Subversion Repositories Kolibri OS

Rev

Blame | Last modification | View Log | Download | RSS feed

  1. /* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */
  2. /* @(#)e_j1.c 5.1 93/09/24 */
  3. /*
  4.  * ====================================================
  5.  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  6.  *
  7.  * Developed at SunPro, a Sun Microsystems, Inc. business.
  8.  * Permission to use, copy, modify, and distribute this
  9.  * software is freely granted, provided that this notice
  10.  * is preserved.
  11.  * ====================================================
  12.  */
  13.  
  14. #if defined(LIBM_SCCS) && !defined(lint)
  15. static char rcsid[] = "$Id: e_j1.c,v 1.6 1994/08/18 23:05:33 jtc Exp $";
  16. #endif
  17.  
  18. /* __ieee754_j1(x), __ieee754_y1(x)
  19.  * Bessel function of the first and second kinds of order zero.
  20.  * Method -- j1(x):
  21.  *      1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
  22.  *      2. Reduce x to |x| since j1(x)=-j1(-x),  and
  23.  *         for x in (0,2)
  24.  *              j1(x) = x/2 + x*z*R0/S0,  where z = x*x;
  25.  *         (precision:  |j1/x - 1/2 - R0/S0 |<2**-61.51 )
  26.  *         for x in (2,inf)
  27.  *              j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
  28.  *              y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
  29.  *         where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
  30.  *         as follow:
  31.  *              cos(x1) =  cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
  32.  *                      =  1/sqrt(2) * (sin(x) - cos(x))
  33.  *              sin(x1) =  sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
  34.  *                      = -1/sqrt(2) * (sin(x) + cos(x))
  35.  *         (To avoid cancellation, use
  36.  *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
  37.  *          to compute the worse one.)
  38.  *         
  39.  *      3 Special cases
  40.  *              j1(nan)= nan
  41.  *              j1(0) = 0
  42.  *              j1(inf) = 0
  43.  *             
  44.  * Method -- y1(x):
  45.  *      1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
  46.  *      2. For x<2.
  47.  *         Since
  48.  *              y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
  49.  *         therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
  50.  *         We use the following function to approximate y1,
  51.  *              y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
  52.  *         where for x in [0,2] (abs err less than 2**-65.89)
  53.  *              U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
  54.  *              V(z) = 1  + v0[0]*z + ... + v0[4]*z^5
  55.  *         Note: For tiny x, 1/x dominate y1 and hence
  56.  *              y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
  57.  *      3. For x>=2.
  58.  *              y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
  59.  *         where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
  60.  *         by method mentioned above.
  61.  */
  62.  
  63. #include "math.h"
  64. #include "math_private.h"
  65.  
  66. #ifdef __STDC__
  67. static double pone(double), qone(double);
  68. #else
  69. static double pone(), qone();
  70. #endif
  71.  
  72. #ifdef __STDC__
  73. static const double
  74. #else
  75. static double
  76. #endif
  77. huge    = 1e300,
  78. one     = 1.0,
  79. invsqrtpi=  5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
  80. tpi      =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
  81.         /* R0/S0 on [0,2] */
  82. r00  = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
  83. r01  =  1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
  84. r02  = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
  85. r03  =  4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */
  86. s01  =  1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
  87. s02  =  1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
  88. s03  =  1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
  89. s04  =  5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
  90. s05  =  1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */
  91.  
  92. #ifdef __STDC__
  93. static const double zero    = 0.0;
  94. #else
  95. static double zero    = 0.0;
  96. #endif
  97.  
  98. #ifdef __STDC__
  99.         double __ieee754_j1(double x)
  100. #else
  101.         double __ieee754_j1(x)
  102.         double x;
  103. #endif
  104. {
  105.         double z, s,c,ss,cc,r,u,v,y;
  106.         int32_t hx,ix;
  107.  
  108.         GET_HIGH_WORD(hx,x);
  109.         ix = hx&0x7fffffff;
  110.         if(ix>=0x7ff00000) return one/x;
  111.         y = fabs(x);
  112.         if(ix >= 0x40000000) {  /* |x| >= 2.0 */
  113.                 s = sin(y);
  114.                 c = cos(y);
  115.                 ss = -s-c;
  116.                 cc = s-c;
  117.                 if(ix<0x7fe00000) {  /* make sure y+y not overflow */
  118.                     z = cos(y+y);
  119.                     if ((s*c)>zero) cc = z/ss;
  120.                     else            ss = z/cc;
  121.                 }
  122.         /*
  123.          * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
  124.          * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
  125.          */
  126.                 if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y);
  127.                 else {
  128.                     u = pone(y); v = qone(y);
  129.                     z = invsqrtpi*(u*cc-v*ss)/sqrt(y);
  130.                 }
  131.                 if(hx<0) return -z;
  132.                 else     return  z;
  133.         }
  134.         if(ix<0x3e400000) {     /* |x|<2**-27 */
  135.             if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
  136.         }
  137.         z = x*x;
  138.         r =  z*(r00+z*(r01+z*(r02+z*r03)));
  139.         s =  one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
  140.         r *= x;
  141.         return(x*0.5+r/s);
  142. }
  143.  
