11dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 21dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* @(#)e_j1.c 1.3 95/01/18 */ 31dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* 41dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 51dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 61dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 71dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Developed at SunSoft, a Sun Microsystems, Inc. business. 81dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Permission to use, copy, modify, and distribute this 91dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * software is freely granted, provided that this notice 101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * is preserved. 111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#ifndef lint 151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic char rcsid[] = "$FreeBSD: src/lib/msun/src/e_j1.c,v 1.8 2005/02/04 18:26:06 das Exp $"; 161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#endif 171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* __ieee754_j1(x), __ieee754_y1(x) 191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Bessel function of the first and second kinds of order zero. 201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Method -- j1(x): 211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... 221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 2. Reduce x to |x| since j1(x)=-j1(-x), and 231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * for x in (0,2) 241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * j1(x) = x/2 + x*z*R0/S0, where z = x*x; 251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) 261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * for x in (2,inf) 271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) 281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) 291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) 301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * as follow: 311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) 321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * = 1/sqrt(2) * (sin(x) - cos(x)) 331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * = -1/sqrt(2) * (sin(x) + cos(x)) 351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * (To avoid cancellation, use 361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * to compute the worse one.) 381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 3 Special cases 401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * j1(nan)= nan 411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * j1(0) = 0 421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * j1(inf) = 0 431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Method -- y1(x): 451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN 461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 2. For x<2. 471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Since 481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) 491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. 501dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * We use the following function to approximate y1, 511dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * where for x in [0,2] (abs err less than 2**-65.89) 531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Note: For tiny x, 1/x dominate y1 and hence 561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) 571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 3. For x>=2. 581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) 591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) 601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * by method mentioned above. 611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math.h" 641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math_private.h" 651dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 661dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic double pone(double), qone(double); 671dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double 691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecthuge = 1e300, 701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectone = 1.0, 711dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectinvsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ 721dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecttpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 731dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* R0/S0 on [0,2] */ 741dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectr00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ 751dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectr01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ 761dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectr02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ 771dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectr03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ 781dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projects01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ 791dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projects02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ 801dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projects03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ 811dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projects04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ 821dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projects05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ 831dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 841dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double zero = 0.0; 851dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 861dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectdouble 871dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project__ieee754_j1(double x) 881dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project{ 891dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project double z, s,c,ss,cc,r,u,v,y; 901dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project int32_t hx,ix; 911dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 921dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_HIGH_WORD(hx,x); 931dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ix = hx&0x7fffffff; 941dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix>=0x7ff00000) return one/x; 951dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project y = fabs(x); 961dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix >= 0x40000000) { /* |x| >= 2.0 */ 971dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s = sin(y); 981dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project c = cos(y); 991dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ss = -s-c; 1001dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project cc = s-c; 1011dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix<0x7fe00000) { /* make sure y+y not overflow */ 1021dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = cos(y+y); 1031dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if ((s*c)>zero) cc = z/ss; 1041dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else ss = z/cc; 1051dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1061dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* 1071dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) 1081dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) 1091dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 1101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y); 1111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else { 1121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u = pone(y); v = qone(y); 1131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = invsqrtpi*(u*cc-v*ss)/sqrt(y); 1141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx<0) return -z; 1161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else return z; 1171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix<0x3e400000) { /* |x|<2**-27 */ 1191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ 1201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = x*x; 1221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project r = z*(r00+z*(r01+z*(r02+z*r03))); 1231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); 1241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project r *= x; 1251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return(x*0.5+r/s); 1261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project} 1271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double U0[5] = { 1291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ 1301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ 1311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ 1321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ 1331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ 1341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 1351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double V0[5] = { 1361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ 1371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ 1381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ 1391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ 1401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ 1411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 1421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectdouble 1441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project__ieee754_y1(double x) 1451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project{ 1461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project double z, s,c,ss,cc,u,v; 1471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project int32_t hx,ix,lx; 1481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project EXTRACT_WORDS(hx,lx,x); 1501dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ix = 0x7fffffff&hx; 1511dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ 1521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix>=0x7ff00000) return one/(x+x*x); 1531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if((ix|lx)==0) return -one/zero; 1541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(hx<0) return zero/zero; 1551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix >= 0x40000000) { /* |x| >= 2.0 */ 1561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s = sin(x); 1571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project c = cos(x); 1581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ss = -s-c; 1591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project cc = s-c; 1601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix<0x7fe00000) { /* make sure x+x not overflow */ 1611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = cos(x+x); 1621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if ((s*c)>zero) cc = z/ss; 1631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else ss = z/cc; 1641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1651dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) 1661dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * where x0 = x-3pi/4 1671dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Better formula: 1681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) 1691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * = 1/sqrt(2) * (sin(x) - cos(x)) 1701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 1711dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * = -1/sqrt(2) * (cos(x) + sin(x)) 1721dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * To avoid cancellation, use 1731dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 1741dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * to compute the worse one. 1751dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 1761dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); 1771dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else { 1781dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u = pone(x); v = qone(x); 1791dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = invsqrtpi*(u*ss+v*cc)/sqrt(x); 1801dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1811dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return z; 1821dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1831dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix<=0x3c900000) { /* x < 2**-54 */ 1841dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return(-tpi/x); 1851dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 1861dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = x*x; 1871dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); 1881dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); 1891dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); 1901dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project} 1911dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1921dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* For x >= 8, the asymptotic expansions of pone is 1931dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. 