>If the first argument is infinite, then an infinity of the same sign is returned. + * <li>If the first argument is zero, then a zero of the same sign is returned. + * </ul> + * + * @param d number to be scaled by a power of two. + * @param scaleFactor power of 2 used to scale {@code d} + * @return {@code d} × 2<sup>{@code scaleFactor}</sup> + * @since 1.6 + */ + @SuppressWarnings("deprecation") + public static double scalb(double d, int scaleFactor) { + return sun.misc.FpUtils.scalb(d, scaleFactor); + } + + /** + * Return {@code f} × 2<sup>{@code scaleFactor}</sup> rounded as if performed by a single + * correctly rounded floating-point multiply to a member of the float value set. See the Java + * Language Specification for a discussion of floating-point value sets. If the exponent of the + * result is between {@link Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the answer is + * calculated exactly. If the exponent of the result would be larger than + * {@code Float.MAX_EXPONENT}, an infinity is returned. Note that if the result is subnormal, + * precision may be lost; that is, when {@code scalb(x, n)} is subnormal, + * {@code scalb(scalb(x, n), -n)} may not equal <i>x</i>. When the result is non-NaN, the result + * has the same sign as {@code f}. + * + * <p> + * Special cases: + * <ul> + * <li>If the first argument is NaN, NaN is returned. + * <li>If the first argument is infinite, then an infinity of the same sign is returned. + * <li>If the first argument is zero, then a zero of the same sign is returned. + * </ul> + * + * @param f number to be scaled by a power of two. + * @param scaleFactor power of 2 used to scale {@code f} + * @return {@code f} × 2<sup>{@code scaleFactor}</sup> + * @since 1.6 + */ + @SuppressWarnings("deprecation") + public static float scalb(float f, int scaleFactor) { + return sun.misc.FpUtils.scalb(f, scaleFactor); + } + + public static double setHhighbitsAddSome(double x, long highadd) { + return setHhighbitsAddSome(Double.doubleToRawLongBits(x), highadd); + } + + public static double setHhighbitsORSome(double x, long highOR) { + return Double.longBitsToDouble(Double.doubleToRawLongBits(x) | (highOR << 32)); + } + + public static double setHhighbitsAddSome(long xl, long highadd) { + return Double.longBitsToDouble((xl & clearHighmask) | (xl + highadd)); + } + + private static int __HI(double x) { + return (int) (Double.doubleToRawLongBits(x) >> 32); + } + + private static int __LO(double x) { + return (int) Double.doubleToRawLongBits(x); + } + + private static double clearLow32bits(double x) { + return Double.longBitsToDouble(Double.doubleToRawLongBits(x) & 0xFFFFFFFF00000000L); + } + + private static double setHigh32bits(double x, long newhigh) { + return setHigh32bits(Double.doubleToRawLongBits(x), newhigh); + } + + private static double setHigh32bitsXOR(double x, long toXor) { + return Double.longBitsToDouble((Double.doubleToRawLongBits(x)) ^ toXor); + } + + private static double addToHighBits(double x, long toadd) { + return addToHighBits(Double.doubleToRawLongBits(x), toadd); + } + + private static double addToHighBits(long x, long toadd) { + return Double.longBitsToDouble((x & clearHighmask) | (((x >> 32) + toadd) << 32)); + } + + private static double setHigh32bits(long x, long newhigh) { + return Double.longBitsToDouble((x & clearHighmask) | (newhigh << 32)); + } + + private static double setHigh32bitsDontMask(long x, long newhigh) { + return Double.longBitsToDouble(x | (newhigh << 32)); + } + + private static double setHigh32bits(long newhigh) { + return Double.longBitsToDouble((newhigh << 32)); + } + + private static double ldexp(double x, int exp) { + double r = x; + // set exponent of result to exp + long ir = Double.doubleToRawLongBits(r); + long oldexp = Math.getExponent(r); + long newexpbits = (oldexp + exp + DoubleConsts.EXP_BIAS) << (DoubleConsts.SIGNIFICAND_WIDTH - 1); + // clear exp bits to zero + ir &= ~DoubleConsts.EXP_BIT_MASK; + ir |= newexpbits; + return Double.longBitsToDouble(ir); + } + + @SuppressWarnings("deprecation") + private static double fmod(double x, double y) { + int ir, iy; + double r, w; + + if ((y == 0.0) || FpUtils.isNaN(y) || !FpUtils.isFinite(x)) { + return (x * y) / (x * y); + } + + r = Math.abs(x); + double absy = Math.abs(y); + iy = getExponent(absy); + while (r >= absy) { + ir = getExponent(r); + w = ldexp(absy, ir - iy); + r -= (w <= r ? w : w * 0.5); + } + return (x >= 0.0 ? r : -r); + } + +} \ No newline at end of file
