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| Rev | Author | Line No. | Line |
|---|---|---|---|
| 2 | pj | 1 | /* @(#)e_j0.c 5.1 93/09/24 */ |
| 2 | /* |
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| 3 | * ==================================================== |
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| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 5 | * |
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| 6 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 7 | * Permission to use, copy, modify, and distribute this |
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| 8 | * software is freely granted, provided that this notice |
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| 9 | * is preserved. |
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| 10 | * ==================================================== |
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| 11 | */ |
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| 12 | |||
| 13 | #ifndef lint |
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| 14 | static char rcsid[] = "$\Id: e_j0.c,v 1.2 1995/05/30 05:48:18 rgrimes Exp $"; |
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| 15 | #endif |
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| 16 | |||
| 17 | /* __ieee754_j0(x), __ieee754_y0(x) |
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| 18 | * Bessel function of the first and second kinds of order zero. |
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| 19 | * Method -- j0(x): |
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| 20 | * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... |
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| 21 | * 2. Reduce x to |x| since j0(x)=j0(-x), and |
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| 22 | * for x in (0,2) |
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| 23 | * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; |
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| 24 | * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) |
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| 25 | * for x in (2,inf) |
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| 26 | * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) |
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| 27 | * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) |
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| 28 | * as follow: |
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| 29 | * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) |
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| 30 | * = 1/sqrt(2) * (cos(x) + sin(x)) |
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| 31 | * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) |
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| 32 | * = 1/sqrt(2) * (sin(x) - cos(x)) |
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| 33 | * (To avoid cancellation, use |
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| 34 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
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| 35 | * to compute the worse one.) |
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| 36 | * |
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| 37 | * 3 Special cases |
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| 38 | * j0(nan)= nan |
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| 39 | * j0(0) = 1 |
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| 40 | * j0(inf) = 0 |
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| 41 | * |
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| 42 | * Method -- y0(x): |
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| 43 | * 1. For x<2. |
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| 44 | * Since |
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| 45 | * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) |
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| 46 | * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. |
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| 47 | * We use the following function to approximate y0, |
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| 48 | * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 |
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| 49 | * where |
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| 50 | * U(z) = u00 + u01*z + ... + u06*z^6 |
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| 51 | * V(z) = 1 + v01*z + ... + v04*z^4 |
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| 52 | * with absolute approximation error bounded by 2**-72. |
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| 53 | * Note: For tiny x, U/V = u0 and j0(x)~1, hence |
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| 54 | * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) |
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| 55 | * 2. For x>=2. |
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| 56 | * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) |
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| 57 | * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) |
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| 58 | * by the method mentioned above. |
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| 59 | * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. |
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| 60 | */ |
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| 61 | |||
| 62 | #include "math.h" |
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| 63 | #include "math_private.h" |
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| 64 | |||
| 65 | #ifdef __STDC__ |
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| 66 | static double pzero(double), qzero(double); |
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| 67 | #else |
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| 68 | static double pzero(), qzero(); |
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| 69 | #endif |
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| 70 | |||
| 71 | #ifdef __STDC__ |
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| 72 | static const double |
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| 73 | #else |
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| 74 | static double |
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| 75 | #endif |
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| 76 | huge = 1e300, |
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| 77 | one = 1.0, |
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| 78 | invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ |
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| 79 | tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
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| 80 | /* R0/S0 on [0, 2.00] */ |
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| 81 | R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ |
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| 82 | R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ |
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| 83 | R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ |
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| 84 | R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ |
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| 85 | S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ |
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| 86 | S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ |
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| 87 | S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ |
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| 88 | S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ |
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| 89 | |||
| 90 | #ifdef __STDC__ |
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| 91 | static const double zero = 0.0; |
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| 92 | #else |
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| 93 | static double zero = 0.0; |
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| 94 | #endif |
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| 95 | |||
| 96 | #ifdef __STDC__ |
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| 97 | double __ieee754_j0(double x) |
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| 98 | #else |
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| 99 | double __ieee754_j0(x) |
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| 100 | double x; |
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| 101 | #endif |
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| 102 | { |
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| 103 | double z, s,c,ss,cc,r,u,v; |
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| 104 | int32_t hx,ix; |
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| 105 | |||
| 106 | GET_HIGH_WORD(hx,x); |
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| 107 | ix = hx&0x7fffffff; |
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| 108 | if(ix>=0x7ff00000) return one/(x*x); |
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| 109 | x = fabs(x); |
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| 110 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
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| 111 | s = sin(x); |
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| 112 | c = cos(x); |
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| 113 | ss = s-c; |
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| 114 | cc = s+c; |
