1 2 /* @(#)e_j0.c 1.3 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, 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 /* __ieee754_j0(x), __ieee754_y0(x) 15 * Bessel function of the first and second kinds of order zero. 16 * Method -- ieee_j0(x): 17 * 1. For tiny x, we use ieee_j0(x) = 1 - x^2/4 + x^4/64 - ... 18 * 2. Reduce x to |x| since ieee_j0(x)=ieee_j0(-x), and 19 * for x in (0,2) 20 * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; 21 * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) 22 * for x in (2,inf) 23 * j0(x) = ieee_sqrt(2/(pi*x))*(p0(x)*ieee_cos(x0)-q0(x)*ieee_sin(x0)) 24 * where x0 = x-pi/4. It is better to compute ieee_sin(x0),cos(x0) 25 * as follow: 26 * cos(x0) = ieee_cos(x)cos(pi/4)+ieee_sin(x)sin(pi/4) 27 * = 1/ieee_sqrt(2) * (ieee_cos(x) + ieee_sin(x)) 28 * sin(x0) = ieee_sin(x)cos(pi/4)-ieee_cos(x)sin(pi/4) 29 * = 1/ieee_sqrt(2) * (ieee_sin(x) - ieee_cos(x)) 30 * (To avoid cancellation, use 31 * sin(x) +- ieee_cos(x) = -ieee_cos(2x)/(ieee_sin(x) -+ ieee_cos(x)) 32 * to compute the worse one.) 33 * 34 * 3 Special cases 35 * j0(nan)= nan 36 * j0(0) = 1 37 * j0(inf) = 0 38 * 39 * Method -- ieee_y0(x): 40 * 1. For x<2. 41 * Since 42 * y0(x) = 2/pi*(ieee_j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) 43 * therefore ieee_y0(x)-2/pi*ieee_j0(x)*ln(x) is an even function. 44 * We use the following function to approximate y0, 45 * y0(x) = U(z)/V(z) + (2/pi)*(ieee_j0(x)*ln(x)), z= x^2 46 * where 47 * U(z) = u00 + u01*z + ... + u06*z^6 48 * V(z) = 1 + v01*z + ... + v04*z^4 49 * with absolute approximation error bounded by 2**-72. 50 * Note: For tiny x, U/V = u0 and ieee_j0(x)~1, hence 51 * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) 52 * 2. For x>=2. 53 * y0(x) = ieee_sqrt(2/(pi*x))*(p0(x)*ieee_cos(x0)+q0(x)*ieee_sin(x0)) 54 * where x0 = x-pi/4. It is better to compute ieee_sin(x0),cos(x0) 55 * by the method mentioned above. 56 * 3. Special cases: ieee_y0(0)=-inf, ieee_y0(x<0)=NaN, ieee_y0(inf)=0. 57 */ 58 59 #include "fdlibm.h" 60 61 #ifdef __STDC__ 62 static double pzero(double), qzero(double); 63 #else 64 static double pzero(), qzero(); 65 #endif 66 67 #ifdef __STDC__ 68 static const double 69 #else 70 static double 71 #endif 72 huge = 1e300, 73 one = 1.0, 74 invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ 75 tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 76 /* R0/S0 on [0, 2.00] */ 77 R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ 78 R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ 79 R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ 80 R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ 81 S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ 82 S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ 83 S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ 84 S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ 85 86 static double zero = 0.0; 87 88 #ifdef __STDC__ __ieee754_j0(double x)89 double __ieee754_j0(double x) 90 #else 91 double __ieee754_j0(x) 92 double x; 93 #endif 94 { 95 double z, s,c,ss,cc,r,u,v; 96 int hx,ix; 97 98 hx = __HI(x); 99 ix = hx&0x7fffffff; 100 if(ix>=0x7ff00000) return one/(x*x); 101 x = ieee_fabs(x); 102 if(ix >= 0x40000000) { /* |x| >= 2.0 */ 103 s = ieee_sin(x); 104 c = ieee_cos(x); 105 ss = s-c; 106 cc = s+c; 107 if(ix<0x7fe00000) { /* make sure x+x not overflow */ 108 z = -ieee_cos(x+x); 109 if ((s*c)<zero) cc = z/ss; 110 else ss = z/cc; 111 } 112 /* 113 * ieee_j0(x) = 1/ieee_sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / ieee_sqrt(x) 114 * ieee_y0(x) = 1/ieee_sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / ieee_sqrt(x) 115 */ 116 if(ix>0x48000000) z = (invsqrtpi*cc)/ieee_sqrt(x); 117 else { 118 u = pzero(x); v = qzero(x); 119 z = invsqrtpi*(u*cc-v*ss)/ieee_sqrt(x); 120 } 121 return z; 122 } 123 if(ix<0x3f200000) { /* |x| < 2**-13 */ 124 if(huge+x>one) { /* raise inexact if x != 0 */ 125 if(ix<0x3e400000) return one; /* |x|<2**-27 */ 126 else return one - 0.25*x*x; 127 } 128 } 129 z = x*x; 130 r = z*(R02+z*(R03+z*(R04+z*R05))); 131 s = one+z*(S01+z*(S02+z*(S03+z*S04))); 132 if(ix < 0x3FF00000) { /* |x| < 1.00 */ 133 return one + z*(-0.25+(r/s)); 134 } else { 135 u = 0.5*x; 136 return((one+u)*(one-u)+z*(r/s)); 137 } 138 } 139 140 #ifdef __STDC__ 141 static const double 142 #else 143 static double 144 #endif 145 u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ 146 u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ 147 u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ 148 u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ 149 u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ 150 u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ 151 u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ 152 v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ 153 v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ 154 v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ 155 v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ 156 157 #ifdef __STDC__ __ieee754_y0(double x)158 double __ieee754_y0(double x) 159 #else 160 double __ieee754_y0(x) 161 double x; 162 #endif 163 { 164 double z, s,c,ss,cc,u,v; 165 int hx,ix,lx; 166 167 hx = __HI(x); 168 ix = 0x7fffffff&hx; 169 lx = __LO(x); 170 /* Y0(NaN) is NaN, ieee_y0(-inf) is Nan, ieee_y0(inf) is 0 */ 171 if(ix>=0x7ff00000) return one/(x+x*x); 172 if((ix|lx)==0) return -one/zero; 173 if(hx<0) return zero/zero; 174 if(ix >= 0x40000000) { /* |x| >= 2.0 */ 175 /* ieee_y0(x) = ieee_sqrt(2/(pi*x))*(p0(x)*ieee_sin(x0)+q0(x)*ieee_cos(x0)) 176 * where x0 = x-pi/4 177 * Better formula: 178 * ieee_cos(x0) = ieee_cos(x)cos(pi/4)+ieee_sin(x)sin(pi/4) 179 * = 1/ieee_sqrt(2) * (ieee_sin(x) + ieee_cos(x)) 180 * ieee_sin(x0) = ieee_sin(x)cos(3pi/4)-ieee_cos(x)sin(3pi/4) 181 * = 1/ieee_sqrt(2) * (ieee_sin(x) - ieee_cos(x)) 182 * To avoid cancellation, use 183 * ieee_sin(x) +- ieee_cos(x) = -ieee_cos(2x)/(ieee_sin(x) -+ ieee_cos(x)) 184 * to compute the worse one. 185 */ 186 s = ieee_sin(x); 187 c = ieee_cos(x); 188 ss = s-c; 189 cc = s+c; 190 /* 191 * ieee_j0(x) = 1/ieee_sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / ieee_sqrt(x) 192 * ieee_y0(x) = 1/ieee_sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / ieee_sqrt(x) 193 */ 194 if(ix<0x7fe00000) { /* make sure x+x not overflow */ 195 z = -ieee_cos(x+x); 196 if ((s*c)<zero) cc = z/ss; 197 else ss = z/cc; 198 } 199 if(ix>0x48000000) z = (invsqrtpi*ss)/ieee_sqrt(x); 200 else { 201 u = pzero(x); v = qzero(x); 202 z = invsqrtpi*(u*ss+v*cc)/ieee_sqrt(x); 203 } 204 return z; 205 } 206 if(ix<=0x3e400000) { /* x < 2**-27 */ 207 return(u00 + tpi*__ieee754_log(x)); 208 } 209 z = x*x; 210 u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); 211 v = one+z*(v01+z*(v02+z*(v03+z*v04))); 212 return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); 213 } 214 215 /* The asymptotic expansions of pzero is 216 * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. 217 * For x >= 2, We approximate pzero by 218 * pzero(x) = 1 + (R/S) 219 * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 220 * S = 1 + pS0*s^2 + ... + pS4*s^10 221 * and 222 * | pzero(x)-1-R/S | <= 2 ** ( -60.26) 223 */ 224 #ifdef __STDC__ 225 static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 226 #else 227 static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 228 #endif 229 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 230 -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ 231 -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ 232 -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ 233 -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ 234 -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ 235 }; 236 #ifdef __STDC__ 237 static const double pS8[5] = { 238 #else 239 static double pS8[5] = { 240 #endif 241 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ 242 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ 243 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ 244 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ 245 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ 246 }; 247 248 #ifdef __STDC__ 249 static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 250 #else 251 static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 252 #endif 253 -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ 254 -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ 255 -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ 256 -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ 257 -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ 258 -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ 259 }; 260 #ifdef __STDC__ 261 static const double pS5[5] = { 262 #else 263 static double pS5[5] = { 264 #endif 265 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ 266 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ 267 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ 268 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ 269 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ 270 }; 271 272 #ifdef __STDC__ 273 static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 274 #else 275 static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 276 #endif 277 -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ 278 -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ 279 -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ 280 -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ 281 -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ 282 -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ 283 }; 284 #ifdef __STDC__ 285 static const double pS3[5] = { 286 #else 287 static double pS3[5] = { 288 #endif 289 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ 290 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ 291 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ 292 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ 293 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ 294 }; 295 296 #ifdef __STDC__ 297 static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 298 #else 299 static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 300 #endif 301 -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ 302 -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ 303 -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ 304 -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ 305 -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ 306 -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ 307 }; 308 #ifdef __STDC__ 309 static const double pS2[5] = { 310 #else 311 static double pS2[5] = { 312 #endif 313 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ 314 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ 315 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ 316 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ 317 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ 318 }; 319 320 #ifdef __STDC__ pzero(double x)321 static double pzero(double x) 322 #else 323 static double pzero(x) 324 double x; 325 #endif 326 { 327 #ifdef __STDC__ 328 const double *p,*q; 329 #else 330 double *p,*q; 331 #endif 332 double z,r,s; 333 int ix; 334 ix = 0x7fffffff&__HI(x); 335 if(ix>=0x40200000) {p = pR8; q= pS8;} 336 else if(ix>=0x40122E8B){p = pR5; q= pS5;} 337 else if(ix>=0x4006DB6D){p = pR3; q= pS3;} 338 else if(ix>=0x40000000){p = pR2; q= pS2;} 339 z = one/(x*x); 340 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 341 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); 342 return one+ r/s; 343 } 344 345 346 /* For x >= 8, the asymptotic expansions of qzero is 347 * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. 