Mon, 23 Jun 2008 14:11:12 -0700
6708714: Optimize long LShift on 32-bits x86
Summary: For small (1-3 bits) left long shifts in 32-bits VM use sets of add+addc instructions instead of shld+shl on new AMD cpus.
Reviewed-by: never
Contributed-by: shrinivas.joshi@amd.com
duke@435 | 1 | /* |
duke@435 | 2 | * Copyright 2005 Sun Microsystems, Inc. All Rights Reserved. |
duke@435 | 3 | * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
duke@435 | 4 | * |
duke@435 | 5 | * This code is free software; you can redistribute it and/or modify it |
duke@435 | 6 | * under the terms of the GNU General Public License version 2 only, as |
duke@435 | 7 | * published by the Free Software Foundation. |
duke@435 | 8 | * |
duke@435 | 9 | * This code is distributed in the hope that it will be useful, but WITHOUT |
duke@435 | 10 | * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
duke@435 | 11 | * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
duke@435 | 12 | * version 2 for more details (a copy is included in the LICENSE file that |
duke@435 | 13 | * accompanied this code). |
duke@435 | 14 | * |
duke@435 | 15 | * You should have received a copy of the GNU General Public License version |
duke@435 | 16 | * 2 along with this work; if not, write to the Free Software Foundation, |
duke@435 | 17 | * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
duke@435 | 18 | * |
duke@435 | 19 | * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara, |
duke@435 | 20 | * CA 95054 USA or visit www.sun.com if you need additional information or |
duke@435 | 21 | * have any questions. |
duke@435 | 22 | * |
duke@435 | 23 | */ |
duke@435 | 24 | |
duke@435 | 25 | #include "incls/_precompiled.incl" |
duke@435 | 26 | #include "incls/_sharedRuntimeTrans.cpp.incl" |
duke@435 | 27 | |
duke@435 | 28 | // This file contains copies of the fdlibm routines used by |
duke@435 | 29 | // StrictMath. It turns out that it is almost always required to use |
duke@435 | 30 | // these runtime routines; the Intel CPU doesn't meet the Java |
duke@435 | 31 | // specification for sin/cos outside a certain limited argument range, |
duke@435 | 32 | // and the SPARC CPU doesn't appear to have sin/cos instructions. It |
duke@435 | 33 | // also turns out that avoiding the indirect call through function |
duke@435 | 34 | // pointer out to libjava.so in SharedRuntime speeds these routines up |
duke@435 | 35 | // by roughly 15% on both Win32/x86 and Solaris/SPARC. |
duke@435 | 36 | |
duke@435 | 37 | // Enabling optimizations in this file causes incorrect code to be |
duke@435 | 38 | // generated; can not figure out how to turn down optimization for one |
duke@435 | 39 | // file in the IDE on Windows |
duke@435 | 40 | #ifdef WIN32 |
duke@435 | 41 | # pragma optimize ( "", off ) |
duke@435 | 42 | #endif |
duke@435 | 43 | |
duke@435 | 44 | #include <math.h> |
duke@435 | 45 | |
duke@435 | 46 | // VM_LITTLE_ENDIAN is #defined appropriately in the Makefiles |
duke@435 | 47 | // [jk] this is not 100% correct because the float word order may different |
duke@435 | 48 | // from the byte order (e.g. on ARM) |
duke@435 | 49 | #ifdef VM_LITTLE_ENDIAN |
duke@435 | 50 | # define __HI(x) *(1+(int*)&x) |
duke@435 | 51 | # define __LO(x) *(int*)&x |
duke@435 | 52 | #else |
duke@435 | 53 | # define __HI(x) *(int*)&x |
duke@435 | 54 | # define __LO(x) *(1+(int*)&x) |
duke@435 | 55 | #endif |
duke@435 | 56 | |
duke@435 | 57 | double copysign(double x, double y) { |
duke@435 | 58 | __HI(x) = (__HI(x)&0x7fffffff)|(__HI(y)&0x80000000); |
duke@435 | 59 | return x; |
duke@435 | 60 | } |
duke@435 | 61 | |
duke@435 | 62 | /* |
duke@435 | 63 | * ==================================================== |
duke@435 | 64 | * Copyright (C) 1998 by Sun Microsystems, Inc. All rights reserved. |
duke@435 | 65 | * |
duke@435 | 66 | * Developed at SunSoft, a Sun Microsystems, Inc. business. |
duke@435 | 67 | * Permission to use, copy, modify, and distribute this |
duke@435 | 68 | * software is freely granted, provided that this notice |
duke@435 | 69 | * is preserved. |
duke@435 | 70 | * ==================================================== |
duke@435 | 71 | */ |
duke@435 | 72 | |
duke@435 | 73 | /* |
duke@435 | 74 | * scalbn (double x, int n) |
duke@435 | 75 | * scalbn(x,n) returns x* 2**n computed by exponent |
duke@435 | 76 | * manipulation rather than by actually performing an |
