Updated math code from the uClibc 0.9.33 release
This commit is contained in:
Sam Lantinga
parent
554d129015
commit
fd9bdc8766
18 changed files with 945 additions and 1198 deletions
596
src/libm/e_pow.c
596
src/libm/e_pow.c
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@ -1,4 +1,3 @@
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/* @(#)e_pow.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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@ -10,10 +9,6 @@
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* ====================================================
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*/
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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $";
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#endif
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/* __ieee754_pow(x,y) return x**y
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*
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* n
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@ -26,25 +21,26 @@ static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $";
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* 3. Return x**y = 2**n*exp(y'*log2)
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*
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* Special cases:
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* 1. (anything) ** 0 is 1
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* 2. (anything) ** 1 is itself
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* 3. (anything) ** NAN is NAN
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* 4. NAN ** (anything except 0) is NAN
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* 5. +-(|x| > 1) ** +INF is +INF
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* 6. +-(|x| > 1) ** -INF is +0
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* 7. +-(|x| < 1) ** +INF is +0
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* 8. +-(|x| < 1) ** -INF is +INF
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* 9. +-1 ** +-INF is NAN
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* 10. +0 ** (+anything except 0, NAN) is +0
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* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
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* 12. +0 ** (-anything except 0, NAN) is +INF
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* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
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* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
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* 15. +INF ** (+anything except 0,NAN) is +INF
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* 16. +INF ** (-anything except 0,NAN) is +0
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* 17. -INF ** (anything) = -0 ** (-anything)
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* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
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* 19. (-anything except 0 and inf) ** (non-integer) is NAN
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* 1. +-1 ** anything is 1.0
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* 2. +-1 ** +-INF is 1.0
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* 3. (anything) ** 0 is 1
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* 4. (anything) ** 1 is itself
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* 5. (anything) ** NAN is NAN
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* 6. NAN ** (anything except 0) is NAN
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* 7. +-(|x| > 1) ** +INF is +INF
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* 8. +-(|x| > 1) ** -INF is +0
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* 9. +-(|x| < 1) ** +INF is +0
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* 10 +-(|x| < 1) ** -INF is +INF
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* 11. +0 ** (+anything except 0, NAN) is +0
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* 12. -0 ** (+anything except 0, NAN, odd integer) is +0
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* 13. +0 ** (-anything except 0, NAN) is +INF
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* 14. -0 ** (-anything except 0, NAN, odd integer) is +INF
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* 15. -0 ** (odd integer) = -( +0 ** (odd integer) )
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* 16. +INF ** (+anything except 0,NAN) is +INF
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* 17. +INF ** (-anything except 0,NAN) is +0
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* 18. -INF ** (anything) = -0 ** (-anything)
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* 19. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
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* 20. (-anything except 0 and inf) ** (non-integer) is NAN
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*
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* Accuracy:
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* pow(x,y) returns x**y nearly rounded. In particular
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@ -62,281 +58,281 @@ static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $";
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#include "math_libm.h"
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#include "math_private.h"
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libm_hidden_proto(scalbn)
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libm_hidden_proto(fabs)
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#ifdef __STDC__
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static const double
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static const double
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bp[] = {1.0, 1.5,},
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dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
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dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
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zero = 0.0,
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one = 1.0,
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two = 2.0,
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two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
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huge = 1.0e300,
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tiny = 1.0e-300,
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/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
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L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
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L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
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L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
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L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
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L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
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L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
