runtime/MathCommon.cpp

   1 /*
   2  * Copyright (C) 2015 Apple Inc. All rights reserved.
   3  *
   4  * Redistribution and use in source and binary forms, with or without
   5  * modification, are permitted provided that the following conditions
   6  * are met:
   7  * 1. Redistributions of source code must retain the above copyright
   8  *    notice, this list of conditions and the following disclaimer.
   9  * 2. Redistributions in binary form must reproduce the above copyright
  10  *    notice, this list of conditions and the following disclaimer in the
  11  *    documentation and/or other materials provided with the distribution.
  12  *
  13  * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
  14  * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  15  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
  16  * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL APPLE INC. OR
  17  * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
  18  * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
  19  * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
  20  * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
  21  * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  22  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
  23  * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  24  */
  25
  26 #include "config.h"
  27 #include "MathCommon.h"
  28
  29 #include <cmath>
  30 #include "PureNaN.h"
  31
  32 namespace JSC {
  33
  34 #if PLATFORM(IOS) && CPU(ARM_THUMB2)
  35
  36 // The following code is taken from netlib.org:
  37 //   http://www.netlib.org/fdlibm/fdlibm.h
  38 //   http://www.netlib.org/fdlibm/e_pow.c
  39 //   http://www.netlib.org/fdlibm/s_scalbn.c
  40 //
  41 // And was originally distributed under the following license:
  42
  43 /*
  44  * ====================================================
  45  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  46  *
  47  * Developed at SunSoft, a Sun Microsystems, Inc. business.
  48  * Permission to use, copy, modify, and distribute this
  49  * software is freely granted, provided that this notice
  50  * is preserved.
  51  * ====================================================
  52  */
  53 /*
  54  * ====================================================
  55  * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
  56  *
  57  * Permission to use, copy, modify, and distribute this
  58  * software is freely granted, provided that this notice
  59  * is preserved.
  60  * ====================================================
  61  */
  62
  63 /* __ieee754_pow(x,y) return x**y
  64  *
  65  *              n
  66  * Method:  Let x =  2   * (1+f)
  67  *    1. Compute and return log2(x) in two pieces:
  68  *        log2(x) = w1 + w2,
  69  *       where w1 has 53-24 = 29 bit trailing zeros.
  70  *    2. Perform y*log2(x) = n+y' by simulating muti-precision
  71  *       arithmetic, where |y'|<=0.5.
  72  *    3. Return x**y = 2**n*exp(y'*log2)
  73  *
  74  * Special cases:
  75  *    1.  (anything) ** 0  is 1
  76  *    2.  (anything) ** 1  is itself
  77  *    3.  (anything) ** NAN is NAN
  78  *    4.  NAN ** (anything except 0) is NAN
  79  *    5.  +-(|x| > 1) **  +INF is +INF
  80  *    6.  +-(|x| > 1) **  -INF is +0
  81  *    7.  +-(|x| < 1) **  +INF is +0
  82  *    8.  +-(|x| < 1) **  -INF is +INF
  83  *    9.  +-1         ** +-INF is NAN
  84  *    10. +0 ** (+anything except 0, NAN)               is +0
  85  *    11. -0 ** (+anything except 0, NAN, odd integer)  is +0
  86  *    12. +0 ** (-anything except 0, NAN)               is +INF
  87  *    13. -0 ** (-anything except 0, NAN, odd integer)  is +INF
  88  *    14. -0 ** (odd integer) = -( +0 ** (odd integer) )
  89  *    15. +INF ** (+anything except 0,NAN) is +INF
  90  *    16. +INF ** (-anything except 0,NAN) is +0
  91  *    17. -INF ** (anything)  = -0 ** (-anything)
  92  *    18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
  93  *    19. (-anything except 0 and inf) ** (non-integer) is NAN
  94  *
  95  * Accuracy:
  96  *    pow(x,y) returns x**y nearly rounded. In particular
  97  *            pow(integer,integer)
  98  *    always returns the correct integer provided it is
  99  *    representable.
 100  *
 101  * Constants :
 102  * The hexadecimal values are the intended ones for the following
 103  * constants. The decimal values may be used, provided that the
 104  * compiler will convert from decimal to binary accurately enough
 105  * to produce the hexadecimal values shown.
