| File: | jdk/src/hotspot/share/runtime/sharedRuntimeTrans.cpp |
| Warning: | line 450, column 31 Value stored to 'i1' is never read |
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| 1 | /* |
| 2 | * Copyright (c) 2005, 2017, Oracle and/or its affiliates. All rights reserved. |
| 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 | * |
| 19 | * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| 20 | * or visit www.oracle.com if you need additional information or have any |
| 21 | * questions. |
| 22 | * |
| 23 | */ |
| 24 | |
| 25 | #include "precompiled.hpp" |
| 26 | #include "jni.h" |
| 27 | #include "runtime/interfaceSupport.inline.hpp" |
| 28 | #include "runtime/sharedRuntime.hpp" |
| 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 warning( disable: 4748 ) // /GS can not protect parameters and local variables from local buffer overrun because optimizations are disabled in function |
| 44 | # pragma optimize ( "", off ) |
| 45 | #endif |
| 46 | |
| 47 | #include "runtime/sharedRuntimeMath.hpp" |
| 48 | |
| 49 | /* __ieee754_log(x) |
| 50 | * Return the logarithm 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 | |
| 118 | hx = high(x); /* high word of x */ |
| 119 | lx = low(x); /* low word of x */ |
| 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 */ |
| 127 | hx = high(x); /* high word of x */ |
| 128 | } |
| 129 | if (hx >= 0x7ff00000) return x+x; |
| 130 | k += (hx>>20)-1023; |
| 131 | hx &= 0x000fffff; |
| 132 | i = (hx+0x95f64)&0x100000; |
| 133 | set_high(&x, hx|(i^0x3ff00000)); /* normalize x or x/2 */ |
| 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))jdouble SharedRuntime::dlog(jdouble x) { NoHandleMark __hm; ; os::verify_stack_alignment(); NoSafepointVerifier __nsv; |
| 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 | |
| 212 | hx = high(x); /* high word of x */ |
| 213 | lx = low(x); /* low word of x */ |
| 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 */ |
| 221 | hx = high(x); /* high word of x */ |
| 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); |
| 228 | set_high(&x, hx); |
| 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))jdouble SharedRuntime::dlog10(jdouble x) { NoHandleMark __hm; ; os::verify_stack_alignment(); NoSafepointVerifier __nsv; |
| 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 | |
| 323 | hx = high(x); /* high word of x */ |
| 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) { |
| 330 | if(((hx&0xfffff)|low(x))!=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) { |
| 361 | set_high(&y, high(y) + (k<<20)); /* add k to y's exponent */ |
| 362 | return y; |
| 363 | } else { |
| 364 | set_high(&y, high(y) + ((k+1000)<<20)); /* add k to y's exponent */ |
| 365 | return y*twom1000; |
| 366 | } |
| 367 | } |
| 368 | |
| 369 | JRT_LEAF(jdouble, SharedRuntime::dexp(jdouble x))jdouble SharedRuntime::dexp(jdouble x) { NoHandleMark __hm; ; os::verify_stack_alignment(); NoSafepointVerifier __nsv; |
| 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; |
Value stored to 'i1' is never read | |
| 451 | hx = high(x); lx = low(x); |
| 452 | hy = high(y); ly = low(y); |
| 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) { |
| 511 | #ifdef CAN_USE_NAN_DEFINE1 |
| 512 | z = NAN(__builtin_nanf ("")); |
| 513 | #else |
| 514 | z = (z-z)/(z-z); /* (-1)**non-int is NaN */ |
| 515 | #endif |
| 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 */ |
| 526 | if((n|yisint)==0) |
| 527 | #ifdef CAN_USE_NAN_DEFINE1 |
| 528 | return NAN(__builtin_nanf ("")); |
| 529 | #else |
| 530 | return (x-x)/(x-x); |
| 531 | #endif |
| 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; |
| 552 | set_low(&t1, 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) |
| 559 | {ax *= two53; n -= 53; ix = high(ax); } |
| 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;} |
| 567 | set_high(&ax, ix); |
| 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; |
| 574 | set_low(&s_h, 0); |
| 575 | /* t_h=ax+bp[k] High */ |
| 576 | t_h = zeroX; |
| 577 | set_high(&t_h, ((ix>>1)|0x20000000)+0x00080000+(k<<18)); |
| 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; |
| 586 | set_low(&t_h, 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; |
| 593 | set_low(&p_h, 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); |
| 600 | set_low(&t1, 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; |
| 606 | set_low(&y1, 0); |
| 607 | p_l = (y-y1)*t1+y*t2; |
| 608 | p_h = y1*t1; |
| 609 | z = p_l+p_h; |
| 610 | j = high(z); |
| 611 | i = low(z); |
| 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; |
| 635 | set_high(&t, (n&~(0x000fffff>>k))); |
| 636 | n = ((n&0x000fffff)|0x00100000)>>(20-k); |
| 637 | if(j<0) n = -n; |
| 638 | p_h -= t; |
| 639 | } |
| 640 | t = p_l+p_h; |
| 641 | set_low(&t, 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); |
| 650 | j = high(z); |
| 651 | j += (n<<20); |
| 652 | if((j>>20)<=0) z = scalbnA(z,n); /* subnormal output */ |
| 653 | else set_high(&z, high(z) + (n<<20)); |
| 654 | return s*z; |
| 655 | } |
| 656 | |
| 657 | |
| 658 | JRT_LEAF(jdouble, SharedRuntime::dpow(jdouble x, jdouble y))jdouble SharedRuntime::dpow(jdouble x, jdouble y) { NoHandleMark __hm; ; os::verify_stack_alignment(); NoSafepointVerifier __nsv ; |
| 659 | return __ieee754_pow(x, y); |
| 660 | JRT_END} |
| 661 | |
| 662 | #ifdef WIN32 |
| 663 | # pragma optimize ( "", on ) |
| 664 | #endif |