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e_j1.c
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00001 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
00002  *
00003  * ***** BEGIN LICENSE BLOCK *****
00004  * Version: MPL 1.1/GPL 2.0/LGPL 2.1
00005  *
00006  * The contents of this file are subject to the Mozilla Public License Version
00007  * 1.1 (the "License"); you may not use this file except in compliance with
00008  * the License. You may obtain a copy of the License at
00009  * http://www.mozilla.org/MPL/
00010  *
00011  * Software distributed under the License is distributed on an "AS IS" basis,
00012  * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
00013  * for the specific language governing rights and limitations under the
00014  * License.
00015  *
00016  * The Original Code is Mozilla Communicator client code, released
00017  * March 31, 1998.
00018  *
00019  * The Initial Developer of the Original Code is
00020  * Sun Microsystems, Inc.
00021  * Portions created by the Initial Developer are Copyright (C) 1998
00022  * the Initial Developer. All Rights Reserved.
00023  *
00024  * Contributor(s):
00025  *
00026  * Alternatively, the contents of this file may be used under the terms of
00027  * either of the GNU General Public License Version 2 or later (the "GPL"),
00028  * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
00029  * in which case the provisions of the GPL or the LGPL are applicable instead
00030  * of those above. If you wish to allow use of your version of this file only
00031  * under the terms of either the GPL or the LGPL, and not to allow others to
00032  * use your version of this file under the terms of the MPL, indicate your
00033  * decision by deleting the provisions above and replace them with the notice
00034  * and other provisions required by the GPL or the LGPL. If you do not delete
00035  * the provisions above, a recipient may use your version of this file under
00036  * the terms of any one of the MPL, the GPL or the LGPL.
00037  *
00038  * ***** END LICENSE BLOCK ***** */
00039 
00040 /* @(#)e_j1.c 1.3 95/01/18 */
00041 /*
00042  * ====================================================
00043  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00044  *
00045  * Developed at SunSoft, a Sun Microsystems, Inc. business.
00046  * Permission to use, copy, modify, and distribute this
00047  * software is freely granted, provided that this notice 
00048  * is preserved.
00049  * ====================================================
00050  */
00051 
00052 /* __ieee754_j1(x), __ieee754_y1(x)
00053  * Bessel function of the first and second kinds of order zero.
00054  * Method -- j1(x):
00055  *     1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
00056  *     2. Reduce x to |x| since j1(x)=-j1(-x),  and
00057  *        for x in (0,2)
00058  *            j1(x) = x/2 + x*z*R0/S0,  where z = x*x;
00059  *        (precision:  |j1/x - 1/2 - R0/S0 |<2**-61.51 )
00060  *        for x in (2,inf)
00061  *            j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
00062  *            y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
00063  *        where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
00064  *        as follow:
00065  *            cos(x1) =  cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
00066  *                   =  1/sqrt(2) * (sin(x) - cos(x))
00067  *            sin(x1) =  sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
00068  *                   = -1/sqrt(2) * (sin(x) + cos(x))
00069  *        (To avoid cancellation, use
00070  *            sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
00071  *         to compute the worse one.)
00072  *        
00073  *     3 Special cases
00074  *            j1(nan)= nan
00075  *            j1(0) = 0
00076  *            j1(inf) = 0
00077  *            
00078  * Method -- y1(x):
00079  *     1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN 
00080  *     2. For x<2.
00081  *        Since 
00082  *            y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
00083  *        therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
00084  *        We use the following function to approximate y1,
00085  *            y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
00086  *        where for x in [0,2] (abs err less than 2**-65.89)
00087  *            U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
00088  *            V(z) = 1  + v0[0]*z + ... + v0[4]*z^5
00089  *        Note: For tiny x, 1/x dominate y1 and hence
00090  *            y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
00091  *     3. For x>=2.
00092  *            y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
00093  *        where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
00094  *        by method mentioned above.
