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00001 /* @(#)e_j0.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 /* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/26, 00013 for performance improvement on pipelined processors. 00014 */ 00015 00016 #if defined(LIBM_SCCS) && !defined(lint) 00017 static char rcsid[] = "$NetBSD: e_j0.c,v 1.8 1995/05/10 20:45:23 jtc Exp $"; 00018 #endif 00019 00020 /* __ieee754_j0(x), __ieee754_y0(x) 00021 * Bessel function of the first and second kinds of order zero. 00022 * Method -- j0(x): 00023 * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... 00024 * 2. Reduce x to |x| since j0(x)=j0(-x), and 00025 * for x in (0,2) 00026 * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; 00027 * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) 00028 * for x in (2,inf) 00029 * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) 00030 * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) 00031 * as follow: 00032 * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) 00033 * = 1/sqrt(2) * (cos(x) + sin(x)) 00034 * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) 00035 * = 1/sqrt(2) * (sin(x) - cos(x)) 00036 * (To avoid cancellation, use 00037 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 00038 * to compute the worse one.) 00039 * 00040 * 3 Special cases 00041 * j0(nan)= nan 00042 * j0(0) = 1 00043 * j0(inf) = 0 00044 * 00045 * Method -- y0(x): 00046 * 1. For x<2. 00047 * Since 00048 * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) 00049 * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. 00050 * We use the following function to approximate y0, 00051 * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 00052 * where 00053 * U(z) = u00 + u01*z + ... + u06*z^6 00054 * V(z) = 1 + v01*z + ... + v04*z^4 00055 * with absolute approximation error bounded by 2**-72. 00056 * Note: For tiny x, U/V = u0 and j0(x)~1, hence 00057 * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) 00058 * 2. For x>=2. 00059 * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) 00060 * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) 00061 * by the method mentioned above. 00062 * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. 00063 */ 00064 00065 #include "math.h" 00066 #include "ieee754.h" 00067 00068 #ifdef __STDC__ 00069 static double pzero(double), qzero(double); 00070 #else 00071 static double pzero(), qzero(); 00072 #endif 00073 00074 #ifdef __STDC__ 00075 static const double 00076 #else 00077 static double 00078 #endif 00079 huge = 1e300, 00080 one = 1.0, 00081 invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ 00082 tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 00083 /* R0/S0 on [0, 2.00] */ 00084 R[] = {0.0, 0.0, 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ 00085 -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ 00086 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ 00087 -4.61832688532103189199e-09}, /* 0xBE33D5E7, 0x73D63FCE */ 00088 S[] = {0.0, 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ 00089 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ 00090 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ 00091 1.16614003333790000205e-09}; /* 0x3E1408BC, 0xF4745D8F */ 00092 00093 #ifdef __STDC__ 00094 static const double zero = 0.0; 00095 #else 00096 static double zero = 0.0; 00097 #endif 00098 00099 #ifdef __STDC__ 00100 double __ieee754_j0(double x) 00101 #else 00102 double __ieee754_j0(x) 00103 double x; 00104 #endif 00105 { 00106 double z, s,c,ss,cc,r,u,v,r1,r2,s1,s2,z2,z4; 00107 int32_t hx,ix; 00108 00109 GET_HIGH_WORD(hx,x); 00110 ix = hx&0x7fffffff; 00111 if(ix>=0x7ff00000) return one/(x*x); 00112 x = fabs(x); 00113 if(ix >= 0x40000000) { /* |x| >= 2.0 */ 00114 __sincos (x, &s, &c); 00115 ss = s-c; 00116 cc = s+c; 00117 if(ix<0x7fe00000) { /* make sure x+x not overflow */ 00118 z = -__cos(x+x); 00119 if ((s*c)<zero) cc = z/ss; 00120 else ss = z/cc; 00121 } 00122 /* 00123 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) 00124 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) 00125 */ 00126 if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(x); 00127 else { 00128 u = pzero(x); v = qzero(x); 00129 z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(x); 00130 } 00131 return z; 00132 } 00133 if(ix<0x3f200000) { /* |x| < 2**-13 */ 00134 if(huge+x>one) { /* raise inexact if x != 0 */ 00135 if(ix<0x3e400000) return one; /* |x|<2**-27 */ 00136 else return one - 0.25*x*x; 00137 } 00138 } 00139 z = x*x; 00140 #ifdef DO_NOT_USE_THIS 00141 r = z*(R02+z*(R03+z*(R04+z*R05))); 00142 s = one+z*(S01+z*(S02+z*(S03+z*S04))); 00143 #else 00144 r1 = z*R[2]; z2=z*z; 00145 r2 = R[3]+z*R[4]; z4=z2*z2; 