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 /* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/26, 13 for performance improvement on pipelined processors. 14 */ 15 16 #if defined(LIBM_SCCS) && !defined(lint) 17 static char rcsid[] = "$NetBSD: e_j1.c,v 1.8 1995/05/10 20:45:27 jtc Exp $"; 18 #endif 19 20 /* __ieee754_j1(x), __ieee754_y1(x) 21 * Bessel function of the first and second kinds of order zero. 22 * Method -- j1(x): 23 * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... 24 * 2. Reduce x to |x| since j1(x)=-j1(-x), and 25 * for x in (0,2) 26 * j1(x) = x/2 + x*z*R0/S0, where z = x*x; 27 * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) 28 * for x in (2,inf) 29 * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) 30 * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) 31 * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) 32 * as follow: 33 * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) 34 * = 1/sqrt(2) * (sin(x) - cos(x)) 35 * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 36 * = -1/sqrt(2) * (sin(x) + cos(x)) 37 * (To avoid cancellation, use 38 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 39 * to compute the worse one.) 40 * 41 * 3 Special cases 42 * j1(nan)= nan 43 * j1(0) = 0 44 * j1(inf) = 0 45 * 46 * Method -- y1(x): 47 * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN 48 * 2. For x<2. 49 * Since 50 * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) 51 * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. 52 * We use the following function to approximate y1, 53 * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 54 * where for x in [0,2] (abs err less than 2**-65.89) 55 * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 56 * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 57 * Note: For tiny x, 1/x dominate y1 and hence 58 * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) 59 * 3. For x>=2. 60 * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) 61 * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) 62 * by method mentioned above. 63 */ 64 65 #include "math.h" 66 #include "ieee754.h" 67 68 #ifdef __STDC__ 69 static double pone(double), qone(double); 70 #else 71 static double pone(), qone(); 72 #endif 73 74 #ifdef __STDC__ 75 static const double 76 #else 77 static double 78 #endif 79 huge = 1e300, 80 one = 1.0, 81 invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ 82 tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 83 /* R0/S0 on [0,2] */ 84 R[] = {-6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ 85 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ 86 -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ 87 4.96727999609584448412e-08}, /* 0x3E6AAAFA, 0x46CA0BD9 */ 88 S[] = {0.0, 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ 89 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ 90 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ 91 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ 92 1.23542274426137913908e-11}; /* 0x3DAB2ACF, 0xCFB97ED8 */ 93 94 #ifdef __STDC__ 95 static const double zero = 0.0; 96 #else 97 static double zero = 0.0; 98 #endif 99 100 #ifdef __STDC__ __ieee754_j1(double x)101 double __ieee754_j1(double x) 102 #else 103 double __ieee754_j1(x) 104 double x; 105 #endif 106 { 107 double z, s,c,ss,cc,r,u,v,y,r1,r2,s1,s2,s3,z2,z4; 108 int32_t hx,ix; 109 110 GET_HIGH_WORD(hx,x); 111 ix = hx&0x7fffffff; 112 if(ix>=0x7ff00000) return one/x; 113 y = fabs(x); 114 if(ix >= 0x40000000) { /* |x| >= 2.0 */ 115 __sincos (y, &s, &c); 116 ss = -s-c; 117 cc = s-c; 118 if(ix<0x7fe00000) { /* make sure y+y not overflow */ 119 z = __cos(y+y); 120 if ((s*c)>zero) cc = z/ss; 121 else ss = z/cc; 122 } 123 /* 124 * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) 125 * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) 126 */ 127 if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(y); 128 else { 129 u = pone(y); v = qone(y); 130 z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(y); 131 } 132 if(hx<0) return -z; 133 else return z; 134 } 135 if(ix<0x3e400000) { /* |x|<2**-27 */ 136 if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ 137 } 138 z = x*x; 139 #ifdef DO_NOT_USE_THIS 140 r = z*(r00+z*(r01+z*(r02+z*r03))); 141 s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); 142 r *= x; 143 #else 144 r1 = z*R[0]; z2=z*z; 145 r2 = R[1]+z*R[2]; z4=z2*z2; 146 r = r1 + z2*r2 + z4*R[3]; 147 r *= x; 148 s1 = one+z*S[1]; 149 s2 = S[2]+z*S[3]; 150 s3 = S[4]+z*S[5]; 151 s = s1 + z2*s2 + z4*s3; 152 #endif 153 return(x*0.5+r/s); 154 } 155 156 #ifdef __STDC__ 157 static const double U0[5] = { 158 #else 159 static double U0[5] = { 160 #endif 161 -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ 162 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ 163 -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ 164 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ 165 -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ 166 }; 167 #ifdef __STDC__ 168 static const double V0[5] = { 169 #else 170 static double V0[5] = { 171 #endif 172 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ 173 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ 174 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ 175 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ 176 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ 177 }; 178 179 #ifdef __STDC__ __ieee754_y1(double x)180 double __ieee754_y1(double x) 181 #else 182 double __ieee754_y1(x) 183 double x; 184 #endif 185 { 186 double z, s,c,ss,cc,u,v,u1,u2,v1,v2,v3,z2,z4; 187 int32_t hx,ix,lx; 188 189 EXTRACT_WORDS(hx,lx,x); 190 ix = 0x7fffffff&hx; 191 /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ 192 if(ix>=0x7ff00000) return one/(x+x*x); 193 if((ix|lx)==0) return -HUGE_VAL+x; /* -inf and overflow exception. */; 