duke@435 | 77 | * exponentiation or a multiplication. |
duke@435 | 78 | */ |
duke@435 | 79 | |
duke@435 | 80 | static const double |
duke@435 | 81 | two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ |
duke@435 | 82 | twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ |
duke@435 | 83 | hugeX = 1.0e+300, |
duke@435 | 84 | tiny = 1.0e-300; |
duke@435 | 85 | |
duke@435 | 86 | double scalbn (double x, int n) { |
duke@435 | 87 | int k,hx,lx; |
duke@435 | 88 | hx = __HI(x); |
duke@435 | 89 | lx = __LO(x); |
duke@435 | 90 | k = (hx&0x7ff00000)>>20; /* extract exponent */ |
duke@435 | 91 | if (k==0) { /* 0 or subnormal x */ |
duke@435 | 92 | if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ |
duke@435 | 93 | x *= two54; |
duke@435 | 94 | hx = __HI(x); |
duke@435 | 95 | k = ((hx&0x7ff00000)>>20) - 54; |
duke@435 | 96 | if (n< -50000) return tiny*x; /*underflow*/ |
duke@435 | 97 | } |
duke@435 | 98 | if (k==0x7ff) return x+x; /* NaN or Inf */ |
duke@435 | 99 | k = k+n; |
duke@435 | 100 | if (k > 0x7fe) return hugeX*copysign(hugeX,x); /* overflow */ |
duke@435 | 101 | if (k > 0) /* normal result */ |
duke@435 | 102 | {__HI(x) = (hx&0x800fffff)|(k<<20); return x;} |
duke@435 | 103 | if (k <= -54) { |
duke@435 | 104 | if (n > 50000) /* in case integer overflow in n+k */ |
duke@435 | 105 | return hugeX*copysign(hugeX,x); /*overflow*/ |
duke@435 | 106 | else return tiny*copysign(tiny,x); /*underflow*/ |
duke@435 | 107 | } |
duke@435 | 108 | k += 54; /* subnormal result */ |
duke@435 | 109 | __HI(x) = (hx&0x800fffff)|(k<<20); |
duke@435 | 110 | return x*twom54; |
duke@435 | 111 | } |
duke@435 | 112 | |
duke@435 | 113 | /* __ieee754_log(x) |
duke@435 | 114 | * Return the logrithm of x |
duke@435 | 115 | * |
duke@435 | 116 | * Method : |
duke@435 | 117 | * 1. Argument Reduction: find k and f such that |
duke@435 | 118 | * x = 2^k * (1+f), |
duke@435 | 119 | * where sqrt(2)/2 < 1+f < sqrt(2) . |
duke@435 | 120 | * |
duke@435 | 121 | * 2. Approximation of log(1+f). |
duke@435 | 122 | * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) |
duke@435 | 123 | * = 2s + 2/3 s**3 + 2/5 s**5 + ....., |
duke@435 | 124 | * = 2s + s*R |
duke@435 | 125 | * We use a special Reme algorithm on [0,0.1716] to generate |
duke@435 | 126 | * a polynomial of degree 14 to approximate R The maximum error |
duke@435 | 127 | * of this polynomial approximation is bounded by 2**-58.45. In |
duke@435 | 128 | * other words, |
duke@435 | 129 | * 2 4 6 8 10 12 14 |
duke@435 | 130 | * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s |
duke@435 | 131 | * (the values of Lg1 to Lg7 are listed in the program) |
duke@435 | 132 | * and |
duke@435 | 133 | * | 2 14 | -58.45 |
duke@435 | 134 | * | Lg1*s +...+Lg7*s - R(z) | <= 2 |
duke@435 | 135 | * | | |
duke@435 | 136 | * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. |
duke@435 | 137 | * In order to guarantee error in log below 1ulp, we compute log |
duke@435 | 138 | * by |
duke@435 | 139 | * log(1+f) = f - s*(f - R) (if f is not too large) |
duke@435 | 140 | * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) |
duke@435 | 141 | * |
duke@435 | 142 | * 3. Finally, log(x) = k*ln2 + log(1+f). |
duke@435 | 143 | * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) |
duke@435 | 144 | * Here ln2 is split into two floating point number: |
duke@435 | 145 | * ln2_hi + ln2_lo, |
duke@435 | 146 | * where n*ln2_hi is always exact for |n| < 2000. |
duke@435 | 147 | * |
duke@435 | 148 | * Special cases: |
duke@435 | 149 | * log(x) is NaN with signal if x < 0 (including -INF) ; |
duke@435 | 150 | * log(+INF) is +INF; log(0) is -INF with signal; |
duke@435 | 151 | * log(NaN) is that NaN with no signal. |
duke@435 | 152 | * |
duke@435 | 153 | * Accuracy: |
duke@435 | 154 | * according to an error analysis, the error is always less than |
duke@435 | 155 | * 1 ulp (unit in the last place). |
duke@435 | 156 | * |
duke@435 | 157 | * Constants: |
duke@435 | 158 | * The hexadecimal values are the intended ones for the following |
duke@435 | 159 | * constants. The decimal values may be used, provided that the |
duke@435 | 160 | * compiler will convert from decimal to binary accurately enough |
duke@435 | 161 | * to produce the hexadecimal values shown. |
duke@435 | 162 | */ |
duke@435 | 163 | |
duke@435 | 164 | static const double |
duke@435 | 165 | ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ |
duke@435 | 166 | ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ |
duke@435 | 167 | Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ |
duke@435 | 168 | Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ |
duke@435 | 169 | Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ |
duke@435 | 170 | Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ |
duke@435 | 171 | Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ |
duke@435 | 172 | Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ |
duke@435 | 173 | Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ |
duke@435 | 174 | |
duke@435 | 175 | static double zero = 0.0; |
duke@435 | 176 | |
duke@435 | 177 | static double __ieee754_log(double x) { |
duke@435 | 178 | double hfsq,f,s,z,R,w,t1,t2,dk; |
duke@435 | 179 | int k,hx,i,j; |
duke@435 | 180 | unsigned lx; |
duke@435 | 181 | |
duke@435 | 182 | hx = __HI(x); /* high word of x */ |
duke@435 | 183 | lx = __LO(x); /* low word of x */ |
duke@435 | 184 | |
duke@435 | 185 | k=0; |
duke@435 | 186 | if (hx < 0x00100000) { /* x < 2**-1022 */ |
duke@435 | 187 | if (((hx&0x7fffffff)|lx)==0) |
duke@435 | 188 | return -two54/zero; /* log(+-0)=-inf */ |
duke@435 | 189 | if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ |
duke@435 | 190 | k -= 54; x *= two54; /* subnormal number, scale up x */ |
duke@435 | 191 | hx = __HI(x); /* high word of x */ |
duke@435 | 192 | } |
duke@435 | 193 | if (hx >= 0x7ff00000) return x+x; |
duke@435 | 194 | k += (hx>>20)-1023; |
duke@435 | 195 | hx &= 0x000fffff; |
duke@435 | 196 | i = (hx+0x95f64)&0x100000; |
duke@435 | 197 | __HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */ |
duke@435 | 198 | k += (i>>20); |
duke@435 | 199 | f = x-1.0; |
duke@435 | 200 | if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ |
duke@435 | 201 | if(f==zero) { |
duke@435 | 202 | if (k==0) return zero; |
duke@435 | 203 | else {dk=(double)k; return dk*ln2_hi+dk*ln2_lo;} |
duke@435 | 204 | } |
duke@435 | 205 | R = f*f*(0.5-0.33333333333333333*f); |
duke@435 | 206 | if(k==0) return f-R; else {dk=(double)k; |
duke@435 | 207 | return dk*ln2_hi-((R-dk*ln2_lo)-f);} |
duke@435 | 208 | } |
duke@435 | 209 | s = f/(2.0+f); |
duke@435 | 210 | dk = (double)k; |
duke@435 | 211 | z = s*s; |
duke@435 | 212 | i = hx-0x6147a; |
duke@435 | 213 | w = z*z; |
duke@435 | 214 | j = 0x6b851-hx; |
duke@435 | 215 | t1= w*(Lg2+w*(Lg4+w*Lg6)); |
duke@435 | 216 | t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); |
duke@435 | 217 | i |= j; |
duke@435 | 218 | R = t2+t1; |
duke@435 | 219 | if(i>0) { |
duke@435 | 220 | hfsq=0.5*f*f; |
duke@435 | 221 | if(k==0) return f-(hfsq-s*(hfsq+R)); else |
duke@435 | 222 | return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); |
duke@435 | 223 | } else { |
duke@435 | 224 | if(k==0) return f-s*(f-R); else |
duke@435 | 225 | return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); |
duke@435 | 226 | } |
duke@435 | 227 | } |
duke@435 | 228 | |
duke@435 | 229 | JRT_LEAF(jdouble, SharedRuntime::dlog(jdouble x)) |
duke@435 | 230 | return __ieee754_log(x); |
duke@435 | 231 | JRT_END |
duke@435 | 232 | |
duke@435 | 233 | /* __ieee754_log10(x) |
duke@435 | 234 | * Return the base 10 logarithm of x |
duke@435 | 235 | * |
duke@435 | 236 | * Method : |
duke@435 | 237 | * Let log10_2hi = leading 40 bits of log10(2) and |
duke@435 | 238 | * log10_2lo = log10(2) - log10_2hi, |
duke@435 | 239 | * ivln10 = 1/log(10) rounded. |
duke@435 | 240 | * Then |
duke@435 | 241 | * n = ilogb(x), |
duke@435 | 242 | * if(n<0) n = n+1; |
duke@435 | 243 | * x = scalbn(x,-n); |
duke@435 | 244 | * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) |
duke@435 | 245 | * |
duke@435 | 246 | * Note 1: |
duke@435 | 247 | * To guarantee log10(10**n)=n, where 10**n is normal, the rounding |
duke@435 | 248 | * mode must set to Round-to-Nearest. |
duke@435 | 249 | * Note 2: |
duke@435 | 250 | * [1/log(10)] rounded to 53 bits has error .198 ulps; |
duke@435 | 251 | * log10 is monotonic at all binary break points. |
duke@435 | 252 | * |
duke@435 | 253 | * Special cases: |
duke@435 | 254 | * log10(x) is NaN with signal if x < 0; |
duke@435 | 255 | * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; |
duke@435 | 256 | * log10(NaN) is that NaN with no signal; |
duke@435 | 257 | * log10(10**N) = N for N=0,1,...,22. |
duke@435 | 258 | * |
