e_j1.c 16 KB

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  1. /* @(#)e_j1.c 5.1 93/09/24 */
  2. /*
  3. * ====================================================
  4. * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  5. *
  6. * Developed at SunPro, a Sun Microsystems, Inc. business.
  7. * Permission to use, copy, modify, and distribute this
  8. * software is freely granted, provided that this notice
  9. * is preserved.
  10. * ====================================================
  11. */
  12. #if defined(LIBM_SCCS) && !defined(lint)
  13. static char rcsid[] = "$NetBSD: e_j1.c,v 1.8 1995/05/10 20:45:27 jtc Exp $";
  14. #endif
  15. /* __ieee754_j1(x), __ieee754_y1(x)
  16. * Bessel function of the first and second kinds of order zero.
  17. * Method -- j1(x):
  18. * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ...
  19. * 2. Reduce x to |x| since j1(x)=-j1(-x), and
  20. * for x in (0,2)
  21. * j1(x) = x/2 + x*z*R0/S0, where z = x*x;
  22. * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 )
  23. * for x in (2,inf)
  24. * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1))
  25. * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
  26. * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
  27. * as follow:
  28. * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
  29. * = 1/sqrt(2) * (sin(x) - cos(x))
  30. * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
  31. * = -1/sqrt(2) * (sin(x) + cos(x))
  32. * (To avoid cancellation, use
  33. * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
  34. * to compute the worse one.)
  35. *
  36. * 3 Special cases
  37. * j1(nan)= nan
  38. * j1(0) = 0
  39. * j1(inf) = 0
  40. *
  41. * Method -- y1(x):
  42. * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN
  43. * 2. For x<2.
  44. * Since
  45. * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...)
  46. * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function.
  47. * We use the following function to approximate y1,
  48. * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2
  49. * where for x in [0,2] (abs err less than 2**-65.89)
  50. * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4
  51. * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5
  52. * Note: For tiny x, 1/x dominate y1 and hence
  53. * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54)
  54. * 3. For x>=2.
  55. * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1))
  56. * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1)
  57. * by method mentioned above.
  58. */
  59. #include "math.h"
  60. #include "math_private.h"
  61. libm_hidden_proto(sin)
  62. libm_hidden_proto(cos)
  63. libm_hidden_proto(sqrt)
  64. libm_hidden_proto(fabs)
  65. #ifdef __STDC__
  66. static double pone(double), qone(double);
  67. #else
  68. static double pone(), qone();
  69. #endif
  70. #ifdef __STDC__
  71. static const double
  72. #else
  73. static double
  74. #endif
  75. huge = 1e300,
  76. one = 1.0,
  77. invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */
  78. tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
  79. /* R0/S0 on [0,2] */
  80. r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */
  81. r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */
  82. r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */
  83. r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */
  84. s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */
  85. s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */
  86. s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */
  87. s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */
  88. s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */
  89. #ifdef __STDC__
  90. static const double zero = 0.0;
  91. #else
  92. static double zero = 0.0;
  93. #endif
  94. #ifdef __STDC__
  95. double attribute_hidden __ieee754_j1(double x)
  96. #else
  97. double attribute_hidden __ieee754_j1(x)
  98. double x;
  99. #endif
  100. {
  101. double z, s,c,ss,cc,r,u,v,y;
  102. int32_t hx,ix;
  103. GET_HIGH_WORD(hx,x);
  104. ix = hx&0x7fffffff;
  105. if(ix>=0x7ff00000) return one/x;
  106. y = fabs(x);
  107. if(ix >= 0x40000000) { /* |x| >= 2.0 */
  108. s = sin(y);
  109. c = cos(y);
  110. ss = -s-c;
  111. cc = s-c;
  112. if(ix<0x7fe00000) { /* make sure y+y not overflow */
  113. z = cos(y+y);
  114. if ((s*c)>zero) cc = z/ss;
  115. else ss = z/cc;
  116. }
  117. /*
  118. * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x)
  119. * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x)
  120. */
  121. if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y);
  122. else {
  123. u = pone(y); v = qone(y);
  124. z = invsqrtpi*(u*cc-v*ss)/sqrt(y);
  125. }
  126. if(hx<0) return -z;
  127. else return z;
  128. }
  129. if(ix<0x3e400000) { /* |x|<2**-27 */
  130. if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */
  131. }
  132. z = x*x;
  133. r = z*(r00+z*(r01+z*(r02+z*r03)));
  134. s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05))));
  135. r *= x;
  136. return(x*0.5+r/s);
  137. }
  138. #ifdef __STDC__
  139. static const double U0[5] = {
  140. #else
  141. static double U0[5] = {
  142. #endif
  143. -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */
  144. 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */
  145. -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */
  146. 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */
  147. -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */
  148. };
  149. #ifdef __STDC__
  150. static const double V0[5] = {
  151. #else
  152. static double V0[5] = {
  153. #endif
  154. 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */
  155. 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */
  156. 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */
  157. 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */
  158. 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */
  159. };
  160. #ifdef __STDC__
  161. double attribute_hidden __ieee754_y1(double x)
  162. #else
  163. double attribute_hidden __ieee754_y1(x)
  164. double x;
  165. #endif
  166. {
  167. double z, s,c,ss,cc,u,v;
  168. int32_t hx,ix,lx;
  169. EXTRACT_WORDS(hx,lx,x);
  170. ix = 0x7fffffff&hx;
  171. /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */
  172. if(ix>=0x7ff00000) return one/(x+x*x);
  173. if((ix|lx)==0) return -one/zero;
