runtime/MathObject.cpp

   1 /*
   2  *  Copyright (C) 1999-2000 Harri Porten (porten@kde.org)
   3  *  Copyright (C) 2007, 2008 Apple Inc. All Rights Reserved.
   4  *
   5  *  This library is free software; you can redistribute it and/or
   6  *  modify it under the terms of the GNU Lesser General Public
   7  *  License as published by the Free Software Foundation; either
   8  *  version 2 of the License, or (at your option) any later version.
   9  *
  10  *  This library is distributed in the hope that it will be useful,
  11  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
  12  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  13  *  Lesser General Public License for more details.
  14  *
  15  *  You should have received a copy of the GNU Lesser General Public
  16  *  License along with this library; if not, write to the Free Software
  17  *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  18  *
  19  */
  20
  21 #include "config.h"
  22 #include "MathObject.h"
  23
  24 #include "Lookup.h"
  25 #include "ObjectPrototype.h"
  26 #include "Operations.h"
  27 #include <time.h>
  28 #include <wtf/Assertions.h>
  29 #include <wtf/MathExtras.h>
  30 #include <wtf/RandomNumber.h>
  31 #include <wtf/RandomNumberSeed.h>
  32
  33 namespace JSC {
  34
  35 ASSERT_CLASS_FITS_IN_CELL(MathObject);
  36
  37 static EncodedJSValue JSC_HOST_CALL mathProtoFuncAbs(ExecState*);
  38 static EncodedJSValue JSC_HOST_CALL mathProtoFuncACos(ExecState*);
  39 static EncodedJSValue JSC_HOST_CALL mathProtoFuncASin(ExecState*);
  40 static EncodedJSValue JSC_HOST_CALL mathProtoFuncATan(ExecState*);
  41 static EncodedJSValue JSC_HOST_CALL mathProtoFuncATan2(ExecState*);
  42 static EncodedJSValue JSC_HOST_CALL mathProtoFuncCeil(ExecState*);
  43 static EncodedJSValue JSC_HOST_CALL mathProtoFuncCos(ExecState*);
  44 static EncodedJSValue JSC_HOST_CALL mathProtoFuncExp(ExecState*);
  45 static EncodedJSValue JSC_HOST_CALL mathProtoFuncFloor(ExecState*);
  46 static EncodedJSValue JSC_HOST_CALL mathProtoFuncLog(ExecState*);
  47 static EncodedJSValue JSC_HOST_CALL mathProtoFuncMax(ExecState*);
  48 static EncodedJSValue JSC_HOST_CALL mathProtoFuncMin(ExecState*);
  49 static EncodedJSValue JSC_HOST_CALL mathProtoFuncPow(ExecState*);
  50 static EncodedJSValue JSC_HOST_CALL mathProtoFuncRandom(ExecState*);
  51 static EncodedJSValue JSC_HOST_CALL mathProtoFuncRound(ExecState*);
  52 static EncodedJSValue JSC_HOST_CALL mathProtoFuncSin(ExecState*);
  53 static EncodedJSValue JSC_HOST_CALL mathProtoFuncSqrt(ExecState*);
  54 static EncodedJSValue JSC_HOST_CALL mathProtoFuncTan(ExecState*);
  55
  56 }
  57
  58 #include "MathObject.lut.h"
  59
  60 namespace JSC {
  61
  62 ASSERT_HAS_TRIVIAL_DESTRUCTOR(MathObject);
  63
  64 const ClassInfo MathObject::s_info = { "Math", &JSNonFinalObject::s_info, 0, ExecState::mathTable, CREATE_METHOD_TABLE(MathObject) };
  65
  66 /* Source for MathObject.lut.h
  67 @begin mathTable
  68   abs           mathProtoFuncAbs               DontEnum|Function 1
  69   acos          mathProtoFuncACos              DontEnum|Function 1
  70   asin          mathProtoFuncASin              DontEnum|Function 1
  71   atan          mathProtoFuncATan              DontEnum|Function 1
  72   atan2         mathProtoFuncATan2             DontEnum|Function 2
  73   ceil          mathProtoFuncCeil              DontEnum|Function 1
