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| Rev | Author | Line No. | Line |
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| 2 | pj | 1 | /* @(#)e_j1.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_j1.c,v 1.2 1995/05/30 05:48:20 rgrimes Exp $"; |
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| 15 | #endif |
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| 16 | |||
| 17 | /* __ieee754_j1(x), __ieee754_y1(x) |
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| 18 | * Bessel function of the first and second kinds of order zero. |
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| 19 | * Method -- j1(x): |
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| 20 | * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... |
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| 21 | * 2. Reduce x to |x| since j1(x)=-j1(-x), and |
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| 22 | * for x in (0,2) |
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| 23 | * j1(x) = x/2 + x*z*R0/S0, where z = x*x; |
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| 24 | * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) |
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| 25 | * for x in (2,inf) |
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| 26 | * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) |
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| 27 | * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) |
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| 28 | * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) |
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| 29 | * as follow: |
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| 30 | * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) |
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| 31 | * = 1/sqrt(2) * (sin(x) - cos(x)) |
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| 32 | * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) |
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| 33 | * = -1/sqrt(2) * (sin(x) + cos(x)) |
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| 34 | * (To avoid cancellation, use |
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| 35 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
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| 36 | * to compute the worse one.) |
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| 37 | * |
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| 38 | * 3 Special cases |
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| 39 | * j1(nan)= nan |
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| 40 | * j1(0) = 0 |
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| 41 | * j1(inf) = 0 |
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| 42 | * |
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| 43 | * Method -- y1(x): |
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| 44 | * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN |
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| 45 | * 2. For x<2. |
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| 46 | * Since |
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| 47 | * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) |
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| 48 | * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. |
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| 49 | * We use the following function to approximate y1, |
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| 50 | * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 |
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| 51 | * where for x in [0,2] (abs err less than 2**-65.89) |
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| 52 | * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 |
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| 53 | * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 |
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| 54 | * Note: For tiny x, 1/x dominate y1 and hence |
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| 55 | * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) |
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| 56 | * 3. For x>=2. |
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| 57 | * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) |
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| 58 | * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) |
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| 59 | * by method mentioned above. |
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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 pone(double), qone(double); |
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| 67 | #else |
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| 68 | static double pone(), qone(); |
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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] */ |
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| 81 | r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ |
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| 82 | r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ |
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| 83 | r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ |
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| 84 | r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ |
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| 85 | s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ |
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| 86 | s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ |
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| 87 | s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ |
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| 88 | s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ |
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| 89 | s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ |
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| 90 | |||
| 91 | #ifdef __STDC__ |
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| 92 | static const double zero = 0.0; |
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| 93 | #else |
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| 94 | static double zero = 0.0; |
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| 95 | #endif |
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| 96 | |||
| 97 | #ifdef __STDC__ |
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| 98 | double __ieee754_j1(double x) |
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| 99 | #else |
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| 100 | double __ieee754_j1(x) |
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| 101 | double x; |
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| 102 | #endif |
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| 103 | { |
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| 104 | double z, s,c,ss,cc,r,u,v,y; |
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| 105 | int32_t hx,ix; |
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| 106 | |||
| 107 | GET_HIGH_WORD(hx,x); |
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| 108 | ix = hx&0x7fffffff; |
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| 109 | if(ix>=0x7ff00000) return one/x; |
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| 110 | y = fabs(x); |
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| 111 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
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| 112 | s = sin(y); |
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| 113 | c = cos(y); |
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| 114 | ss = -s-c; |
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| 115 | cc = s-c; |
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| 116 | if(ix<0x7fe00000) { /* make sure y+y not overflow */ |
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| 117 | z = cos(y+y); |
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| 118 | if ((s*c)>zero) cc = z/ss; |
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| 119 | else ss = z/cc; |
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| 120 | } |
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| 121 | /* |
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| 122 | * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) |
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| 123 | * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) |
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| 124 | */ |
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| 125 | if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y); |
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| 126 | else { |
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| 127 | u = pone(y); v = qone(y); |
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| 128 | z = invsqrtpi*(u*cc-v*ss)/sqrt(y); |
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| 129 | } |
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| 130 | if(hx<0) return -z; |
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| 131 | else return z; |
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| 132 | } |
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| 133 | if(ix<0x3e400000) { /* |x|<2**-27 */ |
