Details | Last modification | View Log | RSS feed
| Rev | Author | Line No. | Line |
|---|---|---|---|
| 4973 | right-hear | 1 | /* Copyright (C) 1994 DJ Delorie, see COPYING.DJ for details */ |
| 2 | /* e_j0f.c -- float version of e_j0.c. |
||
| 3 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
||
| 4 | */ |
||
| 5 | |||
| 6 | /* |
||
| 7 | * ==================================================== |
||
| 8 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
||
| 9 | * |
||
| 10 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
||
| 11 | * Permission to use, copy, modify, and distribute this |
||
| 12 | * software is freely granted, provided that this notice |
||
| 13 | * is preserved. |
||
| 14 | * ==================================================== |
||
| 15 | */ |
||
| 16 | |||
| 17 | #if defined(LIBM_SCCS) && !defined(lint) |
||
| 18 | static char rcsid[] = "$Id: e_j0f.c,v 1.2 1994/08/18 23:05:32 jtc Exp $"; |
||
| 19 | #endif |
||
| 20 | |||
| 21 | #include "math.h" |
||
| 22 | #include "math_private.h" |
||
| 23 | |||
| 24 | #ifdef __STDC__ |
||
| 25 | static float pzerof(float), qzerof(float); |
||
| 26 | #else |
||
| 27 | static float pzerof(), qzerof(); |
||
| 28 | #endif |
||
| 29 | |||
| 30 | #ifdef __STDC__ |
||
| 31 | static const float |
||
| 32 | #else |
||
| 33 | static float |
||
| 34 | #endif |
||
| 35 | huge = 1e30, |
||
| 36 | one = 1.0, |
||
| 37 | invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ |
||
| 38 | tpi = 6.3661974669e-01, /* 0x3f22f983 */ |
||
| 39 | /* R0/S0 on [0, 2.00] */ |
||
| 40 | R02 = 1.5625000000e-02, /* 0x3c800000 */ |
||
| 41 | R03 = -1.8997929874e-04, /* 0xb947352e */ |
||
| 42 | R04 = 1.8295404516e-06, /* 0x35f58e88 */ |
||
| 43 | R05 = -4.6183270541e-09, /* 0xb19eaf3c */ |
||
| 44 | S01 = 1.5619102865e-02, /* 0x3c7fe744 */ |
||
| 45 | S02 = 1.1692678527e-04, /* 0x38f53697 */ |
||
| 46 | S03 = 5.1354652442e-07, /* 0x3509daa6 */ |
||
| 47 | S04 = 1.1661400734e-09; /* 0x30a045e8 */ |
||
| 48 | |||
| 49 | #ifdef __STDC__ |
||
| 50 | static const float zero = 0.0; |
||
| 51 | #else |
||
| 52 | static float zero = 0.0; |
||
| 53 | #endif |
||
| 54 | |||
| 55 | #ifdef __STDC__ |
||
| 56 | float __ieee754_j0f(float x) |
||
| 57 | #else |
||
| 58 | float __ieee754_j0f(x) |
||
| 59 | float x; |
||
| 60 | #endif |
||
| 61 | { |
||
| 62 | float z, s,c,ss,cc,r,u,v; |
||
| 63 | int32_t hx,ix; |
||
| 64 | |||
| 65 | GET_FLOAT_WORD(hx,x); |
||
| 66 | ix = hx&0x7fffffff; |
||
| 67 | if(ix>=0x7f800000) return one/(x*x); |
||
| 68 | x = fabsf(x); |
||
| 69 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
||
| 70 | s = sinf(x); |
||
| 71 | c = cosf(x); |
||
| 72 | ss = s-c; |
||
| 73 | cc = s+c; |
||
| 74 | if(ix<0x7f000000) { /* make sure x+x not overflow */ |
||
| 75 | z = -cosf(x+x); |
||
| 76 | if ((s*c) |
||
| 77 | else ss = z/cc; |
