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glibc  2.9
e_j1.c
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00001 /* @(#)e_j1.c 5.1 93/09/24 */
00002 /*
00003  * ====================================================
00004  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
00005  *
00006  * Developed at SunPro, a Sun Microsystems, Inc. business.
00007  * Permission to use, copy, modify, and distribute this
00008  * software is freely granted, provided that this notice
00009  * is preserved.
00010  * ====================================================
00011  */
00012 /* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/26,
00013    for performance improvement on pipelined processors.
00014 */
00015 
00016 #if defined(LIBM_SCCS) && !defined(lint)
00017 static char rcsid[] = "$NetBSD: e_j1.c,v 1.8 1995/05/10 20:45:27 jtc Exp $";
00018 #endif
00019 
00020 /* __ieee754_j1(x), __ieee754_y1(x)
00021  * Bessel function of the first and second kinds of order zero.
00022  * Method -- j1(x):
00023  *     1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
00024  *     2. Reduce x to |x| since j1(x)=-j1(-x),  and
00025  *        for x in (0,2)
00026  *            j1(x) = x/2 + x*z*R0/S0,  where z = x*x;
00027  *        (precision:  |j1/x - 1/2 - R0/S0 |<2**-61.51 )
00028  *        for x in (2,inf)
00029  *            j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
00030  *            y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
00031  *        where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
00032  *        as follow:
00033  *            cos(x1) =  cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
00034  *                   =  1/sqrt(2) * (sin(x) - cos(x))
00035  *            sin(x1) =  sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
00036  *                   = -1/sqrt(2) * (sin(x) + cos(x))
00037  *        (To avoid cancellation, use
00038  *            sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
00039  *         to compute the worse one.)
00040  *
00041  *     3 Special cases
00042  *            j1(nan)= nan
00043  *            j1(0) = 0
00044  *            j1(inf) = 0
00045  *
00046  * Method -- y1(x):
00047  *     1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
00048  *     2. For x<2.
00049  *        Since
00050  *            y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
00051  *        therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
00052  *        We use the following function to approximate y1,
00053  *            y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
00054  *        where for x in [0,2] (abs err less than 2**-65.89)
00055  *            U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
00056  *            V(z) = 1  + v0[0]*z + ... + v0[4]*z^5
00057  *        Note: For tiny x, 1/x dominate y1 and hence
00058  *            y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
00059  *     3. For x>=2.
00060  *            y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
00061  *        where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
00062  *        by method mentioned above.
00063  */
00064 
00065 #include "math.h"
00066 #include "math_private.h"
00067 
00068 #ifdef __STDC__
00069 static double pone(double), qone(double);
00070 #else
00071 static double pone(), qone();
00072 #endif
00073 
00074 #ifdef __STDC__
00075 static const double
00076 #else
00077 static double
00078 #endif
00079 huge    = 1e300,
00080 one    = 1.0,
00081 invsqrtpi=  5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
00082 tpi      =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
00083        /* R0/S0 on [0,2] */
00084 R[]  = {-6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
00085   1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
00086  -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
00087   4.96727999609584448412e-08}, /* 0x3E6AAAFA, 0x46CA0BD9 */
00088 S[]  =  {0.0, 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
00089   1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
00090   1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
00091   5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
00092   1.23542274426137913908e-11}; /* 0x3DAB2ACF, 0xCFB97ED8 */
00093 
00094 #ifdef __STDC__
00095 static const double zero    = 0.0;
00096 #else
00097 static double zero    = 0.0;
00098 #endif
00099 
00100 #ifdef __STDC__