00146 r = r1 + z2*r2 + z4*R[5]; 00147 s1 = one+z*S[1]; 00148 s2 = S[2]+z*S[3]; 00149 s = s1 + z2*s2 + z4*S[4]; 00150 #endif 00151 if(ix < 0x3FF00000) { /* |x| < 1.00 */ 00152 return one + z*(-0.25+(r/s)); 00153 } else { 00154 u = 0.5*x; 00155 return((one+u)*(one-u)+z*(r/s)); 00156 } 00157 } 00158 00159 #ifdef __STDC__ 00160 static const double 00161 #else 00162 static double 00163 #endif 00164 U[] = {-7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ 00165 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ 00166 -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ 00167 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ 00168 -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ 00169 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ 00170 -3.98205194132103398453e-11}, /* 0xBDC5E43D, 0x693FB3C8 */ 00171 V[] = {1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ 00172 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ 00173 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ 00174 4.41110311332675467403e-10}; /* 0x3DFE5018, 0x3BD6D9EF */ 00175 00176 #ifdef __STDC__ 00177 double __ieee754_y0(double x) 00178 #else 00179 double __ieee754_y0(x) 00180 double x; 00181 #endif 00182 { 00183 double z, s,c,ss,cc,u,v,z2,z4,z6,u1,u2,u3,v1,v2; 00184 int32_t hx,ix,lx; 00185 00186 EXTRACT_WORDS(hx,lx,x); 00187 ix = 0x7fffffff&hx; 00188 /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0, y0(0) is -inf. */ 00189 if(ix>=0x7ff00000) return one/(x+x*x); 00190 if((ix|lx)==0) return -HUGE_VAL+x; /* -inf and overflow exception. */ 00191 if(hx<0) return zero/(zero*x); 00192 if(ix >= 0x40000000) { /* |x| >= 2.0 */ 00193 /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) 00194 * where x0 = x-pi/4 00195 * Better formula: 00196 * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) 00197 * = 1/sqrt(2) * (sin(x) + cos(x)) 00198 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) 00199 * = 1/sqrt(2) * (sin(x) - cos(x)) 00200 * To avoid cancellation, use 00201 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) 00202 * to compute the worse one. 00203 */ 00204 __sincos (x, &s, &c); 00205 ss = s-c; 00206 cc = s+c; 00207 /* 00208 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) 00209 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) 00210 */ 00211 if(ix<0x7fe00000) { /* make sure x+x not overflow */ 00212 z = -__cos(x+x); 00213 if ((s*c)<zero) cc = z/ss; 00214 else ss = z/cc; 00215 } 00216 if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x); 00217 else { 00218 u = pzero(x); v = qzero(x); 00219 z = invsqrtpi*(u*ss+v*cc)/__ieee754_sqrt(x); 00220 } 00221 return z; 00222 } 00223 if(ix<=0x3e400000) { /* x < 2**-27 */ 00224 return(U[0] + tpi*__ieee754_log(x)); 00225 } 00226 z = x*x; 00227 #ifdef DO_NOT_USE_THIS 00228 u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); 00229 v = one+z*(v01+z*(v02+z*(v03+z*v04))); 00230 #else 00231 u1 = U[0]+z*U[1]; z2=z*z; 00232 u2 = U[2]+z*U[3]; z4=z2*z2; 00233 u3 = U[4]+z*U[5]; z6=z4*z2; 00234 u = u1 + z2*u2 + z4*u3 + z6*U[6]; 00235 v1 = one+z*V[0]; 00236 v2 = V[1]+z*V[2]; 00237 v = v1 + z2*v2 + z4*V[3]; 00238 #endif 00239 return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); 00240 } 00241 00242 /* The asymptotic expansions of pzero is 00243 * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. 00244 * For x >= 2, We approximate pzero by 00245 * pzero(x) = 1 + (R/S) 00246 * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 00247 * S = 1 + pS0*s^2 + ... + pS4*s^10 00248 * and 00249 * | pzero(x)-1-R/S | <= 2 ** ( -60.26) 00250 */ 00251 #ifdef __STDC__ 00252 static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 00253 #else 00254 static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 00255 #endif 00256 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 00257 -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ 00258 -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ 00259 -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ 00260 -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ 00261 -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ 00262 }; 00263 #ifdef __STDC__ 00264 static const double pS8[5] = { 00265 #else 00266 static double pS8[5] = { 00267 #endif 00268 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ 00269 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ 00270 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ 00271 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ 00272 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ 00273 }; 00274 00275 #ifdef __STDC__ 00276 static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 00277 #else 00278 static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 