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| 134 | if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ |
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| 135 | } |
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| 136 | z = x*x; |
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| 137 | r = z*(r00+z*(r01+z*(r02+z*r03))); |
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| 138 | s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); |
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| 139 | r *= x; |
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| 140 | return(x*0.5+r/s); |
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| 141 | } |
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| 142 | |||
| 143 | #ifdef __STDC__ |
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| 144 | static const double U0[5] = { |
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| 145 | #else |
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| 146 | static double U0[5] = { |
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| 147 | #endif |
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| 148 | -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ |
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| 149 | 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ |
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| 150 | -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ |
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| 151 | 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ |
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| 152 | -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ |
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| 153 | }; |
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| 154 | #ifdef __STDC__ |
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| 155 | static const double V0[5] = { |
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| 156 | #else |
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| 157 | static double V0[5] = { |
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| 158 | #endif |
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| 159 | 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ |
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| 160 | 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ |
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| 161 | 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ |
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| 162 | 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ |
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| 163 | 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ |
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| 164 | }; |
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| 165 | |||
| 166 | #ifdef __STDC__ |
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| 167 | double __ieee754_y1(double x) |
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| 168 | #else |
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| 169 | double __ieee754_y1(x) |
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| 170 | double x; |
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| 171 | #endif |
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| 172 | { |
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| 173 | double z, s,c,ss,cc,u,v; |
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| 174 | int32_t hx,ix,lx; |
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| 175 | |||
| 176 | EXTRACT_WORDS(hx,lx,x); |
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| 177 | ix = 0x7fffffff&hx; |
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| 178 | /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ |
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| 179 | if(ix>=0x7ff00000) return one/(x+x*x); |
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| 180 | if((ix|lx)==0) return -one/zero; |
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| 181 | if(hx<0) return zero/zero; |
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| 182 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
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| 183 | s = sin(x); |
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| 184 | c = cos(x); |
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| 185 | ss = -s-c; |
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| 186 | cc = s-c; |
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| 187 | if(ix<0x7fe00000) { /* make sure x+x not overflow */ |
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| 188 | z = cos(x+x); |
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| 189 | if ((s*c)>zero) cc = z/ss; |
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| 190 | else ss = z/cc; |
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| 191 | } |
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| 192 | /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) |
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| 193 | * where x0 = x-3pi/4 |
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| 194 | * Better formula: |
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| 195 | * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) |
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| 196 | * = 1/sqrt(2) * (sin(x) - cos(x)) |
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| 197 | * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) |
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| 198 | * = -1/sqrt(2) * (cos(x) + sin(x)) |
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| 199 | * To avoid cancellation, use |
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| 200 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
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| 201 | * to compute the worse one. |
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| 202 | */ |
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| 203 | if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); |
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| 204 | else { |
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| 205 | u = pone(x); v = qone(x); |
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| 206 | z = invsqrtpi*(u*ss+v*cc)/sqrt(x); |
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| 207 | } |
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| 208 | return z; |
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| 209 | } |
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| 210 | if(ix<=0x3c900000) { /* x < 2**-54 */ |
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| 211 | return(-tpi/x); |
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| 212 | } |
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| 213 | z = x*x; |
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| 214 | u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); |
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| 215 | v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); |
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| 216 | return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); |
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| 217 | } |
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| 218 | |||
| 219 | /* For x >= 8, the asymptotic expansions of pone is |
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| 220 | * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. |
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| 221 | * We approximate pone by |
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| 222 | * pone(x) = 1 + (R/S) |
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| 223 | * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 |
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| 224 | * S = 1 + ps0*s^2 + ... + ps4*s^10 |
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| 225 | * and |
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| 226 | * | pone(x)-1-R/S | <= 2 ** ( -60.06) |
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| 227 | */ |
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| 228 | |||
| 229 | #ifdef __STDC__ |
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| 230 | static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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| 231 | #else |
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| 232 | static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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| 233 | #endif |
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| 234 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
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| 235 | 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ |
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| 236 | 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ |
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| 237 | 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ |
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| 238 | 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ |
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| 239 | 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ |
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| 240 | }; |
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| 241 | #ifdef __STDC__ |