00095  */
00096 
00097 #include "fdlibm.h"
00098 
00099 #ifdef __STDC__
00100 static double pone(double), qone(double);
00101 #else
00102 static double pone(), qone();
00103 #endif
00104 
00105 #ifdef __STDC__
00106 static const double 
00107 #else
00108 static double 
00109 #endif
00110 really_big    = 1e300,
00111 one    = 1.0,
00112 invsqrtpi=  5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
00113 tpi      =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
00114        /* R0/S0 on [0,2] */
00115 r00  = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
00116 r01  =  1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
00117 r02  = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
00118 r03  =  4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */
00119 s01  =  1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
00120 s02  =  1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
00121 s03  =  1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
00122 s04  =  5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
00123 s05  =  1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */
00124 
00125 static double zero    = 0.0;
00126 
00127 #ifdef __STDC__
00128        double __ieee754_j1(double x) 
00129 #else
00130        double __ieee754_j1(x) 
00131        double x;
00132 #endif
00133 {
00134         fd_twoints un;
00135        double z, s,c,ss,cc,r,u,v,y;
00136        int hx,ix;
00137 
00138         un.d = x;
00139        hx = __HI(un);
00140        ix = hx&0x7fffffff;
00141        if(ix>=0x7ff00000) return one/x;
00142        y = fd_fabs(x);
00143        if(ix >= 0x40000000) {      /* |x| >= 2.0 */
00144               s = fd_sin(y);
00145               c = fd_cos(y);
00146               ss = -s-c;
00147               cc = s-c;
00148               if(ix<0x7fe00000) {  /* make sure y+y not overflow */
00149                   z = fd_cos(y+y);
00150                   if ((s*c)>zero) cc = z/ss;
00151                   else          ss = z/cc;
00152               }
00153        /*
00154         * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
00155         * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
00156         */
00157               if(ix>0x48000000) z = (invsqrtpi*cc)/fd_sqrt(y);
00158               else {
00159                   u = pone(y); v = qone(y);
00160                   z = invsqrtpi*(u*cc-v*ss)/fd_sqrt(y);
00161               }
00162               if(hx<0) return -z;
00163               else    return  z;
00164        }
00165        if(ix<0x3e400000) {  /* |x|<2**-27 */
00166            if(really_big+x>one) return 0.5*x;/* inexact if x!=0 necessary */
00167        }
00168        z = x*x;
00169        r =  z*(r00+z*(r01+z*(r02+z*r03)));
00170        s =  one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
00171        r *= x;
00172        return(x*0.5+r/s);
00173 }
00174 
00175 #ifdef __STDC__
00176 static const double U0[5] = {
00177 #else
00178 static double U0[5] = {
00179 #endif
00180  -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
00181   5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
00182  -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
00183   2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
00184  -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
00185 };
00186 #ifdef __STDC__
00187 static const double V0[5] = {
00188 #else
00189 static double V0[5] = {
00190 #endif
00191   1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
00192   2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
00193   1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
00194   6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
00195   1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
00196 };
00197 
00198 #ifdef __STDC__
00199        double __ieee754_y1(double x) 
00200 #else
00201        double __ieee754_y1(x) 
00202        double x;
00203 #endif
00204 {
00205         fd_twoints un;
00206        double z, s,c,ss,cc,u,v;
00207        int hx,ix,lx;
00208 
00209         un.d = x;
00210         hx = __HI(un);
00211         ix = 0x7fffffff&hx;
00212         lx = __LO(un);
00213     /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
00214        if(ix>=0x7ff00000) return  one/(x+x*x); 
00215         if((ix|lx)==0) return -one/zero;
00216         if(hx<0) return zero/zero;
00217         if(ix >= 0x40000000) {  /* |x| >= 2.0 */
00218                 s = fd_sin(x);
00219                 c = fd_cos(x);
00220                 ss = -s-c;
00221                 cc = s-c;
00222                 if(ix<0x7fe00000) {  /* make sure x+x not overflow */
00223                     z = fd_cos(x+x);
00224                     if ((s*c)>zero) cc = z/ss;
00225                     else            ss = z/cc;
00226                 }
00227         /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
00228          * where x0 = x-3pi/4
00229          *      Better formula:
00230          *              cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
00231          *                      =  1/sqrt(2) * (sin(x) - cos(x))
00232          *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
00233          *                      = -1/sqrt(2) * (cos(x) + sin(x))
00234          * To avoid cancellation, use
00235          *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
00236          * to compute the worse one.
00237          */
00238                 if(ix>0x48000000) z = (invsqrtpi*ss)/fd_sqrt(x);
00239                 else {
00240                     u = pone(x); v = qone(x);
00241                     z = invsqrtpi*(u*ss+v*cc)/fd_sqrt(x);
00242                 }
00243                 return z;
00244         } 
00245         if(ix<=0x3c900000) {    /* x < 2**-54 */
00246             return(-tpi/x);
00247         } 
00248         z = x*x;
00249         u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
00250         v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
00251         return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
00252 }
00253 
00254 /* For x >= 8, the asymptotic expansions of pone is
00255  *     1 + 15/128 s^2 - 4725/2^15 s^4 - ...,     where s = 1/x.