1941dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * We approximate pone by 1951dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * pone(x) = 1 + (R/S) 1961dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 1971dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * S = 1 + ps0*s^2 + ... + ps4*s^10 1981dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * and 1991dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * | pone(x)-1-R/S | <= 2 ** ( -60.06) 2001dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 2011dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2021dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 2031dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 2041dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ 2051dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ 2061dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ 2071dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ 2081dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ 2091dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 2101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double ps8[5] = { 2111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ 2121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ 2131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ 2141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ 2151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ 2161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 2171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 2191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ 2201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ 2211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ 2221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ 2231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ 2241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ 2251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 2261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double ps5[5] = { 2271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ 2281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ 2291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ 2301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ 2311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ 2321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 2331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double pr3[6] = { 2351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ 2361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ 2371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ 2381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ 2391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ 2401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ 2411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 2421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double ps3[5] = { 2431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ 2441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ 2451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ 2461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ 2471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ 2481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 2491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2501dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 2511dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ 2521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ 2531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ 2541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ 2551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ 2561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ 2571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 2581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double ps2[5] = { 2591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ 2601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ 2611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ 2621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ 2631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ 2641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 2651dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2661dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project static double pone(double x) 2671dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project{ 2681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project const double *p,*q; 2691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project double z,r,s; 2701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project int32_t ix; 2711dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_HIGH_WORD(ix,x); 2721dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ix &= 0x7fffffff; 2731dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix>=0x40200000) {p = pr8; q= ps8;} 2741dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if(ix>=0x40122E8B){p = pr5; q= ps5;} 2751dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if(ix>=0x4006DB6D){p = pr3; q= ps3;} 2761dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if(ix>=0x40000000){p = pr2; q= ps2;} 2771dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = one/(x*x); 2781dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 2791dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); 2801dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return one+ r/s; 2811dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project} 2821dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2831dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2841dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* For x >= 8, the asymptotic expansions of qone is 2851dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. 2861dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * We approximate pone by 2871dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * qone(x) = s*(0.375 + (R/S)) 2881dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 2891dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * S = 1 + qs1*s^2 + ... + qs6*s^12 2901dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * and 2911dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) 2921dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 2931dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2941dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 2951dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 2961dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ 2971dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ 2981dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ 2991dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ 3001dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ 3011dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 3021dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double qs8[6] = { 3031dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ 3041dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ 3051dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ 3061dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ 3071dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ 3081dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ 3091dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 3101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 3111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 3121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ 3131dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ 3141dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ 3151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ 3161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ 3171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ 3181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 3191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double qs5[6] = { 3201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ 3211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ 3221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ 3231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ 3241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ 3251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ 3261dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 3271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 3281dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double qr3[6] = { 3291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ 3301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ 3311dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ 3321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ 3331dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ 3341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ 3351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 3361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double qs3[6] = { 3371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ 3381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ 3391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ 3401dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ 3411dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ 3421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ 3431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 3441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 3451dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 3461dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ 3471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ 3481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ 3491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ 3501dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ 3511dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ 3521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 3531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectstatic const double qs2[6] = { 3541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ 3551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ 3561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ 3571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ 3581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ 3591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ 3601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project}; 3611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 3621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project static double qone(double x) 3631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project{ 3641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project const double *p,*q; 3651dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project double s,r,z; 3661dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project int32_t ix; 3671dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_HIGH_WORD(ix,x); 3681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ix &= 0x7fffffff; 3691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix>=0x40200000) {p = qr8; q= qs8;} 3701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if(ix>=0x40122E8B){p = qr5; q= qs5;} 3711dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if(ix>=0x4006DB6D){p = qr3; q= qs3;} 3721dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else if(ix>=0x40000000){p = qr2; q= qs2;} 3731dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = one/(x*x); 3741dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 3751dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); 3761dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return (.375 + r/s)/x; 3771dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project} 378