duke@435 | 259 | * Constants: |
duke@435 | 260 | * The hexadecimal values are the intended ones for the following constants. |
duke@435 | 261 | * The decimal values may be used, provided that the compiler will convert |
duke@435 | 262 | * from decimal to binary accurately enough to produce the hexadecimal values |
duke@435 | 263 | * shown. |
duke@435 | 264 | */ |
duke@435 | 265 | |
duke@435 | 266 | static const double |
duke@435 | 267 | ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ |
duke@435 | 268 | log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ |
duke@435 | 269 | log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ |
duke@435 | 270 | |
duke@435 | 271 | static double __ieee754_log10(double x) { |
duke@435 | 272 | double y,z; |
duke@435 | 273 | int i,k,hx; |
duke@435 | 274 | unsigned lx; |
duke@435 | 275 | |
duke@435 | 276 | hx = __HI(x); /* high word of x */ |
duke@435 | 277 | lx = __LO(x); /* low word of x */ |
duke@435 | 278 | |
duke@435 | 279 | k=0; |
duke@435 | 280 | if (hx < 0x00100000) { /* x < 2**-1022 */ |
duke@435 | 281 | if (((hx&0x7fffffff)|lx)==0) |
duke@435 | 282 | return -two54/zero; /* log(+-0)=-inf */ |
duke@435 | 283 | if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ |
duke@435 | 284 | k -= 54; x *= two54; /* subnormal number, scale up x */ |
duke@435 | 285 | hx = __HI(x); /* high word of x */ |
duke@435 | 286 | } |
duke@435 | 287 | if (hx >= 0x7ff00000) return x+x; |
duke@435 | 288 | k += (hx>>20)-1023; |
duke@435 | 289 | i = ((unsigned)k&0x80000000)>>31; |
duke@435 | 290 | hx = (hx&0x000fffff)|((0x3ff-i)<<20); |
duke@435 | 291 | y = (double)(k+i); |
duke@435 | 292 | __HI(x) = hx; |
duke@435 | 293 | z = y*log10_2lo + ivln10*__ieee754_log(x); |
duke@435 | 294 | return z+y*log10_2hi; |
duke@435 | 295 | } |
duke@435 | 296 | |
duke@435 | 297 | JRT_LEAF(jdouble, SharedRuntime::dlog10(jdouble x)) |
duke@435 | 298 | return __ieee754_log10(x); |
duke@435 | 299 | JRT_END |
duke@435 | 300 | |
duke@435 | 301 | |
duke@435 | 302 | /* __ieee754_exp(x) |
duke@435 | 303 | * Returns the exponential of x. |
duke@435 | 304 | * |
duke@435 | 305 | * Method |
duke@435 | 306 | * 1. Argument reduction: |
duke@435 | 307 | * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. |
duke@435 | 308 | * Given x, find r and integer k such that |
duke@435 | 309 | * |
duke@435 | 310 | * x = k*ln2 + r, |r| <= 0.5*ln2. |
duke@435 | 311 | * |
duke@435 | 312 | * Here r will be represented as r = hi-lo for better |
duke@435 | 313 | * accuracy. |
duke@435 | 314 | * |
duke@435 | 315 | * 2. Approximation of exp(r) by a special rational function on |
duke@435 | 316 | * the interval [0,0.34658]: |
duke@435 | 317 | * Write |
duke@435 | 318 | * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... |
duke@435 | 319 | * We use a special Reme algorithm on [0,0.34658] to generate |
duke@435 | 320 | * a polynomial of degree 5 to approximate R. The maximum error |
duke@435 | 321 | * of this polynomial approximation is bounded by 2**-59. In |
duke@435 | 322 | * other words, |
duke@435 | 323 | * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 |
duke@435 | 324 | * (where z=r*r, and the values of P1 to P5 are listed below) |
duke@435 | 325 | * and |
duke@435 | 326 | * | 5 | -59 |
duke@435 | 327 | * | 2.0+P1*z+...+P5*z - R(z) | <= 2 |
duke@435 | 328 | * | | |
duke@435 | 329 | * The computation of exp(r) thus becomes |
duke@435 | 330 | * 2*r |
duke@435 | 331 | * exp(r) = 1 + ------- |
duke@435 | 332 | * R - r |
duke@435 | 333 | * r*R1(r) |
duke@435 | 334 | * = 1 + r + ----------- (for better accuracy) |
duke@435 | 335 | * 2 - R1(r) |
duke@435 | 336 | * where |
duke@435 | 337 | * 2 4 10 |
duke@435 | 338 | * R1(r) = r - (P1*r + P2*r + ... + P5*r ). |
duke@435 | 339 | * |
duke@435 | 340 | * 3. Scale back to obtain exp(x): |
duke@435 | 341 | * From step 1, we have |
duke@435 | 342 | * exp(x) = 2^k * exp(r) |
duke@435 | 343 | * |
duke@435 | 344 | * Special cases: |
duke@435 | 345 | * exp(INF) is INF, exp(NaN) is NaN; |
duke@435 | 346 | * exp(-INF) is 0, and |
duke@435 | 347 | * for finite argument, only exp(0)=1 is exact. |
duke@435 | 348 | * |
duke@435 | 349 | * Accuracy: |
duke@435 | 350 | * according to an error analysis, the error is always less than |
duke@435 | 351 | * 1 ulp (unit in the last place). |
duke@435 | 352 | * |
duke@435 | 353 | * Misc. info. |
duke@435 | 354 | * For IEEE double |
