Mercurial > hg > graal-compiler
annotate src/share/vm/runtime/sharedRuntimeTrans.cpp @ 20527:8cb56c8cb30d
Merge
| author | jiangli |
|---|---|
| date | Mon, 15 Sep 2014 16:39:00 -0400 |
| parents | a073be2ce5c2 |
| children | 7848fc12602b |
| rev | line source |
|---|---|
| 0 | 1 /* |
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2 * Copyright (c) 2005, 2014, 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 | |
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43 # pragma warning( disable: 4748 ) // /GS can not protect parameters and local variables from local buffer overrun because optimizations are disabled in function |
| 0 | 44 # pragma optimize ( "", off ) |
| 45 #endif | |
| 46 | |
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47 #include "runtime/sharedRuntimeMath.hpp" |
| 0 | 48 |
| 49 /* __ieee754_log(x) | |
| 50 * Return the logrithm of x | |
| 51 * | |
| 52 * Method : | |
| 53 * 1. Argument Reduction: find k and f such that | |
| 54 * x = 2^k * (1+f), | |
| 55 * where sqrt(2)/2 < 1+f < sqrt(2) . | |
| 56 * | |
| 57 * 2. Approximation of log(1+f). | |
| 58 * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) | |
| 59 * = 2s + 2/3 s**3 + 2/5 s**5 + ....., | |
| 60 * = 2s + s*R | |
| 61 * We use a special Reme algorithm on [0,0.1716] to generate | |
| 62 * a polynomial of degree 14 to approximate R The maximum error | |
| 63 * of this polynomial approximation is bounded by 2**-58.45. In | |
| 64 * other words, | |
| 65 * 2 4 6 8 10 12 14 | |
| 66 * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s | |
| 67 * (the values of Lg1 to Lg7 are listed in the program) | |
| 68 * and | |
| 69 * | 2 14 | -58.45 | |
| 70 * | Lg1*s +...+Lg7*s - R(z) | <= 2 | |
| 71 * | | | |
| 72 * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. | |
| 73 * In order to guarantee error in log below 1ulp, we compute log | |
| 74 * by | |
| 75 * log(1+f) = f - s*(f - R) (if f is not too large) | |
| 76 * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) | |
| 77 * | |
| 78 * 3. Finally, log(x) = k*ln2 + log(1+f). | |
| 79 * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) | |
| 80 * Here ln2 is split into two floating point number: | |
| 81 * ln2_hi + ln2_lo, | |
| 82 * where n*ln2_hi is always exact for |n| < 2000. | |
| 83 * | |
| 84 * Special cases: | |
| 85 * log(x) is NaN with signal if x < 0 (including -INF) ; | |
| 86 * log(+INF) is +INF; log(0) is -INF with signal; | |
| 87 * log(NaN) is that NaN with no signal. | |
| 88 * | |
| 89 * Accuracy: | |
| 90 * according to an error analysis, the error is always less than | |
| 91 * 1 ulp (unit in the last place). | |
| 92 * | |
| 93 * Constants: | |
| 94 * The hexadecimal values are the intended ones for the following | |
| 95 * constants. The decimal values may be used, provided that the | |
| 96 * compiler will convert from decimal to binary accurately enough | |
| 97 * to produce the hexadecimal values shown. | |
| 98 */ | |
| 99 | |
| 100 static const double | |
| 101 ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ | |
| 102 ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ | |
| 103 Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ | |
| 104 Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ | |
| 105 Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ | |
| 106 Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ | |
| 107 Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ | |
| 108 Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ | |
| 109 Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ | |
| 110 | |
| 111 static double zero = 0.0; | |
| 112 | |
| 113 static double __ieee754_log(double x) { | |
| 114 double hfsq,f,s,z,R,w,t1,t2,dk; | |
| 115 int k,hx,i,j; | |
| 116 unsigned lx; | |
| 117 | |
