11dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* e_powf.c -- float version of e_pow.c. 21dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 31dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 41dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 51dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* 61dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 71dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 81dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 91dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Developed at SunPro, a Sun Microsystems, Inc. business. 101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Permission to use, copy, modify, and distribute this 111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * software is freely granted, provided that this notice 121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * is preserved. 131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 16a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <sys/cdefs.h> 17a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes__FBSDID("$FreeBSD$"); 181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math.h" 201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math_private.h" 211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const float 231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectbp[] = {1.0, 1.5,}, 241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectdp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ 251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectdp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ 261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectzero = 0.0, 271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectone = 1.0, 281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecttwo = 2.0, 291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecttwo24 = 16777216.0, /* 0x4b800000 */ 301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecthuge = 1.0e30, 311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecttiny = 1.0e-30, 321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ 331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectL1 = 6.0000002384e-01, /* 0x3f19999a */ 341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectL2 = 4.2857143283e-01, /* 0x3edb6db7 */ 351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectL3 = 3.3333334327e-01, /* 0x3eaaaaab */ 361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectL4 = 2.7272811532e-01, /* 0x3e8ba305 */ 371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectL5 = 2.3066075146e-01, /* 0x3e6c3255 */ 381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectL6 = 2.0697501302e-01, /* 0x3e53f142 */ 391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectP1 = 1.6666667163e-01, /* 0x3e2aaaab */ 401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectP2 = -2.7777778450e-03, /* 0xbb360b61 */ 411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectP3 = 6.6137559770e-05, /* 0x388ab355 */ 421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectP4 = -1.6533901999e-06, /* 0xb5ddea0e */ 431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectP5 = 4.1381369442e-08, /* 0x3331bb4c */ 441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectlg2 = 6.9314718246e-01, /* 0x3f317218 */ 451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectlg2_h = 6.93145752e-01, /* 0x3f317200 */ 461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectlg2_l = 1.42860654e-06, /* 0x35bfbe8c */ 471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */ 481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectcp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */ 49a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughescp_h = 9.6191406250e-01, /* 0x3f764000 =12b cp */ 50a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughescp_l = -1.1736857402e-04, /* 0xb8f623c6 =tail of cp_h */ 511dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */ 521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/ 531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ 541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectfloat 561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project__ieee754_powf(float x, float y) 571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project{ 581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project float z,ax,z_h,z_l,p_h,p_l; 591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project float y1,t1,t2,r,s,sn,t,u,v,w; 601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project int32_t i,j,k,yisint,n; 611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project int32_t hx,hy,ix,iy,is; 621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_FLOAT_WORD(hx,x); 641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_FLOAT_WORD(hy,y); 651dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ix = hx&0x7fffffff; iy = hy&0x7fffffff; 661dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 671dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* y==zero: x**0 = 1 */ 681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(iy==0) return one; 691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 70a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* x==1: 1**y = 1, even if y is NaN */ 71a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if (hx==0x3f800000) return one; 72a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes 73a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* y!=zero: result is NaN if either arg is NaN */ 741dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix > 0x7f800000 || 751dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project iy > 0x7f800000) 76a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return (x+0.0F)+(y+0.0F); 771dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 781dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* determine if y is an odd int when x < 0 791dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * yisint = 0 ... y is not an integer 801dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * yisint = 1 ... y is an odd int 811dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * yisint = 2 ... y is an even int 821dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 831dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project yisint = 0; 841dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx<0) { 851dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(iy>=0x4b800000) yisint = 2; /* even integer y */ 861dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if(iy>=0x3f800000) { 871dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k = (iy>>23)-0x7f; /* exponent */ 881dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project j = iy>>(23-k); 891dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if((j<<(23-k))==iy) yisint = 2-(j&1); 901dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 911dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 921dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 931dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* special value of y */ 941dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (iy==0x7f800000) { /* y is +-inf */ 951dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (ix==0x3f800000) 96a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes return one; /* (-1)**+-inf is NaN */ 971dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */ 981dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return (hy>=0)? y: zero; 991dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else /* (|x|<1)**-,+inf = inf,0 */ 1001dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return (hy<0)?-y: zero; 1011dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1021dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(iy==0x3f800000) { /* y is +-1 */ 1031dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hy<0) return one/x; else return x; 1041dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1051dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hy==0x40000000) return x*x; /* y is 2 */ 1061dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hy==0x3f000000) { /* y is 0.5 */ 1071dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx>=0) /* x >= +0 */ 1081dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return __ieee754_sqrtf(x); 1091dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ax = fabsf(x); 1121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* special value of x */ 1131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix==0x7f800000||ix==0||ix==0x3f800000){ 1141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = ax; /*x is +-0,+-inf,+-1*/ 1151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hy<0) z = one/z; /* z = (1/|x|) */ 1161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx<0) { 1171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(((ix-0x3f800000)|yisint)==0) { 1181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = (z-z)/(z-z); /* (-1)**non-int is NaN */ 1191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } else if(yisint==1) 1201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = -z; /* (x<0)**odd = -(|x|**odd) */ 1211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return z; 1231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project n = ((u_int32_t)hx>>31)-1; 1261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* (x<0)**(non-int) is NaN */ 1281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if((n|yisint)==0) return (x-x)/(x-x); 1291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */ 1311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if((n|(yisint-1))==0) sn = -one;/* (-ve)**(odd int) */ 1321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* |y| is huge */ 1341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(iy>0x4d000000) { /* if |y| > 2**27 */ 1351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* over/underflow if x is not close to one */ 1361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix<0x3f7ffff8) return (hy<0)? sn*huge*huge:sn*tiny*tiny; 1371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix>0x3f800007) return (hy>0)? sn*huge*huge:sn*tiny*tiny; 1381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* now |1-x| is tiny <= 2**-20, suffice to compute 1391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project log(x) by x-x^2/2+x^3/3-x^4/4 */ 1401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = ax-1; /* t has 20 trailing zeros */ 1411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25)); 1421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u = ivln2_h*t; /* ivln2_h has 16 sig. bits */ 1431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project v = t*ivln2_l-w*ivln2; 1441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t1 = u+v; 1451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_FLOAT_WORD(is,t1); 1461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_FLOAT_WORD(t1,is&0xfffff000); 1471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t2 = v-(t1-u); 1481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } else { 1491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project float s2,s_h,s_l,t_h,t_l; 1501dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project n = 0; 1511dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* take care subnormal number */ 1521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix<0x00800000) 1531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); } 1541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project n += ((ix)>>23)-0x7f; 1551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project j = ix&0x007fffff; 1561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* determine interval */ 1571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ix = j|0x3f800000; /* normalize ix */ 1581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */ 1591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */ 1601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else {k=0;n+=1;ix -= 0x00800000;} 1611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_FLOAT_WORD(ax,ix); 1621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ 1641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ 1651dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project v = one/(ax+bp[k]); 1661dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s = u*v; 1671dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s_h = s; 1681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_FLOAT_WORD(is,s_h); 1691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_FLOAT_WORD(s_h,is&0xfffff000); 1701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* t_h=ax+bp[k] High */ 1711dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project is = ((ix>>1)&0xfffff000)|0x20000000; 1721dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_FLOAT_WORD(t_h,is+0x00400000+(k<<21)); 1731dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t_l = ax - (t_h-bp[k]); 1741dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s_l = v*((u-s_h*t_h)-s_h*t_l); 1751dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* compute log(ax) */ 1761dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s2 = s*s; 1771dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); 1781dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project r += s_l*(s_h+s); 1791dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s2 = s_h*s_h; 1801dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t_h = (float)3.0+s2+r; 1811dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_FLOAT_WORD(is,t_h); 1821dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_FLOAT_WORD(t_h,is&0xfffff000); 1831dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t_l = r-((t_h-(float)3.0)-s2); 1841dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* u+v = s*(1+...) */ 1851dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u = s_h*t_h; 1861dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project v = s_l*t_h+t_l*s; 1871dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* 2/(3log2)*(s+...) */ 1881dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project p_h = u+v; 1891dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_FLOAT_WORD(is,p_h); 1901dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_FLOAT_WORD(p_h,is&0xfffff000); 1911dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project p_l = v-(p_h-u); 1921dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ 1931dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z_l = cp_l*p_h+p_l*cp+dp_l[k]; 1941dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ 1951dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = (float)n; 1961dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t1 = (((z_h+z_l)+dp_h[k])+t); 1971dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_FLOAT_WORD(is,t1); 1981dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_FLOAT_WORD(t1,is&0xfffff000); 1991dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t2 = z_l-(((t1-t)-dp_h[k])-z_h); 2001dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 2011dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2021dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ 2031dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_FLOAT_WORD(is,y); 2041dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_FLOAT_WORD(y1,is&0xfffff000); 2051dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project p_l = (y-y1)*t1+y*t2; 2061dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project p_h = y1*t1; 2071dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = p_l+p_h; 2081dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_FLOAT_WORD(j,z); 2091dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (j>0x43000000) /* if z > 128 */ 2101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return sn*huge*huge; /* overflow */ 2111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if (j==0x43000000) { /* if z == 128 */ 2121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */ 2131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 2141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */ 2151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return sn*tiny*tiny; /* underflow */ 2161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if (j==0xc3160000){ /* z == -150 */ 2171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(p_l<=z-p_h) return sn*tiny*tiny; /* underflow */ 2181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 2191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* 2201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * compute 2**(p_h+p_l) 2211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 2221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project i = j&0x7fffffff; 2231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k = (i>>23)-0x7f; 2241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project n = 0; 2251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */ 2261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project n = j+(0x00800000>>(k+1)); 2271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */ 2281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_FLOAT_WORD(t,n&~(0x007fffff>>k)); 2291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project n = ((n&0x007fffff)|0x00800000)>>(23-k); 2301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(j<0) n = -n; 2311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project p_h -= t; 2321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 2331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = p_l+p_h; 2341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_FLOAT_WORD(is,t); 2351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_FLOAT_WORD(t,is&0xffff8000); 2361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u = t*lg2_h; 2371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project v = (p_l-(t-p_h))*lg2+t*lg2_l; 2381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = u+v; 2391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project w = v-(z-u); 2401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = z*z; 2411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); 2421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project r = (z*t1)/(t1-two)-(w+z*w); 2431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = one-(r-z); 2441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_FLOAT_WORD(j,z); 2451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project j += (n<<23); 2461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if((j>>23)<=0) z = scalbnf(z,n); /* subnormal output */ 2471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else SET_FLOAT_WORD(z,j); 2481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return sn*z; 2491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project} 250