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| Rev | Author | Line No. | Line |
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| 3362 | Serge | 1 | |
| 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 | |||
| 14 | * Bessel function of the first and second kinds of order zero. |
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| 15 | * Method -- j0(x): |
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| 16 | * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... |
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| 17 | * 2. Reduce x to |x| since j0(x)=j0(-x), and |
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| 18 | * for x in (0,2) |
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| 19 | * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; |
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| 20 | * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) |
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| 21 | * for x in (2,inf) |
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| 22 | * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) |
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| 23 | * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) |
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| 24 | * as follow: |
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| 25 | * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) |
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| 26 | * = 1/sqrt(2) * (cos(x) + sin(x)) |
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| 27 | * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) |
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| 28 | * = 1/sqrt(2) * (sin(x) - cos(x)) |
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| 29 | * (To avoid cancellation, use |
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| 30 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
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| 31 | * to compute the worse one.) |
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| 32 | * |
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| 33 | * 3 Special cases |
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| 34 | * j0(nan)= nan |
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| 35 | * j0(0) = 1 |
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| 36 | * j0(inf) = 0 |
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| 37 | * |
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| 38 | * Method -- y0(x): |
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| 39 | * 1. For x<2. |
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| 40 | * Since |
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| 41 | * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) |
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| 42 | * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. |
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| 43 | * We use the following function to approximate y0, |
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| 44 | * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 |
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| 45 | * where |
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| 46 | * U(z) = u00 + u01*z + ... + u06*z^6 |
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| 47 | * V(z) = 1 + v01*z + ... + v04*z^4 |
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| 48 | * with absolute approximation error bounded by 2**-72. |
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| 49 | * Note: For tiny x, U/V = u0 and j0(x)~1, hence |
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| 50 | * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) |
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| 51 | * 2. For x>=2. |
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| 52 | * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) |
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| 53 | * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) |
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| 54 | * by the method mentioned above. |
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| 55 | * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. |
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| 56 | */ |
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| 57 | |||
| 58 | |||
| 59 | |||
| 60 | |||
| 61 | |||
| 62 | |||
| 63 | static double pzero(double), qzero(double); |
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| 64 | #else |
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| 65 | static double pzero(), qzero(); |
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| 66 | #endif |
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| 67 | |||
| 68 | |||
| 69 | static const double |
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| 70 | #else |
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| 71 | static double |
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| 72 | #endif |
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| 73 | huge = 1e300, |
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| 74 | one = 1.0, |
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| 75 | invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ |
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| 76 | tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
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| 77 | /* R0/S0 on [0, 2.00] */ |
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| 78 | R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ |
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| 79 | R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ |
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| 80 | R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ |
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| 81 | R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ |
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| 82 | S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ |
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| 83 | S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ |
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| 84 | S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ |
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| 85 | S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ |
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| 86 | |||
| 87 | |||
| 88 | static const double zero = 0.0; |
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| 89 | #else |
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| 90 | static double zero = 0.0; |
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| 91 | #endif |
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| 92 | |||
| 93 | |||
| 94 | double __ieee754_j0(double x) |
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| 95 | #else |
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| 96 | double __ieee754_j0(x) |
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| 97 | double x; |
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| 98 | #endif |
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| 99 | { |
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| 100 | double z, s,c,ss,cc,r,u,v; |
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| 101 | __int32_t hx,ix; |
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| 102 | |||
| 103 | |||
| 104 | ix = hx&0x7fffffff; |
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| 105 | if(ix>=0x7ff00000) return one/(x*x); |
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| 106 | x = fabs(x); |
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| 107 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
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| 108 | s = sin(x); |
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| 109 | c = cos(x); |
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| 110 | ss = s-c; |
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| 111 | cc = s+c; |
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| 112 | if(ix<0x7fe00000) { /* make sure x+x not overflow */ |
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| 113 | z = -cos(x+x); |
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| 114 | if ((s*c) |
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| 115 | else ss = z/cc; |
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| 116 | } |
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| 117 | /* |
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| 118 | * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) |
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| 119 | * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) |
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| 120 | */ |
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| 121 | if(ix>0x48000000) z = (invsqrtpi*cc)/__ieee754_sqrt(x); |
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| 122 | else { |
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| 123 | u = pzero(x); v = qzero(x); |
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| 124 | z = invsqrtpi*(u*cc-v*ss)/__ieee754_sqrt(x); |
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| 125 | } |
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| 126 | return z; |
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| 127 | } |
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| 128 | if(ix<0x3f200000) { /* |x| < 2**-13 */ |
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| 129 | if(huge+x>one) { /* raise inexact if x != 0 */ |
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| 130 | if(ix<0x3e400000) return one; /* |x|<2**-27 */ |
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| 131 | else return one - 0.25*x*x; |
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| 132 | } |
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| 133 | } |
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| 134 | z = x*x; |
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| 135 | r = z*(R02+z*(R03+z*(R04+z*R05))); |
