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annotate src/share/vm/runtime/sharedRuntimeTrans.cpp @ 1972:f95d63e2154a
6989984: Use standard include model for Hospot
Summary: Replaced MakeDeps and the includeDB files with more standardized solutions.
Reviewed-by: coleenp, kvn, kamg
| author | stefank |
|---|---|
| date | Tue, 23 Nov 2010 13:22:55 -0800 |
| parents | 126ea7725993 |
| children | 63a4eb8bcd23 bdd155477289 |
| rev | line source |
|---|---|
| 0 | 1 /* |
| 1972 | 2 * Copyright (c) 2005, 2010, Oracle and/or its affiliates. All rights reserved. |
| 0 | 3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| 4 * | |
| 5 * This code is free software; you can redistribute it and/or modify it | |
| 6 * under the terms of the GNU General Public License version 2 only, as | |
| 7 * published by the Free Software Foundation. | |
| 8 * | |
| 9 * This code is distributed in the hope that it will be useful, but WITHOUT | |
| 10 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 11 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 12 * version 2 for more details (a copy is included in the LICENSE file that | |
| 13 * accompanied this code). | |
| 14 * | |
| 15 * You should have received a copy of the GNU General Public License version | |
| 16 * 2 along with this work; if not, write to the Free Software Foundation, | |
| 17 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. | |
| 18 * | |
|
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19 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
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20 * or visit www.oracle.com if you need additional information or have any |
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21 * questions. |
| 0 | 22 * |
| 23 */ | |
| 24 | |
| 1972 | 25 #include "precompiled.hpp" |
| 26 #include "prims/jni.h" | |
| 27 #include "runtime/interfaceSupport.hpp" | |
| 28 #include "runtime/sharedRuntime.hpp" | |
| 0 | 29 |
| 30 // This file contains copies of the fdlibm routines used by | |
| 31 // StrictMath. It turns out that it is almost always required to use | |
| 32 // these runtime routines; the Intel CPU doesn't meet the Java | |
| 33 // specification for sin/cos outside a certain limited argument range, | |
| 34 // and the SPARC CPU doesn't appear to have sin/cos instructions. It | |
| 35 // also turns out that avoiding the indirect call through function | |
| 36 // pointer out to libjava.so in SharedRuntime speeds these routines up | |
| 37 // by roughly 15% on both Win32/x86 and Solaris/SPARC. | |
| 38 | |
| 39 // Enabling optimizations in this file causes incorrect code to be | |
| 40 // generated; can not figure out how to turn down optimization for one | |
| 41 // file in the IDE on Windows | |
| 42 #ifdef WIN32 | |
| 43 # pragma optimize ( "", off ) | |
| 44 #endif | |
| 45 | |
| 46 #include <math.h> | |
| 47 | |
| 48 // VM_LITTLE_ENDIAN is #defined appropriately in the Makefiles | |
| 49 // [jk] this is not 100% correct because the float word order may different | |
| 50 // from the byte order (e.g. on ARM) | |
| 51 #ifdef VM_LITTLE_ENDIAN | |
| 52 # define __HI(x) *(1+(int*)&x) | |
| 53 # define __LO(x) *(int*)&x | |
| 54 #else | |
| 55 # define __HI(x) *(int*)&x | |
| 56 # define __LO(x) *(1+(int*)&x) | |
| 57 #endif | |
| 58 | |
| 59 double copysign(double x, double y) { | |
| 60 __HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000); | |
| 61 return x; | |
| 62 } | |
| 63 | |
| 64 /* | |
| 65 * ==================================================== | |
|
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66 * Copyright (c) 1998 Oracle and/or its affiliates. All rights reserved. |
| 0 | 67 * |