||
| 78 | } |
||
| 79 | /* |
||
| 80 | * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) |
||
| 81 | * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) |
||
| 82 | */ |
||
| 83 | if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(x); |
||
| 84 | else { |
||
| 85 | u = pzerof(x); v = qzerof(x); |
||
| 86 | z = invsqrtpi*(u*cc-v*ss)/sqrtf(x); |
||
| 87 | } |
||
| 88 | return z; |
||
| 89 | } |
||
| 90 | if(ix<0x39000000) { /* |x| < 2**-13 */ |
||
| 91 | if(huge+x>one) { /* raise inexact if x != 0 */ |
||
| 92 | if(ix<0x32000000) return one; /* |x|<2**-27 */ |
||
| 93 | else return one - (float)0.25*x*x; |
||
| 94 | } |
||
| 95 | } |
||
| 96 | z = x*x; |
||
| 97 | r = z*(R02+z*(R03+z*(R04+z*R05))); |
||
| 98 | s = one+z*(S01+z*(S02+z*(S03+z*S04))); |
||
| 99 | if(ix < 0x3F800000) { /* |x| < 1.00 */ |
||
| 100 | return one + z*((float)-0.25+(r/s)); |
||
| 101 | } else { |
||
| 102 | u = (float)0.5*x; |
||
| 103 | return((one+u)*(one-u)+z*(r/s)); |
||
| 104 | } |
||
| 105 | } |
||
| 106 | |||
| 107 | #ifdef __STDC__ |
||
| 108 | static const float |
||
| 109 | #else |
||
| 110 | static float |
||
| 111 | #endif |
||
| 112 | u00 = -7.3804296553e-02, /* 0xbd9726b5 */ |
||
| 113 | u01 = 1.7666645348e-01, /* 0x3e34e80d */ |
||
| 114 | u02 = -1.3818567619e-02, /* 0xbc626746 */ |
||
| 115 | u03 = 3.4745343146e-04, /* 0x39b62a69 */ |
||
| 116 | u04 = -3.8140706238e-06, /* 0xb67ff53c */ |
||
| 117 | u05 = 1.9559013964e-08, /* 0x32a802ba */ |
||
| 118 | u06 = -3.9820518410e-11, /* 0xae2f21eb */ |
||
| 119 | v01 = 1.2730483897e-02, /* 0x3c509385 */ |
||
| 120 | v02 = 7.6006865129e-05, /* 0x389f65e0 */ |
||
| 121 | v03 = 2.5915085189e-07, /* 0x348b216c */ |
||
| 122 | v04 = 4.4111031494e-10; /* 0x2ff280c2 */ |
||
| 123 | |||
| 124 | #ifdef __STDC__ |
||
| 125 | float __ieee754_y0f(float x) |
||
| 126 | #else |
||
| 127 | float __ieee754_y0f(x) |
||
| 128 | float x; |
||
| 129 | #endif |
||
| 130 | { |
||
| 131 | float z, s,c,ss,cc,u,v; |
||
| 132 | int32_t hx,ix; |
||
| 133 | |||
| 134 | GET_FLOAT_WORD(hx,x); |
||
| 135 | ix = 0x7fffffff&hx; |
||
| 136 | /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ |
||
| 137 | if(ix>=0x7f800000) return one/(x+x*x); |
||
| 138 | if(ix==0) return -one/zero; |
||
| 139 | if(hx<0) return zero/zero; |
||
| 140 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
||
| 141 | /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) |
||
| 142 | * where x0 = x-pi/4 |
||
| 143 | * Better formula: |
||
| 144 | * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) |
||
| 145 | * = 1/sqrt(2) * (sin(x) + cos(x)) |
||
| 146 | * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) |
||
| 147 | * = 1/sqrt(2) * (sin(x) - cos(x)) |
||
| 148 | * To avoid cancellation, use |
||
| 149 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
||