00256  * We approximate pone by
00257  *     pone(x) = 1 + (R/S)
00258  * where  R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
00259  *       S = 1 + ps0*s^2 + ... + ps4*s^10
00260  * and
00261  *     | pone(x)-1-R/S | <= 2  ** ( -60.06)
00262  */
00263 
00264 #ifdef __STDC__
00265 static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
00266 #else
00267 static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
00268 #endif
00269   0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
00270   1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
00271   1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
00272   4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
00273   3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
00274   7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
00275 };
00276 #ifdef __STDC__
00277 static const double ps8[5] = {
00278 #else
00279 static double ps8[5] = {
00280 #endif
00281   1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
00282   3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
00283   3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
00284   9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
00285   3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
00286 };
00287 
00288 #ifdef __STDC__
00289 static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
00290 #else
00291 static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
00292 #endif
00293   1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
00294   1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
00295   6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
00296   1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
00297   5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
00298   5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
00299 };
00300 #ifdef __STDC__
00301 static const double ps5[5] = {
00302 #else
00303 static double ps5[5] = {
00304 #endif
00305   5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
00306   9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
00307   5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
00308   7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
00309   1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
00310 };
00311 
00312 #ifdef __STDC__
00313 static const double pr3[6] = {
00314 #else
00315 static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
00316 #endif
00317   3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
00318   1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
00319   3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
00320   3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
00321   9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
00322   4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
00323 };
00324 #ifdef __STDC__
00325 static const double ps3[5] = {
00326 #else
00327 static double ps3[5] = {
00328 #endif
00329   3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
00330   3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
00331   1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
00332   8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
00333   1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
00334 };
00335 
00336 #ifdef __STDC__
00337 static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
00338 #else
00339 static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
00340 #endif
00341   1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
00342   1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
00343   2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
00344   1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
00345   1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
00346   5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
00347 };
00348 #ifdef __STDC__
00349 static const double ps2[5] = {
00350 #else
00351 static double ps2[5] = {
00352 #endif
00353   2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
00354   1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
00355   2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
00356   1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
00357   8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
00358 };
00359 
00360 #ifdef __STDC__
00361        static double pone(double x)
00362 #else
00363        static double pone(x)
00364        double x;
00365 #endif
00366 {
00367 #ifdef __STDC__
00368        const double *p,*q;
00369 #else
00370        double *p,*q;
00371 #endif
00372         fd_twoints un;
00373        double z,r,s;
00374         int ix;
00375         un.d = x;
00376         ix = 0x7fffffff&__HI(un);
00377         if(ix>=0x40200000)     {p = pr8; q= ps8;}
00378         else if(ix>=0x40122E8B){p = pr5; q= ps5;}
00379         else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
00380         else if(ix>=0x40000000){p = pr2; q= ps2;}
00381         z = one/(x*x);
00382         r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
00383         s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
00384         return one+ r/s;
00385 }
00386               
00387 
00388 /* For x >= 8, the asymptotic expansions of qone is
00389  *     3/8 s - 105/1024 s^3 - ..., where s = 1/x.
00390  * We approximate pone by
00391  *     qone(x) = s*(0.375 + (R/S))
00392  * where  R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
00393  *       S = 1 + qs1*s^2 + ... + qs6*s^12
00394  * and
00395  *     | qone(x)/s -0.375-R/S | <= 2  ** ( -61.13)
00396  */
00397 
00398 #ifdef __STDC__
00399 static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
00400 #else
00401 static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
00402 #endif
00403   0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
00404  -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
00405  -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
00406  -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
00407  -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
00408  -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
00409 };
00410 #ifdef __STDC__
00411 static const double qs8[6] = {
00412 #else
00413 static double qs8[6] = {
00414 #endif
00415   1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
00416   7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
00417   1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
00418   7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
00419   6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
00420  -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
00421 };
00422 
00423 #ifdef __STDC__
00424 static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
00425 #else
00426 static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
00427 #endif
00428  -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
00429  -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
00430  -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
00431  -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
00432  -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
00433  -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
00434 };
00435 #ifdef __STDC__
00436 static const double qs5[6] = {
00437 #else
00438 static double qs5[6] = {
00439 #endif
00440   8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
00441   1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
00442   1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
00443   4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
00444   2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
00445  -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
00446 };
00447 
00448 #ifdef __STDC__
00449 static const double qr3[6] = {
00450 #else
00451 static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
00452 #endif
00453  -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
00454  -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
00455  -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
00456  -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
00457  -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
00458  -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
00459 };
00460 #ifdef __STDC__
00461 static const double qs3[6] = {
00462 #else
00463 static double qs3[6] = {
00464 #endif
00465   4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
00466   6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
00467   3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
00468   5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
00469   1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
00470  -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
00471 };
00472 
00473 #ifdef __STDC__
00474 static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
00475 #else
00476 static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
00477 #endif
00478  -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
00479  -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
00480  -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
00481  -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
00482  -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
00483  -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
00484 };
00485 #ifdef __STDC__
00486 static const double qs2[6] = {
00487 #else
00488 static double qs2[6] = {
00489 #endif
00490   2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
00491   2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
00492   7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
00493   7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
00494   1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
00495  -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
00496 };
00497 
00498 #ifdef __STDC__
00499        static double qone(double x)
00500 #else
00501        static double qone(x)
00502        double x;
00503 #endif
00504 {
00505 #ifdef __STDC__
00506        const double *p,*q;
00507 #else
00508        double *p,*q;
00509 #endif
00510         fd_twoints un;
00511        double  s,r,z;
00512        int ix;
00513         un.d = x;
00514        ix = 0x7fffffff&__HI(un);
00515        if(ix>=0x40200000)     {p = qr8; q= qs8;}
00516        else if(ix>=0x40122E8B){p = qr5; q= qs5;}
00517        else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
00518        else if(ix>=0x40000000){p = qr2; q= qs2;}
00519        z = one/(x*x);
00520        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
00521        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
00522        return (.375 + r/s)/x;
00523 }