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| 242 | static const double ps8[5] = { |
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| 243 | #else |
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| 244 | static double ps8[5] = { |
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| 245 | #endif |
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| 246 | 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ |
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| 247 | 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ |
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| 248 | 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ |
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| 249 | 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ |
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| 250 | 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ |
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| 251 | }; |
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| 252 | |||
| 253 | #ifdef __STDC__ |
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| 254 | static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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| 255 | #else |
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| 256 | static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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| 257 | #endif |
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| 258 | 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ |
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| 259 | 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ |
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| 260 | 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ |
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| 261 | 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ |
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| 262 | 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ |
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| 263 | 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ |
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| 264 | }; |
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| 265 | #ifdef __STDC__ |
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| 266 | static const double ps5[5] = { |
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| 267 | #else |
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| 268 | static double ps5[5] = { |
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| 269 | #endif |
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| 270 | 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ |
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| 271 | 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ |
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| 272 | 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ |
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| 273 | 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ |
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| 274 | 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ |
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| 275 | }; |
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| 276 | |||
| 277 | #ifdef __STDC__ |
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| 278 | static const double pr3[6] = { |
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| 279 | #else |
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| 280 | static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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| 281 | #endif |
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| 282 | 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ |
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| 283 | 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ |
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| 284 | 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ |
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| 285 | 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ |
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| 286 | 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ |
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| 287 | 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ |
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| 288 | }; |
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| 289 | #ifdef __STDC__ |
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| 290 | static const double ps3[5] = { |
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| 291 | #else |
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| 292 | static double ps3[5] = { |
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| 293 | #endif |
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| 294 | 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ |
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| 295 | 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ |
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| 296 | 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ |
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| 297 | 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ |
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| 298 | 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ |
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| 299 | }; |
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| 300 | |||
| 301 | #ifdef __STDC__ |
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| 302 | static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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| 303 | #else |
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| 304 | static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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| 305 | #endif |
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| 306 | 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ |
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| 307 | 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ |
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| 308 | 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ |
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| 309 | 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ |
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| 310 | 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ |
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| 311 | 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ |
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| 312 | }; |
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| 313 | #ifdef __STDC__ |
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| 314 | static const double ps2[5] = { |
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| 315 | #else |
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| 316 | static double ps2[5] = { |
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| 317 | #endif |
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| 318 | 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ |
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| 319 | 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ |
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| 320 | 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ |
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| 321 | 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ |
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| 322 | 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ |
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| 323 | }; |
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| 324 | |||
| 325 | #ifdef __STDC__ |
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| 326 | static double pone(double x) |
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| 327 | #else |
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| 328 | static double pone(x) |
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| 329 | double x; |
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| 330 | #endif |
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| 331 | { |
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| 332 | #ifdef __STDC__ |
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| 333 | const double *p,*q; |
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| 334 | #else |
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| 335 | double *p,*q; |
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| 336 | #endif |
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| 337 | double z,r,s; |
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| 338 | int32_t ix; |
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| 339 | GET_HIGH_WORD(ix,x); |
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| 340 | ix &= 0x7fffffff; |
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| 341 | if(ix>=0x40200000) {p = pr8; q= ps8;} |
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| 342 | else if(ix>=0x40122E8B){p = pr5; q= ps5;} |
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| 343 | else if(ix>=0x4006DB6D){p = pr3; q= ps3;} |
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| 344 | else if(ix>=0x40000000){p = pr2; q= ps2;} |
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| 345 | z = one/(x*x); |