| 68 * Developed at SunSoft, a Sun Microsystems, Inc. business. | |
| 69 * Permission to use, copy, modify, and distribute this | |
| 70 * software is freely granted, provided that this notice | |
| 71 * is preserved. | |
| 72 * ==================================================== | |
| 73 */ | |
| 74 | |
| 75 /* | |
| 76 * scalbn (double x, int n) | |
| 77 * scalbn(x,n) returns x* 2**n computed by exponent | |
| 78 * manipulation rather than by actually performing an | |
| 79 * exponentiation or a multiplication. | |
| 80 */ | |
| 81 | |
| 82 static const double | |
| 83 two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ | |
| 84 twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ | |
| 85 hugeX = 1.0e+300, | |
| 86 tiny = 1.0e-300; | |
| 87 | |
| 88 double scalbn (double x, int n) { | |
| 89 int k,hx,lx; | |
| 90 hx = __HI(x); | |
| 91 lx = __LO(x); | |
| 92 k = (hx&0x7ff00000)>>20; /* extract exponent */ | |
| 93 if (k==0) { /* 0 or subnormal x */ | |
| 94 if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ | |
| 95 x *= two54; | |
| 96 hx = __HI(x); | |
| 97 k = ((hx&0x7ff00000)>>20) - 54; | |
| 98 if (n< -50000) return tiny*x; /*underflow*/ | |
| 99 } | |
| 100 if (k==0x7ff) return x+x; /* NaN or Inf */ | |
| 101 k = k+n; | |
| 102 if (k > 0x7fe) return hugeX*copysign(hugeX,x); /* overflow */ | |
| 103 if (k > 0) /* normal result */ | |
| 104 {__HI(x) = (hx&0x800fffff)|(k<<20); return x;} | |
| 105 if (k <= -54) { | |
| 106 if (n > 50000) /* in case integer overflow in n+k */ | |
| 107 return hugeX*copysign(hugeX,x); /*overflow*/ | |
| 108 else return tiny*copysign(tiny,x); /*underflow*/ | |
| 109 } | |
| 110 k += 54; /* subnormal result */ | |
| 111 __HI(x) = (hx&0x800fffff)|(k<<20); | |
| 112 return x*twom54; | |
| 113 } | |
| 114 | |
| 115 /* __ieee754_log(x) | |
| 116 * Return the logrithm of x | |
| 117 * | |
| 118 * Method : | |
| 119 * 1. Argument Reduction: find k and f such that | |
| 120 * x = 2^k * (1+f), | |
| 121 * where sqrt(2)/2 < 1+f < sqrt(2) . | |
| 122 * | |
| 123 * 2. Approximation of log(1+f). | |
| 124 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) | |
| 125 * = 2s + 2/3 s**3 + 2/5 s**5 + ....., | |
| 126 * = 2s + s*R | |
| 127 * We use a special Reme algorithm on [0,0.1716] to generate | |
| 128 * a polynomial of degree 14 to approximate R The maximum error | |
| 129 * of this polynomial approximation is bounded by 2**-58.45. In | |
| 130 * other words, | |
| 131 * 2 4 6 8 10 12 14 | |
| 132 * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s | |
| 133 * (the values of Lg1 to Lg7 are listed in the program) | |
| 134 * and | |
| 135 * | 2 14 | -58.45 | |
| 136 * | Lg1*s +...+Lg7*s - R(z) | <= 2 | |
| 137 * | | | |
| 138 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. | |
| 139 * In order to guarantee error in log below 1ulp, we compute log | |
| 140 * by | |
| 141 * log(1+f) = f - s*(f - R) (if f is not too large) | |
| 142 * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) | |
| 143 * | |
| 144 * 3. Finally, log(x) = k*ln2 + log(1+f). | |
| 145 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) | |
| 146 * Here ln2 is split into two floating point number: | |
| 147 * ln2_hi + ln2_lo, | |
| 148 * where n*ln2_hi is always exact for |n| < 2000. | |
| 149 * | |
| 150 * Special cases: | |
| 151 * log(x) is NaN with signal if x < 0 (including -INF) ; | |
| 152 * log(+INF) is +INF; log(0) is -INF with signal; | |
| 153 * log(NaN) is that NaN with no signal. | |
| 154 * | |
| 155 * Accuracy: | |
| 156 * according to an error analysis, the error is always less than | |
| 157 * 1 ulp (unit in the last place). | |
| 158 * | |
| 159 * Constants: | |
