[444] | 1 | |
---|
| 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 | /* j1(x), y1(x) |
---|
| 15 | * Bessel function of the first and second kinds of order zero. |
---|
| 16 | * Method -- j1(x): |
---|
| 17 | * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... |
---|
| 18 | * 2. Reduce x to |x| since j1(x)=-j1(-x), and |
---|
| 19 | * for x in (0,2) |
---|
| 20 | * j1(x) = x/2 + x*z*R0/S0, where z = x*x; |
---|
| 21 | * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) |
---|
| 22 | * for x in (2,inf) |
---|
| 23 | * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) |
---|
| 24 | * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) |
---|
| 25 | * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) |
---|
| 26 | * as follow: |
---|
| 27 | * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) |
---|
| 28 | * = 1/sqrt(2) * (sin(x) - cos(x)) |
---|
| 29 | * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) |
---|
| 30 | * = -1/sqrt(2) * (sin(x) + cos(x)) |
---|
| 31 | * (To avoid cancellation, use |
---|
| 32 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
---|
| 33 | * to compute the worse one.) |
---|
| 34 | * |
---|
| 35 | * 3 Special cases |
---|
| 36 | * j1(nan)= nan |
---|
| 37 | * j1(0) = 0 |
---|
| 38 | * j1(inf) = 0 |
---|
| 39 | * |
---|
| 40 | * Method -- y1(x): |
---|
| 41 | * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN |
---|
| 42 | * 2. For x<2. |
---|
| 43 | * Since |
---|
| 44 | * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) |
---|
| 45 | * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. |
---|
| 46 | * We use the following function to approximate y1, |
---|
| 47 | * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 |
---|
| 48 | * where for x in [0,2] (abs err less than 2**-65.89) |
---|
| 49 | * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 |
---|
| 50 | * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 |
---|
| 51 | * Note: For tiny x, 1/x dominate y1 and hence |
---|
| 52 | * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) |
---|
| 53 | * 3. For x>=2. |
---|
| 54 | * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) |
---|
| 55 | * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) |
---|
| 56 | * by method mentioned above. |
---|
| 57 | */ |
---|
| 58 | |
---|
| 59 | #include "fdlibm.h" |
---|
| 60 | |
---|
| 61 | #ifndef _DOUBLE_IS_32BITS |
---|
| 62 | |
---|
| 63 | #ifdef __STDC__ |
---|
| 64 | static double pone(double), qone(double); |
---|
| 65 | #else |
---|
| 66 | static double pone(), qone(); |
---|
| 67 | #endif |
---|
| 68 | |
---|
| 69 | #ifdef __STDC__ |
---|
| 70 | static const double |
---|
| 71 | #else |
---|
| 72 | static double |
---|
| 73 | #endif |
---|
| 74 | huge = 1e300, |
---|
| 75 | one = 1.0, |
---|
| 76 | invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ |
---|
| 77 | tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
---|
| 78 | /* R0/S0 on [0,2] */ |
---|
| 79 | r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ |
---|
| 80 | r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ |
---|
| 81 | r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ |
---|
| 82 | r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ |
---|
| 83 | s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ |
---|
| 84 | s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ |
---|
| 85 | s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ |
---|
| 86 | s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ |
---|
| 87 | s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ |
---|
| 88 | |
---|
| 89 | #ifdef __STDC__ |
---|
| 90 | static const double zero = 0.0; |
---|
| 91 | #else |
---|
| 92 | static double zero = 0.0; |
---|
| 93 | #endif |
---|
| 94 | |
---|
| 95 | #ifdef __STDC__ |
---|
| 96 | double j1(double x) |
---|
| 97 | #else |
---|
| 98 | double j1(x) |
---|
| 99 | double x; |
---|
| 100 | #endif |
---|
| 101 | { |
---|
| 102 | double z, s,c,ss,cc,r,u,v,y; |
---|
| 103 | __int32_t hx,ix; |
---|
| 104 | |
---|
| 105 | GET_HIGH_WORD(hx,x); |
---|
| 106 | ix = hx&0x7fffffff; |
---|
| 107 | if(ix>=0x7ff00000) return one/x; |
---|
| 108 | y = fabs(x); |
---|
| 109 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
