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_j0.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_j0(x), __ieee754_y0(x) 53 * Bessel function of the first and second kinds of order zero. 54 * Method -- j0(x): 55 * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... 56 * 2. Reduce x to |x| since j0(x)=j0(-x), and 57 * for x in (0,2) 58 * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; 59 * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) 60 * for x in (2,inf) 61 * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) 62 * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) 63 * as follow: 64 * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) 65 * = 1/sqrt(2) * (cos(x) + sin(x)) 66 * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) 67 * = 1/sqrt(2) * (sin(x) - cos(x)) 68 * (To avoid cancellation, use 69 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 70 * to compute the worse one.) 71 * 72 * 3 Special cases 73 * j0(nan)= nan 74 * j0(0) = 1 75 * j0(inf) = 0 76 * 77 * Method -- y0(x): 78 * 1. For x<2. 79 * Since 80 * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) 81 * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. 82 * We use the following function to approximate y0, 83 * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 84 * where 85 * U(z) = u00 + u01*z + ... + u06*z^6 86 * V(z) = 1 + v01*z + ... + v04*z^4 87 * with absolute approximation error bounded by 2**-72. 88 * Note: For tiny x, U/V = u0 and j0(x)~1, hence 89 * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) 90 * 2. For x>=2. 91 * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) 92 * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) 93 * by the method mentioned above. 94 * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. 95 */ 96 97 #include "fdlibm.h" 98 99 #ifdef __STDC__ 100 static double pzero(double), qzero(double); 101 #else 102 static double pzero(), qzero(); 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, 2.00] */ 115 R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ 116 R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ 117 R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ 118 R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ 119 S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ 120 S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ 121 S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ 122 S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ 123 124 static double zero = 0.0; 125 126 #ifdef __STDC__ __ieee754_j0(double x)127 double __ieee754_j0(double x) 128 #else 129 double __ieee754_j0(x) 130 double x; 131 #endif 132 { 133 fd_twoints un; 134 double z, s,c,ss,cc,r,u,v; 135 int hx,ix; 136 137 un.d = x; 138 hx = __HI(un); 139 ix = hx&0x7fffffff; 140 if(ix>=0x7ff00000) return one/(x*x); 141 x = fd_fabs(x); 142 if(ix >= 0x40000000) { /* |x| >= 2.0 */ 143 s = fd_sin(x); 144 c = fd_cos(x); 145 ss = s-c; 146 cc = s+c; 147 if(ix<0x7fe00000) { /* make sure x+x not overflow */ 148 z = -fd_cos(x+x); 149 if ((s*c)<zero) cc = z/ss; 150 else ss = z/cc; 151 } 152 /* 153 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) 154 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) 155 */ 156 if(ix>0x48000000) z = (invsqrtpi*cc)/fd_sqrt(x); 157 else { 158 u = pzero(x); v = qzero(x); 159 z = invsqrtpi*(u*cc-v*ss)/fd_sqrt(x); 160 } 161 return z; 162 } 163 if(ix<0x3f200000) { /* |x| < 2**-13 */ 164 if(really_big+x>one) { /* raise inexact if x != 0 */ 165 if(ix<0x3e400000) return one; /* |x|<2**-27 */ 166 else return one - 0.25*x*x; 167 } 168 } 169 z = x*x; 170 r = z*(R02+z*(R03+z*(R04+z*R05))); 171 s = one+z*(S01+z*(S02+z*(S03+z*S04))); 172 if(ix < 0x3FF00000) { /* |x| < 1.00 */ 173 return one + z*(-0.25+(r/s)); 174 } else { 175 u = 0.5*x; 176 return((one+u)*(one-u)+z*(r/s)); 177 } 178 } 179 180 #ifdef __STDC__ 181 static const double 182 #else 183 static double 184 #endif 185 u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ 186 u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ 187 u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ 188 u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ 189 u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ 190 u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ 191 u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ 192 v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ 193 v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ 194 v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ 195 v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ 196 197 #ifdef __STDC__ __ieee754_y0(double x)198 double __ieee754_y0(double x) 199 #else 200 double __ieee754_y0(x) 201 double x; 202 #endif 203 { 204 fd_twoints un; 205 double z, s,c,ss,cc,u,v; 206 int hx,ix,lx; 207 208 un.d = x; 209 hx = __HI(un); 210 ix = 0x7fffffff&hx; 211 lx = __LO(un); 212 /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ 213 if(ix>=0x7ff00000) return one/(x+x*x); 214 if((ix|lx)==0) return -one/zero; 215 if(hx<0) return zero/zero; 216 if(ix >= 0x40000000) { /* |x| >= 2.0 */ 217 /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) 218 * where x0 = x-pi/4 219 * Better formula: 220 * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) 221 * = 1/sqrt(2) * (sin(x) + cos(x)) 222 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 223 * = 1/sqrt(2) * (sin(x) - cos(x)) 224 * To avoid cancellation, use 225 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 226 * to compute the worse one. 227 */ 228 s = fd_sin(x); 229 c = fd_cos(x); 230 ss = s-c; 231 cc = s+c; 232 /* 233 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) 234 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) 235 */ 236 if(ix<0x7fe00000) { /* make sure x+x not overflow */ 237 z = -fd_cos(x+x); 238 if ((s*c)<zero) cc = z/ss; 239 else ss = z/cc; 240 } 241 if(ix>0x48000000) z = (invsqrtpi*ss)/fd_sqrt(x); 242 else { 243 u = pzero(x); v = qzero(x); 244 z = invsqrtpi*(u*ss+v*cc)/fd_sqrt(x); 245 } 246 return z; 247 } 248 if(ix<=0x3e400000) { /* x < 2**-27 */ 249 return(u00 + tpi*__ieee754_log(x)); 250 } 251 z = x*x; 252 u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); 253 v = one+z*(v01+z*(v02+z*(v03+z*v04))); 254 return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); 255 } 256 257 /* The asymptotic expansions of pzero is 258 * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. 259 * For x >= 2, We approximate pzero by 260 * pzero(x) = 1 + (R/S) 261 * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 262 * S = 1 + pS0*s^2 + ... + pS4*s^10 263 * and 264 * | pzero(x)-1-R/S | <= 2 ** ( -60.26) 265 */ 266 #ifdef __STDC__ 267 static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 268 #else 269 static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 270 #endif 271 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 272 -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ 273 -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ 274 -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ 275 -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ 276 -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ 277 }; 278 #ifdef __STDC__ 279 static const double pS8[5] = { 280 #else 281 static double pS8[5] = { 282 #endif 283 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ 284 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ 285 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ 286 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ 287 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ 288 }; 289 290 #ifdef __STDC__ 291 static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 292 #else 293 static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 294 #endif 295 -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ 296 -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ 297 -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ 298 -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ 299 -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ 300 -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ 301 }; 302 #ifdef __STDC__ 303 static const double pS5[5] = { 304 #else 305 static double pS5[5] = { 306 #endif 307 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ 308 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ 309 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ 310 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ 311 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ 312 }; 313 314 #ifdef __STDC__ 315 static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 316 #else 317 static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 318 #endif 319 -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ 320 -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ 321 -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ 322 -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ 323 -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ 324 -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ 325 }; 326 #ifdef __STDC__ 327 static const double pS3[5] = { 328 #else 329 static double pS3[5] = { 330 #endif 331 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ 332 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ 333 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ 334 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ 335 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ 336 }; 337 338 #ifdef __STDC__ 339 static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 340 #else 341 static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 342 #endif 343 -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ 344 -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ 345 -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ 346 -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ 347 -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ 348 -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ 349 }; 350 #ifdef __STDC__ 351 static const double pS2[5] = { 352 #else 353 static double pS2[5] = { 354 #endif 355 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ 356 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ 357 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ 358 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ 359 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ 360 }; 361 362 #ifdef __STDC__ pzero(double x)363 static double pzero(double x) 364 #else 365 static double pzero(x) 366 double x; 367 #endif 368 { 369 #ifdef __STDC__ 370 const double *p,*q; 371 #else 372 double *p,*q; 373 #endif 374 fd_twoints u; 375 double z,r,s; 376 int ix; 377 u.d = x; 378 ix = 0x7fffffff&__HI(u); 379 if(ix>=0x40200000) {p = pR8; q= pS8;} 380 else if(ix>=0x40122E8B){p = pR5; q= pS5;} 381 else if(ix>=0x4006DB6D){p = pR3; q= pS3;} 382 else if(ix>=0x40000000){p = pR2; q= pS2;} 383 z = one/(x*x); 384 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 385 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); 386 return one+ r/s; 387 } 388 389 390 /* For x >= 8, the asymptotic expansions of qzero is 391 * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. 392 * We approximate pzero by 393 * qzero(x) = s*(-1.25 + (R/S)) 394 * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 395 * S = 1 + qS0*s^2 + ... + qS5*s^12 396 * and 397 * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) 398 */ 399 #ifdef __STDC__ 400 static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 401 #else 402 static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 403 #endif 404 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 405 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ 406 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ 407 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ 408 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ 409 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ 410 }; 411 #ifdef __STDC__ 412 static const double qS8[6] = { 413 #else 414 static double qS8[6] = { 415 #endif 416 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ 417 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ 418 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ 419 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ 420 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ 421 -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ 422 }; 423 424 #ifdef __STDC__ 425 static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 426 #else 427 static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 428 #endif 429 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ 430 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ 431 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ 432 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ 433 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ 434 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ 435 }; 436 #ifdef __STDC__ 437 static const double qS5[6] = { 438 #else 439 static double qS5[6] = { 440 #endif 441 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ 442 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ 443 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ 444 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ 445 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ 446 -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ 447 }; 448 449 #ifdef __STDC__ 450 static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 451 #else 452 static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 453 #endif 454 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ 455 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ 456 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ 457 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ 458 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ 459 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ 460 }; 461 #ifdef __STDC__ 462 static const double qS3[6] = { 463 #else 464 static double qS3[6] = { 465 #endif 466 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ 467 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ 468 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ 469 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ 470 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ 471 -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ 472 }; 473 474 #ifdef __STDC__ 475 static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 476 #else 477 static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 478 #endif 479 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ 480 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ 481 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ 482 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ 483 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ 484 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ 485 }; 486 #ifdef __STDC__ 487 static const double qS2[6] = { 488 #else 489 static double qS2[6] = { 490 #endif 491 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ 492 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ 493 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ 494 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ 495 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ 496 -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ 497 }; 498 499 #ifdef __STDC__ qzero(double x)500 static double qzero(double x) 501 #else 502 static double qzero(x) 503 double x; 504 #endif 505 { 506 #ifdef __STDC__ 507 const double *p,*q; 508 #else 509 double *p,*q; 510 #endif 511 fd_twoints u; 512 double s,r,z; 513 int ix; 514 u.d = x; 515 ix = 0x7fffffff&__HI(u); 516 if(ix>=0x40200000) {p = qR8; q= qS8;} 517 else if(ix>=0x40122E8B){p = qR5; q= qS5;} 518 else if(ix>=0x4006DB6D){p = qR3; q= qS3;} 519 else if(ix>=0x40000000){p = qR2; q= qS2;} 520 z = one/(x*x); 521 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 522 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); 523 return (-.125 + r/s)/x; 524 } 525