duke@435 | 355 | * if x > 7.09782712893383973096e+02 then exp(x) overflow |
duke@435 | 356 | * if x < -7.45133219101941108420e+02 then exp(x) underflow |
duke@435 | 357 | * |
duke@435 | 358 | * Constants: |
duke@435 | 359 | * The hexadecimal values are the intended ones for the following |
duke@435 | 360 | * constants. The decimal values may be used, provided that the |
duke@435 | 361 | * compiler will convert from decimal to binary accurately enough |
duke@435 | 362 | * to produce the hexadecimal values shown. |
duke@435 | 363 | */ |
duke@435 | 364 | |
duke@435 | 365 | static const double |
duke@435 | 366 | one = 1.0, |
duke@435 | 367 | halF[2] = {0.5,-0.5,}, |
duke@435 | 368 | twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/ |
duke@435 | 369 | o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ |
duke@435 | 370 | u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ |
duke@435 | 371 | ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ |
duke@435 | 372 | -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */ |
duke@435 | 373 | ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ |
duke@435 | 374 | -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ |
duke@435 | 375 | invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ |
duke@435 | 376 | P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ |
duke@435 | 377 | P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ |
duke@435 | 378 | P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ |
duke@435 | 379 | P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ |
duke@435 | 380 | P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ |
duke@435 | 381 | |
duke@435 | 382 | static double __ieee754_exp(double x) { |
duke@435 | 383 | double y,hi=0,lo=0,c,t; |
duke@435 | 384 | int k=0,xsb; |
duke@435 | 385 | unsigned hx; |
duke@435 | 386 | |
duke@435 | 387 | hx = __HI(x); /* high word of x */ |
duke@435 | 388 | xsb = (hx>>31)&1; /* sign bit of x */ |
duke@435 | 389 | hx &= 0x7fffffff; /* high word of |x| */ |
duke@435 | 390 | |
duke@435 | 391 | /* filter out non-finite argument */ |
duke@435 | 392 | if(hx >= 0x40862E42) { /* if |x|>=709.78... */ |
duke@435 | 393 | if(hx>=0x7ff00000) { |
duke@435 | 394 | if(((hx&0xfffff)|__LO(x))!=0) |
duke@435 | 395 | return x+x; /* NaN */ |
duke@435 | 396 | else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ |
duke@435 | 397 | } |
duke@435 | 398 | if(x > o_threshold) return hugeX*hugeX; /* overflow */ |
duke@435 | 399 | if(x < u_threshold) return twom1000*twom1000; /* underflow */ |
duke@435 | 400 | } |
duke@435 | 401 | |
duke@435 | 402 | /* argument reduction */ |
duke@435 | 403 | if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ |
duke@435 | 404 | if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ |
duke@435 | 405 | hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; |
duke@435 | 406 | } else { |
duke@435 | 407 | k = (int)(invln2*x+halF[xsb]); |
duke@435 | 408 | t = k; |
duke@435 | 409 | hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ |
duke@435 | 410 | lo = t*ln2LO[0]; |
duke@435 | 411 | } |
duke@435 | 412 | x = hi - lo; |
duke@435 | 413 | } |
duke@435 | 414 | else if(hx < 0x3e300000) { /* when |x|<2**-28 */ |
duke@435 | 415 | if(hugeX+x>one) return one+x;/* trigger inexact */ |
duke@435 | 416 | } |
duke@435 | 417 | else k = 0; |
duke@435 | 418 | |
duke@435 | 419 | /* x is now in primary range */ |
duke@435 | 420 | t = x*x; |
duke@435 | 421 | c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); |
duke@435 | 422 | if(k==0) return one-((x*c)/(c-2.0)-x); |
duke@435 | 423 | else y = one-((lo-(x*c)/(2.0-c))-hi); |
duke@435 | 424 | if(k >= -1021) { |
duke@435 | 425 | __HI(y) += (k<<20); /* add k to y's exponent */ |
duke@435 | 426 | return y; |
duke@435 | 427 | } else { |
duke@435 | 428 | __HI(y) += ((k+1000)<<20);/* add k to y's exponent */ |
duke@435 | 429 | return y*twom1000; |
duke@435 | 430 | } |
duke@435 | 431 | } |
duke@435 | 432 | |
duke@435 | 433 | JRT_LEAF(jdouble, SharedRuntime::dexp(jdouble x)) |
duke@435 | 434 | return __ieee754_exp(x); |
duke@435 | 435 | JRT_END |
duke@435 | 436 | |
duke@435 | 437 | /* __ieee754_pow(x,y) return x**y |
duke@435 | 438 | * |
duke@435 | 439 | * n |
duke@435 | 440 | * Method: Let x = 2 * (1+f) |
duke@435 | 441 | * 1. Compute and return log2(x) in two pieces: |
duke@435 | 442 | * log2(x) = w1 + w2, |