  74   cos           mathProtoFuncCos               DontEnum|Function 1
  75   exp           mathProtoFuncExp               DontEnum|Function 1
  76   floor         mathProtoFuncFloor             DontEnum|Function 1
  77   log           mathProtoFuncLog               DontEnum|Function 1
  78   max           mathProtoFuncMax               DontEnum|Function 2
  79   min           mathProtoFuncMin               DontEnum|Function 2
  80   pow           mathProtoFuncPow               DontEnum|Function 2
  81   random        mathProtoFuncRandom            DontEnum|Function 0
  82   round         mathProtoFuncRound             DontEnum|Function 1
  83   sin           mathProtoFuncSin               DontEnum|Function 1
  84   sqrt          mathProtoFuncSqrt              DontEnum|Function 1
  85   tan           mathProtoFuncTan               DontEnum|Function 1
  86 @end
  87 */
  88
  89 MathObject::MathObject(JSGlobalObject* globalObject, Structure* structure)
  90     : JSNonFinalObject(globalObject->globalData(), structure)
  91 {
  92 }
  93
  94 void MathObject::finishCreation(ExecState* exec, JSGlobalObject* globalObject)
  95 {
  96     Base::finishCreation(globalObject->globalData());
  97     ASSERT(inherits(&s_info));
  98
  99     putDirectWithoutTransition(exec->globalData(), Identifier(exec, "E"), jsNumber(exp(1.0)), DontDelete | DontEnum | ReadOnly);
 100     putDirectWithoutTransition(exec->globalData(), Identifier(exec, "LN2"), jsNumber(log(2.0)), DontDelete | DontEnum | ReadOnly);
 101     putDirectWithoutTransition(exec->globalData(), Identifier(exec, "LN10"), jsNumber(log(10.0)), DontDelete | DontEnum | ReadOnly);
 102     putDirectWithoutTransition(exec->globalData(), Identifier(exec, "LOG2E"), jsNumber(1.0 / log(2.0)), DontDelete | DontEnum | ReadOnly);
 103     putDirectWithoutTransition(exec->globalData(), Identifier(exec, "LOG10E"), jsNumber(0.4342944819032518), DontDelete | DontEnum | ReadOnly); // See ECMA-262 15.8.1.5
 104     putDirectWithoutTransition(exec->globalData(), Identifier(exec, "PI"), jsNumber(piDouble), DontDelete | DontEnum | ReadOnly);
 105     putDirectWithoutTransition(exec->globalData(), Identifier(exec, "SQRT1_2"), jsNumber(sqrt(0.5)), DontDelete | DontEnum | ReadOnly);
 106     putDirectWithoutTransition(exec->globalData(), Identifier(exec, "SQRT2"), jsNumber(sqrt(2.0)), DontDelete | DontEnum | ReadOnly);
 107 }
 108
 109 bool MathObject::getOwnPropertySlot(JSCell* cell, ExecState* exec, const Identifier& propertyName, PropertySlot &slot)
 110 {
 111     return getStaticFunctionSlot<JSObject>(exec, ExecState::mathTable(exec), jsCast<MathObject*>(cell), propertyName, slot);
 112 }
 113
 114 bool MathObject::getOwnPropertyDescriptor(JSObject* object, ExecState* exec, const Identifier& propertyName, PropertyDescriptor& descriptor)
 115 {
 116     return getStaticFunctionDescriptor<JSObject>(exec, ExecState::mathTable(exec), jsCast<MathObject*>(object), propertyName, descriptor);
 117 }
 118
 119 // ------------------------------ Functions --------------------------------
 120
 121 EncodedJSValue JSC_HOST_CALL mathProtoFuncAbs(ExecState* exec)
 122 {
 123     return JSValue::encode(jsNumber(fabs(exec->argument(0).toNumber(exec))));
 124 }
 125
 126 EncodedJSValue JSC_HOST_CALL mathProtoFuncACos(ExecState* exec)
 127 {
 128     return JSValue::encode(jsDoubleNumber(acos(exec->argument(0).toNumber(exec))));