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P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
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P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
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P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
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P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
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P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
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lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
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lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
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lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
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ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
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cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
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cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
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cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
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ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
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ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
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ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
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double attribute_hidden __ieee754_pow(double x, double y)
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{
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double z,ax,z_h,z_l,p_h,p_l;
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double y1,t1,t2,r,s,t,u,v,w;
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int32_t i,j,k,yisint,n;
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int32_t hx,hy,ix,iy;
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u_int32_t lx,ly;
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EXTRACT_WORDS(hx,lx,x);
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/* x==1: 1**y = 1 (even if y is NaN) */
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if (hx==0x3ff00000 && lx==0) {
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return x;
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}
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ix = hx&0x7fffffff;
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EXTRACT_WORDS(hy,ly,y);
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iy = hy&0x7fffffff;
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/* y==zero: x**0 = 1 */
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if((iy|ly)==0) return one;
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/* +-NaN return x+y */
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if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
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iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
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return x+y;
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/* determine if y is an odd int when x < 0
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* yisint = 0 ... y is not an integer
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* yisint = 1 ... y is an odd int
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* yisint = 2 ... y is an even int
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*/
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yisint = 0;
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if(hx<0) {
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if(iy>=0x43400000) yisint = 2; /* even integer y */
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else if(iy>=0x3ff00000) {
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k = (iy>>20)-0x3ff; /* exponent */
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if(k>20) {
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j = ly>>(52-k);
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if((j<<(52-k))==ly) yisint = 2-(j&1);
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} else if(ly==0) {
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j = iy>>(20-k);
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if((j<<(20-k))==iy) yisint = 2-(j&1);
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}
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}
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}
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/* special value of y */
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if(ly==0) {
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if (iy==0x7ff00000) { /* y is +-inf */
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if (((ix-0x3ff00000)|lx)==0)
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return one; /* +-1**+-inf is 1 (yes, weird rule) */
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if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
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return (hy>=0) ? y : zero;
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/* (|x|<1)**-,+inf = inf,0 */
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return (hy<0) ? -y : zero;
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}
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if(iy==0x3ff00000) { /* y is +-1 */
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if(hy<0) return one/x; else return x;
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}
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if(hy==0x40000000) return x*x; /* y is 2 */
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if(hy==0x3fe00000) { /* y is 0.5 */
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if(hx>=0) /* x >= +0 */
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return __ieee754_sqrt(x);
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}
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}
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ax = fabs(x);
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/* special value of x */
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if(lx==0) {
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if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
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z = ax; /*x is +-0,+-inf,+-1*/
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if(hy<0) z = one/z; /* z = (1/|x|) */
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if(hx<0) {
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if(((ix-0x3ff00000)|yisint)==0) {
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z = (z-z)/(z-z); /* (-1)**non-int is NaN */
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} else if(yisint==1)
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z = -z; /* (x<0)**odd = -(|x|**odd) */
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}
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return z;
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}
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}
