src/libm/e_pow.c
 author Sam Lantinga Tue, 10 Dec 2019 13:09:52 -0800 changeset 13329 732a469df95c parent 12420 4a6c91d9cc33 permissions -rw-r--r--
 slouken@2756 ` 1` ```/* ``` slouken@2756 ` 2` ``` * ==================================================== ``` slouken@2756 ` 3` ``` * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. ``` slouken@2756 ` 4` ``` * ``` slouken@2756 ` 5` ``` * Developed at SunPro, a Sun Microsystems, Inc. business. ``` slouken@2756 ` 6` ``` * Permission to use, copy, modify, and distribute this ``` slouken@2756 ` 7` ``` * software is freely granted, provided that this notice ``` slouken@2756 ` 8` ``` * is preserved. ``` slouken@2756 ` 9` ``` * ==================================================== ``` slouken@2756 ` 10` ``` */ ``` slouken@2756 ` 11` slouken@2756 ` 12` ```/* __ieee754_pow(x,y) return x**y ``` slouken@2756 ` 13` ``` * ``` slouken@2756 ` 14` ``` * n ``` slouken@2756 ` 15` ``` * Method: Let x = 2 * (1+f) ``` slouken@2756 ` 16` ``` * 1. Compute and return log2(x) in two pieces: ``` slouken@2756 ` 17` ``` * log2(x) = w1 + w2, ``` slouken@2756 ` 18` ``` * where w1 has 53-24 = 29 bit trailing zeros. ``` slouken@2756 ` 19` ``` * 2. Perform y*log2(x) = n+y' by simulating muti-precision ``` slouken@2756 ` 20` ``` * arithmetic, where |y'|<=0.5. ``` slouken@2756 ` 21` ``` * 3. Return x**y = 2**n*exp(y'*log2) ``` slouken@2756 ` 22` ``` * ``` slouken@2756 ` 23` ``` * Special cases: ``` slouken@11683 ` 24` ``` * 1. +-1 ** anything is 1.0 ``` slouken@11683 ` 25` ``` * 2. +-1 ** +-INF is 1.0 ``` slouken@11683 ` 26` ``` * 3. (anything) ** 0 is 1 ``` slouken@11683 ` 27` ``` * 4. (anything) ** 1 is itself ``` slouken@11683 ` 28` ``` * 5. (anything) ** NAN is NAN ``` slouken@11683 ` 29` ``` * 6. NAN ** (anything except 0) is NAN ``` slouken@11683 ` 30` ``` * 7. +-(|x| > 1) ** +INF is +INF ``` slouken@11683 ` 31` ``` * 8. +-(|x| > 1) ** -INF is +0 ``` slouken@11683 ` 32` ``` * 9. +-(|x| < 1) ** +INF is +0 ``` slouken@11683 ` 33` ``` * 10 +-(|x| < 1) ** -INF is +INF ``` slouken@11683 ` 34` ``` * 11. +0 ** (+anything except 0, NAN) is +0 ``` slouken@11683 ` 35` ``` * 12. -0 ** (+anything except 0, NAN, odd integer) is +0 ``` slouken@11683 ` 36` ``` * 13. +0 ** (-anything except 0, NAN) is +INF ``` slouken@11683 ` 37` ``` * 14. -0 ** (-anything except 0, NAN, odd integer) is +INF ``` slouken@11683 ` 38` ``` * 15. -0 ** (odd integer) = -( +0 ** (odd integer) ) ``` slouken@11683 ` 39` ``` * 16. +INF ** (+anything except 0,NAN) is +INF ``` slouken@11683 ` 40` ``` * 17. +INF ** (-anything except 0,NAN) is +0 ``` slouken@11683 ` 41` ``` * 18. -INF ** (anything) = -0 ** (-anything) ``` slouken@11683 ` 42` ``` * 19. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) ``` slouken@11683 ` 43` ``` * 20. (-anything except 0 and inf) ** (non-integer) is NAN ``` slouken@2756 ` 44` ``` * ``` slouken@2756 ` 45` ``` * Accuracy: ``` slouken@2756 ` 46` ``` * pow(x,y) returns x**y nearly rounded. In particular ``` slouken@2756 ` 47` ``` * pow(integer,integer) ``` slouken@2756 ` 48` ``` * always returns the correct integer provided it is ``` slouken@2756 ` 49` ``` * representable. ``` slouken@2756 ` 50` ``` * ``` slouken@2756 ` 51` ``` * Constants : ``` slouken@2756 ` 52` ``` * The hexadecimal values are the intended ones for the following ``` slouken@2756 ` 53` ``` * constants. The decimal values may be used, provided that the ``` slouken@2756 ` 54` ``` * compiler will convert from decimal to binary accurately enough ``` slouken@2756 ` 55` ``` * to produce the hexadecimal values shown. ``` slouken@2756 ` 56` ``` */ ``` slouken@2756 ` 57` slouken@6044 ` 58` ```#include "math_libm.h" ``` slouken@2756 ` 59` ```#include "math_private.h" ``` slouken@2756 ` 60` slouken@11711 ` 61` ```#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */ ``` slouken@11711 ` 62` ```/* C4756: overflow in constant arithmetic */ ``` slouken@11711 ` 63` ```#pragma warning ( disable : 4756 ) ``` slouken@11711 ` 64` ```#endif ``` slouken@11711 ` 65` sezeroz@12420 ` 66` ```#ifdef __WATCOMC__ /* Watcom defines huge=__huge */ ``` sezeroz@12420 ` 67` ```#undef huge ``` sezeroz@12420 ` 68` ```#endif ``` sezeroz@12420 ` 69` slouken@11683 ` 70` ```static const double ``` slouken@11683 ` 71` ```bp[] = {1.0, 1.5,}, ``` slouken@11683 ` 72` ```dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ ``` slouken@11683 ` 73` ```dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ ``` slouken@11683 ` 74` ```zero = 0.0, ``` slouken@11683 ` 75` ```one = 1.0, ``` slouken@11683 ` 76` ```two = 2.0, ``` slouken@11683 ` 77` ```two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ ``` slouken@11683 ` 78` ```huge = 1.0e300, ``` slouken@11683 ` 79` ```tiny = 1.0e-300, ``` slouken@11683 ` 80` ``` /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ ``` slouken@11683 ` 81` ```L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ ``` slouken@11683 ` 82` ```L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ ``` slouken@11683 ` 83` ```L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ ``` slouken@11683 ` 84` ```L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ ``` slouken@11683 ` 85` ```L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ ``` slouken@11683 ` 86` ```L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ ``` slouken@11683 ` 87` ```P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ ``` slouken@11683 ` 88` ```P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ ``` slouken@11683 ` 89` ```P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ ``` slouken@11683 ` 90` ```P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ ``` slouken@11683 ` 91` ```P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ ``` slouken@11683 ` 92` ```lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ ``` slouken@11683 ` 93` ```lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ ``` slouken@11683 ` 94` ```lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ ``` slouken@11683 ` 95` ```ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ ``` slouken@11683 ` 96` ```cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ ``` slouken@11683 ` 97` ```cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ ``` slouken@11683 ` 98` ```cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ ``` slouken@11683 ` 