 129 }
 130
 131 EncodedJSValue JSC_HOST_CALL mathProtoFuncASin(ExecState* exec)
 132 {
 133     return JSValue::encode(jsDoubleNumber(asin(exec->argument(0).toNumber(exec))));
 134 }
 135
 136 EncodedJSValue JSC_HOST_CALL mathProtoFuncATan(ExecState* exec)
 137 {
 138     return JSValue::encode(jsDoubleNumber(atan(exec->argument(0).toNumber(exec))));
 139 }
 140
 141 EncodedJSValue JSC_HOST_CALL mathProtoFuncATan2(ExecState* exec)
 142 {
 143     double arg0 = exec->argument(0).toNumber(exec);
 144     double arg1 = exec->argument(1).toNumber(exec);
 145     return JSValue::encode(jsDoubleNumber(atan2(arg0, arg1)));
 146 }
 147
 148 EncodedJSValue JSC_HOST_CALL mathProtoFuncCeil(ExecState* exec)
 149 {
 150     return JSValue::encode(jsNumber(ceil(exec->argument(0).toNumber(exec))));
 151 }
 152
 153 EncodedJSValue JSC_HOST_CALL mathProtoFuncCos(ExecState* exec)
 154 {
 155     return JSValue::encode(jsDoubleNumber(cos(exec->argument(0).toNumber(exec))));
 156 }
 157
 158 EncodedJSValue JSC_HOST_CALL mathProtoFuncExp(ExecState* exec)
 159 {
 160     return JSValue::encode(jsDoubleNumber(exp(exec->argument(0).toNumber(exec))));
 161 }
 162
 163 EncodedJSValue JSC_HOST_CALL mathProtoFuncFloor(ExecState* exec)
 164 {
 165     return JSValue::encode(jsNumber(floor(exec->argument(0).toNumber(exec))));
 166 }
 167
 168 EncodedJSValue JSC_HOST_CALL mathProtoFuncLog(ExecState* exec)
 169 {
 170     return JSValue::encode(jsDoubleNumber(log(exec->argument(0).toNumber(exec))));
 171 }
 172
 173 EncodedJSValue JSC_HOST_CALL mathProtoFuncMax(ExecState* exec)
 174 {
 175     unsigned argsCount = exec->argumentCount();
 176     double result = -std::numeric_limits<double>::infinity();
 177     for (unsigned k = 0; k < argsCount; ++k) {
 178         double val = exec->argument(k).toNumber(exec);
 179         if (isnan(val)) {
 180             result = std::numeric_limits<double>::quiet_NaN();
 181             break;
 182         }
 183         if (val > result || (val == 0 && result == 0 && !signbit(val)))
 184             result = val;
 185     }
 186     return JSValue::encode(jsNumber(result));
 187 }
 188
 189 EncodedJSValue JSC_HOST_CALL mathProtoFuncMin(ExecState* exec)
 190 {
 191     unsigned argsCount = exec->argumentCount();
 192     double result = +std::numeric_limits<double>::infinity();
 193     for (unsigned k = 0; k < argsCount; ++k) {
 194         double val = exec->argument(k).toNumber(exec);
 195         if (isnan(val)) {
 196             result = std::numeric_limits<double>::quiet_NaN();
 197             break;
 198         }
 199         if (val < result || (val == 0 && result == 0 && signbit(val)))
 200             result = val;
 201     }
 202     return JSValue::encode(jsNumber(result));
 203 }
 204
 205 #if CPU(ARM_THUMB2)
 206
 207 static double fdlibmPow(double x, double y);
 208
 209 static ALWAYS_INLINE bool isDenormal(double x)
 210 {
 211         static const uint64_t signbit = 0x8000000000000000ULL;
 212         static const uint64_t minNormal = 0x0001000000000000ULL;
 213         return (bitwise_cast<uint64_t>(x) & ~signbit) - 1 < minNormal - 1;
 214 }
 215
 216 static ALWAYS_INLINE bool isEdgeCase(double x)
 217 {
 218         static const uint64_t signbit = 0x8000000000000000ULL;
 219         static const uint64_t infinity = 0x7fffffffffffffffULL;
 220         return (bitwise_cast<uint64_t>(x) & ~signbit) - 1 >= infinity - 1;