| 160 * The hexadecimal values are the intended ones for the following | |
| 161 * constants. The decimal values may be used, provided that the | |
| 162 * compiler will convert from decimal to binary accurately enough | |
| 163 * to produce the hexadecimal values shown. | |
| 164 */ | |
| 165 | |
| 166 static const double | |
| 167 ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ | |
| 168 ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ | |
| 169 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ | |
| 170 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ | |
| 171 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ | |
| 172 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ | |
| 173 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ | |
| 174 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ | |
| 175 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ | |
| 176 | |
| 177 static double zero = 0.0; | |
| 178 | |
| 179 static double __ieee754_log(double x) { | |
| 180 double hfsq,f,s,z,R,w,t1,t2,dk; | |
| 181 int k,hx,i,j; | |
| 182 unsigned lx; | |
| 183 | |
| 184 hx = __HI(x); /* high word of x */ | |
| 185 lx = __LO(x); /* low word of x */ | |
| 186 | |
| 187 k=0; | |
| 188 if (hx < 0x00100000) { /* x < 2**-1022 */ | |
| 189 if (((hx&0x7fffffff)|lx)==0) | |
| 190 return -two54/zero; /* log(+-0)=-inf */ | |
| 191 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ | |
| 192 k -= 54; x *= two54; /* subnormal number, scale up x */ | |
| 193 hx = __HI(x); /* high word of x */ | |
| 194 } | |
| 195 if (hx >= 0x7ff00000) return x+x; | |
| 196 k += (hx>>20)-1023; | |
| 197 hx &= 0x000fffff; | |
| 198 i = (hx+0x95f64)&0x100000; | |
| 199 __HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */ | |
| 200 k += (i>>20); | |
| 201 f = x-1.0; | |
| 202 if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ | |
| 203 if(f==zero) { | |
| 204 if (k==0) return zero; | |
| 205 else {dk=(double)k; return dk*ln2_hi+dk*ln2_lo;} | |
| 206 } | |
| 207 R = f*f*(0.5-0.33333333333333333*f); | |
| 208 if(k==0) return f-R; else {dk=(double)k; | |
| 209 return dk*ln2_hi-((R-dk*ln2_lo)-f);} | |
| 210 } | |
| 211 s = f/(2.0+f); | |
| 212 dk = (double)k; | |
| 213 z = s*s; | |
| 214 i = hx-0x6147a; | |
| 215 w = z*z; | |
| 216 j = 0x6b851-hx; | |
| 217 t1= w*(Lg2+w*(Lg4+w*Lg6)); | |
| 218 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); | |
| 219 i |= j; | |
| 220 R = t2+t1; | |
| 221 if(i>0) { | |
| 222 hfsq=0.5*f*f; | |
| 223 if(k==0) return f-(hfsq-s*(hfsq+R)); else | |
| 224 return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); | |
| 225 } else { | |
| 226 if(k==0) return f-s*(f-R); else | |
| 227 return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); | |
| 228 } | |
| 229 } | |
| 230 | |
| 231 JRT_LEAF(jdouble, SharedRuntime::dlog(jdouble x)) | |
| 232 return __ieee754_log(x); | |
| 233 JRT_END | |
| 234 | |
| 235 /* __ieee754_log10(x) | |
| 236 * Return the base 10 logarithm of x | |
| 237 * | |
| 238 * Method : | |
| 239 * Let log10_2hi = leading 40 bits of log10(2) and | |
| 240 * log10_2lo = log10(2) - log10_2hi, | |
| 241 * ivln10 = 1/log(10) rounded. | |
| 242 * Then | |
| 243 * n = ilogb(x), | |
| 244 * if(n<0) n = n+1; | |
| 245 * x = scalbn(x,-n); | |
| 246 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) | |
| 247 * | |
| 248 * Note 1: | |
| 249 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding | |
| 250 * mode must set to Round-to-Nearest. | |
| 251 * Note 2: | |
| 252 * [1/log(10)] rounded to 53 bits has error .198 ulps; | |
| 253 * log10 is monotonic at all binary break points. | |
| 254 * | |
| 255 * Special cases: | |
| 256 * log10(x) is NaN with signal if x < 0; | |
| 257 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; | |
