e_j0.c revision 50476
12116Sjkh/* @(#)e_j0.c 5.1 93/09/24 */ 22116Sjkh/* 32116Sjkh * ==================================================== 42116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 52116Sjkh * 62116Sjkh * Developed at SunPro, a Sun Microsystems, Inc. business. 72116Sjkh * Permission to use, copy, modify, and distribute this 88870Srgrimes * software is freely granted, provided that this notice 92116Sjkh * is preserved. 102116Sjkh * ==================================================== 112116Sjkh */ 122116Sjkh 132116Sjkh#ifndef lint 1450476Speterstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/e_j0.c 50476 1999-08-28 00:22:10Z peter $"; 152116Sjkh#endif 162116Sjkh 172116Sjkh/* __ieee754_j0(x), __ieee754_y0(x) 182116Sjkh * Bessel function of the first and second kinds of order zero. 192116Sjkh * Method -- j0(x): 202116Sjkh * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... 212116Sjkh * 2. Reduce x to |x| since j0(x)=j0(-x), and 222116Sjkh * for x in (0,2) 232116Sjkh * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; 242116Sjkh * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) 252116Sjkh * for x in (2,inf) 262116Sjkh * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) 272116Sjkh * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) 282116Sjkh * as follow: 292116Sjkh * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) 302116Sjkh * = 1/sqrt(2) * (cos(x) + sin(x)) 312116Sjkh * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) 322116Sjkh * = 1/sqrt(2) * (sin(x) - cos(x)) 332116Sjkh * (To avoid cancellation, use 342116Sjkh * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 352116Sjkh * to compute the worse one.) 368870Srgrimes * 372116Sjkh * 3 Special cases 382116Sjkh * j0(nan)= nan 392116Sjkh * j0(0) = 1 402116Sjkh * j0(inf) = 0 418870Srgrimes * 422116Sjkh * Method -- y0(x): 432116Sjkh * 1. For x<2. 448870Srgrimes * Since 452116Sjkh * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) 462116Sjkh * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. 472116Sjkh * We use the following function to approximate y0, 482116Sjkh * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 498870Srgrimes * where 502116Sjkh * U(z) = u00 + u01*z + ... + u06*z^6 512116Sjkh * V(z) = 1 + v01*z + ... + v04*z^4 522116Sjkh * with absolute approximation error bounded by 2**-72. 532116Sjkh * Note: For tiny x, U/V = u0 and j0(x)~1, hence 542116Sjkh * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) 552116Sjkh * 2. For x>=2. 562116Sjkh * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) 572116Sjkh * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) 582116Sjkh * by the method mentioned above. 592116Sjkh * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. 602116Sjkh */ 612116Sjkh 622116Sjkh#include "math.h" 632116Sjkh#include "math_private.h" 642116Sjkh 652116Sjkh#ifdef __STDC__ 662116Sjkhstatic double pzero(double), qzero(double); 672116Sjkh#else 682116Sjkhstatic double pzero(), qzero(); 692116Sjkh#endif 702116Sjkh 712116Sjkh#ifdef __STDC__ 728870Srgrimesstatic const double 732116Sjkh#else 748870Srgrimesstatic double 752116Sjkh#endif 762116Sjkhhuge = 1e300, 772116Sjkhone = 1.0, 782116Sjkhinvsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ 792116Sjkhtpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 802116Sjkh /* R0/S0 on [0, 2.00] */ 812116SjkhR02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ 822116SjkhR03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ 832116SjkhR04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ 842116SjkhR05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ 852116SjkhS01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ 862116SjkhS02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ 872116SjkhS03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ 882116SjkhS04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ 892116Sjkh 902116Sjkh#ifdef __STDC__ 912116Sjkhstatic const double zero = 0.0; 922116Sjkh#else 932116Sjkhstatic double zero = 0.0; 942116Sjkh#endif 952116Sjkh 962116Sjkh#ifdef __STDC__ 978870Srgrimes double __ieee754_j0(double