---|
| 110 | s = sin(y); |
---|
| 111 | c = cos(y); |
---|
| 112 | ss = -s-c; |
---|
| 113 | cc = s-c; |
---|
| 114 | if(ix<0x7fe00000) { /* make sure y+y not overflow */ |
---|
| 115 | z = cos(y+y); |
---|
| 116 | if ((s*c)>zero) cc = z/ss; |
---|
| 117 | else ss = z/cc; |
---|
| 118 | } |
---|
| 119 | /* |
---|
| 120 | * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) |
---|
| 121 | * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) |
---|
| 122 | */ |
---|
| 123 | if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y); |
---|
| 124 | else { |
---|
| 125 | u = pone(y); v = qone(y); |
---|
| 126 | z = invsqrtpi*(u*cc-v*ss)/sqrt(y); |
---|
| 127 | } |
---|
| 128 | if(hx<0) return -z; |
---|
| 129 | else return z; |
---|
| 130 | } |
---|
| 131 | if(ix<0x3e400000) { /* |x|<2**-27 */ |
---|
| 132 | if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ |
---|
| 133 | } |
---|
| 134 | z = x*x; |
---|
| 135 | r = z*(r00+z*(r01+z*(r02+z*r03))); |
---|
| 136 | s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); |
---|
| 137 | r *= x; |
---|
| 138 | return(x*0.5+r/s); |
---|
| 139 | } |
---|
| 140 | |
---|
| 141 | #ifdef __STDC__ |
---|
| 142 | static const double U0[5] = { |
---|
| 143 | #else |
---|
| 144 | static double U0[5] = { |
---|
| 145 | #endif |
---|
| 146 | -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ |
---|
| 147 | 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ |
---|
| 148 | -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ |
---|
| 149 | 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ |
---|
| 150 | -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ |
---|
| 151 | }; |
---|
| 152 | #ifdef __STDC__ |
---|
| 153 | static const double V0[5] = { |
---|
| 154 | #else |
---|
| 155 | static double V0[5] = { |
---|
| 156 | #endif |
---|
| 157 | 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ |
---|
| 158 | 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ |
---|
| 159 | 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ |
---|
| 160 | 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ |
---|
| 161 | 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ |
---|
| 162 | }; |
---|
| 163 | |
---|
| 164 | #ifdef __STDC__ |
---|
| 165 | double y1(double x) |
---|
| 166 | #else |
---|
| 167 | double y1(x) |
---|
| 168 | double x; |
---|
| 169 | #endif |
---|
| 170 | { |
---|
| 171 | double z, s,c,ss,cc,u,v; |
---|
| 172 | __int32_t hx,ix,lx; |
---|
| 173 | |
---|
| 174 | EXTRACT_WORDS(hx,lx,x); |
---|
| 175 | ix = 0x7fffffff&hx; |
---|
| 176 | /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ |
---|
| 177 | if(ix>=0x7ff00000) return one/(x+x*x); |
---|
| 178 | if((ix|lx)==0) return -one/zero; |
---|
| 179 | if(hx<0) return zero/zero; |
---|
| 180 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
---|
| 181 | s = sin(x); |
---|
| 182 | c = cos(x); |
---|
| 183 | ss = -s-c; |
---|
| 184 | cc = s-c; |
---|
| 185 | if(ix<0x7fe00000) { /* make sure x+x not overflow */ |
---|
| 186 | z = cos(x+x); |
---|
| 187 | if ((s*c)>zero) cc = z/ss; |
---|
| 188 | else ss = z/cc; |
---|
| 189 | } |
---|
| 190 | /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) |
---|
| 191 | * where x0 = x-3pi/4 |
---|
| 192 | * Better formula: |
---|
| 193 | * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) |
---|
| 194 | * = 1/sqrt(2) * (sin(x) - cos(x)) |
---|
| 195 | * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) |
---|
| 196 | * = -1/sqrt(2) * (cos(x) + sin(x)) |
---|
| 197 | * To avoid cancellation, use |
---|
| 198 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
---|
| 199 | * to compute the worse one. |
---|
| 200 | */ |
---|
| 201 | if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); |
---|
| 202 | else { |
---|
| 203 | u = pone(x); v = qone(x); |
---|
| 204 | z = invsqrtpi*(u*ss+v*cc)/sqrt(x); |
---|
| 205 | } |
---|
| 206 | return z; |
---|
| 207 | } |
---|
| 208 | if(ix<=0x3c900000) { /* x < 2**-54 */ |
---|
| 209 | return(-tpi/x); |
---|
| 210 | } |
---|
| 211 | z = x*x; |
---|
| 212 | u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); |
---|
| 213 | v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); |
---|