| 258 * log10(NaN) is that NaN with no signal; | |
| 259 * log10(10**N) = N for N=0,1,...,22. | |
| 260 * | |
| 261 * Constants: | |
| 262 * The hexadecimal values are the intended ones for the following constants. | |
| 263 * The decimal values may be used, provided that the compiler will convert | |
| 264 * from decimal to binary accurately enough to produce the hexadecimal values | |
| 265 * shown. | |
| 266 */ | |
| 267 | |
| 268 static const double | |
| 269 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ | |
| 270 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ | |
| 271 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ | |
| 272 | |
| 273 static double __ieee754_log10(double x) { | |
| 274 double y,z; | |
| 275 int i,k,hx; | |
| 276 unsigned lx; | |
| 277 | |
| 278 hx = __HI(x); /* high word of x */ | |
| 279 lx = __LO(x); /* low word of x */ | |
| 280 | |
| 281 k=0; | |
| 282 if (hx < 0x00100000) { /* x < 2**-1022 */ | |
| 283 if (((hx&0x7fffffff)|lx)==0) | |
| 284 return -two54/zero; /* log(+-0)=-inf */ | |
| 285 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ | |
| 286 k -= 54; x *= two54; /* subnormal number, scale up x */ | |
| 287 hx = __HI(x); /* high word of x */ | |
| 288 } | |
| 289 if (hx >= 0x7ff00000) return x+x; | |
| 290 k += (hx>>20)-1023; | |
| 291 i = ((unsigned)k&0x80000000)>>31; | |
| 292 hx = (hx&0x000fffff)|((0x3ff-i)<<20); | |
| 293 y = (double)(k+i); | |
| 294 __HI(x) = hx; | |
| 295 z = y*log10_2lo + ivln10*__ieee754_log(x); | |
| 296 return z+y*log10_2hi; | |
| 297 } | |
| 298 | |
| 299 JRT_LEAF(jdouble, SharedRuntime::dlog10(jdouble x)) | |
| 300 return __ieee754_log10(x); | |
| 301 JRT_END | |
| 302 | |
| 303 | |
| 304 /* __ieee754_exp(x) | |
| 305 * Returns the exponential of x. | |
| 306 * | |
| 307 * Method | |
| 308 * 1. Argument reduction: | |
| 309 * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. | |
| 310 * Given x, find r and integer k such that | |
| 311 * | |
| 312 * x = k*ln2 + r, |r| <= 0.5*ln2. | |
| 313 * | |
| 314 * Here r will be represented as r = hi-lo for better | |
| 315 * accuracy. | |
| 316 * | |
| 317 * 2. Approximation of exp(r) by a special rational function on | |
| 318 * the interval [0,0.34658]: | |
| 319 * Write | |
| 320 * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... | |
| 321 * We use a special Reme algorithm on [0,0.34658] to generate | |
| 322 * a polynomial of degree 5 to approximate R. The maximum error | |
| 323 * of this polynomial approximation is bounded by 2**-59. In | |
| 324 * other words, | |
| 325 * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 | |
| 326 * (where z=r*r, and the values of P1 to P5 are listed below) | |
| 327 * and | |
| 328 * | 5 | -59 | |
| 329 * | 2.0+P1*z+...+P5*z - R(z) | <= 2 | |
| 330 * | | | |
| 331 * The computation of exp(r) thus becomes | |
| 332 * 2*r | |
| 333 * exp(r) = 1 + ------- | |
| 334 * R - r | |
| 335 * r*R1(r) | |
| 336 * = 1 + r + ----------- (for better accuracy) | |
| 337 * 2 - R1(r) | |
| 338 * where | |
| 339 * 2 4 10 | |
| 340 * R1(r) = r - (P1*r + P2*r + ... + P5*r ). | |
| 341 * | |
| 342 * 3. Scale back to obtain exp(x): | |
| 343 * From step 1, we have | |
| 344 * exp(x) = 2^k * exp(r) | |
| 345 * | |
| 346 * Special cases: | |
| 347 * exp(INF) is INF, exp(NaN) is NaN; | |
| 348 * exp(-INF) is 0, and | |
| 349 * for finite argument, only exp(0)=1 is exact. | |
| 350 * | |
| 351 * Accuracy: | |
| 352 * according to an error analysis, the error is always less than | |
| 353 * 1 ulp (unit in the last place). | |
| 354 * | |
| 355 * Misc. info. | |
| 356 * For IEEE double | |
| 357 * if x > 7.09782712893383973096e+02 then exp(x) overflow | |