x) 982116Sjkh#else 998870Srgrimes double __ieee754_j0(x) 1002116Sjkh double x; 1012116Sjkh#endif 1022116Sjkh{ 1032116Sjkh double z, s,c,ss,cc,r,u,v; 1042116Sjkh int32_t hx,ix; 1052116Sjkh 1062116Sjkh GET_HIGH_WORD(hx,x); 1072116Sjkh ix = hx&0x7fffffff; 1082116Sjkh if(ix>=0x7ff00000) return one/(x*x); 1092116Sjkh x = fabs(x); 1102116Sjkh if(ix >= 0x40000000) { /* |x| >= 2.0 */ 1112116Sjkh s = sin(x); 1122116Sjkh c = cos(x); 1132116Sjkh ss = s-c; 1142116Sjkh cc = s+c; 1152116Sjkh if(ix<0x7fe00000) { /* make sure x+x not overflow */ 1162116Sjkh z = -cos(x+x); 1172116Sjkh if ((s*c)<zero) cc = z/ss; 1182116Sjkh else ss = z/cc; 1192116Sjkh } 1202116Sjkh /* 1212116Sjkh * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) 1222116Sjkh * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) 1232116Sjkh */ 1242116Sjkh if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(x); 1252116Sjkh else { 1262116Sjkh u = pzero(x); v = qzero(x); 1272116Sjkh z = invsqrtpi*(u*cc-v*ss)/sqrt(x); 1282116Sjkh } 1292116Sjkh return z; 1302116Sjkh } 1312116Sjkh if(ix<0x3f200000) { /* |x| < 2**-13 */ 1322116Sjkh if(huge+x>one) { /* raise inexact if x != 0 */ 1332116Sjkh if(ix<0x3e400000) return one; /* |x|<2**-27 */ 1342116Sjkh else return one - 0.25*x*x; 1352116Sjkh } 1362116Sjkh } 1372116Sjkh z = x*x; 1382116Sjkh r = z*(R02+z*(R03+z*(R04+z*R05))); 1392116Sjkh s = one+z*(S01+z*(S02+z*(S03+z*S04))); 1402116Sjkh if(ix < 0x3FF00000) { /* |x| < 1.00 */ 1412116Sjkh return one + z*(-0.25+(r/s)); 1422116Sjkh } else { 1432116Sjkh u = 0.5*x; 1442116Sjkh return((one+u)*(one-u)+z*(r/s)); 1452116Sjkh } 1462116Sjkh} 1472116Sjkh 1482116Sjkh#ifdef __STDC__ 1492116Sjkhstatic const double 1502116Sjkh#else 1512116Sjkhstatic double 1522116Sjkh#endif 1532116Sjkhu00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ 1542116Sjkhu01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ 1552116Sjkhu02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ 1562116Sjkhu03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ 1572116Sjkhu04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ 1582116Sjkhu05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ 1592116Sjkhu06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ 1602116Sjkhv01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ 1612116Sjkhv02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ 1622116Sjkhv03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ 1632116Sjkhv04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ 1642116Sjkh 1652116Sjkh#ifdef __STDC__ 1668870Srgrimes double __ieee754_y0(double x) 1672116Sjkh#else 1688870Srgrimes double __ieee754_y0(x) 1692116Sjkh double x; 1702116Sjkh#endif 1712116Sjkh{ 1722116Sjkh double z, s,c,ss,cc,u,v; 1732116Sjkh int32_t hx,ix,lx; 1742116Sjkh 1752116Sjkh EXTRACT_WORDS(hx,lx,x); 1762116Sjkh ix = 0x7fffffff&hx; 1772116Sjkh /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ 1788870Srgrimes if(ix>=0x7ff00000) return one/(x+x*x); 1792116Sjkh if((ix|lx)==0) return -one/zero; 1802116Sjkh if(hx<0) return zero/zero; 1812116Sjkh if(ix >= 0x40000000) { /* |x| >= 2.0 */ 1822116Sjkh /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) 1832116Sjkh * where x0 = x-pi/4 1842116Sjkh * Better formula: 1852116Sjkh * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) 1862116Sjkh * = 1/sqrt(2) * (sin(x) + cos(x)) 1872116Sjkh * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 1882116Sjkh * = 1/sqrt(2) * (sin(x) - cos(x)) 1892116Sjkh * To avoid cancellation, use 1902116Sjkh * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 1912116Sjkh * to compute the worse one. 1922116Sjkh */ 1932116Sjkh s = sin(x); 1942116Sjkh c = cos(x); 1952116Sjkh ss = s-c; 1962116Sjkh cc = s+c; 1972116Sjkh /* 1982116Sjkh * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) 1992116Sjkh * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) 2002116Sjkh */ 2012116Sjkh if(ix<0x7fe00000) { /* make sure x+x not overflow */ 2022116Sjkh z = -cos(x+x); 2032116Sjkh if ((s*c)<zero) cc = z/ss; 2042116Sjkh else ss = z/cc; 2052116Sjkh } 2062116Sjkh if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); 