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_j0.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_j0.c,v 1.6 1994/08/18 23:05:29 jtc Exp $";
  16. #endif
  17.  
  18. /* __ieee754_j0(x), __ieee754_y0(x)
  19.  * Bessel function of the first and second kinds of order zero.
  20.  * Method -- j0(x):
  21.  *      1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ...
  22.  *      2. Reduce x to |x| since j0(x)=j0(-x),  and
  23.  *         for x in (0,2)
  24.  *              j0(x) = 1-z/4+ z^2*R0/S0,  where z = x*x;
  25.  *         (precision:  |j0-1+z/4-z^2R0/S0 |<2**-63.67 )
  26.  *         for x in (2,inf)
  27.  *              j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0))
  28.  *         where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
  29.  *         as follow:
  30.  *              cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
  31.  *                      = 1/sqrt(2) * (cos(x) + sin(x))
  32.  *              sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4)
  33.  *                      = 1/sqrt(2) * (sin(x) - cos(x))
  34.  *         (To avoid cancellation, use
  35.  *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
  36.  *          to compute the worse one.)
  37.  *         
  38.  *      3 Special cases
  39.  *              j0(nan)= nan
  40.  *              j0(0) = 1
  41.  *              j0(inf) = 0
  42.  *             
  43.  * Method -- y0(x):
  44.  *      1. For x<2.
  45.  *         Since
  46.  *              y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...)
  47.  *         therefore y0(x)-2/pi*j0(x)*ln(x) is an even function.
  48.  *         We use the following function to approximate y0,
  49.  *              y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2
  50.  *         where
  51.  *              U(z) = u00 + u01*z + ... + u06*z^6
  52.  *              V(z) = 1  + v01*z + ... + v04*z^4
  53.  *         with absolute approximation error bounded by 2**-72.
  54.  *         Note: For tiny x, U/V = u0 and j0(x)~1, hence
  55.  *              y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27)
  56.  *      2. For x>=2.
  57.  *              y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0))
  58.  *         where x0 = x-pi/4. It is better to compute sin(x0),cos(x0)
  59.  *         by the method mentioned above.
  60.  *      3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0.
  61.  */
  62.  
  63. #include "math.h"
  64. #include "math_private.h"
  65.  
  66. #ifdef __STDC__
  67. static double pzero(double), qzero(double);
  68. #else
  69. static double pzero(), qzero();
  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, 2.00] */
  82. R02  =  1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */
  83. R03  = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */
  84. R04  =  1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */
  85. R05  = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */
  86. S01  =  1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */
  87. S02  =  1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */
  88. S03  =  5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */
  89. S04  =  1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */
  90.  
  91. #ifdef __STDC__
  92. static const double zero = 0.0;
  93. #else
  94. static double zero = 0.0;
  95. #endif
  96.  
  97. #ifdef __STDC__
  98.         double __ieee754_j0(double x)
  99. #else
  100.         double __ieee754_j0(x)
  101.         double x;
  102. #endif
  103. {
  104.         double z, s,c,ss,cc,r,u,v;
  105.         int32_t hx,ix;
  106.  
  107.         GET_HIGH_WORD(hx,x);
  108.         ix = hx&0x7fffffff;
  109.         if(ix>=0x7ff00000) return one/(x*x);
  110.         x = fabs(x);
  111.         if(ix >= 0x40000000) {  /* |x| >= 2.0 */
  112.                 s = sin(x);
  113.                 c = cos(x);
  114.                 ss = s-c;
  115.                 cc = s+c;
  116.                 if(ix<0x7fe00000) {  /* make sure x+x not overflow */
  117.                     z = -cos(x+x);
  118.                     if ((s*c)<zero) cc = z/ss;
  119.                     else            ss = z/cc;
  120.                 }
  121.         /*
  122.          * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
  123.          * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
  124.          */
  125.                 if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(x);
  126.                 else {
  127.                     u = pzero(x); v = qzero(x);
  128.                     z = invsqrtpi*(u*cc-v*ss)/sqrt(x);
  129.                 }
  130.                 return z;
  131.         }
  132.         if(ix<0x3f200000) {     /* |x| < 2**-13 */
  133.             if(huge+x>one) {    /* raise inexact if x != 0 */
  134.                 if(ix<0x3e400000) return one;   /* |x|<2**-27 */
  135.                 else          return one - 0.25*x*x;
  136.             }
  137.         }
  138.         z = x*x;
  139.         r =  z*(R02+z*(R03+z*(R04+z*R05)));
  140.         s =  one+z*(S01+z*(S02+z*(S03+z*S04)));
  141.         if(ix < 0x3FF00000) {   /* |x| < 1.00 */
  142.             return one + z*(-0.25+(r/s));
  143.         } else {
  144.             u = 0.5*x;
  145.             return((one+u)*(one-u)+z*(r/s));
  146.         }
  147. }
  148.  