00101        double __ieee754_j1(double x)
00102 #else
00103        double __ieee754_j1(x)
00104        double x;
00105 #endif
00106 {
00107        double z, s,c,ss,cc,r,u,v,y,r1,r2,s1,s2,s3,z2,z4;
00108        int32_t hx,ix;
00109 
00110        GET_HIGH_WORD(hx,x);
00111        ix = hx&0x7fffffff;
00112        if(ix>=0x7ff00000) return one/x;
00113        y = fabs(x);
00114        if(ix >= 0x40000000) {      /* |x| >= 2.0 */
00115               __sincos (y, &s, &c);
00116               ss = -s-c;
00117               cc = s-c;
00118               if(ix<0x7fe00000) {  /* make sure y+y not overflow */
00119                   z = __cos(y+y);
00120                   if ((s*c)>zero) cc = z/ss;
00121                   else          ss = z/cc;
00122               }
00123        /*
00124         * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
00125         * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
00126         */
00127               if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(y);
00128               else {
00129                   u = pone(y); v = qone(y);
00130                   z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(y);
00131               }
00132               if(hx<0) return -z;
00133               else    return  z;
00134        }
00135        if(ix<0x3e400000) {  /* |x|<2**-27 */
00136            if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
00137        }
00138        z = x*x;
00139 #ifdef DO_NOT_USE_THIS
00140        r =  z*(r00+z*(r01+z*(r02+z*r03)));
00141        s =  one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
00142        r *= x;
00143 #else
00144        r1 = z*R[0]; z2=z*z;
00145        r2 = R[1]+z*R[2]; z4=z2*z2;
00146        r = r1 + z2*r2 + z4*R[3];
00147        r *= x;
00148        s1 = one+z*S[1];
00149        s2 = S[2]+z*S[3];
00150        s3 = S[4]+z*S[5];
00151        s = s1 + z2*s2 + z4*s3;
00152 #endif
00153        return(x*0.5+r/s);
00154 }
00155 
00156 #ifdef __STDC__
00157 static const double U0[5] = {
00158 #else
00159 static double U0[5] = {
00160 #endif
00161  -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
00162   5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
00163  -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
00164   2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
00165  -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
00166 };
00167 #ifdef __STDC__
00168 static const double V0[5] = {
00169 #else
00170 static double V0[5] = {
00171 #endif
00172   1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
00173   2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
00174   1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
00175   6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
00176   1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
00177 };
00178 
00179 #ifdef __STDC__
00180        double __ieee754_y1(double x)
00181 #else
00182        double __ieee754_y1(x)
00183        double x;
00184 #endif
00185 {
00186        double z, s,c,ss,cc,u,v,u1,u2,v1,v2,v3,z2,z4;
00187        int32_t hx,ix,lx;
00188 
00189        EXTRACT_WORDS(hx,lx,x);
00190         ix = 0x7fffffff&hx;
00191     /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
00192        if(ix>=0x7ff00000) return  one/(x+x*x);
00193         if((ix|lx)==0) return -HUGE_VAL+x; /* -inf and overflow exception.  */;
00194         if(hx<0) return zero/(zero*x);
00195         if(ix >= 0x40000000) {  /* |x| >= 2.0 */
00196               __sincos (x, &s, &c);
00197                 ss = -s-c;
00198                 cc = s-c;
00199                 if(ix<0x7fe00000) {  /* make sure x+x not overflow */
00200                     z = __cos(x+x);
00201                     if ((s*c)>zero) cc = z/ss;
00202                     else            ss = z/cc;
00203                 }
00204         /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
00205          * where x0 = x-3pi/4
00206          *      Better formula:
00207          *              cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
00208          *                      =  1/sqrt(2) * (sin(x) - cos(x))
00209          *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
00210          *                      = -1/sqrt(2) * (cos(x) + sin(x))
00211          * To avoid cancellation, use
00212          *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
00213          * to compute the worse one.