 221 }
 222
 223 static ALWAYS_INLINE double mathPow(double x, double y)
 224 {
 225     if (!isDenormal(x) && !isDenormal(y)) {
 226         double libmResult = pow(x,y);
 227         if (libmResult || isEdgeCase(x) || isEdgeCase(y))
 228             return libmResult;
 229     }
 230     return fdlibmPow(x,y);
 231 }
 232
 233 #else
 234
 235 ALWAYS_INLINE double mathPow(double x, double y)
 236 {
 237     return pow(x, y);
 238 }
 239
 240 #endif
 241
 242 EncodedJSValue JSC_HOST_CALL mathProtoFuncPow(ExecState* exec)
 243 {
 244     // ECMA 15.8.2.1.13
 245
 246     double arg = exec->argument(0).toNumber(exec);
 247     double arg2 = exec->argument(1).toNumber(exec);
 248
 249     if (isnan(arg2))
 250         return JSValue::encode(jsNaN());
 251     if (isinf(arg2) && fabs(arg) == 1)
 252         return JSValue::encode(jsNaN());
 253     return JSValue::encode(jsNumber(mathPow(arg, arg2)));
 254 }
 255
 256 EncodedJSValue JSC_HOST_CALL mathProtoFuncRandom(ExecState* exec)
 257 {
 258     return JSValue::encode(jsDoubleNumber(exec->lexicalGlobalObject()->weakRandomNumber()));
 259 }
 260
 261 EncodedJSValue JSC_HOST_CALL mathProtoFuncRound(ExecState* exec)
 262 {
 263     double arg = exec->argument(0).toNumber(exec);
 264     double integer = ceil(arg);
 265     return JSValue::encode(jsNumber(integer - (integer - arg > 0.5)));
 266 }
 267
 268 EncodedJSValue JSC_HOST_CALL mathProtoFuncSin(ExecState* exec)
 269 {
 270     return JSValue::encode(exec->globalData().cachedSin(exec->argument(0).toNumber(exec)));
 271 }
 272
 273 EncodedJSValue JSC_HOST_CALL mathProtoFuncSqrt(ExecState* exec)
 274 {
 275     return JSValue::encode(jsDoubleNumber(sqrt(exec->argument(0).toNumber(exec))));
 276 }
 277
 278 EncodedJSValue JSC_HOST_CALL mathProtoFuncTan(ExecState* exec)
 279 {
 280     return JSValue::encode(jsDoubleNumber(tan(exec->argument(0).toNumber(exec))));
 281 }
 282
 283 #if CPU(ARM_THUMB2)
 284
 285 // The following code is taken from netlib.org:
 286 //   http://www.netlib.org/fdlibm/fdlibm.h
 287 //   http://www.netlib.org/fdlibm/e_pow.c
 288 //   http://www.netlib.org/fdlibm/s_scalbn.c
 289 //
 290 // And was originally distributed under the following license:
 291
 292 /*
 293  * ====================================================
 294  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 295  *
 296  * Developed at SunSoft, a Sun Microsystems, Inc. business.
 297  * Permission to use, copy, modify, and distribute this
 298  * software is freely granted, provided that this notice
 299  * is preserved.
 300  * ====================================================
 301  */
 302 /*
 303  * ====================================================
 304  * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
 305  *
 306  * Permission to use, copy, modify, and distribute this
 307  * software is freely granted, provided that this notice
 308  * is preserved.
 309  * ====================================================
 310  */
 311
 312 /* __ieee754_pow(x,y) return x**y
 313  *
 314  *                    n
 315  * Method:  Let x =  2   * (1+f)
 316  *      1. Compute and return log2(x) in two pieces:
 317  *              log2(x) = w1 + w2,
 318  *         where w1 has 53-24 = 29 bit trailing zeros.
 319  *      2. Perform y*log2(x) = n+y' by simulating muti-precision
 320  *         arithmetic, where |y'|<=0.5.