| 214 | return(x*(u/v) + tpi*(j1(x)*log(x)-one/x)); |
---|
| 215 | } |
---|
| 216 | |
---|
| 217 | /* For x >= 8, the asymptotic expansions of pone is |
---|
| 218 | * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. |
---|
| 219 | * We approximate pone by |
---|
| 220 | * pone(x) = 1 + (R/S) |
---|
| 221 | * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 |
---|
| 222 | * S = 1 + ps0*s^2 + ... + ps4*s^10 |
---|
| 223 | * and |
---|
| 224 | * | pone(x)-1-R/S | <= 2 ** ( -60.06) |
---|
| 225 | */ |
---|
| 226 | |
---|
| 227 | #ifdef __STDC__ |
---|
| 228 | static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
---|
| 229 | #else |
---|
| 230 | static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
---|
| 231 | #endif |
---|
| 232 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
---|
| 233 | 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ |
---|
| 234 | 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ |
---|
| 235 | 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ |
---|
| 236 | 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ |
---|
| 237 | 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ |
---|
| 238 | }; |
---|
| 239 | #ifdef __STDC__ |
---|
| 240 | static const double ps8[5] = { |
---|
| 241 | #else |
---|
| 242 | static double ps8[5] = { |
---|
| 243 | #endif |
---|
| 244 | 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ |
---|
| 245 | 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ |
---|
| 246 | 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ |
---|
| 247 | 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ |
---|
| 248 | 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ |
---|
| 249 | }; |
---|
| 250 | |
---|
| 251 | #ifdef __STDC__ |
---|
| 252 | static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
---|
| 253 | #else |
---|
| 254 | static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
---|
| 255 | #endif |
---|
| 256 | 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ |
---|
| 257 | 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ |
---|
| 258 | 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ |
---|
| 259 | 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ |
---|
| 260 | 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ |
---|
| 261 | 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ |
---|
| 262 | }; |
---|
| 263 | #ifdef __STDC__ |
---|
| 264 | static const double ps5[5] = { |
---|
| 265 | #else |
---|
| 266 | static double ps5[5] = { |
---|
| 267 | #endif |
---|
| 268 | 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ |
---|
| 269 | 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ |
---|
| 270 | 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ |
---|
| 271 | 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ |
---|
| 272 | 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ |
---|
| 273 | }; |
---|
| 274 | |
---|
| 275 | #ifdef __STDC__ |
---|
| 276 | static const double pr3[6] = { |
---|
| 277 | #else |
---|
| 278 | static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
---|
| 279 | #endif |
---|
| 280 | 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ |
---|
| 281 | 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ |
---|
| 282 | 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ |
---|
| 283 | 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ |
---|
| 284 | 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ |
---|
| 285 | 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ |
---|
| 286 | }; |
---|
| 287 | #ifdef __STDC__ |
---|
| 288 | static const double ps3[5] = { |
---|
| 289 | #else |
---|
| 290 | static double ps3[5] = { |
---|
| 291 | #endif |
---|
| 292 | 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ |
---|
| 293 | 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ |
---|
| 294 | 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ |
---|
| 295 | 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ |
---|
| 296 | 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ |
---|
| 297 | }; |
---|
| 298 | |
---|
| 299 | #ifdef __STDC__ |
---|
| 300 | static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
---|
| 301 | #else |
---|