99` ```ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ ``` slouken@11683 ` 100` ```ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ ``` slouken@11683 ` 101` ```ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ ``` slouken@11683 ` 102` slouken@11683 ` 103` ```double attribute_hidden __ieee754_pow(double x, double y) ``` slouken@11683 ` 104` ```{ ``` slouken@11683 ` 105` ``` double z,ax,z_h,z_l,p_h,p_l; ``` slouken@11683 ` 106` ``` double y1,t1,t2,r,s,t,u,v,w; ``` slouken@11683 ` 107` ``` int32_t i,j,k,yisint,n; ``` slouken@11683 ` 108` ``` int32_t hx,hy,ix,iy; ``` slouken@11683 ` 109` ``` u_int32_t lx,ly; ``` slouken@11683 ` 110` slouken@11683 ` 111` ``` EXTRACT_WORDS(hx,lx,x); ``` slouken@11683 ` 112` ``` /* x==1: 1**y = 1 (even if y is NaN) */ ``` slouken@11683 ` 113` ``` if (hx==0x3ff00000 && lx==0) { ``` slouken@11683 ` 114` ``` return x; ``` slouken@11683 ` 115` ``` } ``` slouken@11683 ` 116` ``` ix = hx&0x7fffffff; ``` slouken@11683 ` 117` slouken@11683 ` 118` ``` EXTRACT_WORDS(hy,ly,y); ``` slouken@11683 ` 119` ``` iy = hy&0x7fffffff; ``` slouken@11683 ` 120` slouken@11683 ` 121` ``` /* y==zero: x**0 = 1 */ ``` slouken@11683 ` 122` ``` if((iy|ly)==0) return one; ``` slouken@11683 ` 123` slouken@11683 ` 124` ``` /* +-NaN return x+y */ ``` slouken@11683 ` 125` ``` if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || ``` slouken@11683 ` 126` ``` iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) ``` slouken@11683 ` 127` ``` return x+y; ``` slouken@11683 ` 128` slouken@11683 ` 129` ``` /* determine if y is an odd int when x < 0 ``` slouken@11683 ` 130` ``` * yisint = 0 ... y is not an integer ``` slouken@11683 ` 131` ``` * yisint = 1 ... y is an odd int ``` slouken@11683 ` 132` ``` * yisint = 2 ... y is an even int ``` slouken@11683 ` 133` ``` */ ``` slouken@11683 ` 134` ``` yisint = 0; ``` slouken@11683 ` 135` ``` if(hx<0) { ``` slouken@11683 ` 136` ``` if(iy>=0x43400000) yisint = 2; /* even integer y */ ``` slouken@11683 ` 137` ``` else if(iy>=0x3ff00000) { ``` slouken@11683 ` 138` ``` k = (iy>>20)-0x3ff; /* exponent */ ``` slouken@11683 ` 139` ``` if(k>20) { ``` slouken@11683 ` 140` ``` j = ly>>(52-k); ``` slouken@11683 ` 141` ``` if((j<<(52-k))==ly) yisint = 2-(j&1); ``` slouken@11683 ` 142` ``` } else if(ly==0) { ``` slouken@11683 ` 143` ``` j = iy>>(20-k); ``` slouken@11683 ` 144` ``` if((j<<(20-k))==iy) yisint = 2-(j&1); ``` slouken@11683 ` 145` ``` } ``` slouken@11683 ` 146` ``` } ``` slouken@11683 ` 147` ``` } ``` slouken@11683 ` 148` slouken@11683 ` 149` ``` /* special value of y */ ``` slouken@11683 ` 150` ``` if(ly==0) { ``` slouken@11683 ` 151` ``` if (iy==0x7ff00000) { /* y is +-inf */ ``` slouken@11683 ` 152` ``` if (((ix-0x3ff00000)|lx)==0) ``` slouken@11683 ` 153` ``` return one; /* +-1**+-inf is 1 (yes, weird rule) */ ``` slouken@11683 ` 154` ``` if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */ ``` slouken@11683 ` 155` ``` return (hy>=0) ? y : zero; ``` slouken@11683 ` 156` ``` /* (|x|<1)**-,+inf = inf,0 */ ``` slouken@11683 ` 157` ``` return (hy<0) ? -y : zero; ``` slouken@11683 ` 158` ``` } ``` slouken@11683 ` 159` ``` if(iy==0x3ff00000) { /* y