duke@435 | 443 | * where w1 has 53-24 = 29 bit trailing zeros. |
duke@435 | 444 | * 2. Perform y*log2(x) = n+y' by simulating muti-precision |
duke@435 | 445 | * arithmetic, where |y'|<=0.5. |
duke@435 | 446 | * 3. Return x**y = 2**n*exp(y'*log2) |
duke@435 | 447 | * |
duke@435 | 448 | * Special cases: |
duke@435 | 449 | * 1. (anything) ** 0 is 1 |
duke@435 | 450 | * 2. (anything) ** 1 is itself |
duke@435 | 451 | * 3. (anything) ** NAN is NAN |
duke@435 | 452 | * 4. NAN ** (anything except 0) is NAN |
duke@435 | 453 | * 5. +-(|x| > 1) ** +INF is +INF |
duke@435 | 454 | * 6. +-(|x| > 1) ** -INF is +0 |
duke@435 | 455 | * 7. +-(|x| < 1) ** +INF is +0 |
duke@435 | 456 | * 8. +-(|x| < 1) ** -INF is +INF |
duke@435 | 457 | * 9. +-1 ** +-INF is NAN |
duke@435 | 458 | * 10. +0 ** (+anything except 0, NAN) is +0 |
duke@435 | 459 | * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 |
duke@435 | 460 | * 12. +0 ** (-anything except 0, NAN) is +INF |
duke@435 | 461 | * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF |
duke@435 | 462 | * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) |
duke@435 | 463 | * 15. +INF ** (+anything except 0,NAN) is +INF |
duke@435 | 464 | * 16. +INF ** (-anything except 0,NAN) is +0 |
duke@435 | 465 | * 17. -INF ** (anything) = -0 ** (-anything) |
duke@435 | 466 | * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) |
duke@435 | 467 | * 19. (-anything except 0 and inf) ** (non-integer) is NAN |
duke@435 | 468 | * |
duke@435 | 469 | * Accuracy: |
duke@435 | 470 | * pow(x,y) returns x**y nearly rounded. In particular |
duke@435 | 471 | * pow(integer,integer) |
duke@435 | 472 | * always returns the correct integer provided it is |
duke@435 | 473 | * representable. |
duke@435 | 474 | * |
duke@435 | 475 | * Constants : |
duke@435 | 476 | * The hexadecimal values are the intended ones for the following |
duke@435 | 477 | * constants. The decimal values may be used, provided that the |
duke@435 | 478 | * compiler will convert from decimal to binary accurately enough |
duke@435 | 479 | * to produce the hexadecimal values shown. |
duke@435 | 480 | */ |
duke@435 | 481 | |
duke@435 | 482 | static const double |
duke@435 | 483 | bp[] = {1.0, 1.5,}, |
duke@435 | 484 | dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ |
duke@435 | 485 | dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ |
duke@435 | 486 | zeroX = 0.0, |
duke@435 | 487 | two = 2.0, |
duke@435 | 488 | two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ |
duke@435 | 489 | /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ |
duke@435 | 490 | L1X = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ |
duke@435 | 491 | L2X = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ |
duke@435 | 492 | L3X = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ |
duke@435 | 493 | L4X = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ |
duke@435 | 494 | L5X = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ |
duke@435 | 495 | L6X = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ |
duke@435 | 496 | lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ |
duke@435 | 497 | lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ |
duke@435 | 498 | lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ |
duke@435 | 499 | ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ |
duke@435 | 500 | cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ |
duke@435 | 501 | cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ |
duke@435 | 502 | cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ |
duke@435 | 503 | ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ |
duke@435 | 504 | ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ |
duke@435 | 505 | ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ |
duke@435 | 506 | |
duke@435 | 507 | double __ieee754_pow(double x, double y) { |
duke@435 | 508 | double z,ax,z_h,z_l,p_h,p_l; |
duke@435 | 509 | double y1,t1,t2,r,s,t,u,v,w; |
duke@435 | 510 | int i0,i1,i,j,k,yisint,n; |
duke@435 | 511 | int hx,hy,ix,iy; |
duke@435 | 512 | unsigned lx,ly; |
duke@435 | 513 | |
duke@435 | 514 | i0 = ((*(int*)&one)>>29)^1; i1=1-i0; |
duke@435 | 515 | hx = __HI(x); lx = __LO(x); |
duke@435 | 516 | hy = __HI(y); ly = __LO(y); |
duke@435 | 517 | ix = hx&0x7fffffff; iy = hy&0x7fffffff; |
duke@435 | 518 | |
duke@435 | 519 | /* y==zero: x**0 = 1 */ |