  149. #ifdef __STDC__
  150. static const double
  151. #else
  152. static double
  153. #endif
  154. u00  = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */
  155. u01  =  1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */
  156. u02  = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */
  157. u03  =  3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */
  158. u04  = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */
  159. u05  =  1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */
  160. u06  = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */
  161. v01  =  1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */
  162. v02  =  7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */
  163. v03  =  2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */
  164. v04  =  4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */
  165.  
  166. #ifdef __STDC__
  167.         double __ieee754_y0(double x)
  168. #else
  169.         double __ieee754_y0(x)
  170.         double x;
  171. #endif
  172. {
  173.         double z, s,c,ss,cc,u,v;
  174.         int32_t hx,ix,lx;
  175.  
  176.         EXTRACT_WORDS(hx,lx,x);
  177.         ix = 0x7fffffff&hx;
  178.     /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0  */
  179.         if(ix>=0x7ff00000) return  one/(x+x*x);
  180.         if((ix|lx)==0) return -one/zero;
  181.         if(hx<0) return zero/zero;
  182.         if(ix >= 0x40000000) {  /* |x| >= 2.0 */
  183.         /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))
  184.          * where x0 = x-pi/4
  185.          *      Better formula:
  186.          *              cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)
  187.          *                      =  1/sqrt(2) * (sin(x) + cos(x))
  188.          *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
  189.          *                      =  1/sqrt(2) * (sin(x) - cos(x))
  190.          * To avoid cancellation, use
  191.          *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
  192.          * to compute the worse one.
  193.          */
  194.                 s = sin(x);
  195.                 c = cos(x);
  196.                 ss = s-c;
  197.                 cc = s+c;
  198.         /*
  199.          * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)
  200.          * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)
  201.          */
  202.                 if(ix<0x7fe00000) {  /* make sure x+x not overflow */
  203.                     z = -cos(x+x);
  204.                     if ((s*c)<zero) cc = z/ss;
  205.                     else            ss = z/cc;
  206.                 }
  207.                 if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);
  208.                 else {
  209.                     u = pzero(x); v = qzero(x);
  210.                     z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
  211.                 }
  212.                 return z;
  213.         }
  214.         if(ix<=0x3e400000) {    /* x < 2**-27 */
  215.             return(u00 + tpi*__ieee754_log(x));
  216.         }
  217.         z = x*x;
  218.         u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));
  219.         v = one+z*(v01+z*(v02+z*(v03+z*v04)));
  220.         return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x)));
  221. }
  222.  
  223. /* The asymptotic expansions of pzero is
  224.  *      1 - 9/128 s^2 + 11025/98304 s^4 - ...,  where s = 1/x.
  225.  * For x >= 2, We approximate pzero by
  226.  *      pzero(x) = 1 + (R/S)
  227.  * where  R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10
  228.  *        S = 1 + pS0*s^2 + ... + pS4*s^10
  229.  * and
  230.  *      | pzero(x)-1-R/S | <= 2  ** ( -60.26)
  231.  */
  232. #ifdef __STDC__
  233. static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  234. #else
  235. static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  236. #endif
  237.   0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  238.  -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */
  239.  -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */
  240.  -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */
  241.  -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */
  242.  -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */
  243. };
  244. #ifdef __STDC__
  245. static const double pS8[5] = {
  246. #else
  247. static double pS8[5] = {
  248. #endif
  249.   1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */
  250.   3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */
  251.   4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */
  252.   1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */
  253.   4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */
  254. };
  255.  
  256. #ifdef __STDC__
  257. static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  258. #else
  259. static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  260. #endif
  261.  -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */
  262.  -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */
  263.  -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */
  264.  -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */
  265.  -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */
  266.  -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */
  267. };
  268. #ifdef __STDC__
  269. static const double pS5[5] = {
  270. #else
  271. static double pS5[5] = {
  272. #endif
  273.   6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */
  274.   1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */
  275.   5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */
  276.   9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */
  277.   2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */
  278. };
  279.  
  280. #ifdef __STDC__
  281. static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
  282. #else
  283. static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
  284. #endif
  285.  -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */
  286.  -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */
  287.  -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */
  288.  -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */
  289.  -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */
  290.  -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */
  291. };
  292. #ifdef __STDC__
  293. static const double pS3[5] = {
  294. #else
  295. static double pS3[5] = {
  296. #endif
  297.   3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */
  298.   3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */
  299.   1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */
  300.   1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */
  301.   1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */
  302. };
  303.  