 106  */
 107
 108 #define __HI(x) *(1+(int*)&x)
 109 #define __LO(x) *(int*)&x
 110
 111 static const double
 112 bp[] = {1.0, 1.5,},
 113 dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
 114 dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
 115 zero    =  0.0,
 116 one    =  1.0,
 117 two    =  2.0,
 118 two53    =  9007199254740992.0,    /* 0x43400000, 0x00000000 */
 119 huge    =  1.0e300,
 120 tiny    =  1.0e-300,
 121 /* for scalbn */
 122 two54   =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
 123 twom54  =  5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
 124 /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
 125 L1  =  5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
 126 L2  =  4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
 127 L3  =  3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
 128 L4  =  2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
 129 L5  =  2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
 130 L6  =  2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
 131 P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
 132 P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
 133 P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
 134 P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
 135 P5   =  4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
 136 lg2  =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
 137 lg2_h  =  6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
 138 lg2_l  = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
 139 ovt =  8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
 140 cp    =  9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
 141 cp_h  =  9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
 142 cp_l  = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
 143 ivln2    =  1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
 144 ivln2_h  =  1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
 145 ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
 146
 147 inline double fdlibmScalbn (double x, int n)
 148 {
 149     int  k,hx,lx;
 150     hx = __HI(x);
 151     lx = __LO(x);
 152     k = (hx&0x7ff00000)>>20;        /* extract exponent */
 153     if (k==0) {                /* 0 or subnormal x */
 154         if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
 155         x *= two54;
 156         hx = __HI(x);
 157         k = ((hx&0x7ff00000)>>20) - 54;
 158         if (n< -50000) return tiny*x;     /*underflow*/
 159     }
 160     if (k==0x7ff) return x+x;        /* NaN or Inf */
 161     k = k+n;
 162     if (k >  0x7fe) return huge*copysign(huge,x); /* overflow  */
 163     if (k > 0)                 /* normal result */
 164     {__HI(x) = (hx&0x800fffff)|(k<<20); return x;}
 165     if (k <= -54) {
 166         if (n > 50000)     /* in case integer overflow in n+k */
 167             return huge*copysign(huge,x);    /*overflow*/
 168         else return tiny*copysign(tiny,x);     /*underflow*/
 169     }
 170     k += 54;                /* subnormal result */
 171     __HI(x) = (hx&0x800fffff)|(k<<20);
 172     return x*twom54;
 173 }
 174
 175 static double fdlibmPow(double x, double y)
 176 {
 177     double z,ax,z_h,z_l,p_h,p_l;
 178     double y1,t1,t2,r,s,t,u,v,w;
 179     int i0,i1,i,j,k,yisint,n;
 180     int hx,hy,ix,iy;
 181     unsigned lx,ly;
 182
 183     i0 = ((*(int*)&one)>>29)^1; i1=1-i0;
 184     hx = __HI(x); lx = __LO(x);
 185     hy = __HI(y); ly = __LO(y);
 186     ix = hx&0x7fffffff;  iy = hy&0x7fffffff;
 187
 188     /* y==zero: x**0 = 1 */
 189     if((iy|ly)==0) return one;
 190
 191     /* +-NaN return x+y */
 192     if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
 193        iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
 194         return x+y;
 195
 196     /* determine if y is an odd int when x < 0
 197      * yisint = 0    ... y is not an integer
 198      * yisint = 1    ... y is an odd int
 199      * yisint = 2    ... y is an even int
 200      */
 201     yisint  = 0;
 202     if(hx<0) {