  144. #ifdef __STDC__
  145. static const double U0[5] = {
  146. #else
  147. static double U0[5] = {
  148. #endif
  149.  -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
  150.   5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
  151.  -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
  152.   2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
  153.  -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
  154. };
  155. #ifdef __STDC__
  156. static const double V0[5] = {
  157. #else
  158. static double V0[5] = {
  159. #endif
  160.   1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
  161.   2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
  162.   1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
  163.   6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
  164.   1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
  165. };
  166.  
  167. #ifdef __STDC__
  168.         double __ieee754_y1(double x)
  169. #else
  170.         double __ieee754_y1(x)
  171.         double x;
  172. #endif
  173. {
  174.         double z, s,c,ss,cc,u,v;
  175.         int32_t hx,ix,lx;
  176.  
  177.         EXTRACT_WORDS(hx,lx,x);
  178.         ix = 0x7fffffff&hx;
  179.     /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
  180.         if(ix>=0x7ff00000) return  one/(x+x*x);
  181.         if((ix|lx)==0) return -one/zero;
  182.         if(hx<0) return zero/zero;
  183.         if(ix >= 0x40000000) {  /* |x| >= 2.0 */
  184.                 s = sin(x);
  185.                 c = cos(x);
  186.                 ss = -s-c;
  187.                 cc = s-c;
  188.                 if(ix<0x7fe00000) {  /* make sure x+x not overflow */
  189.                     z = cos(x+x);
  190.                     if ((s*c)>zero) cc = z/ss;
  191.                     else            ss = z/cc;
  192.                 }
  193.         /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
  194.          * where x0 = x-3pi/4
  195.          *      Better formula:
  196.          *              cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
  197.          *                      =  1/sqrt(2) * (sin(x) - cos(x))
  198.          *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
  199.          *                      = -1/sqrt(2) * (cos(x) + sin(x))
  200.          * To avoid cancellation, use
  201.          *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
  202.          * to compute the worse one.
  203.          */
  204.                 if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);
  205.                 else {
  206.                     u = pone(x); v = qone(x);
  207.                     z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
  208.                 }
  209.                 return z;
  210.         }
  211.         if(ix<=0x3c900000) {    /* x < 2**-54 */
  212.             return(-tpi/x);
  213.         }
  214.         z = x*x;
  215.         u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
  216.         v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
  217.         return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
  218. }
  219.  
  220. /* For x >= 8, the asymptotic expansions of pone is
  221.  *      1 + 15/128 s^2 - 4725/2^15 s^4 - ...,   where s = 1/x.
  222.  * We approximate pone by
  223.  *      pone(x) = 1 + (R/S)
  224.  * where  R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
  225.  *        S = 1 + ps0*s^2 + ... + ps4*s^10
  226.  * and
  227.  *      | pone(x)-1-R/S | <= 2  ** ( -60.06)
  228.  */
  229.  
  230. #ifdef __STDC__
  231. static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  232. #else
  233. static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  234. #endif
  235.   0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  236.   1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
  237.   1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
  238.   4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
  239.   3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
  240.   7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
  241. };
  242. #ifdef __STDC__
  243. static const double ps8[5] = {
  244. #else
  245. static double ps8[5] = {
  246. #endif
  247.   1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
  248.   3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
  249.   3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
  250.   9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
  251.   3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
  252. };
  253.  
  254. #ifdef __STDC__
  255. static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  256. #else
  257. static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  258. #endif
  259.   1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
  260.   1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
  261.   6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
  262.   1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
  263.   5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
  264.   5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
  265. };
  266. #ifdef __STDC__
  267. static const double ps5[5] = {
  268. #else
  269. static double ps5[5] = {
  270. #endif
  271.   5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
  272.   9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
  273.   5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
  274.   7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
  275.   1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
  276. };
  277.  
  278. #ifdef __STDC__
  279. static const double pr3[6] = {
  280. #else
  281. static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
  282. #endif
  283.   3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
  284.   1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
  285.   3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
  286.   3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
  287.   9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
  288.   4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
  289. };
  290. #ifdef __STDC__
  291. static const double ps3[5] = {
  292. #else
  293. static double ps3[5] = {
  294. #endif
  295.   3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
  296.   3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
  297.   1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
  298.   8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
  299.   1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
  300. };
  301.  
