11dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* @(#)e_pow.c 1.5 04/04/22 SMI */ 21dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* 31dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 41dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. 51dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 61dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Permission to use, copy, modify, and distribute this 71dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * software is freely granted, provided that this notice 81dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * is preserved. 91dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#ifndef lint 131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic char rcsid[] = "$FreeBSD: src/lib/msun/src/e_pow.c,v 1.11 2005/02/04 18:26:06 das Exp $"; 141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#endif 151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* __ieee754_pow(x,y) return x**y 171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * n 191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Method: Let x = 2 * (1+f) 201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 1. Compute and return log2(x) in two pieces: 211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * log2(x) = w1 + w2, 221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * where w1 has 53-24 = 29 bit trailing zeros. 231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 2. Perform y*log2(x) = n+y' by simulating muti-precision 241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * arithmetic, where |y'|<=0.5. 251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 3. Return x**y = 2**n*exp(y'*log2) 261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Special cases: 281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 1. (anything) ** 0 is 1 291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 2. (anything) ** 1 is itself 301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 3. (anything) ** NAN is NAN 311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 4. NAN ** (anything except 0) is NAN 321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 5. +-(|x| > 1) ** +INF is +INF 331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 6. +-(|x| > 1) ** -INF is +0 341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 7. +-(|x| < 1) ** +INF is +0 351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 8. +-(|x| < 1) ** -INF is +INF 361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 9. +-1 ** +-INF is NAN 371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 10. +0 ** (+anything except 0, NAN) is +0 381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 12. +0 ** (-anything except 0, NAN) is +INF 401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF 411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) 421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 15. +INF ** (+anything except 0,NAN) is +INF 431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 16. +INF ** (-anything except 0,NAN) is +0 441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 17. -INF ** (anything) = -0 ** (-anything) 451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) 461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 19. (-anything except 0 and inf) ** (non-integer) is NAN 471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Accuracy: 491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * pow(x,y) returns x**y nearly rounded. In particular 501dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * pow(integer,integer) 511dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * always returns the correct integer provided it is 521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * representable. 531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Constants : 551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * The hexadecimal values are the intended ones for the following 561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * constants. The decimal values may be used, provided that the 571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * compiler will convert from decimal to binary accurately enough 581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * to produce the hexadecimal values shown. 591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math.h" 621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math_private.h" 631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double 651dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectbp[] = {1.0, 1.5,}, 661dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectdp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ 671dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectdp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ 681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectzero = 0.0, 691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectone = 1.0, 701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecttwo = 2.0, 711dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecttwo53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ 721dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecthuge = 1.0e300, 731dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecttiny = 1.0e-300, 741dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ 751dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectL1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ 761dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectL2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ 771dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectL3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ 781dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectL4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ 791dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectL5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ 801dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectL6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ 811dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectP1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ 821dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectP2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ 831dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectP3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ 841dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectP4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ 851dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source ProjectP5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ 861dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectlg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ 871dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectlg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ 881dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectlg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ 891dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ 901dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectcp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ 911dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectcp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ 921dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectcp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ 931dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ 941dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ 951dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ 961dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 971dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectdouble 981dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project__ieee754_pow(double x, double y) 991dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project{ 1001dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project double z,ax,z_h,z_l,p_h,p_l; 1011dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project double y1,t1,t2,r,s,t,u,v,w; 1021dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project int32_t i,j,k,yisint,n; 1031dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project int32_t hx,hy,ix,iy; 1041dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u_int32_t lx,ly; 1051dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1061dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project EXTRACT_WORDS(hx,lx,x); 1071dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project EXTRACT_WORDS(hy,ly,y); 1081dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ix = hx&0x7fffffff; iy = hy&0x7fffffff; 1091dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* y==zero: x**0 = 1 */ 1111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if((iy|ly)==0) return one; 1121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* +-NaN return x+y */ 1141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || 1151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) 1161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return x+y; 1171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* determine if y is an odd int when x < 0 1191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * yisint = 0 ... y is not an integer 1201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * yisint = 1 ... y is an odd int 1211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * yisint = 2 ... y is an even int 1221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 1231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project yisint = 0; 1241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx<0) { 1251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(iy>=0x43400000) yisint = 2; /* even integer y */ 1261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if(iy>=0x3ff00000) { 1271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k = (iy>>20)-0x3ff; /* exponent */ 1281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(k>20) { 1291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project j = ly>>(52-k); 1301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if((j<<(52-k))==ly) yisint = 2-(j&1); 1311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } else if(ly==0) { 1321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project j = iy>>(20-k); 1331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if((j<<(20-k))==iy) yisint = 2-(j&1); 1341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* special value of y */ 1391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ly==0) { 1401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (iy==0x7ff00000) { /* y is +-inf */ 1411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(((ix-0x3ff00000)|lx)==0) 1421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return y - y; /* inf**+-1 is NaN */ 1431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ 1441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return (hy>=0)? y: zero; 1451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else /* (|x|<1)**-,+inf = inf,0 */ 1461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return (hy<0)?