2072116Sjkh else { 2082116Sjkh u = pzero(x); v = qzero(x); 2092116Sjkh z = invsqrtpi*(u*ss+v*cc)/sqrt(x); 2102116Sjkh } 2112116Sjkh return z; 2122116Sjkh } 2132116Sjkh if(ix<=0x3e400000) { /* x < 2**-27 */ 2142116Sjkh return(u00 + tpi*__ieee754_log(x)); 2152116Sjkh } 2162116Sjkh z = x*x; 2172116Sjkh u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); 2182116Sjkh v = one+z*(v01+z*(v02+z*(v03+z*v04))); 2192116Sjkh return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); 2202116Sjkh} 2212116Sjkh 2222116Sjkh/* The asymptotic expansions of pzero is 2232116Sjkh * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. 2242116Sjkh * For x >= 2, We approximate pzero by 2252116Sjkh * pzero(x) = 1 + (R/S) 2262116Sjkh * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 2272116Sjkh * S = 1 + pS0*s^2 + ... + pS4*s^10 2282116Sjkh * and 2292116Sjkh * | pzero(x)-1-R/S | <= 2 ** ( -60.26) 2302116Sjkh */ 2312116Sjkh#ifdef __STDC__ 2322116Sjkhstatic const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 2332116Sjkh#else 2342116Sjkhstatic double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 2352116Sjkh#endif 2362116Sjkh 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 2372116Sjkh -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ 2382116Sjkh -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ 2392116Sjkh -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ 2402116Sjkh -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ 2412116Sjkh -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ 2422116Sjkh}; 2432116Sjkh#ifdef __STDC__ 2442116Sjkhstatic const double pS8[5] = { 2452116Sjkh#else 2462116Sjkhstatic double pS8[5] = { 2472116Sjkh#endif 2482116Sjkh 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ 2492116Sjkh 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ 2502116Sjkh 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ 2512116Sjkh 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ 2522116Sjkh 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ 2532116Sjkh}; 2542116Sjkh 2552116Sjkh#ifdef __STDC__ 2562116Sjkhstatic const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 2572116Sjkh#else 2582116Sjkhstatic double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 2592116Sjkh#endif 2602116Sjkh -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ 2612116Sjkh -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ 2622116Sjkh -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ 2632116Sjkh -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ 2642116Sjkh -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ 2652116Sjkh -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ 2662116Sjkh}; 2672116Sjkh#ifdef __STDC__ 2682116Sjkhstatic const double pS5[5] = { 2692116Sjkh#else 2702116Sjkhstatic double pS5[5] = { 2712116Sjkh#endif 2722116Sjkh 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ 2732116Sjkh 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ 2742116Sjkh 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ 2752116Sjkh 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ 2762116Sjkh 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ 2772116Sjkh}; 2782116Sjkh 2792116Sjkh#ifdef __STDC__ 2802116Sjkhstatic const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 2812116Sjkh#else 2822116Sjkhstatic double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 2832116Sjkh#endif 2842116Sjkh -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ 2852116Sjkh -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ 2862116Sjkh -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ 2872116Sjkh -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ 2882116Sjkh -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ 2892116Sjkh -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ 2902116Sjkh}; 2912116Sjkh#ifdef __STDC__ 2922116Sjkhstatic const double pS3[5] = { 2932116Sjkh#else 2942116Sjkhstatic double pS3[5] = { 2952116Sjkh#endif 2962116Sjkh 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ 2972116Sjkh 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ 2982116Sjkh 