  174. if(hx<0) return zero/zero;
  175. if(ix >= 0x40000000) { /* |x| >= 2.0 */
  176. s = sin(x);
  177. c = cos(x);
  178. ss = -s-c;
  179. cc = s-c;
  180. if(ix<0x7fe00000) { /* make sure x+x not overflow */
  181. z = cos(x+x);
  182. if ((s*c)>zero) cc = z/ss;
  183. else ss = z/cc;
  184. }
  185. /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0))
  186. * where x0 = x-3pi/4
  187. * Better formula:
  188. * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4)
  189. * = 1/sqrt(2) * (sin(x) - cos(x))
  190. * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)
  191. * = -1/sqrt(2) * (cos(x) + sin(x))
  192. * To avoid cancellation, use
  193. * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))
  194. * to compute the worse one.
  195. */
  196. if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x);
  197. else {
  198. u = pone(x); v = qone(x);
  199. z = invsqrtpi*(u*ss+v*cc)/sqrt(x);
  200. }
  201. return z;
  202. }
  203. if(ix<=0x3c900000) { /* x < 2**-54 */
  204. return(-tpi/x);
  205. }
  206. z = x*x;
  207. u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4])));
  208. v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4]))));
  209. return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x));
  210. }
  211. /* For x >= 8, the asymptotic expansions of pone is
  212. * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x.
  213. * We approximate pone by
  214. * pone(x) = 1 + (R/S)
  215. * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10
  216. * S = 1 + ps0*s^2 + ... + ps4*s^10
  217. * and
  218. * | pone(x)-1-R/S | <= 2 ** ( -60.06)
  219. */
  220. #ifdef __STDC__
  221. static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  222. #else
  223. static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  224. #endif
  225. 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  226. 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */
  227. 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */
  228. 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */
  229. 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */
  230. 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */
  231. };
  232. #ifdef __STDC__
  233. static const double ps8[5] = {
  234. #else
  235. static double ps8[5] = {
  236. #endif
  237. 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */
  238. 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */
  239. 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */
  240. 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */
  241. 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */
  242. };
  243. #ifdef __STDC__
  244. static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  245. #else
  246. static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  247. #endif
  248. 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */
  249. 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */
  250. 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */
  251. 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */
  252. 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */
  253. 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */
  254. };
  255. #ifdef __STDC__
  256. static const double ps5[5] = {
  257. #else
  258. static double ps5[5] = {
  259. #endif
  260. 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */
  261. 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */
  262. 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */
  263. 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */
  264. 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */
  265. };
  266. #ifdef __STDC__
  267. static const double pr3[6] = {
  268. #else
  269. static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
  270. #endif
  271. 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */
  272. 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */
  273. 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */
  274. 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */
  275. 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */
  276. 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */
  277. };
  278. #ifdef __STDC__
  279. static const double ps3[5] = {
  280. #else
  281. static double ps3[5] = {
  282. #endif
  283. 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */
  284. 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */
  285. 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */
  286. 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */
  287. 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */
  288. };
  289. #ifdef __STDC__
  290. static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  291. #else
  292. static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  293. #endif
  294. 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */
  295. 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */
  296. 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */
  297. 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */
  298. 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */
  299. 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */
  300. };
  301. #ifdef __STDC__
  302. static const double ps2[5] = {
  303. #else
  304. static double ps2[5] = {
  305. #endif
  306. 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */
  307. 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */
  308. 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */
  309. 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */
  310. 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */
  311. };
  312. #ifdef __STDC__
  313. static double pone(double x)
  314. #else
  315. static double pone(x)
  316. double x;
  317. #endif
  318. {
  319. #ifdef __STDC__
  320. const double *p=0,*q=0;
  321. #else
  322. double *p,*q;
  323. #endif
  324. double z,r,s;
  325. int32_t ix;
  326. GET_HIGH_WORD(ix,x);
  327. ix &= 0x7fffffff;
  328. if(ix>=0x40200000) {p = pr8; q= ps8;}
  329. else if(ix>=0x40122E8B){p = pr5; q= ps5;}
  330. else if(ix>=0x4006DB6D){p = pr3; q= ps3;}
  331. else if(ix>=0x40000000){p = pr2; q= ps2;}
  332. z = one/(x*x);
  333. r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
  334. s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));
  335. return one+ r/s;
  336. }
  337. /* For x >= 8, the asymptotic expansions of qone is
  338. * 3/8 s - 105/1024 s^3 - ..., where s = 1/x.
