| 1 |
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*- |
| 2 |
* |
| 3 |
* ***** BEGIN LICENSE BLOCK ***** |
| 4 |
* Version: MPL 1.1/GPL 2.0/LGPL 2.1 |
| 5 |
* |
| 6 |
* The contents of this file are subject to the Mozilla Public License Version |
| 7 |
* 1.1 (the "License"); you may not use this file except in compliance with |
| 8 |
* the License. You may obtain a copy of the License at |
| 9 |
* http://www.mozilla.org/MPL/ |
| 10 |
* |
| 11 |
* Software distributed under the License is distributed on an "AS IS" basis, |
| 12 |
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License |
| 13 |
* for the specific language governing rights and limitations under the |
| 14 |
* License. |
| 15 |
* |
| 16 |
* The Original Code is Mozilla Communicator client code, released |
| 17 |
* March 31, 1998. |
| 18 |
* |
| 19 |
* The Initial Developer of the Original Code is |
| 20 |
* Sun Microsystems, Inc. |
| 21 |
* Portions created by the Initial Developer are Copyright (C) 1998 |
| 22 |
* the Initial Developer. All Rights Reserved. |
| 23 |
* |
| 24 |
* Contributor(s): |
| 25 |
* |
| 26 |
* Alternatively, the contents of this file may be used under the terms of |
| 27 |
* either of the GNU General Public License Version 2 or later (the "GPL"), |
| 28 |
* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), |
| 29 |
* in which case the provisions of the GPL or the LGPL are applicable instead |
| 30 |
* of those above. If you wish to allow use of your version of this file only |
| 31 |
* under the terms of either the GPL or the LGPL, and not to allow others to |
| 32 |
* use your version of this file under the terms of the MPL, indicate your |
| 33 |
* decision by deleting the provisions above and replace them with the notice |
| 34 |
* and other provisions required by the GPL or the LGPL. If you do not delete |
| 35 |
* the provisions above, a recipient may use your version of this file under |
| 36 |
* the terms of any one of the MPL, the GPL or the LGPL. |
| 37 |
* |
| 38 |
* ***** END LICENSE BLOCK ***** */ |
| 39 |
|
| 40 |
/* @(#)e_j1.c 1.3 95/01/18 */ |
| 41 |
/* |
| 42 |
* ==================================================== |
| 43 |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 44 |
* |
| 45 |
* Developed at SunSoft, a Sun Microsystems, Inc. business. |
| 46 |
* Permission to use, copy, modify, and distribute this |
| 47 |
* software is freely granted, provided that this notice |
| 48 |
* is preserved. |
| 49 |
* ==================================================== |
| 50 |
*/ |
| 51 |
|
| 52 |
/* __ieee754_j1(x), __ieee754_y1(x) |
| 53 |
* Bessel function of the first and second kinds of order zero. |
| 54 |
* Method -- j1(x): |
| 55 |
* 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... |
| 56 |
* 2. Reduce x to |x| since j1(x)=-j1(-x), and |
| 57 |
* for x in (0,2) |
| 58 |
* j1(x) = x/2 + x*z*R0/S0, where z = x*x; |
| 59 |
* (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) |
| 60 |
* for x in (2,inf) |
| 61 |
* j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) |
| 62 |
* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) |
| 63 |
* where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) |
| 64 |
* as follow: |
| 65 |
* cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) |
| 66 |
* = 1/sqrt(2) * (sin(x) - cos(x)) |
| 67 |
* sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) |
| 68 |
* = -1/sqrt(2) * (sin(x) + cos(x)) |
| 69 |
* (To avoid cancellation, use |
| 70 |
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
| 71 |
* to compute the worse one.) |
| 72 |
* |
| 73 |
* 3 Special cases |
| 74 |
* j1(nan)= nan |
| 75 |
* j1(0) = 0 |
| 76 |
* j1(inf) = 0 |
| 77 |
* |
| 78 |
* Method -- y1(x): |
| 79 |
* 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN |
| 80 |
* 2. For x<2. |
| 81 |
* Since |
| 82 |
* y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) |
| 83 |
* therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. |
| 84 |
* We use the following function to approximate y1, |
| 85 |
* y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 |
| 86 |
* where for x in [0,2] (abs err less than 2**-65.89) |
| 87 |
* U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 |
| 88 |
* V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 |
| 89 |