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/* (x<0)**(non-int) is NaN */
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if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
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/* |y| is huge */
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if(iy>0x41e00000) { /* if |y| > 2**31 */
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if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
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if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
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if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
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}
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/* over/underflow if x is not close to one */
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if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
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if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
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/* now |1-x| is tiny <= 2**-20, suffice to compute
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log(x) by x-x^2/2+x^3/3-x^4/4 */
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t = x-1; /* t has 20 trailing zeros */
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w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
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u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
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v = t*ivln2_l-w*ivln2;
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t1 = u+v;
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SET_LOW_WORD(t1,0);
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t2 = v-(t1-u);
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} else {
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double s2,s_h,s_l,t_h,t_l;
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n = 0;
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/* take care subnormal number */
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if(ix<0x00100000)
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{ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
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n += ((ix)>>20)-0x3ff;
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j = ix&0x000fffff;
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/* determine interval */
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ix = j|0x3ff00000; /* normalize ix */
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if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
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else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
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else {k=0;n+=1;ix -= 0x00100000;}
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SET_HIGH_WORD(ax,ix);
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/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
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u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
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v = one/(ax+bp[k]);
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s = u*v;
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s_h = s;
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SET_LOW_WORD(s_h,0);
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/* t_h=ax+bp[k] High */
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t_h = zero;
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SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
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t_l = ax - (t_h-bp[k]);
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s_l = v*((u-s_h*t_h)-s_h*t_l);
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/* compute log(ax) */
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s2 = s*s;
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r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
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r += s_l*(s_h+s);
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s2 = s_h*s_h;
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t_h = 3.0+s2+r;
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SET_LOW_WORD(t_h,0);
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t_l = r-((t_h-3.0)-s2);
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/* u+v = s*(1+...) */
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u = s_h*t_h;
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v = s_l*t_h+t_l*s;
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/* 2/(3log2)*(s+...) */
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p_h = u+v;
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SET_LOW_WORD(p_h,0);
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p_l = v-(p_h-u);
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z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
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z_l = cp_l*p_h+p_l*cp+dp_l[k];
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/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
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t = (double)n;
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t1 = (((z_h+z_l)+dp_h[k])+t);
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SET_LOW_WORD(t1,0);
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t2 = z_l-(((t1-t)-dp_h[k])-z_h);
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}
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s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
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if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
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s = -one;/* (-ve)**(odd int) */
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/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
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y1 = y;
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SET_LOW_WORD(y1,0);
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p_l = (y-y1)*t1+y*t2;
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p_h = y1*t1;
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z = p_l+p_h;
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EXTRACT_WORDS(j,i,z);
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if (j>=0x40900000) { /* z >= 1024 */
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if(((j-0x40900000)|i)!=0) /* if z > 1024 */
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return s*huge*huge; /* overflow */
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else {
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if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
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}
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} else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
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if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
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return s*tiny*tiny; /* underflow */
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else {