| 358 * if x < -7.45133219101941108420e+02 then exp(x) underflow | |
| 359 * | |
| 360 * Constants: | |
| 361 * The hexadecimal values are the intended ones for the following | |
| 362 * constants. The decimal values may be used, provided that the | |
| 363 * compiler will convert from decimal to binary accurately enough | |
| 364 * to produce the hexadecimal values shown. | |
| 365 */ | |
| 366 | |
| 367 static const double | |
| 368 one = 1.0, | |
| 369 halF[2] = {0.5,-0.5,}, | |
| 370 twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/ | |
| 371 o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ | |
| 372 u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ | |
| 373 ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ | |
| 374 -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */ | |
| 375 ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ | |
| 376 -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ | |
| 377 invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ | |
| 378 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ | |
| 379 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ | |
| 380 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ | |
| 381 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ | |
| 382 P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ | |
| 383 | |
| 384 static double __ieee754_exp(double x) { | |
| 385 double y,hi=0,lo=0,c,t; | |
| 386 int k=0,xsb; | |
| 387 unsigned hx; | |
| 388 | |
| 389 hx = __HI(x); /* high word of x */ | |
| 390 xsb = (hx>>31)&1; /* sign bit of x */ | |
| 391 hx &= 0x7fffffff; /* high word of |x| */ | |
| 392 | |
| 393 /* filter out non-finite argument */ | |
| 394 if(hx >= 0x40862E42) { /* if |x|>=709.78... */ | |
| 395 if(hx>=0x7ff00000) { | |
| 396 if(((hx&0xfffff)|__LO(x))!=0) | |
| 397 return x+x; /* NaN */ | |
| 398 else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ | |
| 399 } | |
| 400 if(x > o_threshold) return hugeX*hugeX; /* overflow */ | |
| 401 if(x < u_threshold) return twom1000*twom1000; /* underflow */ | |
| 402 } | |
| 403 | |
| 404 /* argument reduction */ | |
| 405 if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ | |
| 406 if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ | |
| 407 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; | |
| 408 } else { | |
| 409 k = (int)(invln2*x+halF[xsb]); | |
| 410 t = k; | |
| 411 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ | |
| 412 lo = t*ln2LO[0]; | |
| 413 } | |
| 414 x = hi - lo; | |
| 415 } | |
| 416 else if(hx < 0x3e300000) { /* when |x|<2**-28 */ | |
| 417 if(hugeX+x>one) return one+x;/* trigger inexact */ | |
| 418 } | |
| 419 else k = 0; | |
| 420 | |
| 421 /* x is now in primary range */ | |
| 422 t = x*x; | |
| 423 c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); | |
| 424 if(k==0) return one-((x*c)/(c-2.0)-x); | |
| 425 else y = one-((lo-(x*c)/(2.0-c))-hi); | |
| 426 if(k >= -1021) { | |
| 427 __HI(y) += (k<<20); /* add k to y's exponent */ | |
| 428 return y; | |
| 429 } else { | |
| 430 __HI(y) += ((k+1000)<<20);/* add k to y's exponent */ | |
| 431 return y*twom1000; | |
| 432 } | |
| 433 } | |
| 434 | |
| 435 JRT_LEAF(jdouble, SharedRuntime::dexp(jdouble x)) | |
| 436 return __ieee754_exp(x); | |
| 437 JRT_END | |
| 438 | |
| 439 /* __ieee754_pow(x,y) return x**y | |
| 440 * | |
| 441 * n | |
| 442 * Method: Let x = 2 * (1+f) | |
| 443 * 1. Compute and return log2(x) in two pieces: | |
| 444 * log2(x) = w1 + w2, | |
| 445 * where w1 has 53-24 = 29 bit trailing zeros. | |
| 446 * 2. Perform y*log2(x) = n+y' by simulating muti-precision | |
| 447 * arithmetic, where |y'|<=0.5. | |
| 448 * 3. Return x**y = 2**n*exp(y'*log2) | |