* Note: For tiny x, 1/x dominate y1 and hence |
| 90 |
* y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) |
| 91 |
* 3. For x>=2. |
| 92 |
* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) |
| 93 |
* where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) |
| 94 |
* by method mentioned above. |
| 95 |
*/ |
| 96 |
|
| 97 |
#include "fdlibm.h" |
| 98 |
|
| 99 |
#ifdef __STDC__ |
| 100 |
static double pone(double), qone(double); |
| 101 |
#else |
| 102 |
static double pone(), qone(); |
| 103 |
#endif |
| 104 |
|
| 105 |
#ifdef __STDC__ |
| 106 |
static const double |
| 107 |
#else |
| 108 |
static double |
| 109 |
#endif |
| 110 |
really_big = 1e300, |
| 111 |
one = 1.0, |
| 112 |
invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ |
| 113 |
tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
| 114 |
/* R0/S0 on [0,2] */ |
| 115 |
r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ |
| 116 |
r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ |
| 117 |
r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ |
| 118 |
r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ |
| 119 |
s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ |
| 120 |
s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ |
| 121 |
s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ |
| 122 |
s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ |
| 123 |
s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ |
| 124 |
|
| 125 |
static double zero = 0.0; |
| 126 |
|
| 127 |
#ifdef __STDC__ |
| 128 |
double __ieee754_j1(double x) |
| 129 |
#else |
| 130 |
double __ieee754_j1(x) |
| 131 |
double x; |
| 132 |
#endif |
| 133 |
{ |
| 134 |
fd_twoints un; |
| 135 |
double z, s,c,ss,cc,r,u,v,y; |
| 136 |
int hx,ix; |
| 137 |
|
| 138 |
un.d = x; |
| 139 |
hx = __HI(un); |
| 140 |
ix = hx&0x7fffffff; |
| 141 |
if(ix>=0x7ff00000) return one/x; |
| 142 |
y = fd_fabs(x); |
| 143 |
if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
| 144 |
s = fd_sin(y); |
| 145 |
c = fd_cos(y); |
| 146 |
ss = -s-c; |
| 147 |
cc = s-c; |
| 148 |
if(ix<0x7fe00000) { /* make sure y+y not overflow */ |
| 149 |
z = fd_cos(y+y); |
| 150 |
if ((s*c)>zero) cc = z/ss; |
| 151 |
else ss = z/cc; |
| 152 |
} |
| 153 |
/* |
| 154 |
* j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) |
| 155 |
* y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) |
| 156 |
*/ |
| 157 |
if(ix>0x48000000) z = (invsqrtpi*cc)/fd_sqrt(y); |
| 158 |
else { |
| 159 |
u = pone(y); v = qone(y); |
| 160 |
z = invsqrtpi*(u*cc-v*ss)/fd_sqrt(y); |
| 161 |
} |
| 162 |
if(hx<0) return -z; |
| 163 |
else return z; |
| 164 |
} |
| 165 |
if(ix<0x3e400000) { /* |x|<2**-27 */ |
| 166 |
if(really_big+x>one) return 0.5*x;/* inexact if x!=0 necessary */ |
| 167 |
} |
| 168 |
z = x*x; |
| 169 |
r = z*(r00+z*(r01+z*(r02+z*r03))); |
| 170 |
s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); |
| 171 |
r *= x; |
| 172 |
return(x*0.5+r/s); |
| 173 |
} |
| 174 |
|
| 175 |
#ifdef __STDC__ |
| 176 |
static const double U0[5] = { |
| 177 |
#else |
| 178 |
static double U0[5] = { |
| 179 |
#endif |
| 180 |
-1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ |
| 181 |
5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ |
| 182 |
-1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ |
| 183 |
2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ |
| 184 |
-9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ |
| 185 |
}; |
| 186 |
#ifdef __STDC__ |
| 187 |
static const double V0[5] = { |
| 188 |
#else |
| 189 |
static double V0[5] = { |
| 190 |
#endif |
| 191 |
1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ |
| 192 |
2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ |
| 193 |
1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ |
| 194 |
6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ |
| 195 |
1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ |
| 196 |
}; |
| 197 |
|
| 198 |
#ifdef __STDC__ |
| 199 |
double __ieee754_y1(double x) |
| 200 |
#else |
| 201 |
double __ieee754_y1(x) |
| 202 |
double x; |
| 203 |
#endif |
| 204 |
{ |
| 205 |
fd_twoints un; |
| 206 |
double z, s,c,ss,cc,u,v; |
| 207 |
int hx,ix,lx; |
| 208 |
|
| 209 |
un.d = x; |
| 210 |
hx = __HI(un); |
| 211 |
ix = 0x7fffffff&hx; |
| 212 |
lx = __LO(un); |
| 213 |
/* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ |
| 214 |
if(ix>=0x7ff00000) return one/(x+x*x); |
| 215 |
if((ix|lx)==0) return -one/zero; |
| 216 |
if(hx<0) return zero/zero; |
| 217 |
if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
| 218 |
s = fd_sin(x); |
| 219 |
c = fd_cos(x); |
| 220 |
ss = -s-c; |
| 221 |
cc = s-c; |
| 222 |
if(ix<0x7fe00000) { /* make sure x+x not overflow */ |
| 223 |
z = fd_cos(x+x); |
| 224 |
if ((s*c)>zero) cc = z/ss; |
| 225 |
else ss = z/cc; |
| 226 |
} |
| 227 |
/* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) |
| 228 |
* where x0 = x-3pi/4 |
| 229 |
* Better formula: |
| 230 |
* cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) |
| 231 |
* = 1/sqrt(2) * (sin(x) - cos(x)) |
| 232 |
* sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) |
| 233 |
* = -1/sqrt(2) * (cos(x) + sin(x)) |
| 234 |
* To avoid cancellation, use |
| 235 |
* sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
| 236 |
* to compute the worse one. |
| 237 |
*/ |
| 238 |
if(ix>0x48000000) z = (invsqrtpi*ss)/fd_sqrt(x); |
| 239 |
else { |
| 240 |
u = pone(x); v = qone(x); |
| 241 |
z = invsqrtpi*(u*ss+v*cc)/fd_sqrt(x); |
| 242 |
} |
| 243 |
return z; |
| 244 |
} |
| 245 |
if(ix<=0x3c900000) { /* x < 2**-54 */ |
| 246 |
return(-tpi/x); |
| 247 |
} |
| 248 |
z = x*x; |
| 249 |
u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); |
| 250 |
v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); |
| 251 |
return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); |
| 252 |
} |
| 253 |
|
| 254 |
/* For x >= 8, the asymptotic expansions of pone is |
| 255 |
* 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. |
| 256 |
* We approximate pone by |
| 257 |
* pone(x) = 1 + (R/S) |
| 258 |
* where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 |
| 259 |
* S = 1 + ps0*s^2 + ... + ps4*s^10 |
| 260 |
* and |
| 261 |
* | pone(x)-1-R/S | <= 2 ** ( -60.06) |
| 262 |
*/ |
| 263 |
|
| 264 |
#ifdef __STDC__ |
| 265 |
static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
| 266 |
#else |
| 267 |
static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
| 268 |
#endif |
| 269 |
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
| 270 |
1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ |
| 271 |
1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ |
| 272 |
4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ |
| 273 |
3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ |
| 274 |
7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ |
| 275 |
}; |
| 276 |
#ifdef __STDC__ |
| 277 |
static const double ps8[5] = { |
| 278 |
#else |
| 279 |
static double ps8[5] = { |
| 280 |
#endif |
| 281 |
1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ |
| 282 |
3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ |
| 283 |
3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ |
| 284 |
9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ |
| 285 |
3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ |
| 286 |
}; |
| 287 |
|
| 288 |
#ifdef __STDC__ |
| 289 |
static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
| 290 |
#else |
| 291 |
static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
| 292 |
#endif |
| 293 |
1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ |
| 294 |
1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ |
| 295 |
6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ |
| 296 |
1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ |
| 297 |
5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ |
| 298 |
5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ |
| 299 |
}; |
| 300 |
#ifdef __STDC__ |
| 301 |
static const double ps5[5] = { |
| 302 |
#else |
| 303 |
static double ps5[5] = { |
| 304 |
#endif |
| 305 |
5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ |
| 306 |
9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ |
| 307 |
5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ |
| 308 |
7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ |
| 309 |
1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ |
| 310 |
}; |
| 311 |
|
| 312 |
#ifdef __STDC__ |
| 313 |
static const double pr3[6] = { |
| 314 |
#else |
| 315 |
static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
| 316 |
#endif |
| 317 |
3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ |
| 318 |
1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ |
| 319 |
3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ |
| 320 |
3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ |
| 321 |
9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ |
| 322 |
4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ |
| 323 |
}; |
| 324 |
#ifdef __STDC__ |
| 325 |
static const double ps3[5] = { |
| 326 |
#else |
| 327 |
static double ps3[5] = { |
| 328 |
#endif |
| 329 |
3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ |
| 330 |
3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ |
| 331 |
1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ |
| 332 |
8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ |
| 333 |
1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ |
| 334 |
}; |
| 335 |
|
| 336 |
#ifdef __STDC__ |
| 337 |
static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
| 338 |
#else |
| 339 |
static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
| 340 |
#endif |
| 341 |
1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ |
| 342 |
1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ |
| 343 |
2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ |
| 344 |
1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ |
| 345 |
1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ |
| 346 |
5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ |
| 347 |
}; |
| 348 |
#ifdef __STDC__ |
| 349 |
static const double ps2[5] = { |
| 350 |
#else |
| 351 |
static double ps2[5] = { |
| 352 |
#endif |
| 353 |
2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ |
| 354 |
1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ |
| 355 |
2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ |
| 356 |
1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ |
| 357 |
8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ |
| 358 |
}; |
| 359 |
|
| 360 |
#ifdef __STDC__ |
| 361 |
static double pone(double x) |
| 362 |
#else |
| 363 |
static double pone(x) |
| 364 |
double x; |
| 365 |
#endif |
| 366 |
{ |
| 367 |
#ifdef __STDC__ |
| 368 |
const double *p,*q; |
| 369 |
#else |
| 370 |
double *p,*q; |
| 371 |
#endif |
| 372 |
fd_twoints un; |
| 373 |
double z,r,s; |
| 374 |
int ix; |
| 375 |
un.d = x; |
| 376 |
ix = 0x7fffffff&__HI(un); |
| 377 |
if(ix>=0x40200000) {p = pr8; q= ps8;} |
| 378 |
else if(ix>=0x40122E8B){p = pr5; q= ps5;} |
| 379 |
else if(ix>=0x4006DB6D){p = pr3; q= ps3;} |
| 380 |
else if(ix>=0x40000000){p = pr2; q= ps2;} |
| 381 |
z = one/(x*x); |
| 382 |
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
| 383 |
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); |
| 384 |
return one+ r/s; |
| 385 |
} |
| 386 |
|
| 387 |
|
| 388 |
/* For x >= 8, the asymptotic expansions of qone is |
| 389 |
* 3/8 s - 105/1024 s^3 - ..., where s = 1/x. |
| 390 |
* We approximate pone by |
| 391 |
* qone(x) = s*(0.375 + (R/S)) |
| 392 |
* where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 |
| 393 |
* S = 1 + qs1*s^2 + ... + qs6*s^12 |
| 394 |
* and |
| 395 |
* | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) |
| 396 |
*/ |
| 397 |
|
| 398 |
#ifdef __STDC__ |
| 399 |
static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
| 400 |
#else |
| 401 |
static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
| 402 |
#endif |
| 403 |
0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
| 404 |
-1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ |
| 405 |
-1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ |
| 406 |
-7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ |
| 407 |
-1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ |
| 408 |
-4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ |
| 409 |
}; |
| 410 |
#ifdef __STDC__ |
| 411 |
static const double qs8[6] = { |
| 412 |
#else |
| 413 |
static double qs8[6] = { |
| 414 |
#endif |
| 415 |
1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ |
| 416 |
7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ |
| 417 |
1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ |
| 418 |
7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ |
| 419 |
6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ |
| 420 |
-2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ |
| 421 |
}; |
| 422 |
|
| 423 |
#ifdef __STDC__ |
| 424 |
static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
| 425 |
#else |
| 426 |
static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
| 427 |
#endif |
| 428 |
-2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ |
| 429 |
-1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ |
| 430 |
-8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ |
| 431 |
-1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ |
| 432 |
-1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ |
| 433 |
-2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ |
| 434 |
}; |
| 435 |
#ifdef __STDC__ |
| 436 |
static const double qs5[6] = { |
| 437 |
#else |
| 438 |
static double qs5[6] = { |
| 439 |
#endif |
| 440 |
8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ |
| 441 |
1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ |
| 442 |
1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ |
| 443 |
4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ |
| 444 |
2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ |
| 445 |
-4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ |
| 446 |
}; |
| 447 |
|
| 448 |
#ifdef __STDC__ |
| 449 |
static const double qr3[6] = { |
| 450 |
#else |
| 451 |
static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
| 452 |
#endif |
| 453 |
-5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ |
| 454 |
-1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ |
| 455 |
-4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ |
| 456 |
-5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ |
| 457 |
-2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ |
| 458 |
-2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ |
| 459 |
}; |
| 460 |
#ifdef __STDC__ |
| 461 |
static const double qs3[6] = { |
| 462 |
#else |
| 463 |
static double qs3[6] = { |
| 464 |
#endif |
| 465 |
4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ |
| 466 |
6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ |
| 467 |
3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ |
| 468 |
5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ |
| 469 |
1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ |
| 470 |
-1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ |
| 471 |
}; |
| 472 |
|
| 473 |
#ifdef __STDC__ |
| 474 |
static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
| 475 |
#else |
| 476 |
static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
| 477 |
#endif |
| 478 |
-1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ |
| 479 |
-1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ |
| 480 |
-2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ |
| 481 |
-1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ |
| 482 |
-4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ |
| 483 |
-2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ |
| 484 |
}; |
| 485 |
#ifdef __STDC__ |
| 486 |
static const double qs2[6] = { |
| 487 |
#else |
| 488 |
static double qs2[6] = { |
| 489 |
#endif |
| 490 |
2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ |
| 491 |
2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ |
| 492 |
7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ |
| 493 |
7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ |
| 494 |
1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ |
| 495 |
-4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ |
| 496 |
}; |
| 497 |
|
| 498 |
#ifdef __STDC__ |
| 499 |
static double qone(double x) |
| 500 |
#else |
| 501 |
static double qone(x) |
| 502 |
double x; |
| 503 |
#endif |
| 504 |
{ |
| 505 |
#ifdef __STDC__ |
| 506 |
const double *p,*q; |
| 507 |
#else |
| 508 |
double *p,*q; |
| 509 |
#endif |
| 510 |
fd_twoints un; |
| 511 |
double s,r,z; |
| 512 |
int ix; |
| 513 |
un.d = x; |
| 514 |
ix = 0x7fffffff&__HI(un); |
| 515 |
if(ix>=0x40200000) {p = qr8; q= qs8;} |
| 516 |
else if(ix>=0x40122E8B){p = qr5; q= qs5;} |
| 517 |
else if(ix>=0x4006DB6D){p = qr3; q= qs3;} |
| 518 |
else if(ix>=0x40000000){p = qr2; q= qs2;} |
| 519 |
z = one/(x*x); |
| 520 |
r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
| 521 |
s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); |
| 522 |
return (.375 + r/s)/x; |
| 523 |
} |
Parent Directory
| 
Revision Log