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| 115 | if(ix<0x7fe00000) { /* make sure x+x not overflow */ |
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| 116 | z = -cos(x+x); |
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| 117 | if ((s*c)<zero) cc = z/ss; |
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| 118 | else ss = z/cc; |
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| 119 | } |
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| 120 | /* |
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| 121 | * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) |
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| 122 | * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) |
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| 123 | */ |
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| 124 | if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(x); |
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| 125 | else { |
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| 126 | u = pzero(x); v = qzero(x); |
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| 127 | z = invsqrtpi*(u*cc-v*ss)/sqrt(x); |
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| 128 | } |
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| 129 | return z; |
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| 130 | } |
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| 131 | if(ix<0x3f200000) { /* |x| < 2**-13 */ |
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| 132 | if(huge+x>one) { /* raise inexact if x != 0 */ |
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| 133 | if(ix<0x3e400000) return one; /* |x|<2**-27 */ |
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| 134 | else return one - 0.25*x*x; |
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| 135 | } |
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| 136 | } |
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| 137 | z = x*x; |
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| 138 | r = z*(R02+z*(R03+z*(R04+z*R05))); |
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| 139 | s = one+z*(S01+z*(S02+z*(S03+z*S04))); |
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| 140 | if(ix < 0x3FF00000) { /* |x| < 1.00 */ |
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| 141 | return one + z*(-0.25+(r/s)); |
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| 142 | } else { |
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| 143 | u = 0.5*x; |
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| 144 | return((one+u)*(one-u)+z*(r/s)); |
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| 145 | } |
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| 146 | } |
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| 147 | |||
| 148 | #ifdef __STDC__ |
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| 149 | static const double |
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| 150 | #else |
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| 151 | static double |
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| 152 | #endif |
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| 153 | u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ |
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| 154 | u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ |
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| 155 | u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ |
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| 156 | u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ |
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| 157 | u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ |
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| 158 | u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ |
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| 159 | u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ |
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| 160 | v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ |
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| 161 | v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ |
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| 162 | v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ |
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| 163 | v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ |
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| 164 | |||
| 165 | #ifdef __STDC__ |
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| 166 | double __ieee754_y0(double x) |
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| 167 | #else |
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| 168 | double __ieee754_y0(x) |
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| 169 | double x; |
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| 170 | #endif |
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| 171 | { |
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| 172 | double z, s,c,ss,cc,u,v; |
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| 173 | int32_t hx,ix,lx; |
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| 174 | |||
| 175 | EXTRACT_WORDS(hx,lx,x); |
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| 176 | ix = 0x7fffffff&hx; |
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| 177 | /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ |
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| 178 | if(ix>=0x7ff00000) return one/(x+x*x); |
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| 179 | if((ix|lx)==0) return -one/zero; |
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| 180 | if(hx<0) return zero/zero; |
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| 181 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
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| 182 | /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) |
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| 183 | * where x0 = x-pi/4 |
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| 184 | * Better formula: |
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| 185 | * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) |
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| 186 | * = 1/sqrt(2) * (sin(x) + cos(x)) |
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| 187 | * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) |
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| 188 | * = 1/sqrt(2) * (sin(x) - cos(x)) |
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| 189 | * To avoid cancellation, use |
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| 190 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
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| 191 | * to compute the worse one. |
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| 192 | */ |
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| 193 | s = sin(x); |
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| 194 | c = cos(x); |
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| 195 | ss = s-c; |
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| 196 | cc = s+c; |
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| 197 | /* |
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| 198 | * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) |
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| 199 | * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) |
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| 200 | */ |
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| 201 | if(ix<0x7fe00000) { /* make sure x+x not overflow */ |
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| 202 | z = -cos(x+x); |
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| 203 | if ((s*c)<zero) cc = z/ss; |
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| 204 | else ss = z/cc; |
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| 205 | } |
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| 206 | if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); |
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| 207 | else { |
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| 208 | u = pzero(x); v = qzero(x); |
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| 209 | z = invsqrtpi*(u*ss+v*cc)/sqrt(x); |
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| 210 | } |
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| 211 | return z; |
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| 212 | } |
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| 213 | if(ix<=0x3e400000) { /* x < 2**-27 */ |
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| 214 | return(u00 + tpi*__ieee754_log(x)); |
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| 215 | } |
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| 216 | z = x*x; |
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| 217 | u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); |
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| 218 | v = one+z*(v01+z*(v02+z*(v03+z*v04))); |
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| 219 | return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); |
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| 220 | } |
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| 221 | |||
| 222 | /* The asymptotic expansions of pzero is |
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| 223 | * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. |
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| 224 | * For x >= 2, We approximate pzero by |
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| 225 | * pzero(x) = 1 + (R/S) |
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| 226 | * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 |