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118 hx = high(x); /* high word of x */ |
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119 lx = low(x); /* low word of x */ |
| 0 | 120 |
| 121 k=0; | |
| 122 if (hx < 0x00100000) { /* x < 2**-1022 */ | |
| 123 if (((hx&0x7fffffff)|lx)==0) | |
| 124 return -two54/zero; /* log(+-0)=-inf */ | |
| 125 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ | |
| 126 k -= 54; x *= two54; /* subnormal number, scale up x */ | |
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127 hx = high(x); /* high word of x */ |
| 0 | 128 } |
| 129 if (hx >= 0x7ff00000) return x+x; | |
| 130 k += (hx>>20)-1023; | |
| 131 hx &= 0x000fffff; | |
| 132 i = (hx+0x95f64)&0x100000; | |
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133 set_high(&x, hx|(i^0x3ff00000)); /* normalize x or x/2 */ |
| 0 | 134 k += (i>>20); |
| 135 f = x-1.0; | |
| 136 if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ | |
| 137 if(f==zero) { | |
| 138 if (k==0) return zero; | |
| 139 else {dk=(double)k; return dk*ln2_hi+dk*ln2_lo;} | |
| 140 } | |
| 141 R = f*f*(0.5-0.33333333333333333*f); | |
| 142 if(k==0) return f-R; else {dk=(double)k; | |
| 143 return dk*ln2_hi-((R-dk*ln2_lo)-f);} | |
| 144 } | |
| 145 s = f/(2.0+f); | |
| 146 dk = (double)k; | |
| 147 z = s*s; | |
| 148 i = hx-0x6147a; | |
| 149 w = z*z; | |
| 150 j = 0x6b851-hx; | |
| 151 t1= w*(Lg2+w*(Lg4+w*Lg6)); | |
| 152 t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); | |
| 153 i |= j; | |
| 154 R = t2+t1; | |
| 155 if(i>0) { | |
| 156 hfsq=0.5*f*f; | |
| 157 if(k==0) return f-(hfsq-s*(hfsq+R)); else | |
| 158 return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); | |
| 159 } else { | |
| 160 if(k==0) return f-s*(f-R); else | |
| 161 return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); | |
| 162 } | |
| 163 } | |
| 164 | |
| 165 JRT_LEAF(jdouble, SharedRuntime::dlog(jdouble x)) | |
| 166 return __ieee754_log(x); | |
| 167 JRT_END | |
| 168 | |
| 169 /* __ieee754_log10(x) | |
| 170 * Return the base 10 logarithm of x | |
| 171 * | |
| 172 * Method : | |
| 173 * Let log10_2hi = leading 40 bits of log10(2) and | |
| 174 * log10_2lo = log10(2) - log10_2hi, | |
| 175 * ivln10 = 1/log(10) rounded. | |
| 176 * Then | |
| 177 * n = ilogb(x), | |
| 178 * if(n<0) n = n+1; | |
| 179 * x = scalbn(x,-n); | |
| 180 * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) | |
| 181 * | |
| 182 * Note 1: | |
| 183 * To guarantee log10(10**n)=n, where 10**n is normal, the rounding | |
| 184 * mode must set to Round-to-Nearest. | |
| 185 * Note 2: | |
| 186 * [1/log(10)] rounded to 53 bits has error .198 ulps; | |
| 187 * log10 is monotonic at all binary break points. | |
| 188 * | |
| 189 * Special cases: | |
| 190 * log10(x) is NaN with signal if x < 0; | |
| 191 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; | |
| 192 * log10(NaN) is that NaN with no signal; | |
| 193 * log10(10**N) = N for N=0,1,...,22. | |
| 194 * | |
| 195 * Constants: | |
| 196 * The hexadecimal values are the intended ones for the following constants. | |
| 197 * The decimal values may be used, provided that the compiler will convert | |
| 198 * from decimal to binary accurately enough to produce the hexadecimal values | |
| 199 * shown. | |
| 200 */ | |
| 201 | |
| 202 static const double | |
| 203 ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ | |
| 204 log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ | |
| 205 log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ | |
| 206 | |
| 207 static double __ieee754_log10(double x) { | |
| 208 double y,z; | |
| 209 int i,k,hx; | |
| 210 unsigned lx; | |
| 211 | |
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212 hx = high(x); /* high word of x */ |