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if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
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}
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}
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/*
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* compute 2**(p_h+p_l)
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*/
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i = j&0x7fffffff;
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k = (i>>20)-0x3ff;
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n = 0;
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if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
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n = j+(0x00100000>>(k+1));
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k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
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t = zero;
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SET_HIGH_WORD(t,n&~(0x000fffff>>k));
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n = ((n&0x000fffff)|0x00100000)>>(20-k);
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if(j<0) n = -n;
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p_h -= t;
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}
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t = p_l+p_h;
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SET_LOW_WORD(t,0);
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u = t*lg2_h;
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v = (p_l-(t-p_h))*lg2+t*lg2_l;
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z = u+v;
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w = v-(z-u);
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t = z*z;
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t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
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r = (z*t1)/(t1-two)-(w+z*w);
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z = one-(r-z);
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GET_HIGH_WORD(j,z);
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j += (n<<20);
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if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */
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else SET_HIGH_WORD(z,j);
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return s*z;
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}
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/*
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* wrapper pow(x,y) return x**y
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*/
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#ifndef _IEEE_LIBM
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double pow(double x, double y)
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{
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double z = __ieee754_pow(x, y);
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if (_LIB_VERSION == _IEEE_|| isnan(y))
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return z;
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if (isnan(x)) {
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if (y == 0.0)
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return __kernel_standard(x, y, 42); /* pow(NaN,0.0) */
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return z;
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}
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if (x == 0.0) {
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if (y == 0.0)
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return __kernel_standard(x, y, 20); /* pow(0.0,0.0) */
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if (isfinite(y) && y < 0.0)
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return __kernel_standard(x,y,23); /* pow(0.0,negative) */
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return z;
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}
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if (!isfinite(z)) {
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if (isfinite(x) && isfinite(y)) {
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if (isnan(z))
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return __kernel_standard(x, y, 24); /* pow neg**non-int */
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return __kernel_standard(x, y, 21); /* pow overflow */
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}
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}
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if (z == 0.0 && isfinite(x) && isfinite(y))
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return __kernel_standard(x, y, 22); /* pow underflow */
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return z;
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}
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#else
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static double
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strong_alias(__ieee754_pow, pow)
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#endif
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bp[] = { 1.0, 1.5, }, dp_h[] = {
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0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
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dp_l[] = {
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0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
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|
||||
zero = 0.0, one = 1.0, two = 2.0, two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
|
||||
huge_val = 1.0e300, tiny = 1.0e-300,
|
||||
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
|
||||
L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
|
||||
L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
|
||||
L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
|
||||
L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
|
||||
L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
|
||||
L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
|
||||
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
|
||||
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
|
||||
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
|
||||
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
|
||||
P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
|
||||
lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
|
||||
lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
|
||||
lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
|
||||
ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
|
||||
cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
|
||||
cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
|
||||
cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h */
|
||||
ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
|
||||
ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2 */
|
||||
ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail */
|
||||
|
||||
#ifdef __STDC__
|
||||
double attribute_hidden __ieee754_pow(double x, double y)
|
||||
#else
|
||||
double attribute_hidden __ieee754_pow(x, y)
|
||||
double x, y;
|
||||
#endif
|
||||
{