is +-1 */ ``` slouken@11683 ` 160` ``` if(hy<0) return one/x; else return x; ``` slouken@11683 ` 161` ``` } ``` slouken@11683 ` 162` ``` if(hy==0x40000000) return x*x; /* y is 2 */ ``` slouken@11683 ` 163` ``` if(hy==0x3fe00000) { /* y is 0.5 */ ``` slouken@11683 ` 164` ``` if(hx>=0) /* x >= +0 */ ``` slouken@11683 ` 165` ``` return __ieee754_sqrt(x); ``` slouken@11683 ` 166` ``` } ``` slouken@11683 ` 167` ``` } ``` slouken@11683 ` 168` slouken@11683 ` 169` ``` ax = fabs(x); ``` slouken@11683 ` 170` ``` /* special value of x */ ``` slouken@11683 ` 171` ``` if(lx==0) { ``` slouken@11683 ` 172` ``` if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ ``` slouken@11683 ` 173` ``` z = ax; /*x is +-0,+-inf,+-1*/ ``` slouken@11683 ` 174` ``` if(hy<0) z = one/z; /* z = (1/|x|) */ ``` slouken@11683 ` 175` ``` if(hx<0) { ``` slouken@11683 ` 176` ``` if(((ix-0x3ff00000)|yisint)==0) { ``` slouken@11683 ` 177` ``` z = (z-z)/(z-z); /* (-1)**non-int is NaN */ ``` slouken@11683 ` 178` ``` } else if(yisint==1) ``` slouken@11683 ` 179` ``` z = -z; /* (x<0)**odd = -(|x|**odd) */ ``` slouken@11683 ` 180` ``` } ``` slouken@11683 ` 181` ``` return z; ``` slouken@11683 ` 182` ``` } ``` slouken@11683 ` 183` ``` } ``` slouken@11683 ` 184` slouken@11683 ` 185` ``` /* (x<0)**(non-int) is NaN */ ``` slouken@11683 ` 186` ``` if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); ``` slouken@11683 ` 187` slouken@11683 ` 188` ``` /* |y| is huge */ ``` slouken@11683 ` 189` ``` if(iy>0x41e00000) { /* if |y| > 2**31 */ ``` slouken@11683 ` 190` ``` if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ ``` slouken@11683 ` 191` ``` if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; ``` slouken@11683 ` 192` ``` if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; ``` slouken@11683 ` 193` ``` } ``` slouken@11683 ` 194` ``` /* over/underflow if x is not close to one */ ``` slouken@11683 ` 195` ``` if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; ``` slouken@11683 ` 196` ``` if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; ``` slouken@11683 ` 197` ``` /* now |1-x| is tiny <= 2**-20, suffice to compute ``` slouken@11683 ` 198` ``` log(x) by x-x^2/2+x^3/3-x^4/4 */ ``` slouken@11683 ` 199` ``` t = x-1; /* t has 20 trailing zeros */ ``` slouken@11683 ` 200` ``` w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); ``` slouken@11683 ` 201` ``` u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ ``` slouken@11683 ` 202` ``` v = t*ivln2_l-w*ivln2; ``` slouken@11683 ` 203` ``` t1 = u+v; ``` slouken@11683 ` 204` ``` SET_LOW_WORD(t1,0); ``` slouken@11683 ` 205` ``` t2 = v-(t1-u); ``` slouken@11683 ` 206` ``` } else { ``` slouken@11683 ` 207` ``` double s2,s_h,s_l,t_h,t_l; ``` slouken@11683 ` 208` ``` n = 0; ``` slouken@11683 ` 209` ``` /* take care subnormal number */ ``` slouken@11683 ` 210` ``` if(ix<0x00100000) ``` slouken@11683 ` 211` ``` {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); } ``` slouken@11683 ` 212` ``` n += ((ix)>>20)-0x3ff; ``` slouken@11683 ` 213` ``` j = ix&0x000fffff; ``` slouken@11683 ` 214` ``` /* determine interval */ ``` slouken@11683 ` 215` ``` ix = j|0x3ff00000; /* normalize ix */ ``` slouken@11683 ` 216` ``` if(j<=0x3988E) k=0; /* |x|>1)|0x20000000)+0x00080000+(k<<18)); ``` slouken@11683 ` 230` ``` t_l = ax - (t_h-bp[k]); ``` slouken@11683 ` 231` ``` s_l = v*((u-s_h*t_h)-s_h*t_l); ``` slouken@11683 ` 232` ``` /* compute log(ax) */ ``` slouken@11683 ` 233` ``` s2 = s*s; ``` slouken@11683 ` 234` ``` r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); ``` slouken@11683 ` 235` ``` r += s_l*(s_h+s); ``` slouken@11683 ` 236` ``` s2 = s_h*s_h; ``` slouken@11683 ` 237` ``` t_h = 3.0+s2+r; ``` slouken@11683 ` 238` ``` SET_LOW_WORD(t_h,0); ``` slouken@11683 ` 239` ``` t_l = r-((t_h-3.0)-s2); ``` slouken@11683 ` 240` ``` /* u+v = s*(1+...) */ ``` slouken@11683 ` 241` ``` u = s_h*t_h; ``` slouken@11683 ` 242` ``` v = s_l*t_h+t_l*s; ``` slouken@11683 ` 243` ``` /* 2/(3log2)*(s+...) */ ``` slouken@11683 ` 244` ``` p_h = u+v; ``` slouken@11683 ` 245` ``` SET_LOW_WORD(p_h,0); ``` slouken@11683 ` 246` ``` p_l = v-(p_h-u); ``` slouken@11683 ` 247` ``` z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ ``` slouken@11683 ` 248` ``` z_l = cp_l*p_h+p_l*cp+dp_l[k]; ``` slouken@11683 ` 249` ``` /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ ``` slouken@11683 ` 250` ``` t = (double)n; ``` slouken@11683 ` 251` ``` t1 = (((z_h+z_l)+dp_h[k])+t); ``` slouken@11683 ` 252` ``` SET_LOW_WORD(t1,0); ``` slouken@11683 ` 253` ``` t2 = z_l-(((t1-t)-dp_h[k])-z_h); ``` slouken@11683 ` 254` ``` } ``` slouken@11683 ` 255` slouken@11683 ` 256` ``` s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ ``` slouken@11683 ` 257` ``` if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) ``` slouken@11683 ` 258` ``` s = -one;/* (-ve)**(odd int) */ ``` slouken@11683 ` 259` slouken@11683 ` 260` ``` /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ ``` slouken@11683 ` 261` ``` y1 = y; ``` slouken@11683 ` 262` ``` SET_LOW_WORD(y1,0); ``` slouken@11683 ` 263` ``` p_l = (y-y1)*t1+y*t2; ``` slouken@11683 ` 264` ``` p_h = y1*t1; ``` slouken@11683 ` 265` ``` z = p_l+p_h; ``` slouken@11683 ` 266` ``` EXTRACT_WORDS(j,i,z); ``` slouken@11683 ` 267` ``` if (j>=0x40900000) { /* z >= 1024 */ ``` slouken@11683 ` 268` ``` if(((j-0x40900000)|i)!=0) /* if z > 1024 */ ``` slouken@11683 ` 269` ``` return s*huge*huge; /* overflow */ ``` slouken@11683 ` 270` ``` else { ``` slouken@11683 ` 271` ``` if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ ``` slouken@11683 ` 272` ``` } ``` slouken@11683 ` 273` ``` } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ ``` slouken@11683 ` 274` ``` if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ ``` slouken@11683 ` 275` ``` return s*tiny*tiny; /* underflow */ ``` slouken@11683 ` 276` ``` else { ``` slouken@11683 ` 277` ``` if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ ``` slouken@11683 ` 278` ``` } ``` slouken@11683 ` 279` ``` } ``` slouken@11683 ` 280` ``` /* ``` slouken@11683 ` 281` ``` * compute 2**(p_h+p_l) ``` slouken@11683 ` 282` ``` */ ``` slouken@11683 ` 283` ``` i = j&0x7fffffff; ``` slouken@11683 ` 284` ``` k = (i>>20)-0x3ff; ``` slouken@11683 ` 285` ``` n = 0; ``` slouken@11683 ` 