 321  *      3. Return x**y = 2**n*exp(y'*log2)
 322  *
 323  * Special cases:
 324  *      1.  (anything) ** 0  is 1
 325  *      2.  (anything) ** 1  is itself
 326  *      3.  (anything) ** NAN is NAN
 327  *      4.  NAN ** (anything except 0) is NAN
 328  *      5.  +-(|x| > 1) **  +INF is +INF
 329  *      6.  +-(|x| > 1) **  -INF is +0
 330  *      7.  +-(|x| < 1) **  +INF is +0
 331  *      8.  +-(|x| < 1) **  -INF is +INF
 332  *      9.  +-1         ** +-INF is NAN
 333  *      10. +0 ** (+anything except 0, NAN)               is +0
 334  *      11. -0 ** (+anything except 0, NAN, odd integer)  is +0
 335  *      12. +0 ** (-anything except 0, NAN)               is +INF
 336  *      13. -0 ** (-anything except 0, NAN, odd integer)  is +INF
 337  *      14. -0 ** (odd integer) = -( +0 ** (odd integer) )
 338  *      15. +INF ** (+anything except 0,NAN) is +INF
 339  *      16. +INF ** (-anything except 0,NAN) is +0
 340  *      17. -INF ** (anything)  = -0 ** (-anything)
 341  *      18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
 342  *      19. (-anything except 0 and inf) ** (non-integer) is NAN
 343  *
 344  * Accuracy:
 345  *      pow(x,y) returns x**y nearly rounded. In particular
 346  *                      pow(integer,integer)
 347  *      always returns the correct integer provided it is
 348  *      representable.
 349  *
 350  * Constants :
 351  * The hexadecimal values are the intended ones for the following
 352  * constants. The decimal values may be used, provided that the
 353  * compiler will convert from decimal to binary accurately enough
 354  * to produce the hexadecimal values shown.
 355  */
 356
 357 #define __HI(x) *(1+(int*)&x)
 358 #define __LO(x) *(int*)&x
 359
 360 static const double
 361 bp[] = {1.0, 1.5,},
 362 dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
 363 dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
 364 zero    =  0.0,
 365 one     =  1.0,
 366 two     =  2.0,
 367 two53   =  9007199254740992.0,  /* 0x43400000, 0x00000000 */
 368 huge    =  1.0e300,
 369 tiny    =  1.0e-300,
 370         /* for scalbn */
 371 two54   =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
 372 twom54  =  5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
 373         /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
 374 L1  =  5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
 375 L2  =  4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
 376 L3  =  3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
 377 L4  =  2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
 378 L5  =  2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
 379 L6  =  2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
 380 P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
 381 P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
 382 P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
 383 P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
 384 P5   =  4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
 385 lg2  =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
 386 lg2_h  =  6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
 387 lg2_l  = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
 388 ovt =  8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
 389 cp    =  9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
 390 cp_h  =  9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
 391 cp_l  = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
 392 ivln2    =  1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
 393 ivln2_h  =  1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
 394 ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
 395
 396 inline double fdlibmScalbn (double x, int n)
 397 {
 398         int  k,hx,lx;
 399         hx = __HI(x);
 400         lx = __LO(x);
 401         k = (hx&0x7ff00000)>>20;                /* extract exponent */
 402         if (k==0) {                             /* 0 or subnormal x */
 403             if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
 404             x *= two54;
 405             hx = __HI(x);
 406             k = ((hx&0x7ff00000)>>20) - 54;
 407             if (n< -50000) return tiny*x;       /*underflow*/
 408             }
 409         if (k==0x7ff) return x+x;               /* NaN or Inf */
 410         k = k+n;
 411         if (k >  0x7fe) return huge*copysign(huge,x); /* overflow  */
 412         if (k > 0)                              /* normal result */