00279 #endif 00280 -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ 00281 -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ 00282 -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ 00283 -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ 00284 -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ 00285 -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ 00286 }; 00287 #ifdef __STDC__ 00288 static const double pS5[5] = { 00289 #else 00290 static double pS5[5] = { 00291 #endif 00292 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ 00293 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ 00294 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ 00295 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ 00296 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ 00297 }; 00298 00299 #ifdef __STDC__ 00300 static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 00301 #else 00302 static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 00303 #endif 00304 -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ 00305 -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ 00306 -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ 00307 -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ 00308 -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ 00309 -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ 00310 }; 00311 #ifdef __STDC__ 00312 static const double pS3[5] = { 00313 #else 00314 static double pS3[5] = { 00315 #endif 00316 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ 00317 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ 00318 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ 00319 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ 00320 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ 00321 }; 00322 00323 #ifdef __STDC__ 00324 static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 00325 #else 00326 static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 00327 #endif 00328 -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ 00329 -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ 00330 -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ 00331 -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ 00332 -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ 00333 -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ 00334 }; 00335 #ifdef __STDC__ 00336 static const double pS2[5] = { 00337 #else 00338 static double pS2[5] = { 00339 #endif 00340 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ 00341 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ 00342 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ 00343 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ 00344 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ 00345 }; 00346 00347 #ifdef __STDC__ 00348 static double pzero(double x) 00349 #else 00350 static double pzero(x) 00351 double x; 00352 #endif 00353 { 00354 #ifdef __STDC__ 00355 const double *p = 0,*q = 0; 00356 #else 00357 double *p = 0,*q = 0; 00358 #endif 00359 double z,r,s,z2,z4,r1,r2,r3,s1,s2,s3; 00360 int32_t ix; 00361 GET_HIGH_WORD(ix,x); 00362 ix &= 0x7fffffff; 00363 if(ix>=0x40200000) {p = pR8; q= pS8;} 00364 else if(ix>=0x40122E8B){p = pR5; q= pS5;} 00365 else if(ix>=0x4006DB6D){p = pR3; q= pS3;} 00366 else if(ix>=0x40000000){p = pR2; q= pS2;} 00367 z = one/(x*x); 00368 #ifdef DO_NOT_USE_THIS 00369 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 00370 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); 00371 #else 00372 r1 = p[0]+z*p[1]; z2=z*z; 00373 r2 = p[2]+z*p[3]; z4=z2*z2; 00374 r3 = p[4]+z*p[5]; 00375 r = r1 + z2*r2 + z4*r3; 00376 s1 = one+z*q[0]; 00377 s2 = q[1]+z*q[2]; 00378 s3 = q[3]+z*q[4]; 00379 s = s1 + z2*s2 + z4*s3; 00380 #endif 00381 return one+ r/s; 00382 } 00383 00384 00385 /* For x >= 8, the asymptotic expansions of qzero is 00386 * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. 00387 * We approximate pzero by 00388 * qzero(x) = s*(-1.25 + (R/S)) 00389 * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 00390 * S = 1 + qS0*s^2 + ... + qS5*s^12 00391 * and 00392 * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) 00393 */ 00394 #ifdef __STDC__ 00395 static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 00396 #else 00397 static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 00398 #endif 00399 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 00400 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ 00401 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ 00402 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ 00403 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ 00404 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ 00405 }; 00406 #ifdef __STDC__ 00407 static const double qS8[6] = { 00408 #else 00409 static double qS8[6] = { 00410 #endif 00411 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ 00412 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ 00413 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ 00414 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ 00415 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ 00416 -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ 00417 }; 00418 00419 #ifdef __STDC__ 00420 static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 00421 #else 00422 static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 00423 #endif 00424 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ 00425 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ 00426 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ 00427 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ 00428 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ 00429 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ 00430 }; 00431 #ifdef __STDC__ 00432 static const double qS5[6] = { 00433 #else 00434 static double qS5[6] = { 00435 #endif 00436 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ 00437 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ 00438 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ 00439 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ 00440 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ 00441 -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ 00442 }; 00443 00444 #ifdef __STDC__ 00445 static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 00446 #else 00447 static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 00448 #endif 00449 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ 00450 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ 00451 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ 00452 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ 00453 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ 00454 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ 00455 }; 00456 #ifdef __STDC__ 00457 static const double qS3[6] = { 00458 #else 00459 static double qS3[6] = { 00460 #endif 00461 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ 00462 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ 00463 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ 00464 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ 00465 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ 00466 -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ 00467 }; 00468 00469 #ifdef __STDC__ 00470 static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 00471 #else 00472 static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 00473 #endif 00474 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ 00475 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ 00476 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ 00477 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ 00478 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ 00479 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ 00480 }; 00481 #ifdef __STDC__ 00482 static const double qS2[6] = { 00483 #else 00484 static double qS2[6] = { 00485 #endif 00486 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ 00487 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ 00488 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ 00489 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ 00490 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ 00491 -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ 00492 }; 00493 00494 #ifdef __STDC__ 00495 static double qzero(double x) 00496 #else 00497 static double qzero(x) 00498 double x; 00499 #endif 00500 { 00501 #ifdef __STDC__ 00502 const double *p = 0,*q = 0; 00503 #else 00504 double *p = 0,*q = 0; 00505 #endif 00506 double s,r,z,z2,z4,z6,r1,r2,r3,s1,s2,s3; 00507 int32_t ix; 00508 GET_HIGH_WORD(ix,x); 00509 ix &= 0x7fffffff; 00510 if(ix>=0x40200000) {p = qR8; q= qS8;} 00511 else if(ix>=0x40122E8B){p = qR5; q= qS5;} 00512 else if(ix>=0x4006DB6D){p = qR3; q= qS3;} 00513 else if(ix>=0x40000000){p = qR2; q= qS2;} 00514 z = one/(x*x); 00515 #ifdef DO_NOT_USE_THIS 00516 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); 00517 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); 00518 #else 00519 r1 = p[0]+z*p[1]; z2=z*z; 00520 r2 = p[2]+z*p[3]; z4=z2*z2; 00521 r3 = p[4]+z*p[5]; z6=z4*z2; 00522 r= r1 + z2*r2 + z4*r3; 00523 s1 = one+z*q[0]; 00524 s2 = q[1]+z*q[2]; 00525 s3 = q[3]+z*q[4]; 00526 s = s1 + z2*s2 + z4*s3 +z6*q[5]; 00527 #endif 00528 return (-.125 + r/s)/x; 00529 }
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