  339. * We approximate pone by
  340. * qone(x) = s*(0.375 + (R/S))
  341. * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10
  342. * S = 1 + qs1*s^2 + ... + qs6*s^12
  343. * and
  344. * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13)
  345. */
  346. #ifdef __STDC__
  347. static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  348. #else
  349. static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */
  350. #endif
  351. 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
  352. -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */
  353. -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */
  354. -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */
  355. -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */
  356. -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */
  357. };
  358. #ifdef __STDC__
  359. static const double qs8[6] = {
  360. #else
  361. static double qs8[6] = {
  362. #endif
  363. 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */
  364. 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */
  365. 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */
  366. 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */
  367. 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */
  368. -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */
  369. };
  370. #ifdef __STDC__
  371. static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  372. #else
  373. static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */
  374. #endif
  375. -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */
  376. -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */
  377. -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */
  378. -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */
  379. -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */
  380. -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */
  381. };
  382. #ifdef __STDC__
  383. static const double qs5[6] = {
  384. #else
  385. static double qs5[6] = {
  386. #endif
  387. 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */
  388. 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */
  389. 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */
  390. 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */
  391. 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */
  392. -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */
  393. };
  394. #ifdef __STDC__
  395. static const double qr3[6] = {
  396. #else
  397. static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */
  398. #endif
  399. -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */
  400. -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */
  401. -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */
  402. -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */
  403. -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */
  404. -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */
  405. };
  406. #ifdef __STDC__
  407. static const double qs3[6] = {
  408. #else
  409. static double qs3[6] = {
  410. #endif
  411. 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */
  412. 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */
  413. 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */
  414. 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */
  415. 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */
  416. -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */
  417. };
  418. #ifdef __STDC__
  419. static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  420. #else
  421. static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */
  422. #endif
  423. -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */
  424. -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */
  425. -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */
  426. -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */
  427. -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */
  428. -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */
  429. };
  430. #ifdef __STDC__
  431. static const double qs2[6] = {
  432. #else
  433. static double qs2[6] = {
  434. #endif
  435. 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */
  436. 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */
  437. 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */
  438. 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */
  439. 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */
  440. -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */
  441. };
  442. #ifdef __STDC__
  443. static double qone(double x)
  444. #else
  445. static double qone(x)
  446. double x;
  447. #endif
  448. {
  449. #ifdef __STDC__
  450. const double *p=0,*q=0;
  451. #else
  452. double *p,*q;
  453. #endif
  454. double s,r,z;
  455. int32_t ix;
  456. GET_HIGH_WORD(ix,x);
  457. ix &= 0x7fffffff;
  458. if(ix>=0x40200000) {p = qr8; q= qs8;}
  459. else if(ix>=0x40122E8B){p = qr5; q= qs5;}
  460. else if(ix>=0x4006DB6D){p = qr3; q= qs3;}
  461. else if(ix>=0x40000000){p = qr2; q= qs2;}
  462. z = one/(x*x);
  463. r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));
  464. s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));
  465. return (.375 + r/s)/x;
  466. }