 413             {__HI(x) = (hx&0x800fffff)|(k<<20); return x;}
 414         if (k <= -54) {
 415             if (n > 50000)      /* in case integer overflow in n+k */
 416                 return huge*copysign(huge,x);   /*overflow*/
 417             else return tiny*copysign(tiny,x);  /*underflow*/
 418         }
 419         k += 54;                                /* subnormal result */
 420         __HI(x) = (hx&0x800fffff)|(k<<20);
 421         return x*twom54;
 422 }
 423
 424 double fdlibmPow(double x, double y)
 425 {
 426         double z,ax,z_h,z_l,p_h,p_l;
 427         double y1,t1,t2,r,s,t,u,v,w;
 428         int i0,i1,i,j,k,yisint,n;
 429         int hx,hy,ix,iy;
 430         unsigned lx,ly;
 431
 432         i0 = ((*(int*)&one)>>29)^1; i1=1-i0;
 433         hx = __HI(x); lx = __LO(x);
 434         hy = __HI(y); ly = __LO(y);
 435         ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
 436
 437     /* y==zero: x**0 = 1 */
 438         if((iy|ly)==0) return one;
 439
 440     /* +-NaN return x+y */
 441         if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
 442            iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
 443                 return x+y;
 444
 445     /* determine if y is an odd int when x < 0
 446      * yisint = 0       ... y is not an integer
 447      * yisint = 1       ... y is an odd int
 448      * yisint = 2       ... y is an even int
 449      */
 450         yisint  = 0;
 451         if(hx<0) {
 452             if(iy>=0x43400000) yisint = 2; /* even integer y */
 453             else if(iy>=0x3ff00000) {
 454                 k = (iy>>20)-0x3ff;        /* exponent */
 455                 if(k>20) {
 456                     j = ly>>(52-k);
 457                     if(static_cast<unsigned>(j<<(52-k))==ly) yisint = 2-(j&1);
 458                 } else if(ly==0) {
 459                     j = iy>>(20-k);
 460                     if((j<<(20-k))==iy) yisint = 2-(j&1);
 461                 }
 462             }
 463         }
 464
 465     /* special value of y */
 466         if(ly==0) {
 467             if (iy==0x7ff00000) {       /* y is +-inf */
 468                 if(((ix-0x3ff00000)|lx)==0)
 469                     return  y - y;      /* inf**+-1 is NaN */
 470                 else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
 471                     return (hy>=0)? y: zero;
 472                 else                    /* (|x|<1)**-,+inf = inf,0 */
 473                     return (hy<0)?-y: zero;
 474             }
 475             if(iy==0x3ff00000) {        /* y is  +-1 */
 476                 if(hy<0) return one/x; else return x;
 477             }
 478             if(hy==0x40000000) return x*x; /* y is  2 */
 479             if(hy==0x3fe00000) {        /* y is  0.5 */
 480                 if(hx>=0)       /* x >= +0 */
 481                 return sqrt(x);
 482             }
 483         }
 484
 485         ax   = fabs(x);
 486     /* special value of x */
 487         if(lx==0) {
 488             if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
 489                 z = ax;                 /*x is +-0,+-inf,+-1*/
 490                 if(hy<0) z = one/z;     /* z = (1/|x|) */
 491                 if(hx<0) {
 492                     if(((ix-0x3ff00000)|yisint)==0) {
 493                         z = (z-z)/(z-z); /* (-1)**non-int is NaN */
 494                     } else if(yisint==1)
 495                         z = -z;         /* (x<0)**odd = -(|x|**odd) */
 496                 }
 497                 return z;
 498             }
 499         }
 500
 501         n = (hx>>31)+1;
 502
 503     /* (x<0)**(non-int) is NaN */
 504         if((n|yisint)==0) return (x-x)/(x-x);
 505
 506         s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
 507         if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
 508
 509     /* |y| is huge */
 510         if(iy>0x41e00000) { /* if |y| > 2**31 */
 511             if(iy>0x43f00000){  /* if |y| > 2**64, must o/uflow */
 512                 if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
 513                 if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
 514             }
 515         /* over/underflow if x is not close to one */
 516             if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
 517             if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
 518         /* now |1-x| is tiny <= 2**-20, suffice to compute