duke@435 | 520 | if((iy|ly)==0) return one; |
duke@435 | 521 | |
duke@435 | 522 | /* +-NaN return x+y */ |
duke@435 | 523 | if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || |
duke@435 | 524 | iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) |
duke@435 | 525 | return x+y; |
duke@435 | 526 | |
duke@435 | 527 | /* determine if y is an odd int when x < 0 |
duke@435 | 528 | * yisint = 0 ... y is not an integer |
duke@435 | 529 | * yisint = 1 ... y is an odd int |
duke@435 | 530 | * yisint = 2 ... y is an even int |
duke@435 | 531 | */ |
duke@435 | 532 | yisint = 0; |
duke@435 | 533 | if(hx<0) { |
duke@435 | 534 | if(iy>=0x43400000) yisint = 2; /* even integer y */ |
duke@435 | 535 | else if(iy>=0x3ff00000) { |
duke@435 | 536 | k = (iy>>20)-0x3ff; /* exponent */ |
duke@435 | 537 | if(k>20) { |
duke@435 | 538 | j = ly>>(52-k); |
duke@435 | 539 | if((unsigned)(j<<(52-k))==ly) yisint = 2-(j&1); |
duke@435 | 540 | } else if(ly==0) { |
duke@435 | 541 | j = iy>>(20-k); |
duke@435 | 542 | if((j<<(20-k))==iy) yisint = 2-(j&1); |
duke@435 | 543 | } |
duke@435 | 544 | } |
duke@435 | 545 | } |
duke@435 | 546 | |
duke@435 | 547 | /* special value of y */ |
duke@435 | 548 | if(ly==0) { |
duke@435 | 549 | if (iy==0x7ff00000) { /* y is +-inf */ |
duke@435 | 550 | if(((ix-0x3ff00000)|lx)==0) |
duke@435 | 551 | return y - y; /* inf**+-1 is NaN */ |
duke@435 | 552 | else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ |
duke@435 | 553 | return (hy>=0)? y: zeroX; |
duke@435 | 554 | else /* (|x|<1)**-,+inf = inf,0 */ |
duke@435 | 555 | return (hy<0)?-y: zeroX; |
duke@435 | 556 | } |
duke@435 | 557 | if(iy==0x3ff00000) { /* y is +-1 */ |
duke@435 | 558 | if(hy<0) return one/x; else return x; |
duke@435 | 559 | } |
duke@435 | 560 | if(hy==0x40000000) return x*x; /* y is 2 */ |
duke@435 | 561 | if(hy==0x3fe00000) { /* y is 0.5 */ |
duke@435 | 562 | if(hx>=0) /* x >= +0 */ |
duke@435 | 563 | return sqrt(x); |
duke@435 | 564 | } |
duke@435 | 565 | } |
duke@435 | 566 | |
duke@435 | 567 | ax = fabsd(x); |
duke@435 | 568 | /* special value of x */ |
duke@435 | 569 | if(lx==0) { |
duke@435 | 570 | if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ |
duke@435 | 571 | z = ax; /*x is +-0,+-inf,+-1*/ |
duke@435 | 572 | if(hy<0) z = one/z; /* z = (1/|x|) */ |
duke@435 | 573 | if(hx<0) { |
duke@435 | 574 | if(((ix-0x3ff00000)|yisint)==0) { |
duke@435 | 575 | z = (z-z)/(z-z); /* (-1)**non-int is NaN */ |
duke@435 | 576 | } else if(yisint==1) |
duke@435 | 577 | z = -1.0*z; /* (x<0)**odd = -(|x|**odd) */ |
duke@435 | 578 | } |
duke@435 | 579 | return z; |
duke@435 | 580 | } |
duke@435 | 581 | } |
duke@435 | 582 | |
duke@435 | 583 | n = (hx>>31)+1; |
duke@435 | 584 | |
duke@435 | 585 | /* (x<0)**(non-int) is NaN */ |
duke@435 | 586 | if((n|yisint)==0) return (x-x)/(x-x); |
duke@435 | 587 | |
duke@435 | 588 | s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ |
duke@435 | 589 | if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ |
duke@435 | 590 | |
duke@435 | 591 | /* |y| is huge */ |
duke@435 | 592 | if(iy>0x41e00000) { /* if |y| > 2**31 */ |
duke@435 | 593 | if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ |
duke@435 | 594 | if(ix<=0x3fefffff) return (hy<0)? hugeX*hugeX:tiny*tiny; |
duke@435 | 595 | if(ix>=0x3ff00000) return (hy>0)? hugeX*hugeX:tiny*tiny; |
duke@435 | 596 | } |
duke@435 | 597 | /* over/underflow if x is not close to one */ |
duke@435 | 598 | if(ix<0x3fefffff) return (hy<0)? s*hugeX*hugeX:s*tiny*tiny; |
duke@435 | 599 | if(ix>0x3ff00000) return (hy>0)? s*hugeX*hugeX:s*tiny*tiny; |
duke@435 | 600 | /* now |1-x| is tiny <= 2**-20, suffice to compute |
duke@435 | 601 | log(x) by x-x^2/2+x^3/3-x^4/4 */ |
duke@435 | 602 | t = ax-one; /* t has 20 trailing zeros */ |
duke@435 | 603 | w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); |
duke@435 | 604 | u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ |
duke@435 | 605 | v = t*ivln2_l-w*ivln2; |
duke@435 | 606 | t1 = u+v; |
duke@435 | 607 | __LO(t1) = 0; |
duke@435 | 608 | t2 = v-(t1-u); |
duke@435 | 609 | } else { |
duke@435 | 610 | double ss,s2,s_h,s_l,t_h,t_l; |
duke@435 | 611 | n = 0; |
duke@435 | 612 | /* take care subnormal number */ |
duke@435 | 613 | if(ix<0x00100000) |
duke@435 | 614 | {ax *= two53; n -= 53; ix = __HI(ax); } |
duke@435 | 615 | n += ((ix)>>20)-0x3ff; |
duke@435 | 616 | j = ix&0x000fffff; |