194 if(hx<0) return zero/(zero*x); 195 if(ix >= 0x40000000) { /* |x| >= 2.0 */ 196 __sincos (x, &s, &c); 197 ss = -s-c; 198 cc = s-c; 199 if(ix<0x7fe00000) { /* make sure x+x not overflow */ 200 z = __cos(x+x); 201 if ((s*c)>zero) cc = z/ss; 202 else ss = z/cc; 203 } 204 /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) 205 * where x0 = x-3pi/4 206 * Better formula: 207 * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) 208 * = 1/sqrt(2) * (sin(x) - cos(x)) 209 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 210 * = -1/sqrt(2) * (cos(x) + sin(x)) 211 * To avoid cancellation, use 212 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 213 * to compute the worse one. 214 */ 215 if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x); 216 else { 217 u = pone(x); v = qone(x); 218 z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x); 219 } 220 return z; 221 } 222 if(ix<=0x3c900000) { /* x < 2**-54 */ 223 return(-tpi/x); 224 } 225 z = x*x; 226 #ifdef DO_NOT_USE_THIS 227 u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); 228 v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); 229 #else 230 u1 = U0[0]+z*U0[1];z2=z*z; 231 u2 = U0[2]+z*U0[3];z4=z2*z2; 232 u = u1 + z2*u2 + z4*U0[4]; 233 v1 = one+z*V0[0]; 234 v2 = V0[1]+z*V0[2]; 235 v3 = V0[3]+z*V0[4]; 236 v = v1 + z2*v2 + z4*v3; 237 #endif 238 return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); 239 } 240 241 /* For x >= 8, the asymptotic expansions of pone is 242 * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. 243 * We approximate pone by 244 * pone(x) = 1 + (R/S) 245 * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 246 * S = 1 + ps0*s^2 + ... + ps4*s^10 247 * and 248 * | pone(x)-1-R/S | <= 2 ** ( -60.06) 249 */ 250 251 #ifdef __STDC__ 252 static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 253 #else 254 static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 255 #endif 256 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 257 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ 258 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ 259 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ 260 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ 261 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ 262 }; 263 #ifdef __STDC__ 264 static const double ps8[5] = { 265 #else 266 static double ps8[5] = { 267 #endif 268 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ 269 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ 270 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ 271 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ 272 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ 273 }; 274 275 #ifdef __STDC__ 276 static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 277 #else 278 static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 279 #endif 280 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ 281 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ 282 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ 283 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ 284 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ 285 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ 286 }; 287 #ifdef __STDC__ 288 static const double ps5[5] = { 289 #else 290 static double ps5[5] = { 291 #endif 292 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ 293 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ 294 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ 295 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ 296 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ 297 }; 298 299 #ifdef __STDC__ 300 static const double pr3[6] = { 301 #else 302 static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 303 #endif 304 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ 305 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ 306 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ 307 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ 308 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ 309 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ 310 }; 311 #ifdef __STDC__ 312 static const double ps3[5] = { 313 #else 314 static double ps3[5] = { 315 #endif 316 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ 317 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ 318 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ 319 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ 320 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ 321 }; 322 323 #ifdef __STDC__ 324 static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 325 #else 326 static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 327 #endif 328 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ 329 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ 330 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ 331 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ 332 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ 333 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ 334 }; 335 #ifdef __STDC__ 336 static const double ps2[5] = { 337 #else 338 static double ps2[5] = { 339 #endif 340 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ 341 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ 342 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ 343 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ 344 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ 345 }; 346 347 #ifdef __STDC__ pone(double x)348 static double pone(double x) 349 #else 350 static double pone(x) 351 double x; 352 #endif 353 { 354 #ifdef __STDC__ 355 const double *p = 0,*q = 0; 356 #else 357 double *p = 0,*q = 0; 358 #endif 359 double z,r,s,r1,r2,r3,s1,s2,s3,z2,z4; 360 int32_t ix; 361 GET_HIGH_WORD(ix,x); 362 ix &= 0x7fffffff; 363 if(ix>=0x40200000) {p = pr8; q= ps8;} 364 else if(ix>=0x40122E8B){p = pr5; q= ps5;} 365 else if(ix>=0x4006DB6D){p = pr3; q= ps3;} 366 else if(ix>=0x40000000){p = pr2; q= ps2;} 367 z = one/(x*x); 368 #ifdef DO_NOT_USE_THIS 369 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 370 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); 371 #else 372 r1 = p[0]+z*p[1]; z2=z*z; 373 r2 = p[2]+z*p[3]; z4=z2*z2; 374 r3 = p[4]+z*p[5]; 375 r = r1 + z2*r2 + z4*r3; 376 s1 = one+z*q[0]; 377 s2 = q[1]+z*q[2]; 378 s3 = q[3]+z*q[4]; 379 s = s1 + z2*s2 + z4*s3; 380 #endif 381 return one+ r/s; 382 } 383 384 385 /* For x >= 8, the asymptotic expansions of qone is 386 * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. 