RTAI API: base/math/e_j1.c Source File

00001 /* @(#)e_j1.c 5.1 93/09/24 */ 00002 /* 00003 * ==================================================== 00004 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 00005 * 00006 * Developed at SunPro, a Sun Microsystems, Inc. business. 00007 * Permission to use, copy, modify, and distribute this 00008 * software is freely granted, provided that this notice 00009 * is preserved. 00010 * ==================================================== 00011 */ 00012 00013 #if defined(LIBM_SCCS) && !defined(lint) 00014 static char rcsid[] = "$NetBSD: e_j1.c,v 1.8 1995/05/10 20:45:27 jtc Exp $"; 00015 #endif 00016 00017 /* __ieee754_j1(x), __ieee754_y1(x) 00018 * Bessel function of the first and second kinds of order zero. 00019 * Method -- j1(x): 00020 * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... 00021 * 2. Reduce x to |x| since j1(x)=-j1(-x), and 00022 * for x in (0,2) 00023 * j1(x) = x/2 + x*z*R0/S0, where z = x*x; 00024 * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) 00025 * for x in (2,inf) 00026 * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) 00027 * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) 00028 * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) 00029 * as follow: 00030 * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) 00031 * = 1/sqrt(2) * (sin(x) - cos(x)) 00032 * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 00033 * = -1/sqrt(2) * (sin(x) + cos(x)) 00034 * (To avoid cancellation, use 00035 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 00036 * to compute the worse one.) 00037 * 00038 * 3 Special cases 00039 * j1(nan)= nan 00040 * j1(0) = 0 00041 * j1(inf) = 0 00042 * 00043 * Method -- y1(x): 00044 * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN 00045 * 2. For x<2. 00046 * Since 00047 * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) 00048 * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. 00049 * We use the following function to approximate y1, 00050 * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 00051 * where for x in [0,2] (abs err less than 2**-65.89) 00052 * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 00053 * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 00054 * Note: For tiny x, 1/x dominate y1 and hence 00055 * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) 00056 * 3. For x>=2. 00057 * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) 00058 * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) 00059 * by method mentioned above. 00060 */ 00061 00062 #include "math.h" 00063 #include "mathP.h" 00064 00065 #ifdef __STDC__ 00066 static double pone(double), qone(double); 00067 #else 00068 static double pone(), qone(); 00069 #endif 00070 00071 #ifdef __STDC__ 00072 static const double 00073 #else 00074 static double 00075 #endif 00076 huge = 1e300, 00077 one = 1.0, 00078 invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ 00079 tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 00080 /* R0/S0 on [0,2] */ 00081 r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ 00082 r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ 00083 r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ 00084 r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ 00085 s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ 00086 s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ 00087 s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ 00088 s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ 00089 s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ 00090 00091 #ifdef __STDC__ 00092 static const double zero = 0.0; 00093 #else 00094 static double zero = 0.0; 00095 #endif 00096 00097 #ifdef __STDC__ 00098 double __ieee754_j1(double x) 00099 #else 00100 double __ieee754_j1(x) 00101 double x; 00102 #endif 00103 { 00104 double z, s,c,ss,cc,r,u,v,y; 00105 int32_t hx,ix; 00106 00107 GET_HIGH_WORD(hx,x); 00108 ix = hx&0x7fffffff; 00109 if(ix>=0x7ff00000) return one/x; 00110 y = fabs(x); 00111 if(ix >= 0x40000000) { /* |x| >= 2.0 */ 00112 s = sin(y); 00113 c = cos(y); 00114 ss = -s-c; 00115 cc = s-c; 00116 if(ix<0x7fe00000) { /* make sure y+y not overflow */ 00117 z = cos(y+y); 00118 if ((s*c)>zero) cc = z/ss; 00119 else ss = z/cc; 00120 } 00121 /* 00122 * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) 00123 * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) 00124 */ 00125 if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y); 00126 else { 00127 u = pone(y); v = qone(y); 00128 z = invsqrtpi*(u*cc-v*ss)/sqrt(y); 00129 } 00130 if(hx<0) return -z; 00131 else return z; 00132 } 00133 if(ix<0x3e400000) { /* |x|<2**-27 */ 00134 if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ 00135 } 00136 z = x*x; 00137 r = z*(r00+z*(r01+z*(r02+z*r03))); 00138 s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); 00139 r *= x; 00140 return(x*0.5+r/s); 00141 } 00142 00143 #ifdef __STDC__ 00144 static const double U0[5] = { 00145 #else 00146 static double U0[5] = { 00147 #endif 00148 -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ 00149 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ 00150 -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ 00151 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ 00152 -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ 00153 }; 00154 #ifdef __STDC__ 00155 static const double V0[5] = { 00156 #else 00157 static double V0[5] = { 00158 #endif 00159 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ 00160 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ 00161 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ 00162 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ 00163 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ 00164 }; 00165 00166 #ifdef __STDC__ 00167 double __ieee754_y1(double x) 00168 #else 00169 double __ieee754_y1(x) 00170 double x; 00171 #endif 00172 { 00173 double z, s,c,ss,cc,u,v; 00174 int32_t hx,ix,lx; 00175 00176 EXTRACT_WORDS(hx,lx,x); 00177 ix = 0x7fffffff&hx; 00178 /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ 00179 if(ix>=0x7ff00000) return one/(x+x*x); 00180 if((ix|lx)==0) return -one/zero; 00181 if(hx<0) return zero/zero; 00182 if(ix >= 0x40000000) { /* |x| >= 2.0 */ 00183 s = sin(x); 00184 c = cos(x); 00185 ss = -s-c; 00186 cc = s-c; 00187 if(ix<0x7fe00000) { /* make sure x+x not overflow */ 00188 z = cos(x+x); 00189 if ((s*c)>zero) cc = z/ss; 00190 else ss = z/cc; 00191 } 00192 /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) 00193 * where x0 = x-3pi/4 00194 * Better formula: 00195 * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) 00196 * = 1/sqrt(2) * (sin(x) - cos(x)) 00197 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 00198 * = -1/sqrt(2) * (cos(x) + sin(x)) 00199 * To avoid cancellation, use 00200 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 00201 * to compute the worse one. 00202 */ 00203 if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); 00204 else { 00205 u = pone(x); v = qone(x); 00206 z = invsqrtpi*(u*ss+v*cc)/sqrt(x); 00207 } 00208 return z; 00209 } 00210 if(ix<=0x3c900000) { /* x < 2**-54 */ 00211 return(-tpi/x); 00212 } 00213 z = x*x; 00214 u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); 00215 v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); 00216 return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); 00217 } 00218 00219 /* For x >= 8, the asymptotic expansions of pone is 00220 * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. 00221 * We approximate pone by 00222 * pone(x) = 1 + (R/S) 00223 * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 00224 * S = 1 + ps0*s^2 + ... + ps4*s^10 00225 * and 00226 * | pone(x)-1-R/S | <= 2 ** ( -60.06) 00227 */ 00228 00229 #ifdef __STDC__ 00230 static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 00231 #else 00232 static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 00233 #endif 00234 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 00235 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ 00236 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ 00237 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ 00238 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ 00239 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ 00240 }; 00241 #ifdef __STDC__ 00242 static const double ps8[5] = { 00243 #else 00244 static double ps8[5] = { 00245 #endif 00246 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ 00247 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ 00248 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ 00249 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ 00250 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ 00251 }; 00252 00253 #ifdef __STDC__ 00254 static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 00255 #else 00256 static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 00257 #endif 00258 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ 00259 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ 00260 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ 00261 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ 00262 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ 00263 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ 00264 }; 00265 #ifdef __STDC__ 00266 static const double ps5[5] = { 00267 #else 00268 static double ps5[5] = { 00269 #endif 00270 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ 00271 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ 00272 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ 00273 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ 00274 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ 00275 }; 00276 00277 #ifdef __STDC__ 00278 static const double pr3[6] = { 00279 #else 00280 static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 00281 #endif 00282 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ 00283 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ 00284 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ 00285 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ 00286 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ 00287 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ 00288 }; 00289 #ifdef __STDC__ 00290 static const double ps3[5] = { 00291 #else 00292 static double ps3[5] = { 00293 #endif 00294 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ 00295 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ 00296 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ 00297 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ 00298 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ 00299 }; 00300 00301 #ifdef __STDC__ 00302 static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 00303 #else 00304 static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 00305 #endif 00306 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ 00307 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ 00308 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ 00309 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ 00310 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ 00311 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ 00312 }; 00313 #ifdef __STDC__ 00314 static const double ps2[5] = { 00315 #else 00316 static double ps2[5] = { 00317 #endif 00318 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ 00319 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ 00320 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ 00321 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ 00322 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ 00323 }; 00324 00325 #ifdef __STDC__ 00326 static double pone(double x) 00327 #else 00328 static double pone(x) 00329 double x; 00330 #endif 00331 { 00332 #ifdef __STDC__ 00333 const double *p = 0,*q = 0; 00334 #else 00335 double *p = 0,*q = 0; 00336 #endif 00337 double z,r,s; 00338 int32_t ix; 00339 GET_HIGH_WORD(ix,x); 00340 ix &= 0x7fffffff; 00341 if(ix>=0x40200000) {p = pr8; q= ps8;} 00342 else if(ix>=0x40122E8B){p = pr5; q= ps5;} 00343 else if(ix>=0x4006DB6D){p = pr3; q= ps3;} 00344 else if(ix>=0x40000000){p = pr2; q= ps2;} 00345 z = one/(x*x); 00346 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 00347 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); 00348 return one+ r/s; 00349 } 00350 00351 00352 /* For x >= 8, the asymptotic expansions of qone is 00353 * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. 