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ 2992116Sjkh 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ 3002116Sjkh 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ 3012116Sjkh}; 3022116Sjkh 3032116Sjkh#ifdef __STDC__ 3042116Sjkhstatic const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 3052116Sjkh#else 3062116Sjkhstatic double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 3072116Sjkh#endif 3082116Sjkh -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ 3092116Sjkh -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ 3102116Sjkh -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ 3112116Sjkh -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ 3122116Sjkh -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ 3132116Sjkh -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ 3142116Sjkh}; 3152116Sjkh#ifdef __STDC__ 3162116Sjkhstatic const double pS2[5] = { 3172116Sjkh#else 3182116Sjkhstatic double pS2[5] = { 3192116Sjkh#endif 3202116Sjkh 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ 3212116Sjkh 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ 3222116Sjkh 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ 3232116Sjkh 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ 3242116Sjkh 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ 3252116Sjkh}; 3262116Sjkh 3272116Sjkh#ifdef __STDC__ 3282116Sjkh static double pzero(double x) 3292116Sjkh#else 3302116Sjkh static double pzero(x) 3312116Sjkh double x; 3322116Sjkh#endif 3332116Sjkh{ 3342116Sjkh#ifdef __STDC__ 3352116Sjkh const double *p,*q; 3362116Sjkh#else 3372116Sjkh double *p,*q; 3382116Sjkh#endif 3392116Sjkh double z,r,s; 3402116Sjkh int32_t ix; 3412116Sjkh GET_HIGH_WORD(ix,x); 3422116Sjkh ix &= 0x7fffffff; 3432116Sjkh if(ix>=0x40200000) {p = pR8; q= pS8;} 3442116Sjkh else if(ix>=0x40122E8B){p = pR5; q= pS5;} 3452116Sjkh else if(ix>=0x4006DB6D){p = pR3; q= pS3;} 3462116Sjkh else if(ix>=0x40000000){p = pR2; q= pS2;} 3472116Sjkh z = one/(x*x); 3482116Sjkh r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 3492116Sjkh s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); 3502116Sjkh return one+ r/s; 3512116Sjkh} 3522116Sjkh 3538870Srgrimes 3542116Sjkh/* For x >= 8, the asymptotic expansions of qzero is 3552116Sjkh * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. 3562116Sjkh * We approximate pzero by 3572116Sjkh * qzero(x) = s*(-1.25 + (R/S)) 3582116Sjkh * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 3592116Sjkh * S = 1 + qS0*s^2 + ... + qS5*s^12 3602116Sjkh * and 3612116Sjkh * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) 3622116Sjkh */ 3632116Sjkh#ifdef __STDC__ 3642116Sjkhstatic const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 3652116Sjkh#else 3662116Sjkhstatic double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 3672116Sjkh#endif 3682116Sjkh 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 3692116Sjkh 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ 3702116Sjkh 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ 3712116Sjkh 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ 3722116Sjkh 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ 3732116Sjkh 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ 3742116Sjkh}; 3752116Sjkh#ifdef __STDC__ 3762116Sjkhstatic const double qS8[6] = { 3772116Sjkh#else 3782116Sjkhstatic double qS8[6] = { 3792116Sjkh#endif 3802116Sjkh 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ 3812116Sjkh 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ 3822116Sjkh 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ 3832116Sjkh 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ 3842116Sjkh 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ 3852116Sjkh -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ 3862116Sjkh}; 3872116Sjkh 3882116Sjkh#ifdef __STDC__ 3892116Sjkhstatic const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 3902116Sjkh#else 3912116Sjkhstatic double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 3922116Sjkh#endif 3932116Sjkh 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ 3942116Sjkh 