387 * We approximate pone by 388 * qone(x) = s*(0.375 + (R/S)) 389 * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 390 * S = 1 + qs1*s^2 + ... + qs6*s^12 391 * and 392 * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) 393 */ 394 395 #ifdef __STDC__ 396 static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 397 #else 398 static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 399 #endif 400 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 401 -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ 402 -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ 403 -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ 404 -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ 405 -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ 406 }; 407 #ifdef __STDC__ 408 static const double qs8[6] = { 409 #else 410 static double qs8[6] = { 411 #endif 412 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ 413 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ 414 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ 415 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ 416 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ 417 -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ 418 }; 419 420 #ifdef __STDC__ 421 static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 422 #else 423 static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 424 #endif 425 -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ 426 -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ 427 -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ 428 -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ 429 -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ 430 -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ 431 }; 432 #ifdef __STDC__ 433 static const double qs5[6] = { 434 #else 435 static double qs5[6] = { 436 #endif 437 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ 438 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ 439 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ 440 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ 441 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ 442 -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ 443 }; 444 445 #ifdef __STDC__ 446 static const double qr3[6] = { 447 #else 448 static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 449 #endif 450 -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ 451 -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ 452 -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ 453 -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ 454 -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ 455 -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ 456 }; 457 #ifdef __STDC__ 458 static const double qs3[6] = { 459 #else 460 static double qs3[6] = { 461 #endif 462 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ 463 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ 464 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ 465 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ 466 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ 467 -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ 468 }; 469 470 #ifdef __STDC__ 471 static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 472 #else 473 static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 474 #endif 475 -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ 476 -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ 477 -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ 478 -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ 479 -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ 480 -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ 481 }; 482 #ifdef __STDC__ 483 static const double qs2[6] = { 484 #else 485 static double qs2[6] = { 486 #endif 487 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ 488 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ 489 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ 490 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ 491 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ 492 -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ 493 }; 494 495 #ifdef __STDC__ qone(double x)496 static double qone(double x) 497 #else 498 static double qone(x) 499 double x; 500 #endif 501 { 502 #ifdef __STDC__ 503 const double *p = 0,*q = 0; 504 #else 505 double *p = 0,*q = 0; 506 #endif 507 double s,r,z,r1,r2,r3,s1,s2,s3,z2,z4,z6; 508 int32_t ix; 509 GET_HIGH_WORD(ix,x); 510 ix &= 0x7fffffff; 511 if(ix>=0x40200000) {p = qr8; q= qs8;} 512 else if(ix>=0x40122E8B){p = qr5; q= qs5;} 513 else if(ix>=0x4006DB6D){p = qr3; q= qs3;} 514 else if(ix>=0x40000000){p = qr2; q= qs2;} 515 z = one/(x*x); 516 #ifdef DO_NOT_USE_THIS 517 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 518 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); 519 #else 520 r1 = p[0]+z*p[1]; z2=z*z; 521 r2 = p[2]+z*p[3]; z4=z2*z2; 522 r3 = p[4]+z*p[5]; z6=z4*z2; 523 r = r1 + z2*r2 + z4*r3; 524 s1 = one+z*q[0]; 525 s2 = q[1]+z*q[2]; 526 s3 = q[3]+z*q[4]; 527 s = s1 + z2*s2 + z4*s3 + z6*q[5]; 528 #endif 529 return (.375 + r/s)/x; 530 } 531