| 449 * | |
| 450 * Special cases: | |
| 451 * 1. (anything) ** 0 is 1 | |
| 452 * 2. (anything) ** 1 is itself | |
| 453 * 3. (anything) ** NAN is NAN | |
| 454 * 4. NAN ** (anything except 0) is NAN | |
| 455 * 5. +-(|x| > 1) ** +INF is +INF | |
| 456 * 6. +-(|x| > 1) ** -INF is +0 | |
| 457 * 7. +-(|x| < 1) ** +INF is +0 | |
| 458 * 8. +-(|x| < 1) ** -INF is +INF | |
| 459 * 9. +-1 ** +-INF is NAN | |
| 460 * 10. +0 ** (+anything except 0, NAN) is +0 | |
| 461 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 | |
| 462 * 12. +0 ** (-anything except 0, NAN) is +INF | |
| 463 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF | |
| 464 * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) | |
| 465 * 15. +INF ** (+anything except 0,NAN) is +INF | |
| 466 * 16. +INF ** (-anything except 0,NAN) is +0 | |
| 467 * 17. -INF ** (anything) = -0 ** (-anything) | |
| 468 * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) | |
| 469 * 19. (-anything except 0 and inf) ** (non-integer) is NAN | |
| 470 * | |
| 471 * Accuracy: | |
| 472 * pow(x,y) returns x**y nearly rounded. In particular | |
| 473 * pow(integer,integer) | |
| 474 * always returns the correct integer provided it is | |
| 475 * representable. | |
| 476 * | |
| 477 * Constants : | |
| 478 * The hexadecimal values are the intended ones for the following | |
| 479 * constants. The decimal values may be used, provided that the | |
| 480 * compiler will convert from decimal to binary accurately enough | |
| 481 * to produce the hexadecimal values shown. | |
| 482 */ | |
| 483 | |
| 484 static const double | |
| 485 bp[] = {1.0, 1.5,}, | |
| 486 dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ | |
| 487 dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ | |
| 488 zeroX = 0.0, | |
| 489 two = 2.0, | |
| 490 two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ | |
| 491 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ | |
| 492 L1X = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ | |
| 493 L2X = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ | |
| 494 L3X = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ | |
| 495 L4X = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ | |
| 496 L5X = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ | |
| 497 L6X = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ | |
| 498 lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ | |
| 499 lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ | |
| 500 lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ | |
| 501 ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ | |
| 502 cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ | |
| 503 cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ | |
| 504 cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ | |
| 505 ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ | |
| 506 ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ | |
| 507 ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ | |
| 508 | |
| 509 double __ieee754_pow(double x, double y) { | |
| 510 double z,ax,z_h,z_l,p_h,p_l; | |
| 511 double y1,t1,t2,r,s,t,u,v,w; | |
| 512 int i0,i1,i,j,k,yisint,n; | |
| 513 int hx,hy,ix,iy; | |
| 514 unsigned lx,ly; | |
| 515 | |
| 516 i0 = ((*(int*)&one)>>29)^1; i1=1-i0; | |
| 517 hx = __HI(x); lx = __LO(x); | |
| 518 hy = __HI(y); ly = __LO(y); | |
| 519 ix = hx&0x7fffffff; iy = hy&0x7fffffff; | |
| 520 | |
| 521 /* y==zero: x**0 = 1 */ | |
| 522 if((iy|ly)==0) return one; | |
| 523 | |
| 524 /* +-NaN return x+y */ | |
| 525 if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || | |
| 526 iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) | |
| 527 return x+y; | |