| 150 | * to compute the worse one. |
||
| 151 | */ |
||
| 152 | s = sinf(x); |
||
| 153 | c = cosf(x); |
||
| 154 | ss = s-c; |
||
| 155 | cc = s+c; |
||
| 156 | /* |
||
| 157 | * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) |
||
| 158 | * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) |
||
| 159 | */ |
||
| 160 | if(ix<0x7f000000) { /* make sure x+x not overflow */ |
||
| 161 | z = -cosf(x+x); |
||
| 162 | if ((s*c) |
||
| 163 | else ss = z/cc; |
||
| 164 | } |
||
| 165 | if(ix>0x80000000) z = (invsqrtpi*ss)/sqrtf(x); |
||
| 166 | else { |
||
| 167 | u = pzerof(x); v = qzerof(x); |
||
| 168 | z = invsqrtpi*(u*ss+v*cc)/sqrtf(x); |
||
| 169 | } |
||
| 170 | return z; |
||
| 171 | } |
||
| 172 | if(ix<=0x32000000) { /* x < 2**-27 */ |
||
| 173 | return(u00 + tpi*__ieee754_logf(x)); |
||
| 174 | } |
||
| 175 | z = x*x; |
||
| 176 | u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); |
||
| 177 | v = one+z*(v01+z*(v02+z*(v03+z*v04))); |
||
| 178 | return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x))); |
||
| 179 | } |
||
| 180 | |||
| 181 | /* The asymptotic expansions of pzero is |
||
| 182 | * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. |
||
| 183 | * For x >= 2, We approximate pzero by |
||
| 184 | * pzero(x) = 1 + (R/S) |
||
| 185 | * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 |
||
| 186 | * S = 1 + pS0*s^2 + ... + pS4*s^10 |
||
| 187 | * and |
||
| 188 | * | pzero(x)-1-R/S | <= 2 ** ( -60.26) |
||
| 189 | */ |
||
| 190 | #ifdef __STDC__ |
||
| 191 | static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
||
| 192 | #else |
||
| 193 | static float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
||
| 194 | #endif |
||
| 195 | 0.0000000000e+00, /* 0x00000000 */ |
||
| 196 | -7.0312500000e-02, /* 0xbd900000 */ |
||
| 197 | -8.0816707611e+00, /* 0xc1014e86 */ |
||
| 198 | -2.5706311035e+02, /* 0xc3808814 */ |
||
| 199 | -2.4852163086e+03, /* 0xc51b5376 */ |
||
| 200 | -5.2530439453e+03, /* 0xc5a4285a */ |
||
| 201 | }; |
||
| 202 | #ifdef __STDC__ |
||
| 203 | static const float pS8[5] = { |
||
| 204 | #else |
||
| 205 | static float pS8[5] = { |
||
| 206 | #endif |
||
| 207 | 1.1653436279e+02, /* 0x42e91198 */ |
||
| 208 | 3.8337448730e+03, /* 0x456f9beb */ |
||
| 209 | 4.0597855469e+04, /* 0x471e95db */ |
||
| 210 | 1.1675296875e+05, /* 0x47e4087c */ |
||
| 211 | 4.7627726562e+04, /* 0x473a0bba */ |
||
| 212 | }; |
||
| 213 | #ifdef __STDC__ |
||
| 214 | static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
||
| 215 | #else |
||
| 216 | static float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
||
| 217 | #endif |
||
| 218 | -1.1412546255e-11, /* 0xad48c58a */ |
||
| 219 | -7.0312492549e-02, /* 0xbd8fffff */ |
||
| 220 | -4.1596107483e+00, /* 0xc0851b88 */ |
||
| 221 | -6.7674766541e+01, /* 0xc287597b */ |
||