| 302 | static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
---|
| 303 | #endif |
---|
| 304 | 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ |
---|
| 305 | 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ |
---|
| 306 | 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ |
---|
| 307 | 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ |
---|
| 308 | 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ |
---|
| 309 | 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ |
---|
| 310 | }; |
---|
| 311 | #ifdef __STDC__ |
---|
| 312 | static const double ps2[5] = { |
---|
| 313 | #else |
---|
| 314 | static double ps2[5] = { |
---|
| 315 | #endif |
---|
| 316 | 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ |
---|
| 317 | 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ |
---|
| 318 | 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ |
---|
| 319 | 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ |
---|
| 320 | 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ |
---|
| 321 | }; |
---|
| 322 | |
---|
| 323 | #ifdef __STDC__ |
---|
| 324 | static double pone(double x) |
---|
| 325 | #else |
---|
| 326 | static double pone(x) |
---|
| 327 | double x; |
---|
| 328 | #endif |
---|
| 329 | { |
---|
| 330 | #ifdef __STDC__ |
---|
| 331 | const double *p,*q; |
---|
| 332 | #else |
---|
| 333 | double *p,*q; |
---|
| 334 | #endif |
---|
| 335 | double z,r,s; |
---|
| 336 | __int32_t ix; |
---|
| 337 | GET_HIGH_WORD(ix,x); |
---|
| 338 | ix &= 0x7fffffff; |
---|
| 339 | if(ix>=0x40200000) {p = pr8; q= ps8;} |
---|
| 340 | else if(ix>=0x40122E8B){p = pr5; q= ps5;} |
---|
| 341 | else if(ix>=0x4006DB6D){p = pr3; q= ps3;} |
---|
| 342 | else {p = pr2; q= ps2;} |
---|
| 343 | z = one/(x*x); |
---|
| 344 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
---|
| 345 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); |
---|
| 346 | return one+ r/s; |
---|
| 347 | } |
---|
| 348 | |
---|
| 349 | |
---|
| 350 | /* For x >= 8, the asymptotic expansions of qone is |
---|
| 351 | * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. |
---|
| 352 | * We approximate qone by |
---|
| 353 | * qone(x) = s*(0.375 + (R/S)) |
---|
| 354 | * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 |
---|
| 355 | * S = 1 + qs1*s^2 + ... + qs6*s^12 |
---|
| 356 | * and |
---|
| 357 | * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) |
---|
| 358 | */ |
---|
| 359 | |
---|
| 360 | #ifdef __STDC__ |
---|
| 361 | static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
---|
| 362 | #else |
---|
| 363 | static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
---|
| 364 | #endif |
---|
| 365 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
---|
| 366 | -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ |
---|
| 367 | -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ |
---|
| 368 | -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ |
---|
| 369 | -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ |
---|
| 370 | -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ |
---|
| 371 | }; |
---|
| 372 | #ifdef __STDC__ |
---|
| 373 | static const double qs8[6] = { |
---|
| 374 | #else |
---|
| 375 | static double qs8[6] = { |
---|
| 376 | #endif |
---|
| 377 | 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ |
---|
| 378 | 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ |
---|
| 379 | 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ |
---|
| 380 | 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ |
---|
| 381 | 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ |
---|
| 382 | -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ |
---|
| 383 | }; |
---|
| 384 | |
---|
| 385 | #ifdef __STDC__ |
---|
| 386 | static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
---|
| 387 | #else |
---|
| 388 | static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
---|
| 389 | #endif |
---|
| 390 | -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ |
---|
| 391 | -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ |
---|
| 392 | -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ |
---|
| 393 | -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ |
---|