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| 136 | s = one+z*(S01+z*(S02+z*(S03+z*S04))); |
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| 137 | if(ix < 0x3FF00000) { /* |x| < 1.00 */ |
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| 138 | return one + z*(-0.25+(r/s)); |
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| 139 | } else { |
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| 140 | u = 0.5*x; |
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| 141 | return((one+u)*(one-u)+z*(r/s)); |
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| 142 | } |
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| 143 | } |
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| 144 | |||
| 145 | |||
| 146 | static const double |
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| 147 | #else |
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| 148 | static double |
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| 149 | #endif |
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| 150 | u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ |
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| 151 | u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ |
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| 152 | u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ |
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| 153 | u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ |
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| 154 | u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ |
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| 155 | u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ |
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| 156 | u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ |
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| 157 | v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ |
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| 158 | v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ |
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| 159 | v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ |
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| 160 | v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ |
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| 161 | |||
| 162 | |||
| 163 | double __ieee754_y0(double x) |
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| 164 | #else |
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| 165 | double __ieee754_y0(x) |
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| 166 | double x; |
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| 167 | #endif |
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| 168 | { |
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| 169 | double z, s,c,ss,cc,u,v; |
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| 170 | __int32_t hx,ix,lx; |
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| 171 | |||
| 172 | |||
| 173 | ix = 0x7fffffff&hx; |
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| 174 | /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ |
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| 175 | if(ix>=0x7ff00000) return one/(x+x*x); |
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| 176 | if((ix|lx)==0) return -one/zero; |
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| 177 | if(hx<0) return zero/zero; |
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| 178 | if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
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| 179 | /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) |
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| 180 | * where x0 = x-pi/4 |
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| 181 | * Better formula: |
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| 182 | * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) |
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| 183 | * = 1/sqrt(2) * (sin(x) + cos(x)) |
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| 184 | * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) |
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| 185 | * = 1/sqrt(2) * (sin(x) - cos(x)) |
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| 186 | * To avoid cancellation, use |
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| 187 | * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
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| 188 | * to compute the worse one. |
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| 189 | */ |
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| 190 | s = sin(x); |
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| 191 | c = cos(x); |
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| 192 | ss = s-c; |
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| 193 | cc = s+c; |
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| 194 | /* |
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| 195 | * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) |
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| 196 | * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) |
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| 197 | */ |
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| 198 | if(ix<0x7fe00000) { /* make sure x+x not overflow */ |
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| 199 | z = -cos(x+x); |
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| 200 | if ((s*c) |
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| 201 | else ss = z/cc; |
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| 202 | } |
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| 203 | if(ix>0x48000000) z = (invsqrtpi*ss)/__ieee754_sqrt(x); |
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| 204 | else { |
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| 205 | u = pzero(x); v = qzero(x); |
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| 206 | z = invsqrtpi*(u*ss+v*cc)/__ieee754_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<=0x3e400000) { /* x < 2**-27 */ |
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| 211 | return(u00 + tpi*__ieee754_log(x)); |
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| 212 | } |
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| 213 | z = x*x; |
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| 214 | u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); |
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| 215 | v = one+z*(v01+z*(v02+z*(v03+z*v04))); |
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| 216 | return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); |
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| 217 | } |
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| 218 | |||
| 219 | |||
| 220 | * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. |
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| 221 | * For x >= 2, We approximate pzero by |
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| 222 | * pzero(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 | * | pzero(x)-1-R/S | <= 2 ** ( -60.26) |
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| 227 | */ |
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| 228 | #ifdef __STDC__ |
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| 229 | static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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| 230 | #else |
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| 231 | static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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| 232 | #endif |
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| 233 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
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| 234 | -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ |
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| 235 | -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ |
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| 236 | -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ |
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| 237 | -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ |
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| 238 | -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ |
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| 239 | }; |
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| 240 | #ifdef __STDC__ |
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| 241 | static const double pS8[5] = { |
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| 242 | #else |
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| 243 | static double pS8[5] = { |
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| 244 | #endif |
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| 245 | 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ |
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| 246 | 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ |
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| 247 | 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ |
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| 248 | 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ |
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| 249 | 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ |
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| 250 | }; |
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| 251 | |||
| 252 | |||
| 253 | static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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| 254 | #else |
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| 255 | static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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| 256 | #endif |
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| 257 | -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ |
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| 258 | -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ |
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| 259 | -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ |
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| 260 | -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ |
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| 261 | -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ |
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| 262 | -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ |
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| 263 | }; |
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| 264 | #ifdef __STDC__ |
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| 265 | static const double pS5[5] = { |
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| 266 | #else |
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| 267 | static double pS5[5] = { |
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| 268 | #endif |
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| 269 | 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ |
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| 270 | 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ |
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| 271 | 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ |
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| 272 | 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ |
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| 273 | 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ |
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| 274 | }; |
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| 275 | |||
| 276 | |||
| 277 | static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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| 278 | #else |
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| 279 | static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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| 280 | #endif |
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| 281 | -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ |
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| 282 | -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ |
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| 283 | -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ |
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| 284 | -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ |
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| 285 | -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ |
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| 286 | -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ |
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| 287 | }; |
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| 288 | #ifdef __STDC__ |
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| 289 | static const double pS3[5] = { |
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| 290 | #else |
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| 291 | static double pS3[5] = { |
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| 292 | #endif |
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| 293 | 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ |
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| 294 | 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ |
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| 295 | 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ |
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| 296 | 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ |
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| 297 | 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ |
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| 298 | }; |
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| 299 | |||
| 300 | |||
| 301 | static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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| 302 | #else |
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| 303 | static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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| 304 | #endif |
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| 305 | -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ |
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| 306 | -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ |
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| 307 | -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ |
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| 308 | -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ |
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| 309 | -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ |
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| 310 | -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ |
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| 311 | }; |
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| 312 | #ifdef __STDC__ |
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| 313 | static const double pS2[5] = { |
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| 314 | #else |
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| 315 | static double pS2[5] = { |
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| 316 | #endif |
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| 317 | 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ |
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| 318 | 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ |
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| 319 | 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ |
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| 320 | 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ |
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| 321 | 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ |
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| 322 | }; |
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| 323 | |||
| 324 | |||
| 325 | static double pzero(double x) |
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| 326 | #else |
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| 327 | static double pzero(x) |
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| 328 | double x; |
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| 329 | #endif |
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| 330 | { |
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| 331 | #ifdef __STDC__ |
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| 332 | const double *p,*q; |
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| 333 | #else |
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| 334 | double *p,*q; |
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| 335 | #endif |
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| 336 | double z,r,s; |
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| 337 | __int32_t ix; |
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| 338 | GET_HIGH_WORD(ix,x); |
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| 339 | ix &= 0x7fffffff; |
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| 340 | if(ix>=0x40200000) {p = pR8; q= pS8;} |
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| 341 | else if(ix>=0x40122E8B){p = pR5; q= pS5;} |
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| 342 | else if(ix>=0x4006DB6D){p = pR3; q= pS3;} |
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| 343 | else {p = pR2; q= pS2;} |
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| 344 | z = one/(x*x); |
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| 345 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
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| 346 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); |
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| 347 | return one+ r/s; |
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| 348 | } |
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| 349 | |||
| 350 | |||
| 351 | |||
| 352 | * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. |
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| 353 | * We approximate qzero by |
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| 354 | * qzero(x) = s*(-1.25 + (R/S)) |
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| 355 | * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 |
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| 356 | * S = 1 + qS0*s^2 + ... + qS5*s^12 |
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| 357 | * and |
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| 358 | * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) |
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| 359 | */ |
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| 360 | #ifdef __STDC__ |
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| 361 | static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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| 362 | #else |
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| 363 | static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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| 364 | #endif |
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| 365 | 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
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| 366 | 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ |
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| 367 | 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ |
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| 368 | 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ |
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| 369 | 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ |
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| 370 | 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ |
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| 371 | }; |
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| 372 | #ifdef __STDC__ |