 203         if(iy>=0x43400000) yisint = 2; /* even integer y */
 204         else if(iy>=0x3ff00000) {
 205             k = (iy>>20)-0x3ff;       /* exponent */
 206             if(k>20) {
 207                 j = ly>>(52-k);
 208                 if(static_cast<unsigned>(j<<(52-k))==ly) yisint = 2-(j&1);
 209             } else if(ly==0) {
 210                 j = iy>>(20-k);
 211                 if((j<<(20-k))==iy) yisint = 2-(j&1);
 212             }
 213         }
 214     }
 215
 216     /* special value of y */
 217     if(ly==0) {
 218         if (iy==0x7ff00000) {    /* y is +-inf */
 219             if(((ix-0x3ff00000)|lx)==0)
 220                 return  y - y;    /* inf**+-1 is NaN */
 221             else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
 222                 return (hy>=0)? y: zero;
 223             else            /* (|x|<1)**-,+inf = inf,0 */
 224                 return (hy<0)?-y: zero;
 225         }
 226         if(iy==0x3ff00000) {    /* y is  +-1 */
 227             if(hy<0) return one/x; else return x;
 228         }
 229         if(hy==0x40000000) return x*x; /* y is  2 */
 230         if(hy==0x3fe00000) {    /* y is  0.5 */
 231             if(hx>=0)    /* x >= +0 */
 232                 return sqrt(x);
 233         }
 234     }
 235
 236     ax   = fabs(x);
 237     /* special value of x */
 238     if(lx==0) {
 239         if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
 240             z = ax;            /*x is +-0,+-inf,+-1*/
 241             if(hy<0) z = one/z;    /* z = (1/|x|) */
 242             if(hx<0) {
 243                 if(((ix-0x3ff00000)|yisint)==0) {
 244                     z = (z-z)/(z-z); /* (-1)**non-int is NaN */
 245                 } else if(yisint==1)
 246                     z = -z;        /* (x<0)**odd = -(|x|**odd) */
 247             }
 248             return z;
 249         }
 250     }
 251
 252     n = (hx>>31)+1;
 253
 254     /* (x<0)**(non-int) is NaN */
 255     if((n|yisint)==0) return (x-x)/(x-x);
 256
 257     s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
 258     if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
 259
 260     /* |y| is huge */
 261     if(iy>0x41e00000) { /* if |y| > 2**31 */
 262         if(iy>0x43f00000){    /* if |y| > 2**64, must o/uflow */
 263             if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
 264             if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
 265         }
 266         /* over/underflow if x is not close to one */
 267         if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny;
 268         if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny;
 269         /* now |1-x| is tiny <= 2**-20, suffice to compute
 270          log(x) by x-x^2/2+x^3/3-x^4/4 */
 271         t = ax-one;        /* t has 20 trailing zeros */
 272         w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
 273         u = ivln2_h*t;    /* ivln2_h has 21 sig. bits */
 274         v = t*ivln2_l-w*ivln2;
 275         t1 = u+v;
 276         __LO(t1) = 0;
 277         t2 = v-(t1-u);
 278     } else {
 279         double ss,s2,s_h,s_l,t_h,t_l;
 280         n = 0;
 281         /* take care subnormal number */
 282         if(ix<0x00100000)
 283         {ax *= two53; n -= 53; ix = __HI(ax); }
 284         n  += ((ix)>>20)-0x3ff;
 285         j  = ix&0x000fffff;
 286         /* determine interval */
 287         ix = j|0x3ff00000;        /* normalize ix */
 288         if(j<=0x3988E) k=0;        /* |x|<sqrt(3/2) */
 289         else if(j<0xBB67A) k=1;    /* |x|<sqrt(3)   */
 290         else {k=0;n+=1;ix -= 0x00100000;}
 291         __HI(ax) = ix;
 292
 293         /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
 294         u = ax-bp[k];        /* bp[0]=1.0, bp[1]=1.5 */
 295         v = one/(ax+bp[k]);
 296         ss = u*v;
 297         s_h = ss;
 298         __LO(s_h) = 0;
 299         /* t_h=ax+bp[k] High */
 300         t_h = zero;
 301         __HI(t_h)=((ix>>1)|0x20000000)+0x00080000+(k<<18);
 302         t_l = ax - (t_h-bp[k]);
 303         s_l = v*((u-s_h*t_h)-s_h*t_l);