  302. #ifdef __STDC__
  303. static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  304. #else
  305. static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  306. #endif
  307.   1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
  308.   1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
  309.   2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
  310.   1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
  311.   1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
  312.   5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
  313. };
  314. #ifdef __STDC__
  315. static const double ps2[5] = {
  316. #else
  317. static double ps2[5] = {
  318. #endif
  319.   2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
  320.   1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
  321.   2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
  322.   1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
  323.   8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
  324. };
  325.  
  326. #ifdef __STDC__
  327.         static double pone(double x)
  328. #else
  329.         static double pone(x)
  330.         double x;
  331. #endif
  332. {
  333. #ifdef __STDC__
  334.         const double *p,*q;
  335. #else
  336.         double *p,*q;
  337. #endif
  338.         double z,r,s;
  339.         int32_t ix;
  340.         GET_HIGH_WORD(ix,x);
  341.         ix &= 0x7fffffff;
  342.         if(ix>=0x40200000)     {p = pr8; q= ps8;}
  343.         else if(ix>=0x40122E8B){p = pr5; q= ps5;}
  344.         else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
  345.         else if(ix>=0x40000000){p = pr2; q= ps2;}
  346.         z = one/(x*x);
  347.         r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
  348.         s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
  349.         return one+ r/s;
  350. }
  351.                
  352.  
  353. /* For x >= 8, the asymptotic expansions of qone is
  354.  *      3/8 s - 105/1024 s^3 - ..., where s = 1/x.
  355.  * We approximate pone by
  356.  *      qone(x) = s*(0.375 + (R/S))
  357.  * where  R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
  358.  *        S = 1 + qs1*s^2 + ... + qs6*s^12
  359.  * and
  360.  *      | qone(x)/s -0.375-R/S | <= 2  ** ( -61.13)
  361.  */
  362.  
  363. #ifdef __STDC__
  364. static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  365. #else
  366. static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  367. #endif
  368.   0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  369.  -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
  370.  -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
  371.  -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
  372.  -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
  373.  -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
  374. };
  375. #ifdef __STDC__
  376. static const double qs8[6] = {
  377. #else
  378. static double qs8[6] = {
  379. #endif
  380.   1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
  381.   7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
  382.   1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
  383.   7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
  384.   6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
  385.  -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
  386. };
  387.  
  388. #ifdef __STDC__
  389. static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  390. #else
  391. static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  392. #endif
  393.  -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
  394.  -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
  395.  -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
  396.  -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
  397.  -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
  398.  -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
  399. };
  400. #ifdef __STDC__
  401. static const double qs5[6] = {
  402. #else
  403. static double qs5[6] = {
  404. #endif
  405.   8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
  406.   1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
  407.   1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
  408.   4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
  409.   2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
  410.  -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
  411. };
  412.  
  413. #ifdef __STDC__
  414. static const double qr3[6] = {
  415. #else
  416. static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
  417. #endif
  418.  -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
  419.  -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
  420.  -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
  421.  -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
  422.  -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
  423.  -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
  424. };
  425. #ifdef __STDC__
  426. static const double qs3[6] = {
  427. #else
  428. static double qs3[6] = {
  429. #endif
  430.   4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
  431.   6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
  432.   3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
  433.   5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
  434.   1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
  435.  -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
  436. };
  437.  
  438. #ifdef __STDC__
  439. static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  440. #else
  441. static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  442. #endif
  443.  -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
  444.  -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
  445.  -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
  446.  -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
  447.  -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
  448.  -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
  449. };
  450. #ifdef __STDC__
  451. static const double qs2[6] = {
  452. #else
  453. static double qs2[6] = {
  454. #endif
  455.   2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
  456.   2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
  457.   7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
  458.   7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
  459.   1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
  460.  -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
  461. };
  462.  
  463. #ifdef __STDC__
  464.         static double qone(double x)
  465. #else
  466.         static double qone(x)
  467.         double x;
  468. #endif
  469. {
  470. #ifdef __STDC__
  471.         const double *p,*q;
  472. #else
  473.         double *p,*q;
  474. #endif
  475.         double  s,r,z;
  476.         int32_t ix;
  477.         GET_HIGH_WORD(ix,x);
  478.         ix &= 0x7fffffff;
  479.         if(ix>=0x40200000)     {p = qr8; q= qs8;}
  480.         else if(ix>=0x40122E8B){p = qr5; q= qs5;}
  481.         else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
  482.         else if(ix>=0x40000000){p = qr2; q= qs2;}
  483.         z = one/(x*x);
  484.         r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
  485.         s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
  486.         return (.375 + r/s)/x;
  487. }
  488.