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213 lx = low(x); /* low word of x */ |
| 0 | 214 |
| 215 k=0; | |
| 216 if (hx < 0x00100000) { /* x < 2**-1022 */ | |
| 217 if (((hx&0x7fffffff)|lx)==0) | |
| 218 return -two54/zero; /* log(+-0)=-inf */ | |
| 219 if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ | |
| 220 k -= 54; x *= two54; /* subnormal number, scale up x */ | |
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221 hx = high(x); /* high word of x */ |
| 0 | 222 } |
| 223 if (hx >= 0x7ff00000) return x+x; | |
| 224 k += (hx>>20)-1023; | |
| 225 i = ((unsigned)k&0x80000000)>>31; | |
| 226 hx = (hx&0x000fffff)|((0x3ff-i)<<20); | |
| 227 y = (double)(k+i); | |
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228 set_high(&x, hx); |
| 0 | 229 z = y*log10_2lo + ivln10*__ieee754_log(x); |
| 230 return z+y*log10_2hi; | |
| 231 } | |
| 232 | |
| 233 JRT_LEAF(jdouble, SharedRuntime::dlog10(jdouble x)) | |
| 234 return __ieee754_log10(x); | |
| 235 JRT_END | |
| 236 | |
| 237 | |
| 238 /* __ieee754_exp(x) | |
| 239 * Returns the exponential of x. | |
| 240 * | |
| 241 * Method | |
| 242 * 1. Argument reduction: | |
| 243 * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. | |
| 244 * Given x, find r and integer k such that | |
| 245 * | |
| 246 * x = k*ln2 + r, |r| <= 0.5*ln2. | |
| 247 * | |
| 248 * Here r will be represented as r = hi-lo for better | |
| 249 * accuracy. | |
| 250 * | |
| 251 * 2. Approximation of exp(r) by a special rational function on | |
| 252 * the interval [0,0.34658]: | |
| 253 * Write | |
| 254 * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... | |
| 255 * We use a special Reme algorithm on [0,0.34658] to generate | |
| 256 * a polynomial of degree 5 to approximate R. The maximum error | |
| 257 * of this polynomial approximation is bounded by 2**-59. In | |
| 258 * other words, | |
| 259 * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 | |
| 260 * (where z=r*r, and the values of P1 to P5 are listed below) | |
| 261 * and | |
| 262 * | 5 | -59 | |
| 263 * | 2.0+P1*z+...+P5*z - R(z) | <= 2 | |
| 264 * | | | |
| 265 * The computation of exp(r) thus becomes | |
| 266 * 2*r | |
| 267 * exp(r) = 1 + ------- | |
| 268 * R - r | |
| 269 * r*R1(r) | |
| 270 * = 1 + r + ----------- (for better accuracy) | |
| 271 * 2 - R1(r) | |
| 272 * where | |
| 273 * 2 4 10 | |
| 274 * R1(r) = r - (P1*r + P2*r + ... + P5*r ). | |
| 275 * | |
| 276 * 3. Scale back to obtain exp(x): | |
| 277 * From step 1, we have | |
| 278 * exp(x) = 2^k * exp(r) | |
| 279 * | |
| 280 * Special cases: | |
| 281 * exp(INF) is INF, exp(NaN) is NaN; | |
| 282 * exp(-INF) is 0, and | |
| 283 * for finite argument, only exp(0)=1 is exact. | |
| 284 * | |
| 285 * Accuracy: | |
| 286 * according to an error analysis, the error is always less than | |
| 287 * 1 ulp (unit in the last place). | |
| 288 * | |
| 289 * Misc. info. | |
| 290 * For IEEE double | |
| 291 * if x > 7.09782712893383973096e+02 then exp(x) overflow | |
| 292 * if x < -7.45133219101941108420e+02 then exp(x) underflow | |
| 293 * | |
| 294 * Constants: | |
| 295 * The hexadecimal values are the intended ones for the following | |
| 296 * constants. The decimal values may be used, provided that the | |
| 297 * compiler will convert from decimal to binary accurately enough | |
| 298 * to produce the hexadecimal values shown. | |
| 299 */ | |
| 300 | |
| 301 static const double | |
| 302 one = 1.0, | |
| 303 halF[2] = {0.5,-0.5,}, | |
| 304 twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/ | |
| 305 o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ | |
| 306 u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ | |
| 307 ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ | |
| 308 -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */ | |
| 309 ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ | |
| 310 -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ | |
| 311 invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ | |
| 312 P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ | |
| 313 P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ | |
| 314 P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ | |
| 315 P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ | |
| 316 P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ | |
| 317 | |
| 318 static double __ieee754_exp(double x) { | |
| 319 double y,hi=0,lo=0,c,t; | |
| 320 int k=0,xsb; | |
| 321 unsigned hx; | |
| 322 | |
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323 hx = high(x); /* high word of x */ |
| 0 | 324 xsb = (hx>>31)&1; /* sign bit of x */ |
| 325 hx &= 0x7fffffff; /* high word of |x| */ | |
| 326 | |
| 327 /* filter out non-finite argument */ | |
| 328 if(hx >= 0x40862E42) { /* if |x|>=709.78... */ | |
| 329 if(hx>=0x7ff00000) { | |
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330 if(((hx&0xfffff)|low(x))!=0) |
| 0 | 331 return x+x; /* NaN */ |
| 332 else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ | |
| 333 } | |
| 334 if(x > o_threshold) return hugeX*hugeX; /* overflow */ | |
| 335 if(x < u_threshold) return twom1000*twom1000; /* underflow */ | |
| 336 } | |
| 337 | |
| 338 /* argument reduction */ | |
| 339 if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ | |
| 340 if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ | |
| 341 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; | |
| 342 } else { | |
| 343 k = (int)(invln2*x+halF[xsb]); | |
| 344 t = k; | |
| 345 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ | |
| 346 lo = t*ln2LO[0]; | |
| 347 } | |
| 348 x = hi - lo; | |
| 349 } | |
| 350 else if(hx < 0x3e300000) { /* when |x|<2**-28 */ | |
| 351 if(hugeX+x>one) return one+x;/* trigger inexact */ | |
| 352 } | |
| 353 else k = 0; | |
| 354 | |
| 355 /* x is now in primary range */ | |
| 356 t = x*x; | |
| 357 c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); | |
| 358 if(k==0) return one-((x*c)/(c-2.0)-x); | |
| 359 else y = one-((lo-(x*c)/(2.0-c))-hi); | |
| 360 if(k >= -1021) { | |
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361 set_high(&y, high(y) + (k<<20)); /* add k to y's exponent */ |
| 0 | 362 return y; |
| 363 } else { | |
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364 set_high(&y, high(y) + ((k+1000)<<20)); /* add k to y's exponent */ |
| 0 | 365 return y*twom1000; |
| 366 } | |
| 367 } | |
| 368 | |
| 369 JRT_LEAF(jdouble, SharedRuntime::dexp(jdouble x)) | |
| 370 return __ieee754_exp(x); | |
| 371 JRT_END | |
| 372 | |
| 373 /* __ieee754_pow(x,y) return x**y | |
| 374 * | |
| 375 * n | |
| 376 * Method: Let x = 2 * (1+f) | |
| 377 * 1. Compute and return log2(x) in two pieces: | |
| 378 * log2(x) = w1 + w2, | |
| 379 * where w1 has 53-24 = 29 bit trailing zeros. | |
| 380 * 2. Perform y*log2(x) = n+y' by simulating muti-precision | |
| 381 * arithmetic, where |y'|<=0.5. | |
| 382 * 3. Return x**y = 2**n*exp(y'*log2) | |
| 383 * | |
| 384 * Special cases: | |
| 385 * 1. (anything) ** 0 is 1 | |
| 386 * 2. (anything) ** 1 is itself | |
| 387 * 3. (anything) ** NAN is NAN | |
| 388 * 4. NAN ** (anything except 0) is NAN | |
| 389 * 5. +-(|x| > 1) ** +INF is +INF | |
| 390 * 6. +-(|x| > 1) ** -INF is +0 | |
| 391 * 7. +-(|x| < 1) ** +INF is +0 | |
| 392 * 8. +-(|x| < 1) ** -INF is +INF | |
| 393 * 9. +-1 ** +-INF is NAN | |
| 394 * 10. +0 ** (+anything except 0, NAN) is +0 | |
| 395 * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 | |
| 396 * 12. +0 ** (-anything except 0, NAN) is +INF | |
| 397 * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF | |
| 398 * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) | |
| 399 * 15. +INF ** (+anything except 0,NAN) is +INF | |
| 400 * 16. +INF ** (-anything except 0,NAN) is +0 | |
| 401 * 17. -INF ** (anything) = -0 ** (-anything) | |
| 402 * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) | |
| 403 * 19. (-anything except 0 and inf) ** (non-integer) is NAN | |
| 404 * | |
| 405 * Accuracy: | |
| 406 * pow(x,y) returns x**y nearly rounded. In particular | |
| 407 * pow(integer,integer) | |
| 408 * always returns the correct integer provided it is | |
| 409 * representable. | |
| 410 * | |
| 411 * Constants : | |
| 412 * The hexadecimal values are the intended ones for the following | |
| 413 * constants. The decimal values may be used, provided that the | |
| 414 * compiler will convert from decimal to binary accurately enough | |
| 415 * to produce the hexadecimal values shown. | |
| 416 */ | |
| 417 | |
| 418 static const double | |
| 419 bp[] = {1.0, 1.5,}, | |
| 420 dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ | |
| 421 dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ | |
| 422 zeroX = 0.0, | |
| 423 two = 2.0, | |
| 424 two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ | |
| 425 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ | |
| 426 L1X = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ | |
| 427 L2X = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ | |
| 428 L3X = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ | |
| 429 L4X = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ | |
| 430 L5X = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ | |
| 431 L6X = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ | |
| 432 lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ | |
| 433 lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ | |
| 434 lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ | |
| 435 ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ | |
| 436 cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ | |
| 437 cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ | |
| 438 cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ | |
| 439 ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ | |
| 440 ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ | |
| 441 ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ | |
| 442 | |
| 443 double __ieee754_pow(double x, double y) { | |
| 444 double z,ax,z_h,z_l,p_h,p_l; | |
| 445 double y1,t1,t2,r,s,t,u,v,w; | |
| 446 int i0,i1,i,j,k,yisint,n; | |
| 447 int hx,hy,ix,iy; | |
| 448 unsigned lx,ly; | |
| 449 | |
| 450 i0 = ((*(int*)&one)>>29)^1; i1=1-i0; | |
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451 hx = high(x); lx = low(x); |
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452 hy = high(y); ly = low(y); |
| 0 | 453 ix = hx&0x7fffffff; iy = hy&0x7fffffff; |
| 454 | |
| 455 /* y==zero: x**0 = 1 */ | |
| 456 if((iy|ly)==0) return one; | |
| 457 | |
| 458 /* +-NaN return x+y */ | |
| 459 if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || | |
| 460 iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) | |
| 461 return x+y; | |
| 462 | |
| 463 /* determine if y is an odd int when x < 0 | |
| 464 * yisint = 0 ... y is not an integer | |
| 465 * yisint = 1 ... y is an odd int | |
| 466 * yisint = 2 ... y is an even int | |
| 467 */ | |
| 468 yisint = 0; | |
| 469 if(hx<0) { | |
| 470 if(iy>=0x43400000) yisint = 2; /* even integer y */ | |
| 471 else if(iy>=0x3ff00000) { | |
| 472 k = (iy>>20)-0x3ff; /* exponent */ | |
| 473 if(k>20) { | |
| 474 j = ly>>(52-k); | |
| 475 if((unsigned)(j<<(52-k))==ly) yisint = 2-(j&1); | |
| 476 } else if(ly==0) { | |
| 477 j = iy>>(20-k); | |
| 478 if((j<<(20-k))==iy) yisint = 2-(j&1); | |
| 479 } | |
| 480 } | |
| 481 } | |
| 482 | |
| 483 /* special value of y */ | |