00354 * We approximate pone by 00355 * qone(x) = s*(0.375 + (R/S)) 00356 * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 00357 * S = 1 + qs1*s^2 + ... + qs6*s^12 00358 * and 00359 * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) 00360 */ 00361 00362 #ifdef __STDC__ 00363 static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 00364 #else 00365 static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 00366 #endif 00367 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 00368 -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ 00369 -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ 00370 -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ 00371 -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ 00372 -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ 00373 }; 00374 #ifdef __STDC__ 00375 static const double qs8[6] = { 00376 #else 00377 static double qs8[6] = { 00378 #endif 00379 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ 00380 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ 00381 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ 00382 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ 00383 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ 00384 -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ 00385 }; 00386 00387 #ifdef __STDC__ 00388 static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 00389 #else 00390 static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 00391 #endif 00392 -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ 00393 -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ 00394 -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ 00395 -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ 00396 -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ 00397 -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ 00398 }; 00399 #ifdef __STDC__ 00400 static const double qs5[6] = { 00401 #else 00402 static double qs5[6] = { 00403 #endif 00404 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ 00405 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ 00406 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ 00407 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ 00408 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ 00409 -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ 00410 }; 00411 00412 #ifdef __STDC__ 00413 static const double qr3[6] = { 00414 #else 00415 static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 00416 #endif 00417 -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ 00418 -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ 00419 -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ 00420 -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ 00421 -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ 00422 -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ 00423 }; 00424 #ifdef __STDC__ 00425 static const double qs3[6] = { 00426 #else 00427 static double qs3[6] = { 00428 #endif 00429 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ 00430 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ 00431 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ 00432 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ 00433 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ 00434 -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ 00435 }; 00436 00437 #ifdef __STDC__ 00438 static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 00439 #else 00440 static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 00441 #endif 00442 -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ 00443 -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ 00444 -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ 00445 -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ 00446 -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ 00447 -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ 00448 }; 00449 #ifdef __STDC__ 00450 static const double qs2[6] = { 00451 #else 00452 static double qs2[6] = { 00453 #endif 00454 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ 00455 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ 00456 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ 00457 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ 00458 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ 00459 -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ 00460 }; 00461 00462 #ifdef __STDC__ 00463 static double qone(double x) 00464 #else 00465 static double qone(x) 00466 double x; 00467 #endif 00468 { 00469 #ifdef __STDC__ 00470 const double *p = 0,*q = 0; 00471 #else 00472 double *p = 0,*q = 0; 00473 #endif 00474 double s,r,z; 00475 int32_t ix; 00476 GET_HIGH_WORD(ix,x); 00477 ix &= 0x7fffffff; 00478 if(ix>=0x40200000) {p = qr8; q= qs8;} 00479 else if(ix>=0x40122E8B){p = qr5; q= qs5;} 00480 else if(ix>=0x4006DB6D){p = qr3; q= qs3;} 00481 else if(ix>=0x40000000){p = qr2; q= qs2;} 00482 z = one/(x*x); 00483 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 00484 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); 00485 return (.375 + r/s)/x; 00486 }