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ 3952116Sjkh 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ 3962116Sjkh 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ 3972116Sjkh 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ 3982116Sjkh 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ 3992116Sjkh}; 4002116Sjkh#ifdef __STDC__ 4012116Sjkhstatic const double qS5[6] = { 4022116Sjkh#else 4032116Sjkhstatic double qS5[6] = { 4042116Sjkh#endif 4052116Sjkh 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ 4062116Sjkh 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ 4072116Sjkh 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ 4082116Sjkh 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ 4092116Sjkh 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ 4102116Sjkh -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ 4112116Sjkh}; 4122116Sjkh 4132116Sjkh#ifdef __STDC__ 4142116Sjkhstatic const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 4152116Sjkh#else 4162116Sjkhstatic double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 4172116Sjkh#endif 4182116Sjkh 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ 4192116Sjkh 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ 4202116Sjkh 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ 4212116Sjkh 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ 4222116Sjkh 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ 4232116Sjkh 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ 4242116Sjkh}; 4252116Sjkh#ifdef __STDC__ 4262116Sjkhstatic const double qS3[6] = { 4272116Sjkh#else 4282116Sjkhstatic double qS3[6] = { 4292116Sjkh#endif 4302116Sjkh 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ 4312116Sjkh 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ 4322116Sjkh 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ 4332116Sjkh 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ 4342116Sjkh 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ 4352116Sjkh -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ 4362116Sjkh}; 4372116Sjkh 4382116Sjkh#ifdef __STDC__ 4392116Sjkhstatic const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 4402116Sjkh#else 4412116Sjkhstatic double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 4422116Sjkh#endif 4432116Sjkh 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ 4442116Sjkh 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ 4452116Sjkh 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ 4462116Sjkh 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ 4472116Sjkh 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ 4482116Sjkh 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ 4492116Sjkh}; 4502116Sjkh#ifdef __STDC__ 4512116Sjkhstatic const double qS2[6] = { 4522116Sjkh#else 4532116Sjkhstatic double qS2[6] = { 4542116Sjkh#endif 4552116Sjkh 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ 4562116Sjkh 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ 4572116Sjkh 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ 4582116Sjkh 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ 4592116Sjkh 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ 4602116Sjkh -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ 4612116Sjkh}; 4622116Sjkh 4632116Sjkh#ifdef __STDC__ 4642116Sjkh static double qzero(double x) 4652116Sjkh#else 4662116Sjkh static double qzero(x) 4672116Sjkh double x; 4682116Sjkh#endif 4692116Sjkh{ 4702116Sjkh#ifdef __STDC__ 4712116Sjkh const double *p,*q; 4722116Sjkh#else 4732116Sjkh double *p,*q; 4742116Sjkh#endif 4752116Sjkh double s,r,z; 4762116Sjkh int32_t ix; 4772116Sjkh GET_HIGH_WORD(ix,x); 4782116Sjkh ix &= 0x7fffffff; 4792116Sjkh if(ix>=0x40200000) {p = qR8; q= qS8;} 4802116Sjkh else if(ix>=0x40122E8B){p = qR5; q= qS5;} 4812116Sjkh else if(ix>=0x4006DB6D){p = qR3; q= qS3;} 4822116Sjkh else if(ix>=0x40000000){p = qR2; q= qS2;} 4832116Sjkh z = one/(x*x); 4842116Sjkh r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 4852116Sjkh s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); 4862116Sjkh return (-.125 + r/s)/x; 4872116Sjkh} 488