  304. #ifdef __STDC__
  305. static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  306. #else
  307. static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  308. #endif
  309.  -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */
  310.  -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */
  311.  -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */
  312.  -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */
  313.  -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */
  314.  -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */
  315. };
  316. #ifdef __STDC__
  317. static const double pS2[5] = {
  318. #else
  319. static double pS2[5] = {
  320. #endif
  321.   2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */
  322.   1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */
  323.   2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */
  324.   1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */
  325.   1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */
  326. };
  327.  
  328. #ifdef __STDC__
  329.         static double pzero(double x)
  330. #else
  331.         static double pzero(x)
  332.         double x;
  333. #endif
  334. {
  335. #ifdef __STDC__
  336.         const double *p,*q;
  337. #else
  338.         double *p,*q;
  339. #endif
  340.         double z,r,s;
  341.         int32_t ix;
  342.         GET_HIGH_WORD(ix,x);
  343.         ix &= 0x7fffffff;
  344.         if(ix>=0x40200000)     {p = pR8; q= pS8;}
  345.         else if(ix>=0x40122E8B){p = pR5; q= pS5;}
  346.         else if(ix>=0x4006DB6D){p = pR3; q= pS3;}
  347.         else if(ix>=0x40000000){p = pR2; q= pS2;}
  348.         z = one/(x*x);
  349.         r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
  350.         s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
  351.         return one+ r/s;
  352. }
  353.                
  354.  
  355. /* For x >= 8, the asymptotic expansions of qzero is
  356.  *      -1/8 s + 75/1024 s^3 - ..., where s = 1/x.
  357.  * We approximate pzero by
  358.  *      qzero(x) = s*(-1.25 + (R/S))
  359.  * where  R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10
  360.  *        S = 1 + qS0*s^2 + ... + qS5*s^12
  361.  * and
  362.  *      | qzero(x)/s +1.25-R/S | <= 2  ** ( -61.22)
  363.  */
  364. #ifdef __STDC__
  365. static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  366. #else
  367. static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  368. #endif
  369.   0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  370.   7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */
  371.   1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */
  372.   5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */
  373.   8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */
  374.   3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */
  375. };
  376. #ifdef __STDC__
  377. static const double qS8[6] = {
  378. #else
  379. static double qS8[6] = {
  380. #endif
  381.   1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */
  382.   8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */
  383.   1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */
  384.   8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */
  385.   8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */
  386.  -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */
  387. };
  388.  
  389. #ifdef __STDC__
  390. static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  391. #else
  392. static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  393. #endif
  394.   1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */
  395.   7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */
  396.   5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */
  397.   1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */
  398.   1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */
  399.   1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */
  400. };
  401. #ifdef __STDC__
  402. static const double qS5[6] = {
  403. #else
  404. static double qS5[6] = {
  405. #endif
  406.   8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */
  407.   2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */
  408.   1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */
  409.   5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */
  410.   3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */
  411.  -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */
  412. };
  413.  
  414. #ifdef __STDC__
  415. static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
  416. #else
  417. static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
  418. #endif
  419.   4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */
  420.   7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */
  421.   3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */
  422.   4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */
  423.   1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */
  424.   1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */
  425. };
  426. #ifdef __STDC__
  427. static const double qS3[6] = {
  428. #else
  429. static double qS3[6] = {
  430. #endif
  431.   4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */
  432.   7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */
  433.   3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */
  434.   6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */
  435.   2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */
  436.  -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */
  437. };
  438.  
  439. #ifdef __STDC__
  440. static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  441. #else
  442. static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  443. #endif
  444.   1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */
  445.   7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */
  446.   1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */
  447.   1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */
  448.   3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */
  449.   1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */
  450. };
  451. #ifdef __STDC__
  452. static const double qS2[6] = {
  453. #else
  454. static double qS2[6] = {
  455. #endif
  456.   3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */
  457.   2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */
  458.   8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */
  459.   8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */
  460.   2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */
  461.  -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */
  462. };
  463.  
  464. #ifdef __STDC__
  465.         static double qzero(double x)
  466. #else
  467.         static double qzero(x)
  468.         double x;
  469. #endif
  470. {
  471. #ifdef __STDC__
  472.         const double *p,*q;
  473. #else
  474.         double *p,*q;
  475. #endif
  476.         double s,r,z;
  477.         int32_t ix;
  478.         GET_HIGH_WORD(ix,x);
  479.         ix &= 0x7fffffff;
  480.         if(ix>=0x40200000)     {p = qR8; q= qS8;}
  481.         else if(ix>=0x40122E8B){p = qR5; q= qS5;}
  482.         else if(ix>=0x4006DB6D){p = qR3; q= qS3;}
  483.         else if(ix>=0x40000000){p = qR2; q= qS2;}
  484.         z = one/(x*x);
  485.         r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
  486.         s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
  487.         return (-.125 + r/s)/x;
  488. }
  489.