1141296Sdas 2141296Sdas/* @(#)e_j1.c 1.3 95/01/18 */ 32116Sjkh/* 42116Sjkh * ==================================================== 52116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 62116Sjkh * 7141296Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business. 82116Sjkh * Permission to use, copy, modify, and distribute this 9141296Sdas * software is freely granted, provided that this notice 102116Sjkh * is preserved. 112116Sjkh * ==================================================== 122116Sjkh */ 132116Sjkh 14176451Sdas#include <sys/cdefs.h> 15176451Sdas__FBSDID("$FreeBSD$"); 162116Sjkh 172116Sjkh/* __ieee754_j1(x), __ieee754_y1(x) 182116Sjkh * Bessel function of the first and second kinds of order zero. 192116Sjkh * Method -- j1(x): 202116Sjkh * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... 212116Sjkh * 2. Reduce x to |x| since j1(x)=-j1(-x), and 222116Sjkh * for x in (0,2) 232116Sjkh * j1(x) = x/2 + x*z*R0/S0, where z = x*x; 242116Sjkh * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) 252116Sjkh * for x in (2,inf) 262116Sjkh * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) 272116Sjkh * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) 282116Sjkh * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) 292116Sjkh * as follow: 302116Sjkh * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) 312116Sjkh * = 1/sqrt(2) * (sin(x) - cos(x)) 322116Sjkh * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 332116Sjkh * = -1/sqrt(2) * (sin(x) + cos(x)) 342116Sjkh * (To avoid cancellation, use 352116Sjkh * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 362116Sjkh * to compute the worse one.) 37141296Sdas * 382116Sjkh * 3 Special cases 392116Sjkh * j1(nan)= nan 402116Sjkh * j1(0) = 0 412116Sjkh * j1(inf) = 0 42141296Sdas * 432116Sjkh * Method -- y1(x): 44141296Sdas * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN 452116Sjkh * 2. For x<2. 46141296Sdas * Since 472116Sjkh * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) 482116Sjkh * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. 492116Sjkh * We use the following function to approximate y1, 502116Sjkh * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 512116Sjkh * where for x in [0,2] (abs err less than 2**-65.89) 522116Sjkh * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 532116Sjkh * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 542116Sjkh * Note: For tiny x, 1/x dominate y1 and hence 552116Sjkh * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) 562116Sjkh * 3. For x>=2. 572116Sjkh * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) 582116Sjkh * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) 592116Sjkh * by method mentioned above. 602116Sjkh */ 612116Sjkh 622116Sjkh#include "math.h" 632116Sjkh#include "math_private.h" 642116Sjkh 652116Sjkhstatic double pone(double), qone(double); 662116Sjkh 678870Srgrimesstatic const double 682116Sjkhhuge = 1e300, 692116Sjkhone = 1.0, 702116Sjkhinvsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ 712116Sjkhtpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 722116Sjkh /* R0/S0 on [0,2] */ 732116Sjkhr00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ 742116Sjkhr01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ 752116Sjkhr02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ 762116Sjkhr03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ 772116Sjkhs01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ 782116Sjkhs02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ 792116Sjkhs03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ 802116Sjkhs04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ 812116Sjkhs05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ 822116Sjkh 832116Sjkhstatic const double zero = 0.0; 842116Sjkh 8597413Salfreddouble 8697413Salfred__ieee754_j1(double x) 872116Sjkh{ 882116Sjkh double z, s,c,ss,cc,r,u,v,y; 892116Sjkh int32_t hx,ix; 902116Sjkh 912116Sjkh GET_HIGH_WORD(hx,x); 922116Sjkh ix = hx&0x7fffffff; 932116Sjkh if(ix>=0x7ff00000) return one/x; 942116Sjkh y = fabs(x); 952116Sjkh if(ix >= 0x40000000) { /* |x| >= 2.0 */ 962116Sjkh s = sin(y); 972116Sjkh c = cos(y); 982116Sjkh ss = -s-c; 992116Sjkh cc = s-c; 1002116Sjkh if(ix<0x7fe00000) { /* make sure y+y not overflow */ 1012116Sjkh z = cos(y+y); 1022116Sjkh if ((s*c)>zero) cc = z/ss; 1032116Sjkh else ss = z/cc; 1042116Sjkh } 1052116Sjkh /* 1062116Sjkh * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) 1072116Sjkh * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) 1082116Sjkh */ 1092116Sjkh if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y); 1102116Sjkh else { 1112116Sjkh u = pone(y); v = qone(y); 1122116Sjkh z = invsqrtpi*(u*cc-v*ss)/sqrt(y); 1132116Sjkh } 1142116Sjkh if(hx<0) return -z; 1152116Sjkh else return z; 1162116Sjkh } 1172116Sjkh if(ix<0x3e400000) { /* |x|<2**-27 */ 1182116Sjkh if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ 1192116Sjkh } 1202116Sjkh z = x*x; 1212116Sjkh r = z*(r00+z*(r01+z*(r02+z*r03))); 1222116Sjkh s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); 1232116Sjkh r *= x; 1242116Sjkh return(x*0.5+r/s); 1252116Sjkh} 1262116Sjkh 1272116Sjkhstatic const double U0[5] = { 1282116Sjkh -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ 1292116Sjkh 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ 1302116Sjkh -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ 1312116Sjkh 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ 1322116Sjkh -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ 1332116Sjkh}; 1342116Sjkhstatic const double V0[5] = { 1352116Sjkh 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ 1362116Sjkh 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ 1372116Sjkh 