 304         /* compute log(ax) */
 305         s2 = ss*ss;
 306         r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
 307         r += s_l*(s_h+ss);
 308         s2  = s_h*s_h;
 309         t_h = 3.0+s2+r;
 310         __LO(t_h) = 0;
 311         t_l = r-((t_h-3.0)-s2);
 312         /* u+v = ss*(1+...) */
 313         u = s_h*t_h;
 314         v = s_l*t_h+t_l*ss;
 315         /* 2/(3log2)*(ss+...) */
 316         p_h = u+v;
 317         __LO(p_h) = 0;
 318         p_l = v-(p_h-u);
 319         z_h = cp_h*p_h;        /* cp_h+cp_l = 2/(3*log2) */
 320         z_l = cp_l*p_h+p_l*cp+dp_l[k];
 321         /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
 322         t = (double)n;
 323         t1 = (((z_h+z_l)+dp_h[k])+t);
 324         __LO(t1) = 0;
 325         t2 = z_l-(((t1-t)-dp_h[k])-z_h);
 326     }
 327
 328     /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
 329     y1  = y;
 330     __LO(y1) = 0;
 331     p_l = (y-y1)*t1+y*t2;
 332     p_h = y1*t1;
 333     z = p_l+p_h;
 334     j = __HI(z);
 335     i = __LO(z);
 336     if (j>=0x40900000) {                /* z >= 1024 */
 337         if(((j-0x40900000)|i)!=0)            /* if z > 1024 */
 338             return s*huge*huge;            /* overflow */
 339         else {
 340             if(p_l+ovt>z-p_h) return s*huge*huge;    /* overflow */
 341         }
 342     } else if((j&0x7fffffff)>=0x4090cc00 ) {    /* z <= -1075 */
 343         if(((j-0xc090cc00)|i)!=0)         /* z < -1075 */
 344             return s*tiny*tiny;        /* underflow */
 345         else {
 346             if(p_l<=z-p_h) return s*tiny*tiny;    /* underflow */
 347         }
 348     }
 349     /*
 350      * compute 2**(p_h+p_l)
 351      */
 352     i = j&0x7fffffff;
 353     k = (i>>20)-0x3ff;
 354     n = 0;
 355     if(i>0x3fe00000) {        /* if |z| > 0.5, set n = [z+0.5] */
 356         n = j+(0x00100000>>(k+1));
 357         k = ((n&0x7fffffff)>>20)-0x3ff;    /* new k for n */
 358         t = zero;
 359         __HI(t) = (n&~(0x000fffff>>k));
 360         n = ((n&0x000fffff)|0x00100000)>>(20-k);
 361         if(j<0) n = -n;
 362         p_h -= t;
 363     }
 364     t = p_l+p_h;
 365     __LO(t) = 0;
 366     u = t*lg2_h;
 367     v = (p_l-(t-p_h))*lg2+t*lg2_l;
 368     z = u+v;
 369     w = v-(z-u);
 370     t  = z*z;
 371     t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
 372     r  = (z*t1)/(t1-two)-(w+z*w);
 373     z  = one-(r-z);
 374     j  = __HI(z);
 375     j += (n<<20);
 376     if((j>>20)<=0) z = fdlibmScalbn(z,n);    /* subnormal output */
 377     else __HI(z) += (n<<20);
 378     return s*z;
 379 }
 380
 381 static ALWAYS_INLINE bool isDenormal(double x)
 382 {
 383     static const uint64_t signbit = 0x8000000000000000ULL;
 384     static const uint64_t minNormal = 0x0001000000000000ULL;
 385     return (bitwise_cast<uint64_t>(x) & ~signbit) - 1 < minNormal - 1;
 386 }
 387
 388 static ALWAYS_INLINE bool isEdgeCase(double x)
 389 {
 390     static const uint64_t signbit = 0x8000000000000000ULL;
 391     static const uint64_t infinity = 0x7fffffffffffffffULL;
 392     return (bitwise_cast<uint64_t>(x) & ~signbit) - 1 >= infinity - 1;
 393 }
 394
 395 static ALWAYS_INLINE double mathPowInternal(double x, double y)
 396 {
 397     if (!isDenormal(x) && !isDenormal(y)) {
 398         double libmResult = std::pow(x, y);
 399         if (libmResult || isEdgeCase(x) || isEdgeCase(y))
 400             return libmResult;
 401     }
 402     return fdlibmPow(x, y);
 403 }
 404
 405 #else
 406
 407 ALWAYS_INLINE double mathPowInternal(double x, double y)
 408 {
 409     return pow(x, y);
 410 }
 411
 412 #endif
 413
 414 double JIT_OPERATION operationMathPow(double x, double y)
 415 {
 416     if (std::isnan(y))
 417         return PNaN;
 418     if (std::isinf(y) && fabs(x) == 1)
 419         return PNaN;
 420     return mathPowInternal(x, y);
 421 }
 422
 423 extern "C" {
 424 double jsRound(double value)
 425 {
 426     double integer = ceil(value);
 427     return integer - (integer - value > 0.5);
 428 }
 429 }
 430
 431 } // namespace JSC