286` ``` if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ ``` slouken@11683 ` 287` ``` n = j+(0x00100000>>(k+1)); ``` slouken@11683 ` 288` ``` k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ ``` slouken@11683 ` 289` ``` t = zero; ``` slouken@11683 ` 290` ``` SET_HIGH_WORD(t,n&~(0x000fffff>>k)); ``` slouken@11683 ` 291` ``` n = ((n&0x000fffff)|0x00100000)>>(20-k); ``` slouken@11683 ` 292` ``` if(j<0) n = -n; ``` slouken@11683 ` 293` ``` p_h -= t; ``` slouken@11683 ` 294` ``` } ``` slouken@11683 ` 295` ``` t = p_l+p_h; ``` slouken@11683 ` 296` ``` SET_LOW_WORD(t,0); ``` slouken@11683 ` 297` ``` u = t*lg2_h; ``` slouken@11683 ` 298` ``` v = (p_l-(t-p_h))*lg2+t*lg2_l; ``` slouken@11683 ` 299` ``` z = u+v; ``` slouken@11683 ` 300` ``` w = v-(z-u); ``` slouken@11683 ` 301` ``` t = z*z; ``` slouken@11683 ` 302` ``` t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); ``` slouken@11683 ` 303` ``` r = (z*t1)/(t1-two)-(w+z*w); ``` slouken@11683 ` 304` ``` z = one-(r-z); ``` slouken@11683 ` 305` ``` GET_HIGH_WORD(j,z); ``` slouken@11683 ` 306` ``` j += (n<<20); ``` slouken@11683 ` 307` ``` if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */ ``` slouken@11683 ` 308` ``` else SET_HIGH_WORD(z,j); ``` slouken@11683 ` 309` ``` return s*z; ``` slouken@11683 ` 310` ```} ``` slouken@11683 ` 311` slouken@11683 ` 312` ```/* ``` slouken@11683 ` 313` ``` * wrapper pow(x,y) return x**y ``` slouken@11683 ` 314` ``` */ ``` slouken@11683 ` 315` ```#ifndef _IEEE_LIBM ``` slouken@11683 ` 316` ```double pow(double x, double y) ``` slouken@11683 ` 317` ```{ ``` slouken@11683 ` 318` ``` double z = __ieee754_pow(x, y); ``` slouken@11683 ` 319` ``` if (_LIB_VERSION == _IEEE_|| isnan(y)) ``` slouken@11683 ` 320` ``` return z; ``` slouken@11683 ` 321` ``` if (isnan(x)) { ``` slouken@11683 ` 322` ``` if (y == 0.0) ``` slouken@11683 ` 323` ``` return __kernel_standard(x, y, 42); /* pow(NaN,0.0) */ ``` slouken@11683 ` 324` ``` return z; ``` slouken@11683 ` 325` ``` } ``` slouken@11683 ` 326` ``` if (x == 0.0) { ``` slouken@11683 ` 327` ``` if (y == 0.0) ``` slouken@11683 ` 328` ``` return __kernel_standard(x, y, 20); /* pow(0.0,0.0) */ ``` slouken@11683 ` 329` ``` if (isfinite(y) && y < 0.0) ``` slouken@11683 ` 330` ``` return __kernel_standard(x,y,23); /* pow(0.0,negative) */ ``` slouken@11683 ` 331` ``` return z; ``` slouken@11683 ` 332` ``` } ``` slouken@11683 ` 333` ``` if (!isfinite(z)) { ``` slouken@11683 ` 334` ``` if (isfinite(x) && isfinite(y)) { ``` slouken@11683 ` 335` ``` if (isnan(z)) ``` slouken@11683 ` 336` ``` return __kernel_standard(x, y, 24); /* pow neg**non-int */ ``` slouken@11683 ` 337` ``` return __kernel_standard(x, y, 21); /* pow overflow */ ``` slouken@11683 ` 338` ``` } ``` slouken@11683 ` 339` ``` } ``` slouken@11683 ` 340` ``` if (z == 0.0 && isfinite(x) && isfinite(y)) ``` slouken@11683 ` 341` ``` return __kernel_standard(x, y, 22); /* pow underflow */ ``` slouken@11683 ` 342` ``` return z; ``` slouken@11683 ` 343` ```} ``` slouken@2756 ` 344` ```#else ``` slouken@11683 ` 345` ```strong_alias(__ieee754_pow, pow) ``` slouken@2756 ` 346` ```#endif ``` slouken@11683 ` 347` ```libm_hidden_def(pow) ```