--- a/graal/com.oracle.graal.test/src/com/oracle/graal/test/GraalTest.java Wed Jul 02 13:40:10 2014 -0700 +++ b/graal/com.oracle.graal.test/src/com/oracle/graal/test/GraalTest.java Wed Jul 02 23:40:19 2014 +0200 @@ -28,6 +28,7 @@ import org.junit.*; import org.junit.internal.*; +import static org.junit.Assert.*; /** * Base class for Graal tests. @@ -87,7 +88,11 @@ * @param message the identifying message for the {@link AssertionError} */ protected void assertDeepEquals(String message, Object expected, Object actual) { - assertDeepEquals(message, expected, actual, equalFloatsOrDoublesDelta()); + if (ulpsDelta() > 0) { + assertDeepEquals(message, expected, actual, ulpsDelta()); + } else { + assertDeepEquals(message, expected, actual, equalFloatsOrDoublesDelta()); + } } /** @@ -145,6 +150,61 @@ } /** + * Compares two given values for equality, doing a recursive test if both values are arrays of + * the same type. Uses {@linkplain StrictMath#ulp(float) ULP}s for comparison of floats. + * + * @param message the identifying message for the {@link AssertionError} + * @param ulpsDelta the maximum allowed ulps difference between two doubles or floats for which + * both numbers are still considered equal. + */ + protected void assertDeepEquals(String message, Object expected, Object actual, int ulpsDelta) { + ComparisonCriteria doubleUlpsDeltaCriteria = new ComparisonCriteria() { + @Override + protected void assertElementsEqual(Object e, Object a) { + assertTrue(message, e instanceof Double && a instanceof Double); + // determine acceptable error based on whether it is a normal number or a NaN/Inf + double de = (Double) e; + double epsilon = (!Double.isNaN(de) && Double.isFinite(de) ? ulpsDelta * Math.ulp(de) : 0); + Assert.assertEquals(message, (Double) e, (Double) a, epsilon); + } + }; + + ComparisonCriteria floatUlpsDeltaCriteria = new ComparisonCriteria() { + @Override + protected void assertElementsEqual(Object e, Object a) { + assertTrue(message, e instanceof Float && a instanceof Float); + // determine acceptable error based on whether it is a normal number or a NaN/Inf + float fe = (Float) e; + float epsilon = (!Float.isNaN(fe) && Float.isFinite(fe) ? ulpsDelta * Math.ulp(fe) : 0); + Assert.assertEquals(message, (Float) e, (Float) a, epsilon); + } + }; + + if (expected != null && actual != null) { + Class<?> expectedClass = expected.getClass(); + Class<?> actualClass = actual.getClass(); + if (expectedClass.isArray()) { + Assert.assertEquals(message, expectedClass, actualClass); + if (expected instanceof double[] || expected instanceof Object[]) { + doubleUlpsDeltaCriteria.arrayEquals(message, expected, actual); + return; + } else if (expected instanceof float[] || expected instanceof Object[]) { + floatUlpsDeltaCriteria.arrayEquals(message, expected, actual); + return; + } + } else if (expectedClass.equals(double.class) && actualClass.equals(double.class)) { + doubleUlpsDeltaCriteria.arrayEquals(message, expected, actual); + return; + } else if (expectedClass.equals(float.class) && actualClass.equals(float.class)) { + floatUlpsDeltaCriteria.arrayEquals(message, expected, actual); + return; + } + } + // anything else just use the non-ulps version + assertDeepEquals(message, expected, actual, equalFloatsOrDoublesDelta()); + } + + /** * Gets the value used by {@link #assertDeepEquals(Object, Object)} and * {@link #assertDeepEquals(String, Object, Object)} for the maximum delta between two doubles * or floats for which both numbers are still considered equal. @@ -153,6 +213,11 @@ return 0.0D; } + // unless overridden ulpsDelta is not used + protected int ulpsDelta() { + return 0; + } + @SuppressWarnings("serial") public static class MultiCauseAssertionError extends AssertionError {