duke@435 | 617 | /* determine interval */ |
duke@435 | 618 | ix = j|0x3ff00000; /* normalize ix */ |
duke@435 | 619 | if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */ |
duke@435 | 620 | else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ |
duke@435 | 621 | else {k=0;n+=1;ix -= 0x00100000;} |
duke@435 | 622 | __HI(ax) = ix; |
duke@435 | 623 | |
duke@435 | 624 | /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ |
duke@435 | 625 | u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ |
duke@435 | 626 | v = one/(ax+bp[k]); |
duke@435 | 627 | ss = u*v; |
duke@435 | 628 | s_h = ss; |
duke@435 | 629 | __LO(s_h) = 0; |
duke@435 | 630 | /* t_h=ax+bp[k] High */ |
duke@435 | 631 | t_h = zeroX; |
duke@435 | 632 | __HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18); |
duke@435 | 633 | t_l = ax - (t_h-bp[k]); |
duke@435 | 634 | s_l = v*((u-s_h*t_h)-s_h*t_l); |
duke@435 | 635 | /* compute log(ax) */ |
duke@435 | 636 | s2 = ss*ss; |
duke@435 | 637 | r = s2*s2*(L1X+s2*(L2X+s2*(L3X+s2*(L4X+s2*(L5X+s2*L6X))))); |
duke@435 | 638 | r += s_l*(s_h+ss); |
duke@435 | 639 | s2 = s_h*s_h; |
duke@435 | 640 | t_h = 3.0+s2+r; |
duke@435 | 641 | __LO(t_h) = 0; |
duke@435 | 642 | t_l = r-((t_h-3.0)-s2); |
duke@435 | 643 | /* u+v = ss*(1+...) */ |
duke@435 | 644 | u = s_h*t_h; |
duke@435 | 645 | v = s_l*t_h+t_l*ss; |
duke@435 | 646 | /* 2/(3log2)*(ss+...) */ |
duke@435 | 647 | p_h = u+v; |
duke@435 | 648 | __LO(p_h) = 0; |
duke@435 | 649 | p_l = v-(p_h-u); |
duke@435 | 650 | z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ |
duke@435 | 651 | z_l = cp_l*p_h+p_l*cp+dp_l[k]; |
duke@435 | 652 | /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ |
duke@435 | 653 | t = (double)n; |
duke@435 | 654 | t1 = (((z_h+z_l)+dp_h[k])+t); |
duke@435 | 655 | __LO(t1) = 0; |
duke@435 | 656 | t2 = z_l-(((t1-t)-dp_h[k])-z_h); |
duke@435 | 657 | } |
duke@435 | 658 | |
duke@435 | 659 | /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ |
duke@435 | 660 | y1 = y; |
duke@435 | 661 | __LO(y1) = 0; |
duke@435 | 662 | p_l = (y-y1)*t1+y*t2; |
duke@435 | 663 | p_h = y1*t1; |
duke@435 | 664 | z = p_l+p_h; |
duke@435 | 665 | j = __HI(z); |
duke@435 | 666 | i = __LO(z); |
duke@435 | 667 | if (j>=0x40900000) { /* z >= 1024 */ |
duke@435 | 668 | if(((j-0x40900000)|i)!=0) /* if z > 1024 */ |
duke@435 | 669 | return s*hugeX*hugeX; /* overflow */ |
duke@435 | 670 | else { |
duke@435 | 671 | if(p_l+ovt>z-p_h) return s*hugeX*hugeX; /* overflow */ |
duke@435 | 672 | } |
duke@435 | 673 | } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ |
duke@435 | 674 | if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ |
duke@435 | 675 | return s*tiny*tiny; /* underflow */ |
duke@435 | 676 | else { |
duke@435 | 677 | if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ |
duke@435 | 678 | } |
duke@435 | 679 | } |
duke@435 | 680 | /* |
duke@435 | 681 | * compute 2**(p_h+p_l) |
duke@435 | 682 | */ |
duke@435 | 683 | i = j&0x7fffffff; |
duke@435 | 684 | k = (i>>20)-0x3ff; |
duke@435 | 685 | n = 0; |
duke@435 | 686 | if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ |
duke@435 | 687 | n = j+(0x00100000>>(k+1)); |
duke@435 | 688 | k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ |
duke@435 | 689 | t = zeroX; |
duke@435 | 690 | __HI(t) = (n&~(0x000fffff>>k)); |
duke@435 | 691 | n = ((n&0x000fffff)|0x00100000)>>(20-k); |
duke@435 | 692 | if(j<0) n = -n; |
duke@435 | 693 | p_h -= t; |
duke@435 | 694 | } |
duke@435 | 695 | t = p_l+p_h; |
duke@435 | 696 | __LO(t) = 0; |
duke@435 | 697 | u = t*lg2_h; |
duke@435 | 698 | v = (p_l-(t-p_h))*lg2+t*lg2_l; |
duke@435 | 699 | z = u+v; |
duke@435 | 700 | w = v-(z-u); |
duke@435 | 701 | t = z*z; |
duke@435 | 702 | t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); |
duke@435 | 703 | r = (z*t1)/(t1-two)-(w+z*w); |
duke@435 | 704 | z = one-(r-z); |
duke@435 | 705 | j = __HI(z); |
duke@435 | 706 | j += (n<<20); |
duke@435 | 707 | if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */ |
duke@435 | 708 | else __HI(z) += (n<<20); |
duke@435 | 709 | return s*z; |
duke@435 | 710 | } |
duke@435 | 711 | |
duke@435 | 712 | |
duke@435 | 713 | JRT_LEAF(jdouble, SharedRuntime::dpow(jdouble x, jdouble y)) |
duke@435 | 714 | return __ieee754_pow(x, y); |
duke@435 | 715 | JRT_END |
duke@435 | 716 | |
duke@435 | 717 | #ifdef WIN32 |
duke@435 | 718 | # pragma optimize ( "", on ) |
duke@435 | 719 | #endif |