1 |
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2 /* |
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3 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. |
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4 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
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5 * |
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6 * This code is free software; you can redistribute it and/or modify it |
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7 * under the terms of the GNU General Public License version 2 only, as |
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8 * published by the Free Software Foundation. Oracle designates this |
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9 * particular file as subject to the "Classpath" exception as provided |
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10 * by Oracle in the LICENSE file that accompanied this code. |
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11 * |
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12 * This code is distributed in the hope that it will be useful, but WITHOUT |
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13 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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14 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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15 * version 2 for more details (a copy is included in the LICENSE file that |
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16 * accompanied this code). |
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17 * |
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18 * You should have received a copy of the GNU General Public License version |
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19 * 2 along with this work; if not, write to the Free Software Foundation, |
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20 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
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21 * |
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22 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
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23 * or visit www.oracle.com if you need additional information or have any |
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24 * questions. |
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25 */ |
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26 |
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27 /* __ieee754_j0(x), __ieee754_y0(x) |
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28 * Bessel function of the first and second kinds of order zero. |
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29 * Method -- j0(x): |
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30 * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... |
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31 * 2. Reduce x to |x| since j0(x)=j0(-x), and |
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32 * for x in (0,2) |
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33 * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; |
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34 * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) |
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35 * for x in (2,inf) |
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36 * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) |
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37 * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) |
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38 * as follow: |
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39 * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) |
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40 * = 1/sqrt(2) * (cos(x) + sin(x)) |
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41 * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) |
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42 * = 1/sqrt(2) * (sin(x) - cos(x)) |
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43 * (To avoid cancellation, use |
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44 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
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45 * to compute the worse one.) |
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46 * |
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47 * 3 Special cases |
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48 * j0(nan)= nan |
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49 * j0(0) = 1 |
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50 * j0(inf) = 0 |
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51 * |
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52 * Method -- y0(x): |
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53 * 1. For x<2. |
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54 * Since |
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55 * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) |
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56 * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. |
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57 * We use the following function to approximate y0, |
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58 * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 |
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59 * where |
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60 * U(z) = u00 + u01*z + ... + u06*z^6 |
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61 * V(z) = 1 + v01*z + ... + v04*z^4 |
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62 * with absolute approximation error bounded by 2**-72. |
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63 * Note: For tiny x, U/V = u0 and j0(x)~1, hence |
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64 * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) |
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65 * 2. For x>=2. |
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66 * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) |
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67 * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) |
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68 * by the method mentioned above. |
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69 * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. |
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70 */ |
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71 |
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72 #include "fdlibm.h" |
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73 |
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74 #ifdef __STDC__ |
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75 static double pzero(double), qzero(double); |
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76 #else |
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77 static double pzero(), qzero(); |
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78 #endif |
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79 |
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80 #ifdef __STDC__ |
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81 static const double |
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82 #else |
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83 static double |
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84 #endif |
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85 huge = 1e300, |
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86 one = 1.0, |
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87 invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ |
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88 tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
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89 /* R0/S0 on [0, 2.00] */ |
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90 R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ |
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91 R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ |
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92 R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ |
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93 R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ |
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94 S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ |
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95 S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ |
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96 S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ |
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97 S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ |
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98 |
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99 static double zero = 0.0; |
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100 |
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101 #ifdef __STDC__ |
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102 double __ieee754_j0(double x) |
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103 #else |
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104 double __ieee754_j0(x) |
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105 double x; |
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106 #endif |
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107 { |
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108 double z, s,c,ss,cc,r,u,v; |
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109 int hx,ix; |
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110 |
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111 hx = __HI(x); |
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112 ix = hx&0x7fffffff; |
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113 if(ix>=0x7ff00000) return one/(x*x); |
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114 x = fabs(x); |
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115 if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
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116 s = sin(x); |
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117 c = cos(x); |
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118 ss = s-c; |
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119 cc = s+c; |
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120 if(ix<0x7fe00000) { /* make sure x+x not overflow */ |
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121 z = -cos(x+x); |
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122 if ((s*c)<zero) cc = z/ss; |
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123 else ss = z/cc; |
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124 } |
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125 /* |
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126 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) |
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127 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) |
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128 */ |
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129 if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(x); |
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130 else { |
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131 u = pzero(x); v = qzero(x); |
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132 z = invsqrtpi*(u*cc-v*ss)/sqrt(x); |
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133 } |
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134 return z; |
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135 } |
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136 if(ix<0x3f200000) { /* |x| < 2**-13 */ |
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137 if(huge+x>one) { /* raise inexact if x != 0 */ |
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138 if(ix<0x3e400000) return one; /* |x|<2**-27 */ |
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139 else return one - 0.25*x*x; |
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140 } |
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141 } |
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142 z = x*x; |
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143 r = z*(R02+z*(R03+z*(R04+z*R05))); |
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144 s = one+z*(S01+z*(S02+z*(S03+z*S04))); |
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145 if(ix < 0x3FF00000) { /* |x| < 1.00 */ |
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146 return one + z*(-0.25+(r/s)); |
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147 } else { |
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148 u = 0.5*x; |
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149 return((one+u)*(one-u)+z*(r/s)); |
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150 } |
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151 } |
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152 |
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153 #ifdef __STDC__ |
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154 static const double |
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155 #else |