| 222 | -3.3123129272e+02, /* 0xc3a59d9b */ |
||
| 223 | -3.4643338013e+02, /* 0xc3ad3779 */ |
||
| 224 | }; |
||
| 225 | #ifdef __STDC__ |
||
| 226 | static const float pS5[5] = { |
||
| 227 | #else |
||
| 228 | static float pS5[5] = { |
||
| 229 | #endif |
||
| 230 | 6.0753936768e+01, /* 0x42730408 */ |
||
| 231 | 1.0512523193e+03, /* 0x44836813 */ |
||
| 232 | 5.9789707031e+03, /* 0x45bad7c4 */ |
||
| 233 | 9.6254453125e+03, /* 0x461665c8 */ |
||
| 234 | 2.4060581055e+03, /* 0x451660ee */ |
||
| 235 | }; |
||
| 236 | |||
| 237 | #ifdef __STDC__ |
||
| 238 | static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
||
| 239 | #else |
||
| 240 | static float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
||
| 241 | #endif |
||
| 242 | -2.5470459075e-09, /* 0xb12f081b */ |
||
| 243 | -7.0311963558e-02, /* 0xbd8fffb8 */ |
||
| 244 | -2.4090321064e+00, /* 0xc01a2d95 */ |
||
| 245 | -2.1965976715e+01, /* 0xc1afba52 */ |
||
| 246 | -5.8079170227e+01, /* 0xc2685112 */ |
||
| 247 | -3.1447946548e+01, /* 0xc1fb9565 */ |
||
| 248 | }; |
||
| 249 | #ifdef __STDC__ |
||
| 250 | static const float pS3[5] = { |
||
| 251 | #else |
||
| 252 | static float pS3[5] = { |
||
| 253 | #endif |
||
| 254 | 3.5856033325e+01, /* 0x420f6c94 */ |
||
| 255 | 3.6151397705e+02, /* 0x43b4c1ca */ |
||
| 256 | 1.1936077881e+03, /* 0x44953373 */ |
||
| 257 | 1.1279968262e+03, /* 0x448cffe6 */ |
||
| 258 | 1.7358093262e+02, /* 0x432d94b8 */ |
||
| 259 | }; |
||
| 260 | |||
| 261 | #ifdef __STDC__ |
||
| 262 | static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
||
| 263 | #else |
||
| 264 | static float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
||
| 265 | #endif |
||
| 266 | -8.8753431271e-08, /* 0xb3be98b7 */ |
||
| 267 | -7.0303097367e-02, /* 0xbd8ffb12 */ |
||
| 268 | -1.4507384300e+00, /* 0xbfb9b1cc */ |
||
| 269 | -7.6356959343e+00, /* 0xc0f4579f */ |
||
| 270 | -1.1193166733e+01, /* 0xc1331736 */ |
||
| 271 | -3.2336456776e+00, /* 0xc04ef40d */ |
||
| 272 | }; |
||
| 273 | #ifdef __STDC__ |
||
| 274 | static const float pS2[5] = { |
||
| 275 | #else |
||
| 276 | static float pS2[5] = { |
||
| 277 | #endif |
||
| 278 | 2.2220300674e+01, /* 0x41b1c32d */ |
||
| 279 | 1.3620678711e+02, /* 0x430834f0 */ |
||
| 280 | 2.7047027588e+02, /* 0x43873c32 */ |
||
| 281 | 1.5387539673e+02, /* 0x4319e01a */ |
||
| 282 | 1.4657617569e+01, /* 0x416a859a */ |
||
| 283 | }; |
||
| 284 | |||
| 285 | #ifdef __STDC__ |
||
| 286 | static float pzerof(float x) |
||
| 287 | #else |
||
| 288 | static float pzerof(x) |
||
| 289 | float x; |
||
| 290 | #endif |
||
| 291 | { |
||
| 292 | #ifdef __STDC__ |
||
| 293 | const float *p,*q; |
||
| 294 | #else |
||
| 295 | float *p,*q; |
||
| 296 | #endif |
||
| 297 | float z,r,s; |
||
| 298 | int32_t ix; |
||
| 299 | GET_FLOAT_WORD(ix,x); |
||
| 300 | ix &= 0x7fffffff; |
||