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| 346 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
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| 347 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); |
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| 348 | return one+ r/s; |
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| 349 | } |
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| 350 | |||
| 351 | |||
| 352 | /* For x >= 8, the asymptotic expansions of qone is |
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| 353 | * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. |
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| 354 | * We approximate pone by |
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| 355 | * qone(x) = s*(0.375 + (R/S)) |
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| 356 | * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 |
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| 357 | * S = 1 + qs1*s^2 + ... + qs6*s^12 |
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| 358 | * and |
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| 359 | * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) |
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| 360 | */ |
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| 361 | |||
| 362 | #ifdef __STDC__ |
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| 363 | static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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| 364 | #else |
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| 365 | static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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| 366 | #endif |
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| 367 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
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| 368 | -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ |
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| 369 | -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ |
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| 370 | -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ |
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| 371 | -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ |
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| 372 | -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ |
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| 373 | }; |
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| 374 | #ifdef __STDC__ |
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| 375 | static const double qs8[6] = { |
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| 376 | #else |
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| 377 | static double qs8[6] = { |
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| 378 | #endif |
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| 379 | 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ |
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| 380 | 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ |
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| 381 | 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ |
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| 382 | 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ |
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| 383 | 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ |
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| 384 | -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ |
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| 385 | }; |
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| 386 | |||
| 387 | #ifdef __STDC__ |
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| 388 | static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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| 389 | #else |
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| 390 | static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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| 391 | #endif |
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| 392 | -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ |
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| 393 | -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ |
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| 394 | -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ |
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| 395 | -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ |
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| 396 | -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ |
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| 397 | -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ |
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| 398 | }; |
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| 399 | #ifdef __STDC__ |
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| 400 | static const double qs5[6] = { |
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| 401 | #else |
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| 402 | static double qs5[6] = { |
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| 403 | #endif |
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| 404 | 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ |
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| 405 | 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ |
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| 406 | 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ |
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| 407 | 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ |
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| 408 | 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ |
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| 409 | -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ |
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| 410 | }; |
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| 411 | |||
| 412 | #ifdef __STDC__ |
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| 413 | static const double qr3[6] = { |
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| 414 | #else |
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| 415 | static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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| 416 | #endif |
||
| 417 | -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ |
||
| 418 | -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ |
||
| 419 | -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ |
||
| 420 | -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ |
||
| 421 | -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ |
||
| 422 | -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ |
||
| 423 | }; |
||
| 424 | #ifdef __STDC__ |
||
| 425 | static const double qs3[6] = { |
||
| 426 | #else |
||
| 427 | static double qs3[6] = { |
||
| 428 | #endif |
||
| 429 | 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ |
||
| 430 | 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ |
||
| 431 | 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ |
||
| 432 | 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ |
||
| 433 | 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ |
||
| 434 | -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ |
||
| 435 | }; |
||
| 436 | |||
| 437 | #ifdef __STDC__ |
||
| 438 | static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
||
| 439 | #else |
||
| 440 | static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
||
| 441 | #endif |
||
| 442 | -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ |
||
| 443 | -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ |
||
| 444 | -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ |
||
| 445 | -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ |
||
| 446 | -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ |
||
| 447 | -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ |
||
| 448 | }; |
||
| 449 | #ifdef __STDC__ |
||
| 450 | static const double qs2[6] = { |
||
| 451 | #else |
||
| 452 | static double qs2[6] = { |
||
| 453 | #endif |
||
| 454 | 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ |
||
| 455 | 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ |
||
| 456 | 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ |
||
| 457 | 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ |
||
| 458 | 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ |
||
| 459 | -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ |
||
| 460 | }; |
||
| 461 | |||
| 462 | #ifdef __STDC__ |
||
| 463 | static double qone(double x) |
||
| 464 | #else |
||
| 465 | static double qone(x) |
||
| 466 | double x; |
||
| 467 | #endif |
||
| 468 | { |
||
| 469 | #ifdef __STDC__ |
||
| 470 | const double *p,*q; |
||
| 471 | #else |
||
| 472 | double *p,*q; |
||
| 473 | #endif |
||
| 474 | double s,r,z; |
||
| 475 | int32_t ix; |
||
| 476 | GET_HIGH_WORD(ix,x); |
||
| 477 | ix &= 0x7fffffff; |
||
| 478 | if(ix>=0x40200000) {p = qr8; q= qs8;} |
||
| 479 | else if(ix>=0x40122E8B){p = qr5; q= qs5;} |
||
| 480 | else if(ix>=0x4006DB6D){p = qr3; q= qs3;} |
||
| 481 | else if(ix>=0x40000000){p = qr2; q= qs2;} |
||
| 482 | z = one/(x*x); |
||
| 483 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
||
| 484 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); |
||
| 485 | return (.375 + r/s)/x; |
||
| 486 | } |