| 394 | -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ |
---|
| 395 | -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ |
---|
| 396 | }; |
---|
| 397 | #ifdef __STDC__ |
---|
| 398 | static const double qs5[6] = { |
---|
| 399 | #else |
---|
| 400 | static double qs5[6] = { |
---|
| 401 | #endif |
---|
| 402 | 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ |
---|
| 403 | 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ |
---|
| 404 | 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ |
---|
| 405 | 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ |
---|
| 406 | 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ |
---|
| 407 | -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ |
---|
| 408 | }; |
---|
| 409 | |
---|
| 410 | #ifdef __STDC__ |
---|
| 411 | static const double qr3[6] = { |
---|
| 412 | #else |
---|
| 413 | static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
---|
| 414 | #endif |
---|
| 415 | -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ |
---|
| 416 | -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ |
---|
| 417 | -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ |
---|
| 418 | -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ |
---|
| 419 | -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ |
---|
| 420 | -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ |
---|
| 421 | }; |
---|
| 422 | #ifdef __STDC__ |
---|
| 423 | static const double qs3[6] = { |
---|
| 424 | #else |
---|
| 425 | static double qs3[6] = { |
---|
| 426 | #endif |
---|
| 427 | 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ |
---|
| 428 | 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ |
---|
| 429 | 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ |
---|
| 430 | 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ |
---|
| 431 | 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ |
---|
| 432 | -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ |
---|
| 433 | }; |
---|
| 434 | |
---|
| 435 | #ifdef __STDC__ |
---|
| 436 | static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
---|
| 437 | #else |
---|
| 438 | static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
---|
| 439 | #endif |
---|
| 440 | -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ |
---|
| 441 | -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ |
---|
| 442 | -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ |
---|
| 443 | -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ |
---|
| 444 | -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ |
---|
| 445 | -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ |
---|
| 446 | }; |
---|
| 447 | #ifdef __STDC__ |
---|
| 448 | static const double qs2[6] = { |
---|
| 449 | #else |
---|
| 450 | static double qs2[6] = { |
---|
| 451 | #endif |
---|
| 452 | 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ |
---|
| 453 | 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ |
---|
| 454 | 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ |
---|
| 455 | 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ |
---|
| 456 | 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ |
---|
| 457 | -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ |
---|
| 458 | }; |
---|
| 459 | |
---|
| 460 | #ifdef __STDC__ |
---|
| 461 | static double qone(double x) |
---|
| 462 | #else |
---|
| 463 | static double qone(x) |
---|
| 464 | double x; |
---|
| 465 | #endif |
---|
| 466 | { |
---|
| 467 | #ifdef __STDC__ |
---|
| 468 | const double *p,*q; |
---|
| 469 | #else |
---|
| 470 | double *p,*q; |
---|
| 471 | #endif |
---|
| 472 | double s,r,z; |
---|
| 473 | __int32_t ix; |
---|
| 474 | GET_HIGH_WORD(ix,x); |
---|
| 475 | ix &= 0x7fffffff; |
---|
| 476 | if(ix>=0x40200000) {p = qr8; q= qs8;} |
---|
| 477 | else if(ix>=0x40122E8B){p = qr5; q= qs5;} |
---|
| 478 | else if(ix>=0x4006DB6D){p = qr3; q= qs3;} |
---|
| 479 | else {p = qr2; q= qs2;} |
---|
| 480 | z = one/(x*x); |
---|
| 481 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
---|
| 482 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); |
---|
| 483 | return (.375 + r/s)/x; |
---|
| 484 | } |
---|
| 485 | |
---|
| 486 | #endif /* defined(_DOUBLE_IS_32BITS) */ |
---|