| 301 | if(ix>=0x41000000) {p = pR8; q= pS8;} |
||
| 302 | else if(ix>=0x40f71c58){p = pR5; q= pS5;} |
||
| 303 | else if(ix>=0x4036db68){p = pR3; q= pS3;} |
||
| 304 | else if(ix>=0x40000000){p = pR2; q= pS2;} |
||
| 305 | z = one/(x*x); |
||
| 306 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
||
| 307 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); |
||
| 308 | return one+ r/s; |
||
| 309 | } |
||
| 310 | |||
| 311 | |||
| 312 | /* For x >= 8, the asymptotic expansions of qzero is |
||
| 313 | * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. |
||
| 314 | * We approximate pzero by |
||
| 315 | * qzero(x) = s*(-1.25 + (R/S)) |
||
| 316 | * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 |
||
| 317 | * S = 1 + qS0*s^2 + ... + qS5*s^12 |
||
| 318 | * and |
||
| 319 | * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) |
||
| 320 | */ |
||
| 321 | #ifdef __STDC__ |
||
| 322 | static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
||
| 323 | #else |
||
| 324 | static float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
||
| 325 | #endif |
||
| 326 | 0.0000000000e+00, /* 0x00000000 */ |
||
| 327 | 7.3242187500e-02, /* 0x3d960000 */ |
||
| 328 | 1.1768206596e+01, /* 0x413c4a93 */ |
||
| 329 | 5.5767340088e+02, /* 0x440b6b19 */ |
||
| 330 | 8.8591972656e+03, /* 0x460a6cca */ |
||
| 331 | 3.7014625000e+04, /* 0x471096a0 */ |
||
| 332 | }; |
||
| 333 | #ifdef __STDC__ |
||
| 334 | static const float qS8[6] = { |
||
| 335 | #else |
||
| 336 | static float qS8[6] = { |
||
| 337 | #endif |
||
| 338 | 1.6377603149e+02, /* 0x4323c6aa */ |
||
| 339 | 8.0983447266e+03, /* 0x45fd12c2 */ |
||
| 340 | 1.4253829688e+05, /* 0x480b3293 */ |
||
| 341 | 8.0330925000e+05, /* 0x49441ed4 */ |
||
| 342 | 8.4050156250e+05, /* 0x494d3359 */ |
||
| 343 | -3.4389928125e+05, /* 0xc8a7eb69 */ |
||
| 344 | }; |
||
| 345 | |||
| 346 | #ifdef __STDC__ |
||
| 347 | static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
||
| 348 | #else |
||
| 349 | static float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
||
| 350 | #endif |
||
| 351 | 1.8408595828e-11, /* 0x2da1ec79 */ |
||
| 352 | 7.3242180049e-02, /* 0x3d95ffff */ |
||
| 353 | 5.8356351852e+00, /* 0x40babd86 */ |
||
| 354 | 1.3511157227e+02, /* 0x43071c90 */ |
||
| 355 | 1.0272437744e+03, /* 0x448067cd */ |
||
| 356 | 1.9899779053e+03, /* 0x44f8bf4b */ |
||
| 357 | }; |
||
| 358 | #ifdef __STDC__ |
||
| 359 | static const float qS5[6] = { |
||
| 360 | #else |
||
| 361 | static float qS5[6] = { |
||
| 362 | #endif |
||
| 363 | 8.2776611328e+01, /* 0x42a58da0 */ |
||
| 364 | 2.0778142090e+03, /* 0x4501dd07 */ |
||
| 365 | 1.8847289062e+04, /* 0x46933e94 */ |
||
| 366 | 5.6751113281e+04, /* 0x475daf1d */ |
||
| 367 | 3.5976753906e+04, /* 0x470c88c1 */ |
||
| 368 | -5.3543427734e+03, /* 0xc5a752be */ |
||
| 369 | }; |
||
| 370 | |||
| 371 | #ifdef __STDC__ |
||
| 372 | static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
||
| 373 | #else |
||
| 374 | static float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
||
| 375 | #endif |
||
| 376 | 4.3774099900e-09, /* 0x3196681b */ |
||
| 377 | 7.3241114616e-02, /* 0x3d95ff70 */ |
||
| 378 | 3.3442313671e+00, /* 0x405607e3 */ |
||
| 379 | 4.2621845245e+01, /* 0x422a7cc5 */ |
||
| 380 | 1.7080809021e+02, /* 0x432acedf */ |
||
| 381 | 1.6673394775e+02, /* 0x4326bbe4 */ |
||
| 382 | }; |
||
| 383 | #ifdef __STDC__ |
||
| 384 | static const float qS3[6] = { |
||
| 385 | #else |
||
| 386 | static float qS3[6] = { |
||
| 387 | #endif |
||
| 388 | 4.8758872986e+01, /* 0x42430916 */ |
||
| 389 | 7.0968920898e+02, /* 0x44316c1c */ |
||
| 390 | 3.7041481934e+03, /* 0x4567825f */ |
||
| 391 | 6.4604252930e+03, /* 0x45c9e367 */ |
||
| 392 | 2.5163337402e+03, /* 0x451d4557 */ |
||
| 393 | -1.4924745178e+02, /* 0xc3153f59 */ |
||
| 394 | }; |
||
| 395 | |||
| 396 | #ifdef __STDC__ |
||
| 397 | static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
||
| 398 | #else |
||
| 399 | static float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
||
| 400 | #endif |
||
| 401 | 1.5044444979e-07, /* 0x342189db */ |
||
| 402 | 7.3223426938e-02, /* 0x3d95f62a */ |
||
| 403 | 1.9981917143e+00, /* 0x3fffc4bf */ |
||
| 404 | 1.4495602608e+01, /* 0x4167edfd */ |
||
| 405 | 3.1666231155e+01, /* 0x41fd5471 */ |
||
| 406 | 1.6252708435e+01, /* 0x4182058c */ |
||
| 407 | }; |
||
| 408 | #ifdef __STDC__ |
||
| 409 | static const float qS2[6] = { |
||
| 410 | #else |
||
| 411 | static float qS2[6] = { |
||
| 412 | #endif |
||
| 413 | 3.0365585327e+01, /* 0x41f2ecb8 */ |
||
| 414 | 2.6934811401e+02, /* 0x4386ac8f */ |
||
| 415 | 8.4478375244e+02, /* 0x44533229 */ |
||
| 416 | 8.8293585205e+02, /* 0x445cbbe5 */ |
||
| 417 | 2.1266638184e+02, /* 0x4354aa98 */ |
||
| 418 | -5.3109550476e+00, /* 0xc0a9f358 */ |
||
| 419 | }; |
||
| 420 | |||
| 421 | #ifdef __STDC__ |
||
| 422 | static float qzerof(float x) |
||
| 423 | #else |
||
| 424 | static float qzerof(x) |
||
| 425 | float x; |
||
| 426 | #endif |
||
| 427 | { |
||
| 428 | #ifdef __STDC__ |
||
| 429 | const float *p,*q; |
||
| 430 | #else |
||
| 431 | float *p,*q; |
||
| 432 | #endif |
||
| 433 | float s,r,z; |
||
| 434 | int32_t ix; |
||
| 435 | GET_FLOAT_WORD(ix,x); |
||
| 436 | ix &= 0x7fffffff; |
||
| 437 | if(ix>=0x41000000) {p = qR8; q= qS8;} |
||
| 438 | else if(ix>=0x40f71c58){p = qR5; q= qS5;} |
||
| 439 | else if(ix>=0x4036db68){p = qR3; q= qS3;} |
||
| 440 | else if(ix>=0x40000000){p = qR2; q= qS2;} |
||
| 441 | z = one/(x*x); |
||
| 442 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
||
| 443 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); |
||
| 444 | return (-(float).125 + r/s)/x; |
||
| 445 | } |