| 528 | |
| 529 /* determine if y is an odd int when x < 0 | |
| 530 * yisint = 0 ... y is not an integer | |
| 531 * yisint = 1 ... y is an odd int | |
| 532 * yisint = 2 ... y is an even int | |
| 533 */ | |
| 534 yisint = 0; | |
| 535 if(hx<0) { | |
| 536 if(iy>=0x43400000) yisint = 2; /* even integer y */ | |
| 537 else if(iy>=0x3ff00000) { | |
| 538 k = (iy>>20)-0x3ff; /* exponent */ | |
| 539 if(k>20) { | |
| 540 j = ly>>(52-k); | |
| 541 if((unsigned)(j<<(52-k))==ly) yisint = 2-(j&1); | |
| 542 } else if(ly==0) { | |
| 543 j = iy>>(20-k); | |
| 544 if((j<<(20-k))==iy) yisint = 2-(j&1); | |
| 545 } | |
| 546 } | |
| 547 } | |
| 548 | |
| 549 /* special value of y */ | |
| 550 if(ly==0) { | |
| 551 if (iy==0x7ff00000) { /* y is +-inf */ | |
| 552 if(((ix-0x3ff00000)|lx)==0) | |
| 553 return y - y; /* inf**+-1 is NaN */ | |
| 554 else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ | |
| 555 return (hy>=0)? y: zeroX; | |
| 556 else /* (|x|<1)**-,+inf = inf,0 */ | |
| 557 return (hy<0)?-y: zeroX; | |
| 558 } | |
| 559 if(iy==0x3ff00000) { /* y is +-1 */ | |
| 560 if(hy<0) return one/x; else return x; | |
| 561 } | |
| 562 if(hy==0x40000000) return x*x; /* y is 2 */ | |
| 563 if(hy==0x3fe00000) { /* y is 0.5 */ | |
| 564 if(hx>=0) /* x >= +0 */ | |
| 565 return sqrt(x); | |
| 566 } | |
| 567 } | |
| 568 | |
| 569 ax = fabsd(x); | |
| 570 /* special value of x */ | |
| 571 if(lx==0) { | |
| 572 if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ | |
| 573 z = ax; /*x is +-0,+-inf,+-1*/ | |
| 574 if(hy<0) z = one/z; /* z = (1/|x|) */ | |
| 575 if(hx<0) { | |
| 576 if(((ix-0x3ff00000)|yisint)==0) { | |
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577 #ifdef CAN_USE_NAN_DEFINE |
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578 z = NAN; |
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579 #else |
| 0 | 580 z = (z-z)/(z-z); /* (-1)**non-int is NaN */ |
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581 #endif |
| 0 | 582 } else if(yisint==1) |
| 583 z = -1.0*z; /* (x<0)**odd = -(|x|**odd) */ | |
| 584 } | |
| 585 return z; | |
| 586 } | |
| 587 } | |
| 588 | |
| 589 n = (hx>>31)+1; | |
| 590 | |
| 591 /* (x<0)**(non-int) is NaN */ | |
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592 if((n|yisint)==0) |
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593 #ifdef CAN_USE_NAN_DEFINE |
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594 return NAN; |
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595 #else |
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596 return (x-x)/(x-x); |
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597 #endif |
| 0 | 598 |
| 599 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ | |
| 600 if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ | |
| 601 | |
| 602 /* |y| is huge */ | |
| 603 if(iy>0x41e00000) { /* if |y| > 2**31 */ | |
| 604 if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ | |
| 605 if(ix<=0x3fefffff) return (hy<0)? hugeX*hugeX:tiny*tiny; | |
| 606 if(ix>=0x3ff00000) return (hy>0)? hugeX*hugeX:tiny*tiny; | |
| 607 } | |
| 608 /* over/underflow if x is not close to one */ | |
| 609 if(ix<0x3fefffff) return (hy<0)? s*hugeX*hugeX:s*tiny*tiny; | |
| 610 if(ix>0x3ff00000) return (hy>0)? s*hugeX*hugeX:s*tiny*tiny; | |
| 611 /* now |1-x| is tiny <= 2**-20, suffice to compute | |
| 612 log(x) by x-x^2/2+x^3/3-x^4/4 */ | |
| 613 t = ax-one; /* t has 20 trailing zeros */ | |
| 614 w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); | |
| 615 u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ | |
| 616 v = t*ivln2_l-w*ivln2; | |
| 617 t1 = u+v; | |
| 618 __LO(t1) = 0; | |
| 619 t2 = v-(t1-u); | |
| 620 } else { | |