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| 227 | * S = 1 + pS0*s^2 + ... + pS4*s^10 |
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| 228 | * and |
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| 229 | * | pzero(x)-1-R/S | <= 2 ** ( -60.26) |
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| 230 | */ |
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| 231 | #ifdef __STDC__ |
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| 232 | static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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| 233 | #else |
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| 234 | static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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| 235 | #endif |
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| 236 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
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| 237 | -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ |
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| 238 | -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ |
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| 239 | -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ |
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| 240 | -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ |
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| 241 | -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ |
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| 242 | }; |
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| 243 | #ifdef __STDC__ |
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| 244 | static const double pS8[5] = { |
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| 245 | #else |
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| 246 | static double pS8[5] = { |
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| 247 | #endif |
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| 248 | 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ |
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| 249 | 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ |
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| 250 | 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ |
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| 251 | 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ |
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| 252 | 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ |
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| 253 | }; |
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| 254 | |||
| 255 | #ifdef __STDC__ |
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| 256 | static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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| 257 | #else |
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| 258 | static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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| 259 | #endif |
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| 260 | -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ |
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| 261 | -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ |
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| 262 | -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ |
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| 263 | -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ |
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| 264 | -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ |
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| 265 | -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ |
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| 266 | }; |
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| 267 | #ifdef __STDC__ |
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| 268 | static const double pS5[5] = { |
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| 269 | #else |
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| 270 | static double pS5[5] = { |
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| 271 | #endif |
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| 272 | 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ |
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| 273 | 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ |
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| 274 | 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ |
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| 275 | 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ |
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| 276 | 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ |
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| 277 | }; |
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| 278 | |||
| 279 | #ifdef __STDC__ |
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| 280 | static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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| 281 | #else |
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| 282 | static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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| 283 | #endif |
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| 284 | -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ |
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| 285 | -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ |
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| 286 | -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ |
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| 287 | -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ |
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| 288 | -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ |
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| 289 | -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ |
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| 290 | }; |
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| 291 | #ifdef __STDC__ |
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| 292 | static const double pS3[5] = { |
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| 293 | #else |
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| 294 | static double pS3[5] = { |
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| 295 | #endif |
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| 296 | 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ |
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| 297 | 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ |
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| 298 | 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ |
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| 299 | 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ |
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| 300 | 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ |
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| 301 | }; |
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| 302 | |||
| 303 | #ifdef __STDC__ |
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| 304 | static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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| 305 | #else |
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| 306 | static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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| 307 | #endif |
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| 308 | -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ |
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| 309 | -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ |
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| 310 | -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ |
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| 311 | -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ |
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| 312 | -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ |
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| 313 | -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ |
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| 314 | }; |
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| 315 | #ifdef __STDC__ |
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| 316 | static const double pS2[5] = { |
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| 317 | #else |
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| 318 | static double pS2[5] = { |
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| 319 | #endif |
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| 320 | 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ |
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| 321 | 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ |
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| 322 | 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ |
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| 323 | 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ |
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| 324 | 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ |
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| 325 | }; |
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| 326 | |||
| 327 | #ifdef __STDC__ |
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| 328 | static double pzero(double x) |
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| 329 | #else |
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| 330 | static double pzero(x) |