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ 1382116Sjkh 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ 1392116Sjkh 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ 1402116Sjkh}; 1412116Sjkh 14297413Salfreddouble 14397413Salfred__ieee754_y1(double x) 1442116Sjkh{ 1452116Sjkh double z, s,c,ss,cc,u,v; 1462116Sjkh int32_t hx,ix,lx; 1472116Sjkh 1482116Sjkh EXTRACT_WORDS(hx,lx,x); 1492116Sjkh ix = 0x7fffffff&hx; 1502116Sjkh /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ 151141296Sdas if(ix>=0x7ff00000) return one/(x+x*x); 1522116Sjkh if((ix|lx)==0) return -one/zero; 1532116Sjkh if(hx<0) return zero/zero; 1542116Sjkh if(ix >= 0x40000000) { /* |x| >= 2.0 */ 1552116Sjkh s = sin(x); 1562116Sjkh c = cos(x); 1572116Sjkh ss = -s-c; 1582116Sjkh cc = s-c; 1592116Sjkh if(ix<0x7fe00000) { /* make sure x+x not overflow */ 1602116Sjkh z = cos(x+x); 1612116Sjkh if ((s*c)>zero) cc = z/ss; 1622116Sjkh else ss = z/cc; 1632116Sjkh } 1642116Sjkh /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) 1652116Sjkh * where x0 = x-3pi/4 1662116Sjkh * Better formula: 1672116Sjkh * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) 1682116Sjkh * = 1/sqrt(2) * (sin(x) - cos(x)) 1692116Sjkh * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 1702116Sjkh * = -1/sqrt(2) * (cos(x) + sin(x)) 1712116Sjkh * To avoid cancellation, use 1722116Sjkh * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 1732116Sjkh * to compute the worse one. 1742116Sjkh */ 1752116Sjkh if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); 1762116Sjkh else { 1772116Sjkh u = pone(x); v = qone(x); 1782116Sjkh z = invsqrtpi*(u*ss+v*cc)/sqrt(x); 1792116Sjkh } 1802116Sjkh return z; 181141296Sdas } 1822116Sjkh if(ix<=0x3c900000) { /* x < 2**-54 */ 1832116Sjkh return(-tpi/x); 184141296Sdas } 1852116Sjkh z = x*x; 1862116Sjkh u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); 1872116Sjkh v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); 1882116Sjkh return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); 1892116Sjkh} 1902116Sjkh 1912116Sjkh/* For x >= 8, the asymptotic expansions of pone is 1922116Sjkh * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. 1932116Sjkh * We approximate pone by 1942116Sjkh * pone(x) = 1 + (R/S) 1952116Sjkh * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 1962116Sjkh * S = 1 + ps0*s^2 + ... + ps4*s^10 1972116Sjkh * and 1982116Sjkh * | pone(x)-1-R/S | <= 2 ** ( -60.06) 1992116Sjkh */ 2002116Sjkh 2012116Sjkhstatic const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 2022116Sjkh 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 2032116Sjkh 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ 2042116Sjkh 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ 2052116Sjkh 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ 2062116Sjkh 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ 2072116Sjkh 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ 2082116Sjkh}; 2092116Sjkhstatic const double ps8[5] = { 2102116Sjkh 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ 2112116Sjkh 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ 2122116Sjkh 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ 2132116Sjkh 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ 2142116Sjkh 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ 2152116Sjkh}; 2162116Sjkh 2172116Sjkhstatic const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 2182116Sjkh 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ 2192116Sjkh 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ 2202116Sjkh 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ 2212116Sjkh 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ 2222116Sjkh 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ 2232116Sjkh 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ 2242116Sjkh}; 2252116Sjkhstatic const double ps5[5] = { 2262116Sjkh 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ 2272116Sjkh 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ 2282116Sjkh 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ 2292116Sjkh 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ 2302116Sjkh 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ 2312116Sjkh}; 2322116Sjkh 2332116Sjkhstatic const double pr3[6] = { 2342116Sjkh 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ 2352116Sjkh 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ 2362116Sjkh 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ 2372116Sjkh 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ 2382116Sjkh 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ 2392116Sjkh 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ 2402116Sjkh}; 2412116Sjkhstatic const double ps3[5] = { 2422116Sjkh 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ 2432116Sjkh 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ 2442116Sjkh 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ 2452116Sjkh 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ 2462116Sjkh 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ 2472116Sjkh}; 2482116Sjkh 2492116Sjkhstatic const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 2502116Sjkh 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ 2512116Sjkh 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ 2522116Sjkh 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ 2532116Sjkh 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ 2542116Sjkh 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ 2552116Sjkh 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ 2562116Sjkh}; 2572116Sjkhstatic const double ps2[5] = { 2582116Sjkh 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ 2592116Sjkh 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ 2602116Sjkh 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ 2612116Sjkh 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ 2622116Sjkh 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ 2632116Sjkh}; 2642116Sjkh 2652116Sjkh static double pone(double x) 2662116Sjkh{ 2672116Sjkh const double *p,*q; 2682116Sjkh double z,r,s; 2692116Sjkh int32_t ix; 2702116Sjkh GET_HIGH_WORD(ix,x); 2712116Sjkh ix &= 0x7fffffff; 2722116Sjkh if(ix>=0x40200000) {p = pr8; q= ps8;} 2732116Sjkh else if(ix>=0x40122E8B){p = pr5; q= ps5;} 2742116Sjkh else if(ix>=0x4006DB6D){p = pr3; q= ps3;} 2752116Sjkh else if(ix>=0x40000000){p = pr2; q= ps2;} 2762116Sjkh z = one/(x*x); 2772116Sjkh r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 2782116Sjkh s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); 2792116Sjkh return one+ r/s; 2802116Sjkh} 281141296Sdas 2822116Sjkh 2832116Sjkh/* For x >= 8, the asymptotic expansions of qone is 2842116Sjkh * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. 2852116Sjkh * We approximate pone by 2862116Sjkh * qone(x) = s*(0.375 + (R/S)) 2872116Sjkh * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 2882116Sjkh * S = 1 + qs1*s^2 + ... + qs6*s^12 2892116Sjkh * and 2902116Sjkh * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) 2912116Sjkh */ 2922116Sjkh 2932116Sjkhstatic const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 2942116Sjkh 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 2952116Sjkh -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ 2962116Sjkh -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ 2972116Sjkh -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ 2982116Sjkh -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ 2992116Sjkh -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ 3002116Sjkh}; 3012116Sjkhstatic const double qs8[6] = { 3022116Sjkh 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ 3032116Sjkh 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ 3042116Sjkh 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ 3052116Sjkh 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ 3062116Sjkh 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ 3072116Sjkh -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ 3082116Sjkh}; 3092116Sjkh 3102116Sjkhstatic const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 3112116Sjkh -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ 3122116Sjkh -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ 3132116Sjkh -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ 3142116Sjkh -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ 3152116Sjkh -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ 3162116Sjkh -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ 3172116Sjkh}; 3182116Sjkhstatic const double qs5[6] = { 3192116Sjkh 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ 3202116Sjkh 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ 3212116Sjkh 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ 3222116Sjkh 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ 3232116Sjkh 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ 3242116Sjkh -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ 3252116Sjkh}; 3262116Sjkh 3272116Sjkhstatic const double qr3[6] = { 3282116Sjkh -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ 3292116Sjkh -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ 3302116Sjkh -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ 3312116Sjkh -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ 3322116Sjkh -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ 3332116Sjkh -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ 3342116Sjkh}; 3352116Sjkhstatic const double qs3[6] = { 3362116Sjkh 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ 3372116Sjkh 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ 3382116Sjkh 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ 3392116Sjkh 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ 3402116Sjkh 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ 3412116Sjkh -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ 3422116Sjkh}; 3432116Sjkh 3442116Sjkhstatic const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 3452116Sjkh -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ 3462116Sjkh -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ 3472116Sjkh -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ 3482116Sjkh -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ 3492116Sjkh -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ 3502116Sjkh -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ 3512116Sjkh}; 3522116Sjkhstatic const double qs2[6] = { 3532116Sjkh 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ 3542116Sjkh 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ 3552116Sjkh 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ 3562116Sjkh 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ 3572116Sjkh 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ 3582116Sjkh -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ 3592116Sjkh}; 3602116Sjkh 3612116Sjkh static double qone(double x) 3622116Sjkh{ 3632116Sjkh const double *p,*q; 3642116Sjkh double s,r,z; 3652116Sjkh int32_t ix; 3662116Sjkh GET_HIGH_WORD(ix,x); 3672116Sjkh ix &= 0x7fffffff; 3682116Sjkh if(ix>=0x40200000) {p = qr8; q= qs8;} 3692116Sjkh else if(ix>=0x40122E8B){p = qr5; q= qs5;} 3702116Sjkh else if(ix>=0x4006DB6D){p = qr3; q= qs3;} 3712116Sjkh else if(ix>=0x40000000){p = qr2; q= qs2;} 3722116Sjkh z = one/(x*x); 3732116Sjkh r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 3742116Sjkh s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); 3752116Sjkh return (.375 + r/s)/x; 3762116Sjkh} 377