|
||||
double z, ax, z_h, z_l, p_h, p_l;
|
||||
double y1, t1, t2, r, s, t, u, v, w;
|
||||
int32_t i, j, k, yisint, n;
|
||||
int32_t hx, hy, ix, iy;
|
||||
u_int32_t lx, ly;
|
||||
|
||||
EXTRACT_WORDS(hx, lx, x);
|
||||
EXTRACT_WORDS(hy, ly, y);
|
||||
ix = hx & 0x7fffffff;
|
||||
iy = hy & 0x7fffffff;
|
||||
|
||||
/* y==zero: x**0 = 1 */
|
||||
if ((iy | ly) == 0)
|
||||
return one;
|
||||
|
||||
/* +-NaN return x+y */
|
||||
if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) ||
|
||||
iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0)))
|
||||
return x + y;
|
||||
|
||||
/* determine if y is an odd int when x < 0
|
||||
* yisint = 0 ... y is not an integer
|
||||
* yisint = 1 ... y is an odd int
|
||||
* yisint = 2 ... y is an even int
|
||||
*/
|
||||
yisint = 0;
|
||||
if (hx < 0) {
|
||||
if (iy >= 0x43400000)
|
||||
yisint = 2; /* even integer y */
|
||||
else if (iy >= 0x3ff00000) {
|
||||
k = (iy >> 20) - 0x3ff; /* exponent */
|
||||
if (k > 20) {
|
||||
j = ly >> (52 - k);
|
||||
if ((j << (52 - k)) == ly)
|
||||
yisint = 2 - (j & 1);
|
||||
} else if (ly == 0) {
|
||||
j = iy >> (20 - k);
|
||||
if ((j << (20 - k)) == iy)
|
||||
yisint = 2 - (j & 1);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
/* special value of y */
|
||||
if (ly == 0) {
|
||||
if (iy == 0x7ff00000) { /* y is +-inf */
|
||||
if (((ix - 0x3ff00000) | lx) == 0)
|
||||
return y - y; /* inf**+-1 is NaN */
|
||||
else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */
|
||||
return (hy >= 0) ? y : zero;
|
||||
else /* (|x|<1)**-,+inf = inf,0 */
|
||||
return (hy < 0) ? -y : zero;
|
||||
}
|
||||
if (iy == 0x3ff00000) { /* y is +-1 */
|
||||
if (hy < 0)
|
||||
return one / x;
|
||||
else
|
||||
return x;
|
||||
}
|
||||
if (hy == 0x40000000)
|
||||
return x * x; /* y is 2 */
|
||||
if (hy == 0x3fe00000) { /* y is 0.5 */
|
||||
if (hx >= 0) /* x >= +0 */
|
||||
return __ieee754_sqrt(x);
|
||||
}
|
||||
}
|
||||
|
||||
ax = fabs(x);
|
||||
/* special value of x */
|
||||
if (lx == 0) {
|
||||
if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) {
|
||||
z = ax; /* x is +-0,+-inf,+-1 */
|
||||
if (hy < 0)
|
||||
z = one / z; /* z = (1/|x|) */
|
||||
if (hx < 0) {
|
||||
if (((ix - 0x3ff00000) | yisint) == 0) {
|
||||
z = (z - z) / (z - z); /* (-1)**non-int is NaN */
|
||||
} else if (yisint == 1)
|
||||
z = -z; /* (x<0)**odd = -(|x|**odd) */
|
||||
}
|
||||
return z;
|
||||
}
|
||||
}
|
||||
|
||||
/* (x<0)**(non-int) is NaN */
|
||||
if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0)
|
||||
return (x - x) / (x - x);
|
||||
|
||||
/* |y| is huge */
|
||||
if (iy > 0x41e00000) { /* if |y| > 2**31 */
|
||||
if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */
|
||||
if (ix <= 0x3fefffff)
|
||||
return (hy < 0) ? huge_val * huge_val : tiny * tiny;
|
||||
if (ix >= 0x3ff00000)
|
||||
return (hy > 0) ? huge_val * huge_val : tiny * tiny;
|
||||
}
|
||||
/* over/underflow if x is not close to one */
|
||||
if (ix < 0x3fefffff)
|
||||
return (hy < 0) ? huge_val * huge_val : tiny * tiny;
|
||||
if (ix > 0x3ff00000)
|
||||
return (hy > 0) ? huge_val * huge_val : tiny * tiny;
|
||||
/* now |1-x| is tiny <= 2**-20, suffice to compute
|
||||
log(x) by x-x^2/2+x^3/3-x^4/4 */
|
||||
t = x - 1; /* t has 20 trailing zeros */
|
||||
w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
|
||||
u = ivln2_h * t; /* ivln2_h has 21 sig. bits */
|
||||
v = t * ivln2_l - w * ivln2;
|
||||
t1 = u + v;
|
||||
SET_LOW_WORD(t1, 0);
|
||||
t2 = v - (t1 - u);
|
||||
} else {
|
||||
double s2, s_h, s_l, t_h, t_l;
|
||||
n = 0;
|
||||
/* take care subnormal number */
|
||||
if (ix < 0x00100000) {
|
||||
ax *= two53;
|
||||
n -= 53;
|
||||
GET_HIGH_WORD(ix, ax);
|
||||
}
|
||||
n += ((ix) >> 20) - 0x3ff;
|
||||
j = ix & 0x000fffff;
|
||||
/* determine interval */
|
||||
ix = j | 0x3ff00000; /* normalize ix */
|
||||
if (j <= 0x3988E)
|
||||
k = 0; /* |x|<sqrt(3/2) */
|
||||
else if (j < 0xBB67A)
|
||||
k = 1; /* |x|<sqrt(3) */
|
||||
else {
|
||||
k = 0;
|
||||
n += 1;
|
||||
ix -= 0x00100000;
|
||||
}
|
||||
SET_HIGH_WORD(ax, ix);
|
||||
|
||||
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
|
||||
u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
|
||||
v = one / (ax + bp[k]);
|
||||
s = u * v;
|
||||
s_h = s;
|
||||
SET_LOW_WORD(s_h, 0);
|
||||
/* t_h=ax+bp[k] High */
|
||||
t_h = zero;
|
||||
SET_HIGH_WORD(t_h,
|
||||
((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18));
|
||||
t_l = ax - (t_h - bp[k]);
|
||||
s_l = v * ((u - s_h * t_h) - s_h * t_l);
|
||||
/* compute log(ax) */
|
||||
s2 = s * s;
|
||||
r = s2 * s2 * (L1 +
|
||||
s2 * (L2 +
|
||||
s2 * (L3 +
|
||||
s2 * (L4 + s2 * (L5 + s2 * L6)))));
|
||||
r += s_l * (s_h + s);
|
||||
s2 = s_h * s_h;
|
||||
t_h = 3.0 + s2 + r;
|
||||
SET_LOW_WORD(t_h, 0);
|
||||
t_l = r - ((t_h - 3.0) - s2);
|
||||
/* u+v = s*(1+...) */
|
||||
u = s_h * t_h;
|
||||
v = s_l * t_h + t_l * s;
|
||||
/* 2/(3log2)*(s+...) */
|
||||
p_h = u + v;
|
||||
SET_LOW_WORD(p_h, 0);
|
||||
p_l = v - (p_h - u);
|
||||
z_h = cp_h * p_h; /* cp_h+cp_l = 2/(3*log2) */
|
||||
z_l = cp_l * p_h + p_l * cp + dp_l[k];
|
||||
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
|
||||
t = (double) n;
|
||||
t1 = (((z_h + z_l) + dp_h[k]) + t);
|
||||
SET_LOW_WORD(t1, 0);
|
||||
t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
|
||||
}
|
||||
|
||||
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
|
||||
if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0)
|
||||
s = -one; /* (-ve)**(odd int) */
|
||||
|
||||
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
|
||||
y1 = y;
|
||||
SET_LOW_WORD(y1, 0);
|
||||
p_l = (y - y1) * t1 + y * t2;
|
||||
p_h = y1 * t1;
|
||||
z = p_l + p_h;
|
||||
EXTRACT_WORDS(j, i, z);
|
||||
if (j >= 0x40900000) { /* z >= 1024 */
|
||||
if (((j - 0x40900000) | i) != 0) /* if z > 1024 */
|
||||
return s * huge_val * huge_val; /* overflow */
|
||||
else {
|
||||
if (p_l + ovt > z - p_h)
|
||||
return s * huge_val * huge_val; /* overflow */
|
||||
}
|
||||
} else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */
|
||||
if (((j - 0xc090cc00) | i) != 0) /* z < -1075 */
|
||||
return s * tiny * tiny; /* underflow */
|
||||
else {
|
||||
if (p_l <= z - p_h)
|
||||
return s * tiny * tiny; /* underflow */
|
||||
}
|
||||
}
|
||||
/*
|
||||
* compute 2**(p_h+p_l)
|
||||
*/
|
||||
i = j & 0x7fffffff;
|
||||
k = (i >> 20) - 0x3ff;
|
||||
n = 0;
|
||||
if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
|
||||
n = j + (0x00100000 >> (k + 1));
|
||||
k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */
|
||||
t = zero;
|
||||
SET_HIGH_WORD(t, n & ~(0x000fffff >> k));
|
||||
n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);
|
||||
if (j < 0)
|
||||
n = -n;
|
||||
p_h -= t;
|
||||
}
|
||||
t = p_l + p_h;
|
||||
SET_LOW_WORD(t, 0);
|
||||
u = t * lg2_h;
|
||||
v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
|
||||
z = u + v;
|
||||
w = v - (z - u);
|
||||
t = z * z;
|
||||
t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
|
||||
r = (z * t1) / (t1 - two) - (w + z * w);
|
||||
z = one - (r - z);
|
||||
GET_HIGH_WORD(j, z);
|
||||
j += (n << 20);
|
||||
if ((j >> 20) <= 0)
|
||||
z = scalbn(z, n); /* subnormal output */
|
||||
else
|
||||
SET_HIGH_WORD(z, j);
|
||||
return s * z;
|
||||
}
|
||||
libm_hidden_def(pow)
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue