146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner/* @(#)e_pow.c 5.1 93/09/24 */ 246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner/* 346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * ==================================================== 446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * Developed at SunPro, a Sun Microsystems, Inc. business. 746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * Permission to use, copy, modify, and distribute this 846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * software is freely granted, provided that this notice 946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * is preserved. 1046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * ==================================================== 1146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner */ 1246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 1346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner#if defined(LIBM_SCCS) && !defined(lint) 1446be48730333120a7b939116cef075e61c12c703David 'Digit' Turnerstatic char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; 1546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner#endif 1646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 1746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner/* __ieee754_pow(x,y) return x**y 1846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 1946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * n 2046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * Method: Let x = 2 * (1+f) 2146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 1. Compute and return log2(x) in two pieces: 2246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * log2(x) = w1 + w2, 2346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * where w1 has 53-24 = 29 bit trailing zeros. 2446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 2. Perform y*log2(x) = n+y' by simulating muti-precision 2546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * arithmetic, where |y'|<=0.5. 2646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 3. Return x**y = 2**n*exp(y'*log2) 2746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 2846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * Special cases: 2946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 1. (anything) ** 0 is 1 3046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 2. (anything) ** 1 is itself 3146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 3. (anything) ** NAN is NAN 3246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 4. NAN ** (anything except 0) is NAN 3346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 5. +-(|x| > 1) ** +INF is +INF 3446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 6. +-(|x| > 1) ** -INF is +0 3546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 7. +-(|x| < 1) ** +INF is +0 3646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 8. +-(|x| < 1) ** -INF is +INF 3746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 9. +-1 ** +-INF is NAN 3846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 10. +0 ** (+anything except 0, NAN) is +0 3946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 4046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 12. +0 ** (-anything except 0, NAN) is +INF 4146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF 4246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) 4346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 15. +INF ** (+anything except 0,NAN) is +INF 4446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 16. +INF ** (-anything except 0,NAN) is +0 4546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 17. -INF ** (anything) = -0 ** (-anything) 4646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) 4746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 19. (-anything except 0 and inf) ** (non-integer) is NAN 4846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 4946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * Accuracy: 5046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * pow(x,y) returns x**y nearly rounded. In particular 5146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * pow(integer,integer) 5246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * always returns the correct integer provided it is 5346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * representable. 5446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * 5546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * Constants : 5646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * The hexadecimal values are the intended ones for the following 5746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * constants. The decimal values may be used, provided that the 5846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * compiler will convert from decimal to binary accurately enough 5946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * to produce the hexadecimal values shown. 6046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner */ 6146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 6246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner/*#include "math.h"*/ 6346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner#include "math_private.h" 6446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 6546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner#ifdef __STDC__ 6646be48730333120a7b939116cef075e61c12c703David 'Digit' Turnerstatic const double 6746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner#else 6846be48730333120a7b939116cef075e61c12c703David 'Digit' Turnerstatic double 6946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner#endif 7046be48730333120a7b939116cef075e61c12c703David 'Digit' Turnerbp[] = {1.0, 1.5,}, 7146be48730333120a7b939116cef075e61c12c703David 'Digit' Turnerdp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ 7246be48730333120a7b939116cef075e61c12c703David 'Digit' Turnerdp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ 7346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ 7446be48730333120a7b939116cef075e61c12c703David 'Digit' TurnerL1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ 7546be48730333120a7b939116cef075e61c12c703David 'Digit' TurnerL2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ 7646be48730333120a7b939116cef075e61c12c703David 'Digit' TurnerL3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ 7746be48730333120a7b939116cef075e61c12c703David 'Digit' TurnerL4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ 7846be48730333120a7b939116cef075e61c12c703David 'Digit' TurnerL5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ 7946be48730333120a7b939116cef075e61c12c703David 'Digit' TurnerL6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ 8046be48730333120a7b939116cef075e61c12c703David 'Digit' TurnerP1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ 8146be48730333120a7b939116cef075e61c12c703David 'Digit' TurnerP2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ 8246be48730333120a7b939116cef075e61c12c703David 'Digit' TurnerP3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ 8346be48730333120a7b939116cef075e61c12c703David 'Digit' TurnerP4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ 8446be48730333120a7b939116cef075e61c12c703David 'Digit' TurnerP5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ 8546be48730333120a7b939116cef075e61c12c703David 'Digit' Turnerlg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ 8646be48730333120a7b939116cef075e61c12c703David 'Digit' Turnerlg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ 8746be48730333120a7b939116cef075e61c12c703David 'Digit' Turnerlg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ 8846be48730333120a7b939116cef075e61c12c703David 'Digit' Turnerovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ 8946be48730333120a7b939116cef075e61c12c703David 'Digit' Turnercp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ 9046be48730333120a7b939116cef075e61c12c703David 'Digit' Turnercp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ 9146be48730333120a7b939116cef075e61c12c703David 'Digit' Turnercp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ 9246be48730333120a7b939116cef075e61c12c703David 'Digit' Turnerivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ 9346be48730333120a7b939116cef075e61c12c703David 'Digit' Turnerivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ 9446be48730333120a7b939116cef075e61c12c703David 'Digit' Turnerivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ 9546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 9646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner#ifdef __STDC__ 9746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner double __ieee754_pow(double x, double y) 9846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner#else 9946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner double __ieee754_pow(x,y) 10046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner double x, y; 10146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner#endif 10246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner{ 10346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner double z,ax,z_h,z_l,p_h,p_l; 10446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner double y1,t1,t2,r,s,t,u,v,w; 10546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner int32_t i,j,k,yisint,n; 10646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner int32_t hx,hy,ix,iy; 10746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner u_int32_t lx,ly; 10846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 10946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner EXTRACT_WORDS(hx,lx,x); 11046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner EXTRACT_WORDS(hy,ly,y); 11146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner ix = hx&0x7fffffff; iy = hy&0x7fffffff; 11246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 11346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* y==zero: x**0 = 1 */ 11446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if((iy|ly)==0) return one; 11546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 11646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* +-NaN return x+y */ 11746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || 11846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) 11946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner return x+y; 12046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 12146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* determine if y is an odd int when x < 0 12246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * yisint = 0 ... y is not an integer 12346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * yisint = 1 ... y is an odd int 12446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * yisint = 2 ... y is an even int 12546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner */ 12646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner yisint = 0; 12746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(hx<0) { 12846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(iy>=0x43400000) yisint = 2; /* even integer y */ 12946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner else if(iy>=0x3ff00000) { 13046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner k = (iy>>20)-0x3ff; /* exponent */ 13146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(k>20) { 13246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner j = ly>>(52-k); 13346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if((u_int32_t)(j<<(52-k))==ly) yisint = 2-(j&1); 13446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } else if(ly==0) { 13546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner j = iy>>(20-k); 13646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if((j<<(20-k))==iy) yisint = 2-(j&1); 13746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 13846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 13946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 14046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 14146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* special value of y */ 14246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(ly==0) { 14346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if (iy==0x7ff00000) { /* y is +-inf */ 14446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(((ix-0x3ff00000)|lx)==0) 14546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner return y - y; /* inf**+-1 is NaN */ 14646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ 14746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner return (hy>=0)? y: zero; 14846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner else /* (|x|<1)**-,+inf = inf,0 */ 14946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner return (hy<0)?-y: zero; 15046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 15146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(iy==0x3ff00000) { /* y is +-1 */ 15246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(hy<0) return one/x; else return x; 15346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 15446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(hy==0x40000000) return x*x; /* y is 2 */ 15546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(hy==0x3fe00000) { /* y is 0.5 */ 15646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(hx>=0) /* x >= +0 */ 15746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner return __ieee754_sqrt(x); 15846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 15946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 16046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 16146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner ax = x < 0 ? -x : x; /*fabs(x);*/ 16246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* special value of x */ 16346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(lx==0) { 16446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ 16546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner z = ax; /*x is +-0,+-inf,+-1*/ 16646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(hy<0) z = one/z; /* z = (1/|x|) */ 16746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(hx<0) { 16846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(((ix-0x3ff00000)|yisint)==0) { 16946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner z = (z-z)/(z-z); /* (-1)**non-int is NaN */ 17046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } else if(yisint==1) 17146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner z = -z; /* (x<0)**odd = -(|x|**odd) */ 17246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 17346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner return z; 17446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 17546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 17646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 17746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* (x<0)**(non-int) is NaN */ 17846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); 17946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 18046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* |y| is huge */ 18146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(iy>0x41e00000) { /* if |y| > 2**31 */ 18246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ 18346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; 18446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; 18546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 18646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* over/underflow if x is not close to one */ 18746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; 18846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; 18946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* now |1-x| is tiny <= 2**-20, suffice to compute 19046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner log(x) by x-x^2/2+x^3/3-x^4/4 */ 19146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner t = x-1; /* t has 20 trailing zeros */ 19246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); 19346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ 19446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner v = t*ivln2_l-w*ivln2; 19546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner t1 = u+v; 19646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner SET_LOW_WORD(t1,0); 19746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner t2 = v-(t1-u); 19846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } else { 19946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner double s2,s_h,s_l,t_h,t_l; 20046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner n = 0; 20146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* take care subnormal number */ 20246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(ix<0x00100000) 20346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); } 20446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner n += ((ix)>>20)-0x3ff; 20546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner j = ix&0x000fffff; 20646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* determine interval */ 20746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner ix = j|0x3ff00000; /* normalize ix */ 20846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */ 20946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ 21046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner else {k=0;n+=1;ix -= 0x00100000;} 21146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner SET_HIGH_WORD(ax,ix); 21246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 21346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ 21446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ 21546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner v = one/(ax+bp[k]); 21646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner s = u*v; 21746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner s_h = s; 21846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner SET_LOW_WORD(s_h,0); 21946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* t_h=ax+bp[k] High */ 22046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner t_h = zero; 22146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18)); 22246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner t_l = ax - (t_h-bp[k]); 22346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner s_l = v*((u-s_h*t_h)-s_h*t_l); 22446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* compute log(ax) */ 22546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner s2 = s*s; 22646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); 22746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner r += s_l*(s_h+s); 22846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner s2 = s_h*s_h; 22946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner t_h = 3.0+s2+r; 23046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner SET_LOW_WORD(t_h,0); 23146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner t_l = r-((t_h-3.0)-s2); 23246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* u+v = s*(1+...) */ 23346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner u = s_h*t_h; 23446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner v = s_l*t_h+t_l*s; 23546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* 2/(3log2)*(s+...) */ 23646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner p_h = u+v; 23746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner SET_LOW_WORD(p_h,0); 23846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner p_l = v-(p_h-u); 23946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ 24046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner z_l = cp_l*p_h+p_l*cp+dp_l[k]; 24146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ 24246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner t = (double)n; 24346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner t1 = (((z_h+z_l)+dp_h[k])+t); 24446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner SET_LOW_WORD(t1,0); 24546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner t2 = z_l-(((t1-t)-dp_h[k])-z_h); 24646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 24746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 24846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ 24946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) 25046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner s = -one;/* (-ve)**(odd int) */ 25146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner 25246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ 25346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner y1 = y; 25446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner SET_LOW_WORD(y1,0); 25546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner p_l = (y-y1)*t1+y*t2; 25646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner p_h = y1*t1; 25746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner z = p_l+p_h; 25846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner EXTRACT_WORDS(j,i,z); 25946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if (j>=0x40900000) { /* z >= 1024 */ 26046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(((j-0x40900000)|i)!=0) /* if z > 1024 */ 26146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner return s*huge*huge; /* overflow */ 26246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner else { 26346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ 26446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 26546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ 26646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ 26746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner return s*tiny*tiny; /* underflow */ 26846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner else { 26946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ 27046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 27146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 27246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner /* 27346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner * compute 2**(p_h+p_l) 27446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner */ 27546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner i = j&0x7fffffff; 27646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner k = (i>>20)-0x3ff; 27746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner n = 0; 27846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ 27946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner n = j+(0x00100000>>(k+1)); 28046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ 28146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner t = zero; 28246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner SET_HIGH_WORD(t,n&~(0x000fffff>>k)); 28346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner n = ((n&0x000fffff)|0x00100000)>>(20-k); 28446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if(j<0) n = -n; 28546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner p_h -= t; 28646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner } 28746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner t = p_l+p_h; 28846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner SET_LOW_WORD(t,0); 28946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner u = t*lg2_h; 29046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner v = (p_l-(t-p_h))*lg2+t*lg2_l; 29146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner z = u+v; 29246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner w = v-(z-u); 29346be48730333120a7b939116cef075e61c12c703David 'Digit' Turner t = z*z; 29446be48730333120a7b939116cef075e61c12c703David 'Digit' Turner t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); 29546be48730333120a7b939116cef075e61c12c703David 'Digit' Turner r = (z*t1)/(t1-two)-(w+z*w); 29646be48730333120a7b939116cef075e61c12c703David 'Digit' Turner z = one-(r-z); 29746be48730333120a7b939116cef075e61c12c703David 'Digit' Turner GET_HIGH_WORD(j,z); 29846be48730333120a7b939116cef075e61c12c703David 'Digit' Turner j += (n<<20); 29946be48730333120a7b939116cef075e61c12c703David 'Digit' Turner if((j>>20)<=0) z = SDL_NAME(scalbn)(z,n); /* subnormal output */ 30046be48730333120a7b939116cef075e61c12c703David 'Digit' Turner else SET_HIGH_WORD(z,j); 30146be48730333120a7b939116cef075e61c12c703David 'Digit' Turner return s*z; 30246be48730333120a7b939116cef075e61c12c703David 'Digit' Turner} 303