| 621 double ss,s2,s_h,s_l,t_h,t_l; | |
| 622 n = 0; | |
| 623 /* take care subnormal number */ | |
| 624 if(ix<0x00100000) | |
| 625 {ax *= two53; n -= 53; ix = __HI(ax); } | |
| 626 n += ((ix)>>20)-0x3ff; | |
| 627 j = ix&0x000fffff; | |
| 628 /* determine interval */ | |
| 629 ix = j|0x3ff00000; /* normalize ix */ | |
| 630 if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */ | |
| 631 else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ | |
| 632 else {k=0;n+=1;ix -= 0x00100000;} | |
| 633 __HI(ax) = ix; | |
| 634 | |
| 635 /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ | |
| 636 u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ | |
| 637 v = one/(ax+bp[k]); | |
| 638 ss = u*v; | |
| 639 s_h = ss; | |
| 640 __LO(s_h) = 0; | |
| 641 /* t_h=ax+bp[k] High */ | |
| 642 t_h = zeroX; | |
| 643 __HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18); | |
| 644 t_l = ax - (t_h-bp[k]); | |
| 645 s_l = v*((u-s_h*t_h)-s_h*t_l); | |
| 646 /* compute log(ax) */ | |
| 647 s2 = ss*ss; | |
| 648 r = s2*s2*(L1X+s2*(L2X+s2*(L3X+s2*(L4X+s2*(L5X+s2*L6X))))); | |
| 649 r += s_l*(s_h+ss); | |
| 650 s2 = s_h*s_h; | |
| 651 t_h = 3.0+s2+r; | |
| 652 __LO(t_h) = 0; | |
| 653 t_l = r-((t_h-3.0)-s2); | |
| 654 /* u+v = ss*(1+...) */ | |
| 655 u = s_h*t_h; | |
| 656 v = s_l*t_h+t_l*ss; | |
| 657 /* 2/(3log2)*(ss+...) */ | |
| 658 p_h = u+v; | |
| 659 __LO(p_h) = 0; | |
| 660 p_l = v-(p_h-u); | |
| 661 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ | |
| 662 z_l = cp_l*p_h+p_l*cp+dp_l[k]; | |
| 663 /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ | |
| 664 t = (double)n; | |
| 665 t1 = (((z_h+z_l)+dp_h[k])+t); | |
| 666 __LO(t1) = 0; | |
| 667 t2 = z_l-(((t1-t)-dp_h[k])-z_h); | |
| 668 } | |
| 669 | |
| 670 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ | |
| 671 y1 = y; | |
| 672 __LO(y1) = 0; | |
| 673 p_l = (y-y1)*t1+y*t2; | |
| 674 p_h = y1*t1; | |
| 675 z = p_l+p_h; | |
| 676 j = __HI(z); | |
| 677 i = __LO(z); | |
| 678 if (j>=0x40900000) { /* z >= 1024 */ | |
| 679 if(((j-0x40900000)|i)!=0) /* if z > 1024 */ | |
| 680 return s*hugeX*hugeX; /* overflow */ | |
| 681 else { | |
| 682 if(p_l+ovt>z-p_h) return s*hugeX*hugeX; /* overflow */ | |
| 683 } | |
| 684 } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ | |
| 685 if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ | |
| 686 return s*tiny*tiny; /* underflow */ | |
| 687 else { | |
| 688 if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ | |
| 689 } | |
| 690 } | |
| 691 /* | |
| 692 * compute 2**(p_h+p_l) | |
| 693 */ | |
| 694 i = j&0x7fffffff; | |
| 695 k = (i>>20)-0x3ff; | |
| 696 n = 0; | |
| 697 if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ | |
| 698 n = j+(0x00100000>>(k+1)); | |
| 699 k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ | |
| 700 t = zeroX; | |
| 701 __HI(t) = (n&~(0x000fffff>>k)); | |
| 702 n = ((n&0x000fffff)|0x00100000)>>(20-k); | |
| 703 if(j<0) n = -n; | |
| 704 p_h -= t; | |
| 705 } | |
| 706 t = p_l+p_h; | |
| 707 __LO(t) = 0; | |
| 708 u = t*lg2_h; | |
| 709 v = (p_l-(t-p_h))*lg2+t*lg2_l; | |
| 710 z = u+v; | |
| 711 w = v-(z-u); | |
| 712 t = z*z; | |
| 713 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); | |
| 714 r = (z*t1)/(t1-two)-(w+z*w); | |
| 715 z = one-(r-z); | |
| 716 j = __HI(z); | |
| 717 j += (n<<20); | |
| 718 if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */ | |
| 719 else __HI(z) += (n<<20); | |
| 720 return s*z; | |
| 721 } | |
| 722 | |
| 723 | |
| 724 JRT_LEAF(jdouble, SharedRuntime::dpow(jdouble x, jdouble y)) | |
| 725 return __ieee754_pow(x, y); | |
| 726 JRT_END | |
| 727 | |
| 728 #ifdef WIN32 | |
| 729 # pragma optimize ( "", on ) | |
| 730 #endif |