348 * We approximate pzero by 349 * qzero(x) = s*(-1.25 + (R/S)) 350 * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 351 * S = 1 + qS0*s^2 + ... + qS5*s^12 352 * and 353 * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) 354 */ 355 #ifdef __STDC__ 356 static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 357 #else 358 static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 359 #endif 360 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 361 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ 362 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ 363 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ 364 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ 365 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ 366 }; 367 #ifdef __STDC__ 368 static const double qS8[6] = { 369 #else 370 static double qS8[6] = { 371 #endif 372 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ 373 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ 374 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ 375 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ 376 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ 377 -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ 378 }; 379 380 #ifdef __STDC__ 381 static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 382 #else 383 static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 384 #endif 385 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ 386 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ 387 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ 388 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ 389 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ 390 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ 391 }; 392 #ifdef __STDC__ 393 static const double qS5[6] = { 394 #else 395 static double qS5[6] = { 396 #endif 397 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ 398 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ 399 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ 400 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ 401 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ 402 -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ 403 }; 404 405 #ifdef __STDC__ 406 static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 407 #else 408 static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 409 #endif 410 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ 411 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ 412 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ 413 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ 414 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ 415 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ 416 }; 417 #ifdef __STDC__ 418 static const double qS3[6] = { 419 #else 420 static double qS3[6] = { 421 #endif 422 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ 423 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ 424 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ 425 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ 426 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ 427 -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ 428 }; 429 430 #ifdef __STDC__ 431 static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 432 #else 433 static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 434 #endif 435 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ 436 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ 437 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ 438 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ 439 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ 440 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ 441 }; 442 #ifdef __STDC__ 443 static const double qS2[6] = { 444 #else 445 static double qS2[6] = { 446 #endif 447 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ 448 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ 449 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ 450 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ 451 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ 452 -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ 453 }; 454 455 #ifdef __STDC__ qzero(double x)456 static double qzero(double x) 457 #else 458 static double qzero(x) 459 double x; 460 #endif 461 { 462 #ifdef __STDC__ 463 const double *p,*q; 464 #else 465 double *p,*q; 466 #endif 467 double s,r,z; 468 int ix; 469 ix = 0x7fffffff&__HI(x); 470 if(ix>=0x40200000) {p = qR8; q= qS8;} 471 else if(ix>=0x40122E8B){p = qR5; q= qS5;} 472 else if(ix>=0x4006DB6D){p = qR3; q= qS3;} 473 else if(ix>=0x40000000){p = qR2; q= qS2;} 474 z = one/(x*x); 475 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 476 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); 477 return (-.125 + r/s)/x; 478 } 479