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| 331 | double x; |
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| 332 | #endif |
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| 333 | { |
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| 334 | #ifdef __STDC__ |
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| 335 | const double *p,*q; |
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| 336 | #else |
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| 337 | double *p,*q; |
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| 338 | #endif |
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| 339 | double z,r,s; |
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| 340 | int32_t ix; |
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| 341 | GET_HIGH_WORD(ix,x); |
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| 342 | ix &= 0x7fffffff; |
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| 343 | if(ix>=0x40200000) {p = pR8; q= pS8;} |
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| 344 | else if(ix>=0x40122E8B){p = pR5; q= pS5;} |
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| 345 | else if(ix>=0x4006DB6D){p = pR3; q= pS3;} |
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| 346 | else if(ix>=0x40000000){p = pR2; q= pS2;} |
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| 347 | z = one/(x*x); |
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| 348 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
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| 349 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); |
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| 350 | return one+ r/s; |
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| 351 | } |
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| 352 | |||
| 353 | |||
| 354 | /* For x >= 8, the asymptotic expansions of qzero is |
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| 355 | * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. |
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| 356 | * We approximate pzero by |
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| 357 | * qzero(x) = s*(-1.25 + (R/S)) |
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| 358 | * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 |
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| 359 | * S = 1 + qS0*s^2 + ... + qS5*s^12 |
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| 360 | * and |
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| 361 | * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) |
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| 362 | */ |
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| 363 | #ifdef __STDC__ |
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| 364 | static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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| 365 | #else |
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| 366 | static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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| 367 | #endif |
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| 368 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
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| 369 | 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ |
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| 370 | 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ |
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| 371 | 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ |
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| 372 | 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ |
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| 373 | 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ |
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| 374 | }; |
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| 375 | #ifdef __STDC__ |
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| 376 | static const double qS8[6] = { |
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| 377 | #else |
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| 378 | static double qS8[6] = { |
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| 379 | #endif |
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| 380 | 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ |
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| 381 | 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ |
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| 382 | 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ |
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| 383 | 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ |
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| 384 | 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ |
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| 385 | -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ |
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| 386 | }; |
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| 387 | |||
| 388 | #ifdef __STDC__ |
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| 389 | static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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| 390 | #else |
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| 391 | static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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| 392 | #endif |
||
| 393 | 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ |
||
| 394 | 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ |
||
| 395 | 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ |
||
| 396 | 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ |
||
| 397 | 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ |
||
| 398 | 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ |
||
| 399 | }; |
||
| 400 | #ifdef __STDC__ |
||
| 401 | static const double qS5[6] = { |
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| 402 | #else |
||
| 403 | static double qS5[6] = { |
||
| 404 | #endif |
||
| 405 | 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ |
||
| 406 | 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ |
||
| 407 | 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ |
||
| 408 | 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ |
||
| 409 | 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ |
||
| 410 | -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ |
||
| 411 | }; |
||
| 412 | |||
| 413 | #ifdef __STDC__ |
||
| 414 | static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
||
| 415 | #else |
||
| 416 | static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
||
| 417 | #endif |
||
| 418 | 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ |
||
| 419 | 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ |
||
| 420 | 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ |
||
| 421 | 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ |
||
| 422 | 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ |
||
| 423 | 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ |
||
| 424 | }; |
||
| 425 | #ifdef __STDC__ |
||
| 426 | static const double qS3[6] = { |
||
| 427 | #else |
||
| 428 | static double qS3[6] = { |
||
| 429 | #endif |
||
| 430 | 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ |
||
| 431 | 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ |
||
| 432 | 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ |
||
| 433 | 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ |
||
| 434 | 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ |
||
| 435 | -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ |
||
| 436 | }; |
||
| 437 | |||
| 438 | #ifdef __STDC__ |
||
| 439 | static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
||
| 440 | #else |
||
| 441 | static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
||
| 442 | #endif |
||
| 443 | 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ |
||
| 444 | 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ |
||
| 445 | 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ |
||
| 446 | 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ |
||
| 447 | 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ |
||
| 448 | 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ |
||
| 449 | }; |
||
| 450 | #ifdef __STDC__ |
||
| 451 | static const double qS2[6] = { |
||
| 452 | #else |
||
| 453 | static double qS2[6] = { |
||
| 454 | #endif |
||
| 455 | 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ |
||
| 456 | 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ |
||
| 457 | 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ |
||
| 458 | 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ |
||
| 459 | 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ |
||
| 460 | -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ |
||
| 461 | }; |
||
| 462 | |||
| 463 | #ifdef __STDC__ |
||
| 464 | static double qzero(double x) |
||
| 465 | #else |
||
| 466 | static double qzero(x) |
||
| 467 | double x; |
||
| 468 | #endif |
||
| 469 | { |
||
| 470 | #ifdef __STDC__ |
||
| 471 | const double *p,*q; |
||
| 472 | #else |
||
| 473 | double *p,*q; |
||
| 474 | #endif |
||
| 475 | double s,r,z; |
||
| 476 | int32_t ix; |
||
| 477 | GET_HIGH_WORD(ix,x); |
||
| 478 | ix &= 0x7fffffff; |
||
| 479 | if(ix>=0x40200000) {p = qR8; q= qS8;} |
||
| 480 | else if(ix>=0x40122E8B){p = qR5; q= qS5;} |
||
| 481 | else if(ix>=0x4006DB6D){p = qR3; q= qS3;} |
||
| 482 | else if(ix>=0x40000000){p = qR2; q= qS2;} |
||
| 483 | z = one/(x*x); |
||
| 484 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
||
| 485 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); |
||
| 486 | return (-.125 + r/s)/x; |
||
| 487 | } |