| 484 if(ly==0) { | |
| 485 if (iy==0x7ff00000) { /* y is +-inf */ | |
| 486 if(((ix-0x3ff00000)|lx)==0) | |
| 487 return y - y; /* inf**+-1 is NaN */ | |
| 488 else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ | |
| 489 return (hy>=0)? y: zeroX; | |
| 490 else /* (|x|<1)**-,+inf = inf,0 */ | |
| 491 return (hy<0)?-y: zeroX; | |
| 492 } | |
| 493 if(iy==0x3ff00000) { /* y is +-1 */ | |
| 494 if(hy<0) return one/x; else return x; | |
| 495 } | |
| 496 if(hy==0x40000000) return x*x; /* y is 2 */ | |
| 497 if(hy==0x3fe00000) { /* y is 0.5 */ | |
| 498 if(hx>=0) /* x >= +0 */ | |
| 499 return sqrt(x); | |
| 500 } | |
| 501 } | |
| 502 | |
| 503 ax = fabsd(x); | |
| 504 /* special value of x */ | |
| 505 if(lx==0) { | |
| 506 if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ | |
| 507 z = ax; /*x is +-0,+-inf,+-1*/ | |
| 508 if(hy<0) z = one/z; /* z = (1/|x|) */ | |
| 509 if(hx<0) { | |
| 510 if(((ix-0x3ff00000)|yisint)==0) { | |
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511 #ifdef CAN_USE_NAN_DEFINE |
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512 z = NAN; |
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513 #else |
| 0 | 514 z = (z-z)/(z-z); /* (-1)**non-int is NaN */ |
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515 #endif |
| 0 | 516 } else if(yisint==1) |
| 517 z = -1.0*z; /* (x<0)**odd = -(|x|**odd) */ | |
| 518 } | |
| 519 return z; | |
| 520 } | |
| 521 } | |
| 522 | |
| 523 n = (hx>>31)+1; | |
| 524 | |
| 525 /* (x<0)**(non-int) is NaN */ | |
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526 if((n|yisint)==0) |
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527 #ifdef CAN_USE_NAN_DEFINE |
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528 return NAN; |
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529 #else |
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530 return (x-x)/(x-x); |
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531 #endif |
| 0 | 532 |
| 533 s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ | |
| 534 if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ | |
| 535 | |
| 536 /* |y| is huge */ | |
| 537 if(iy>0x41e00000) { /* if |y| > 2**31 */ | |
| 538 if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ | |
| 539 if(ix<=0x3fefffff) return (hy<0)? hugeX*hugeX:tiny*tiny; | |
| 540 if(ix>=0x3ff00000) return (hy>0)? hugeX*hugeX:tiny*tiny; | |
| 541 } | |
| 542 /* over/underflow if x is not close to one */ | |
| 543 if(ix<0x3fefffff) return (hy<0)? s*hugeX*hugeX:s*tiny*tiny; | |
| 544 if(ix>0x3ff00000) return (hy>0)? s*hugeX*hugeX:s*tiny*tiny; | |
| 545 /* now |1-x| is tiny <= 2**-20, suffice to compute | |
| 546 log(x) by x-x^2/2+x^3/3-x^4/4 */ | |
| 547 t = ax-one; /* t has 20 trailing zeros */ | |
| 548 w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); | |
| 549 u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ | |
| 550 v = t*ivln2_l-w*ivln2; | |
| 551 t1 = u+v; | |
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552 set_low(&t1, 0); |
| 0 | 553 t2 = v-(t1-u); |
| 554 } else { | |
| 555 double ss,s2,s_h,s_l,t_h,t_l; | |
| 556 n = 0; | |
| 557 /* take care subnormal number */ | |
| 558 if(ix<0x00100000) | |
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559 {ax *= two53; n -= 53; ix = high(ax); } |
| 0 | 560 n += ((ix)>>20)-0x3ff; |
| 561 j = ix&0x000fffff; | |
| 562 /* determine interval */ | |
| 563 ix = j|0x3ff00000; /* normalize ix */ | |
| 564 if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */ | |
| 565 else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ | |
| 566 else {k=0;n+=1;ix -= 0x00100000;} | |
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567 set_high(&ax, ix); |
| 0 | 568 |
| 569 /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ | |
| 570 u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ | |
| 571 v = one/(ax+bp[k]); | |
| 572 ss = u*v; | |
| 573 s_h = ss; | |
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574 set_low(&s_h, 0); |
| 0 | 575 /* t_h=ax+bp[k] High */ |
| 576 t_h = zeroX; | |
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577 set_high(&t_h, ((ix>>1)|0x20000000)+0x00080000+(k<<18)); |
| 0 | 578 t_l = ax - (t_h-bp[k]); |
| 579 s_l = v*((u-s_h*t_h)-s_h*t_l); | |
| 580 /* compute log(ax) */ | |
| 581 s2 = ss*ss; | |
| 582 r = s2*s2*(L1X+s2*(L2X+s2*(L3X+s2*(L4X+s2*(L5X+s2*L6X))))); | |
| 583 r += s_l*(s_h+ss); | |
| 584 s2 = s_h*s_h; | |
| 585 t_h = 3.0+s2+r; | |
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586 set_low(&t_h, 0); |
| 0 | 587 t_l = r-((t_h-3.0)-s2); |
| 588 /* u+v = ss*(1+...) */ | |
| 589 u = s_h*t_h; | |
| 590 v = s_l*t_h+t_l*ss; | |
| 591 /* 2/(3log2)*(ss+...) */ | |
| 592 p_h = u+v; | |
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593 set_low(&p_h, 0); |
| 0 | 594 p_l = v-(p_h-u); |
| 595 z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ | |
| 596 z_l = cp_l*p_h+p_l*cp+dp_l[k]; | |
| 597 /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ | |
| 598 t = (double)n; | |
| 599 t1 = (((z_h+z_l)+dp_h[k])+t); | |
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600 set_low(&t1, 0); |
| 0 | 601 t2 = z_l-(((t1-t)-dp_h[k])-z_h); |
| 602 } | |
| 603 | |
| 604 /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ | |
| 605 y1 = y; | |
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606 set_low(&y1, 0); |
| 0 | 607 p_l = (y-y1)*t1+y*t2; |
| 608 p_h = y1*t1; | |
| 609 z = p_l+p_h; | |
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610 j = high(z); |
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611 i = low(z); |
| 0 | 612 if (j>=0x40900000) { /* z >= 1024 */ |
| 613 if(((j-0x40900000)|i)!=0) /* if z > 1024 */ | |
| 614 return s*hugeX*hugeX; /* overflow */ | |
| 615 else { | |
| 616 if(p_l+ovt>z-p_h) return s*hugeX*hugeX; /* overflow */ | |
| 617 } | |
| 618 } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ | |
| 619 if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ | |
| 620 return s*tiny*tiny; /* underflow */ | |
| 621 else { | |
| 622 if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ | |
| 623 } | |
| 624 } | |
| 625 /* | |
| 626 * compute 2**(p_h+p_l) | |
| 627 */ | |
| 628 i = j&0x7fffffff; | |
| 629 k = (i>>20)-0x3ff; | |
| 630 n = 0; | |
| 631 if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ | |
| 632 n = j+(0x00100000>>(k+1)); | |
| 633 k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ | |
| 634 t = zeroX; | |
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635 set_high(&t, (n&~(0x000fffff>>k))); |
| 0 | 636 n = ((n&0x000fffff)|0x00100000)>>(20-k); |
| 637 if(j<0) n = -n; | |
| 638 p_h -= t; | |
| 639 } | |
| 640 t = p_l+p_h; | |
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641 set_low(&t, 0); |
| 0 | 642 u = t*lg2_h; |
| 643 v = (p_l-(t-p_h))*lg2+t*lg2_l; | |
| 644 z = u+v; | |
| 645 w = v-(z-u); | |
| 646 t = z*z; | |
| 647 t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); | |
| 648 r = (z*t1)/(t1-two)-(w+z*w); | |
| 649 z = one-(r-z); | |
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650 j = high(z); |
| 0 | 651 j += (n<<20); |
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652 if((j>>20)<=0) z = scalbnA(z,n); /* subnormal output */ |
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653 else set_high(&z, high(z) + (n<<20)); |
| 0 | 654 return s*z; |
| 655 } | |
| 656 | |
| 657 | |
| 658 JRT_LEAF(jdouble, SharedRuntime::dpow(jdouble x, jdouble y)) | |
| 659 return __ieee754_pow(x, y); | |
| 660 JRT_END | |
| 661 | |
| 662 #ifdef WIN32 | |
| 663 # pragma optimize ( "", on ) | |
| 664 #endif |