 519            log(x) by x-x^2/2+x^3/3-x^4/4 */
 520             t = ax-one;         /* t has 20 trailing zeros */
 521             w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
 522             u = ivln2_h*t;      /* ivln2_h has 21 sig. bits */
 523             v = t*ivln2_l-w*ivln2;
 524             t1 = u+v;
 525             __LO(t1) = 0;
 526             t2 = v-(t1-u);
 527         } else {
 528             double ss,s2,s_h,s_l,t_h,t_l;
 529             n = 0;
 530         /* take care subnormal number */
 531             if(ix<0x00100000)
 532                 {ax *= two53; n -= 53; ix = __HI(ax); }
 533             n  += ((ix)>>20)-0x3ff;
 534             j  = ix&0x000fffff;
 535         /* determine interval */
 536             ix = j|0x3ff00000;          /* normalize ix */
 537             if(j<=0x3988E) k=0;         /* |x|<sqrt(3/2) */
 538             else if(j<0xBB67A) k=1;     /* |x|<sqrt(3)   */
 539             else {k=0;n+=1;ix -= 0x00100000;}
 540             __HI(ax) = ix;
 541
 542         /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
 543             u = ax-bp[k];               /* bp[0]=1.0, bp[1]=1.5 */
 544             v = one/(ax+bp[k]);
 545             ss = u*v;
 546             s_h = ss;
 547             __LO(s_h) = 0;
 548         /* t_h=ax+bp[k] High */
 549             t_h = zero;
 550             __HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18);
 551             t_l = ax - (t_h-bp[k]);
 552             s_l = v*((u-s_h*t_h)-s_h*t_l);
 553         /* compute log(ax) */
 554             s2 = ss*ss;
 555             r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
 556             r += s_l*(s_h+ss);
 557             s2  = s_h*s_h;
 558             t_h = 3.0+s2+r;
 559             __LO(t_h) = 0;
 560             t_l = r-((t_h-3.0)-s2);
 561         /* u+v = ss*(1+...) */
 562             u = s_h*t_h;
 563             v = s_l*t_h+t_l*ss;
 564         /* 2/(3log2)*(ss+...) */
 565             p_h = u+v;
 566             __LO(p_h) = 0;
 567             p_l = v-(p_h-u);
 568             z_h = cp_h*p_h;             /* cp_h+cp_l = 2/(3*log2) */
 569             z_l = cp_l*p_h+p_l*cp+dp_l[k];
 570         /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
 571             t = (double)n;
 572             t1 = (((z_h+z_l)+dp_h[k])+t);
 573             __LO(t1) = 0;
 574             t2 = z_l-(((t1-t)-dp_h[k])-z_h);
 575         }
 576
 577     /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
 578         y1  = y;
 579         __LO(y1) = 0;
 580         p_l = (y-y1)*t1+y*t2;
 581         p_h = y1*t1;
 582         z = p_l+p_h;
 583         j = __HI(z);
 584         i = __LO(z);
 585         if (j>=0x40900000) {                            /* z >= 1024 */
 586             if(((j-0x40900000)|i)!=0)                   /* if z > 1024 */
 587                 return s*huge*huge;                     /* overflow */
 588             else {
 589                 if(p_l+ovt>z-p_h) return s*huge*huge;   /* overflow */
 590             }
 591         } else if((j&0x7fffffff)>=0x4090cc00 ) {        /* z <= -1075 */
 592             if(((j-0xc090cc00)|i)!=0)           /* z < -1075 */
 593                 return s*tiny*tiny;             /* underflow */
 594             else {
 595                 if(p_l<=z-p_h) return s*tiny*tiny;      /* underflow */
 596             }
 597         }
 598     /*
 599      * compute 2**(p_h+p_l)
 600      */
 601         i = j&0x7fffffff;
 602         k = (i>>20)-0x3ff;
 603         n = 0;
 604         if(i>0x3fe00000) {              /* if |z| > 0.5, set n = [z+0.5] */
 605             n = j+(0x00100000>>(k+1));
 606             k = ((n&0x7fffffff)>>20)-0x3ff;     /* new k for n */
 607             t = zero;
 608             __HI(t) = (n&~(0x000fffff>>k));
 609             n = ((n&0x000fffff)|0x00100000)>>(20-k);
 610             if(j<0) n = -n;
 611             p_h -= t;
 612         }
 613         t = p_l+p_h;
 614         __LO(t) = 0;
 615         u = t*lg2_h;
 616         v = (p_l-(t-p_h))*lg2+t*lg2_l;
 617         z = u+v;
 618         w = v-(z-u);
 619         t  = z*z;
 620         t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
 621         r  = (z*t1)/(t1-two)-(w+z*w);
 622         z  = one-(r-z);
 623         j  = __HI(z);
 624         j += (n<<20);
 625         if((j>>20)<=0) z = fdlibmScalbn(z,n);   /* subnormal output */
 626         else __HI(z) += (n<<20);
 627         return s*z;
 628 }
 629
 630 #endif
 631
 632 } // namespace JSC