1 /* 2 * Copyright (c) 2005, 2010, 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 "prims/jni.h" 27 #include "runtime/interfaceSupport.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 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 * ==================================================== 66 * Copyright (c) 1998 Oracle and/or its affiliates. All rights reserved. 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) { 577 #ifdef CAN_USE_NAN_DEFINE 578 z = NAN; 579 #else 580 z = (z-z)/(z-z); /* (-1)**non-int is NaN */ 581 #endif 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 */ 592 if((n|yisint)==0) 593 #ifdef CAN_USE_NAN_DEFINE 594 return NAN; 595 #else 596 return (x-x)/(x-x); 597 #endif 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