-y: zero; 1471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(iy==0x3ff00000) { /* y is +-1 */ 1491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hy<0) return one/x; else return x; 1501dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1511dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hy==0x40000000) return x*x; /* y is 2 */ 1521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hy==0x3fe00000) { /* y is 0.5 */ 1531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx>=0) /* x >= +0 */ 1541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return sqrt(x); 1551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ax = fabs(x); 1591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* special value of x */ 1601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(lx==0) { 1611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ 1621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = ax; /*x is +-0,+-inf,+-1*/ 1631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hy<0) z = one/z; /* z = (1/|x|) */ 1641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx<0) { 1651dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(((ix-0x3ff00000)|yisint)==0) { 1661dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = (z-z)/(z-z); /* (-1)**non-int is NaN */ 1671dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } else if(yisint==1) 1681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = -z; /* (x<0)**odd = -(|x|**odd) */ 1691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return z; 1711dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1721dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1731dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1741dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* CYGNUS LOCAL + fdlibm-5.3 fix: This used to be 1751dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project n = (hx>>31)+1; 1761dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project but ANSI C says a right shift of a signed negative quantity is 1771dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project implementation defined. */ 1781dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project n = ((u_int32_t)hx>>31)-1; 1791dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1801dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* (x<0)**(non-int) is NaN */ 1811dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if((n|yisint)==0) return (x-x)/(x-x); 1821dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1831dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ 1841dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ 1851dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1861dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* |y| is huge */ 1871dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(iy>0x41e00000) { /* if |y| > 2**31 */ 1881dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ 1891dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; 1901dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; 1911dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1921dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* over/underflow if x is not close to one */ 1931dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny; 1941dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny; 1951dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* now |1-x| is tiny <= 2**-20, suffice to compute 1961dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project log(x) by x-x^2/2+x^3/3-x^4/4 */ 1971dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = ax-one; /* t has 20 trailing zeros */ 1981dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); 1991dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ 2001dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project v = t*ivln2_l-w*ivln2; 2011dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t1 = u+v; 2021dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_LOW_WORD(t1,0); 2031dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t2 = v-(t1-u); 2041dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } else { 2051dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project double ss,s2,s_h,s_l,t_h,t_l; 2061dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project n = 0; 2071dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* take care subnormal number */ 2081dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix<0x00100000) 2091dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); } 2101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project n += ((ix)>>20)-0x3ff; 2111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project j = ix&0x000fffff; 2121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* determine interval */ 2131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ix = j|0x3ff00000; /* normalize ix */ 2141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */ 2151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */ 2161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else {k=0;n+=1;ix -= 0x00100000;} 2171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_HIGH_WORD(ax,ix); 2181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */ 2201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */ 2211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project v = one/(ax+bp[k]); 2221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ss = u*v; 2231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s_h = ss; 2241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_LOW_WORD(s_h,0); 2251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* t_h=ax+bp[k] High */ 2261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t_h = zero; 2271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18)); 2281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t_l = ax - (t_h-bp[k]); 2291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s_l = v*((u-s_h*t_h)-s_h*t_l); 2301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* compute log(ax) */ 2311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s2 = ss*ss; 2321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); 2331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project r += s_l*(s_h+ss); 2341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s2 = s_h*s_h; 2351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t_h = 3.0+s2+r; 2361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_LOW_WORD(t_h,0); 2371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t_l = r-((t_h-3.0)-s2); 2381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* u+v = ss*(1+...) */ 2391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u = s_h*t_h; 2401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project v = s_l*t_h+t_l*ss; 2411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* 2/(3log2)*(ss+...) */ 2421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project p_h = u+v; 2431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_LOW_WORD(p_h,0); 2441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project p_l = v-(p_h-u); 2451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ 2461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z_l = cp_l*p_h+p_l*cp+dp_l[k]; 2471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ 2481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = (double)n; 2491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t1 = (((z_h+z_l)+dp_h[k])+t); 2501dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_LOW_WORD(t1,0); 2511dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t2 = z_l-(((t1-t)-dp_h[k])-z_h); 2521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 2531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ 2551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project y1 = y; 2561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_LOW_WORD(y1,0); 2571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project p_l = (y-y1)*t1+y*t2; 2581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project p_h = y1*t1; 2591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = p_l+p_h; 2601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project EXTRACT_WORDS(j,i,z); 2611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (j>=0x40900000) { /* z >= 1024 */ 2621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(((j-0x40900000)|i)!=0) /* if z > 1024 */ 2631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return s*huge*huge; /* overflow */ 2641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else { 2651dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ 2661dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 2671dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ 2681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ 2691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return s*tiny*tiny; /* underflow */ 2701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else { 2711dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ 2721dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 2731dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 2741dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* 2751dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * compute 2**(p_h+p_l) 2761dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 2771dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project i = j&0x7fffffff; 2781dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k = (i>>20)-0x3ff; 2791dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project n = 0; 2801dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ 2811dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project n = j+(0x00100000>>(k+1)); 2821dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ 2831dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = zero; 2841dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_HIGH_WORD(t,n&~(0x000fffff>>k)); 2851dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project n = ((n&0x000fffff)|0x00100000)>>(20-k); 2861dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(j<0) n = -n; 2871dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project p_h -= t; 2881dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 2891dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = p_l+p_h; 2901dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project SET_LOW_WORD(t,0); 2911dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u = t*lg2_h; 2921dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project v = (p_l-(t-p_h))*lg2+t*lg2_l; 2931dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = u+v; 2941dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project w = v-(z-u); 2951dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = z*z; 2961dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); 2971dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project r = (z*t1)/(t1-two)-(w+z*w); 2981dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = one-(r-z); 2991dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_HIGH_WORD(j,z); 3001dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project j += (n<<20); 3011dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */ 3021dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else SET_HIGH_WORD(z,j); 3031dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return s*z; 3041dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project} 305