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| 373 | static const double qS8[6] = { |
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| 374 | #else |
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| 375 | static double qS8[6] = { |
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| 376 | #endif |
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| 377 | 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ |
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| 378 | 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ |
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| 379 | 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ |
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| 380 | 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ |
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| 381 | 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ |
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| 382 | -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ |
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| 383 | }; |
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| 384 | |||
| 385 | |||
| 386 | static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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| 387 | #else |
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| 388 | static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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| 389 | #endif |
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| 390 | 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ |
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| 391 | 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ |
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| 392 | 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ |
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| 393 | 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ |
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| 394 | 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ |
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| 395 | 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ |
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| 396 | }; |
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| 397 | #ifdef __STDC__ |
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| 398 | static const double qS5[6] = { |
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| 399 | #else |
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| 400 | static double qS5[6] = { |
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| 401 | #endif |
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| 402 | 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ |
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| 403 | 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ |
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| 404 | 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ |
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| 405 | 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ |
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| 406 | 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ |
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| 407 | -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ |
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| 408 | }; |
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| 409 | |||
| 410 | |||
| 411 | static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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| 412 | #else |
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| 413 | static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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| 414 | #endif |
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| 415 | 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ |
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| 416 | 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ |
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| 417 | 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ |
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| 418 | 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ |
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| 419 | 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ |
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| 420 | 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ |
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| 421 | }; |
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| 422 | #ifdef __STDC__ |
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| 423 | static const double qS3[6] = { |
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| 424 | #else |
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| 425 | static double qS3[6] = { |
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| 426 | #endif |
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| 427 | 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ |
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| 428 | 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ |
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| 429 | 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ |
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| 430 | 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ |
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| 431 | 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ |
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| 432 | -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ |
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| 433 | }; |
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| 434 | |||
| 435 | |||
| 436 | static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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| 437 | #else |
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| 438 | static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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| 439 | #endif |
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| 440 | 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ |
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| 441 | 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ |
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| 442 | 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ |
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| 443 | 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ |
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| 444 | 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ |
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| 445 | 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ |
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| 446 | }; |
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| 447 | #ifdef __STDC__ |
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| 448 | static const double qS2[6] = { |
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| 449 | #else |
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| 450 | static double qS2[6] = { |
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| 451 | #endif |
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| 452 | 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ |
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| 453 | 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ |
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| 454 | 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ |
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| 455 | 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ |
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| 456 | 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ |
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| 457 | -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ |
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| 458 | }; |
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| 459 | |||
| 460 | |||
| 461 | static double qzero(double x) |
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| 462 | #else |
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| 463 | static double qzero(x) |
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| 464 | double x; |
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| 465 | #endif |
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| 466 | { |
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| 467 | #ifdef __STDC__ |
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| 468 | const double *p,*q; |
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| 469 | #else |
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| 470 | double *p,*q; |
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| 471 | #endif |
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| 472 | double s,r,z; |
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| 473 | __int32_t ix; |
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| 474 | GET_HIGH_WORD(ix,x); |
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| 475 | ix &= 0x7fffffff; |
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| 476 | if(ix>=0x40200000) {p = qR8; q= qS8;} |
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| 477 | else if(ix>=0x40122E8B){p = qR5; q= qS5;} |
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| 478 | else if(ix>=0x4006DB6D){p = qR3; q= qS3;} |
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| 479 | else {p = qR2; q= qS2;} |
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| 480 | z = one/(x*x); |
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| 481 | r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
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| 482 | s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); |
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| 483 | return (-.125 + r/s)/x; |
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| 484 | } |
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| 485 | |||
| 486 | |||
| 487 | > |