00214          */
00215                 if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x);
00216                 else {
00217                     u = pone(x); v = qone(x);
00218                     z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x);
00219                 }
00220                 return z;
00221         }
00222         if(ix<=0x3c900000) {    /* x < 2**-54 */
00223             return(-tpi/x);
00224         }
00225         z = x*x;
00226 #ifdef DO_NOT_USE_THIS
00227         u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
00228         v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
00229 #else
00230        u1 = U0[0]+z*U0[1];z2=z*z;
00231        u2 = U0[2]+z*U0[3];z4=z2*z2;
00232        u  = u1 + z2*u2 + z4*U0[4];
00233        v1 = one+z*V0[0];
00234        v2 = V0[1]+z*V0[2];
00235        v3 = V0[3]+z*V0[4];
00236        v = v1 + z2*v2 + z4*v3;
00237 #endif
00238         return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
00239 }
00240 
00241 /* For x >= 8, the asymptotic expansions of pone is
00242  *     1 + 15/128 s^2 - 4725/2^15 s^4 - ...,     where s = 1/x.
00243  * We approximate pone by
00244  *     pone(x) = 1 + (R/S)
00245  * where  R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
00246  *       S = 1 + ps0*s^2 + ... + ps4*s^10
00247  * and
00248  *     | pone(x)-1-R/S | <= 2  ** ( -60.06)
00249  */
00250 
00251 #ifdef __STDC__
00252 static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
00253 #else
00254 static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
00255 #endif
00256   0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
00257   1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
00258   1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
00259   4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
00260   3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
00261   7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
00262 };
00263 #ifdef __STDC__
00264 static const double ps8[5] = {
00265 #else
00266 static double ps8[5] = {
00267 #endif
00268   1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
00269   3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
00270   3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
00271   9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
00272   3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
00273 };
00274 
00275 #ifdef __STDC__
00276 static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
00277 #else
00278 static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
00279 #endif
00280   1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
00281   1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
00282   6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
00283   1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
00284   5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
00285   5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
00286 };
00287 #ifdef __STDC__
00288 static const double ps5[5] = {
00289 #else
00290 static double ps5[5] = {
00291 #endif
00292   5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
00293   9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
00294   5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
00295   7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
00296   1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
00297 };
00298 
00299 #ifdef __STDC__
00300 static const double pr3[6] = {
00301 #else
00302 static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
00303 #endif
00304   3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
00305   1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
00306   3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
00307   3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
00308   9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
00309   4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
00310 };
00311 #ifdef __STDC__
00312 static const double ps3[5] = {
00313 #else
00314 static double ps3[5] = {
00315 #endif
00316   3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
00317   3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
00318   1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
00319   8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
00320   1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
00321 };
00322 
00323 #ifdef __STDC__
00324 static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
00325 #else
00326 static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
00327 #endif
00328   1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
00329   1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
00330   2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
00331   1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
00332   1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
00333   5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
00334 };
00335 #ifdef __STDC__
00336 static const double ps2[5] = {
00337 #else
00338 static double ps2[5] = {
00339 #endif
00340   2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
00341   1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
00342   2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
00343   1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
00344   8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
00345 };
00346 
00347 #ifdef __STDC__
00348        static double pone(double x)
00349 #else
00350        static double pone(x)
00351        double x;
00352 #endif
00353 {
00354 #ifdef __STDC__
00355        const double *p,*q;
00356 #else
00357        double *p,*q;
00358 #endif
00359        double z,r,s,r1,r2,r3,s1,s2,s3,z2,z4;
00360         int32_t ix;
00361        GET_HIGH_WORD(ix,x);
00362        ix &= 0x7fffffff;
00363         if(ix>=0x40200000)     {p = pr8; q= ps8;}
00364         else if(ix>=0x40122E8B){p = pr5; q= ps5;}
00365         else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
00366         else if(ix>=0x40000000){p = pr2; q= ps2;}
00367         z = one/(x*x);
00368 #ifdef DO_NOT_USE_THIS
00369         r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
00370         s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
00371 #else
00372        r1 = p[0]+z*p[1]; z2=z*z;
00373        r2 = p[2]+z*p[3]; z4=z2*z2;
00374        r3 = p[4]+z*p[5];
00375        r = r1 + z2*r2 + z4*r3;
00376        s1 = one+z*q[0];
00377        s2 = q[1]+z*q[2];
00378        s3 = q[3]+z*q[4];
00379        s = s1 + z2*s2 + z4*s3;
00380 #endif
00381         return one+ r/s;
00382 }
00383 
00384 
00385 /* For x >= 8, the asymptotic expansions of qone is
00386  *     3/8 s - 105/1024 s^3 - ..., where s = 1/x.
00387  * We approximate pone by
00388  *     qone(x) = s*(0.375 + (R/S))
00389  * where  R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
00390  *       S = 1 + qs1*s^2 + ... + qs6*s^12
00391  * and
00392  *     | qone(x)/s -0.375-R/S | <= 2  ** ( -61.13)
00393  */
00394 
00395 #ifdef __STDC__
00396 static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
00397 #else
00398 static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
00399 #endif
00400   0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
00401  -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
00402  -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
00403  -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
00404  -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
00405  -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
00406 };
00407 #ifdef __STDC__
00408 static const double qs8[6] = {
00409 #else
00410 static double qs8[6] = {
00411 #endif
00412   1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
00413   7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
00414   1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
00415   7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
00416   6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
00417  -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
00418 };
00419 
00420 #ifdef __STDC__
00421 static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
00422 #else
00423 static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
00424 #endif
00425  -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
00426  -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
00427  -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
00428  -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
00429  -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
00430  -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
00431 };
00432 #ifdef __STDC__
00433 static const double qs5[6] = {
00434 #else
00435 static double qs5[6] = {
00436 #endif
00437   8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
00438   1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
00439   1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
00440   4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
00441   2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
00442  -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
00443 };
00444 
00445 #ifdef __STDC__
00446 static const double qr3[6] = {
00447 #else
00448 static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
00449 #endif
00450  -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
00451  -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
00452  -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
00453  -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
00454  -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
00455  -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
00456 };
00457 #ifdef __STDC__
00458 static const double qs3[6] = {
00459 #else
00460 static double qs3[6] = {
00461 #endif
00462   4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
00463   6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
00464   3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
00465   5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
00466   1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
00467  -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
00468 };
00469 
00470 #ifdef __STDC__
00471 static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
00472 #else
00473 static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
00474 #endif
00475  -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
00476  -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
00477  -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
00478  -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
00479  -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
00480  -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
00481 };
00482 #ifdef __STDC__
00483 static const double qs2[6] = {
00484 #else
00485 static double qs2[6] = {
00486 #endif
00487   2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
00488   2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
00489   7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
00490   7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
00491   1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
00492  -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
00493 };
00494 
00495 #ifdef __STDC__
00496        static double qone(double x)
00497 #else
00498        static double qone(x)
00499        double x;
00500 #endif
00501 {
00502 #ifdef __STDC__
00503        const double *p,*q;
00504 #else
00505        double *p,*q;
00506 #endif
00507        double  s,r,z,r1,r2,r3,s1,s2,s3,z2,z4,z6;
00508        int32_t ix;
00509        GET_HIGH_WORD(ix,x);
00510        ix &= 0x7fffffff;
00511        if(ix>=0x40200000)     {p = qr8; q= qs8;}
00512        else if(ix>=0x40122E8B){p = qr5; q= qs5;}
00513        else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
00514        else if(ix>=0x40000000){p = qr2; q= qs2;}
00515        z = one/(x*x);
00516 #ifdef DO_NOT_USE_THIS
00517        r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
00518        s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
00519 #else
00520        r1 = p[0]+z*p[1]; z2=z*z;
00521        r2 = p[2]+z*p[3]; z4=z2*z2;
00522        r3 = p[4]+z*p[5]; z6=z4*z2;
00523        r = r1 + z2*r2 + z4*r3;
00524        s1 = one+z*q[0];
00525        s2 = q[1]+z*q[2];
00526        s3 = q[3]+z*q[4];
00527        s = s1 + z2*s2 + z4*s3 + z6*q[5];
00528 #endif
00529        return (.375 + r/s)/x;
00530 }