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156 static double |
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157 #endif |
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158 u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ |
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159 u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ |
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160 u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ |
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161 u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ |
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162 u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ |
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163 u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ |
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164 u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ |
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165 v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ |
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166 v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ |
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167 v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ |
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168 v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ |
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169 |
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170 #ifdef __STDC__ |
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171 double __ieee754_y0(double x) |
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172 #else |
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173 double __ieee754_y0(x) |
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174 double x; |
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175 #endif |
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176 { |
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177 double z, s,c,ss,cc,u,v; |
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178 int hx,ix,lx; |
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179 |
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180 hx = __HI(x); |
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181 ix = 0x7fffffff&hx; |
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182 lx = __LO(x); |
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183 /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ |
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184 if(ix>=0x7ff00000) return one/(x+x*x); |
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185 if((ix|lx)==0) return -one/zero; |
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186 if(hx<0) return zero/zero; |
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187 if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
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188 /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) |
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189 * where x0 = x-pi/4 |
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190 * Better formula: |
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191 * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) |
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192 * = 1/sqrt(2) * (sin(x) + cos(x)) |
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193 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) |
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194 * = 1/sqrt(2) * (sin(x) - cos(x)) |
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195 * To avoid cancellation, use |
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196 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
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197 * to compute the worse one. |
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198 */ |
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199 s = sin(x); |
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200 c = cos(x); |
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201 ss = s-c; |
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202 cc = s+c; |
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203 /* |
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204 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) |
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205 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) |
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206 */ |
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207 if(ix<0x7fe00000) { /* make sure x+x not overflow */ |
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208 z = -cos(x+x); |
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209 if ((s*c)<zero) cc = z/ss; |
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210 else ss = z/cc; |
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211 } |
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212 if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); |
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213 else { |
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214 u = pzero(x); v = qzero(x); |
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215 z = invsqrtpi*(u*ss+v*cc)/sqrt(x); |
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216 } |
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217 return z; |
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218 } |
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219 if(ix<=0x3e400000) { /* x < 2**-27 */ |
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220 return(u00 + tpi*__ieee754_log(x)); |
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221 } |
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222 z = x*x; |
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223 u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); |
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224 v = one+z*(v01+z*(v02+z*(v03+z*v04))); |
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225 return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); |
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226 } |
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227 |
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228 /* The asymptotic expansions of pzero is |
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229 * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. |
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230 * For x >= 2, We approximate pzero by |
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231 * pzero(x) = 1 + (R/S) |
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232 * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 |
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233 * S = 1 + pS0*s^2 + ... + pS4*s^10 |
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234 * and |
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235 * | pzero(x)-1-R/S | <= 2 ** ( -60.26) |
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236 */ |
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237 #ifdef __STDC__ |
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238 static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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239 #else |
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240 static double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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241 #endif |
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242 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
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243 -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ |
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244 -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ |
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245 -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ |
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246 -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ |
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247 -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ |
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248 }; |
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249 #ifdef __STDC__ |
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250 static const double pS8[5] = { |
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251 #else |
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252 static double pS8[5] = { |
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253 #endif |
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254 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ |
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255 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ |
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256 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ |
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257 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ |
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258 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ |
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259 }; |
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260 |
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261 #ifdef __STDC__ |
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262 static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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263 #else |
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264 static double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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265 #endif |
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266 -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ |
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267 -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ |
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268 -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ |
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269 -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ |
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270 -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ |
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271 -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ |
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272 }; |
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273 #ifdef __STDC__ |
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274 static const double pS5[5] = { |
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275 #else |
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276 static double pS5[5] = { |
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277 #endif |
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278 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ |
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279 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ |
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280 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ |
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281 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ |
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282 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ |
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283 }; |
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284 |
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285 #ifdef __STDC__ |
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286 static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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287 #else |
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288 static double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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289 #endif |
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290 -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ |
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291 -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ |
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292 -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ |
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293 -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ |
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294 -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ |
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295 -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ |
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296 }; |
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297 #ifdef __STDC__ |
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298 static const double pS3[5] = { |
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299 #else |
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300 static double pS3[5] = { |
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301 #endif |
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302 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ |
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303 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ |
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304 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ |
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305 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ |
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306 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ |
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307 }; |
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308 |
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309 #ifdef __STDC__ |
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310 static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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311 #else |
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312 static double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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313 #endif |
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314 -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ |
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315 -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ |
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316 -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ |
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317 -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ |
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318 -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ |
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319 -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ |
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320 }; |
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321 #ifdef __STDC__ |
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322 static const double pS2[5] = { |
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323 #else |
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324 static double pS2[5] = { |
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325 #endif |
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326 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ |
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327 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ |
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328 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ |
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329 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ |
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330 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ |
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331 }; |
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332 |
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333 #ifdef __STDC__ |
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334 static double pzero(double x) |
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335 #else |
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336 static double pzero(x) |
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337 double x; |
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338 #endif |
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339 { |
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340 #ifdef __STDC__ |
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341 const double *p=(void*)0,*q=(void*)0; |
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342 #else |
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343 double *p,*q; |
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344 #endif |
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345 double z,r,s; |
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346 int ix; |
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347 ix = 0x7fffffff&__HI(x); |
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348 if(ix>=0x40200000) {p = pR8; q= pS8;} |
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349 else if(ix>=0x40122E8B){p = pR5; q= pS5;} |
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350 else if(ix>=0x4006DB6D){p = pR3; q= pS3;} |
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351 else if(ix>=0x40000000){p = pR2; q= pS2;} |
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352 z = one/(x*x); |
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353 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
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354 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); |
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355 return one+ r/s; |
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356 } |
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357 |
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358 |
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359 /* For x >= 8, the asymptotic expansions of qzero is |
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360 * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. |
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361 * We approximate pzero by |
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362 * qzero(x) = s*(-1.25 + (R/S)) |
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363 * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 |
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364 * S = 1 + qS0*s^2 + ... + qS5*s^12 |
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365 * and |
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366 * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) |
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367 */ |
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368 #ifdef __STDC__ |
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369 static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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370 #else |
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371 static double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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372 #endif |
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373 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
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374 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ |
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375 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ |
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376 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ |
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377 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ |
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378 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ |
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379 }; |
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380 #ifdef __STDC__ |
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381 static const double qS8[6] = { |
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382 #else |
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383 static double qS8[6] = { |
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384 #endif |
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385 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ |
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386 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ |
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387 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ |
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388 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ |
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389 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ |
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390 -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ |
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391 }; |
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392 |
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393 #ifdef __STDC__ |
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394 static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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395 #else |
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396 static double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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397 #endif |
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398 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ |
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399 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ |
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400 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ |
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401 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ |
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402 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ |
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403 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ |
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404 }; |
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405 #ifdef __STDC__ |
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406 static const double qS5[6] = { |
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407 #else |
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408 static double qS5[6] = { |
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409 #endif |
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410 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ |
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411 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ |
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412 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ |
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413 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ |
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414 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ |
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415 -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ |
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416 }; |
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417 |
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418 #ifdef __STDC__ |
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419 static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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420 #else |
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421 static double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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422 #endif |
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423 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ |
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424 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ |
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425 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ |
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426 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ |
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427 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ |
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428 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ |
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429 }; |
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430 #ifdef __STDC__ |
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431 static const double qS3[6] = { |
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432 #else |
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433 static double qS3[6] = { |
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434 #endif |
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435 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ |
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436 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ |
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437 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ |
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438 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ |
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439 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ |
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440 -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ |
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441 }; |
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442 |
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443 #ifdef __STDC__ |
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444 static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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445 #else |
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446 static double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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447 #endif |
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448 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ |
|
449 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ |
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450 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ |
|
451 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ |
|
452 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ |
|
453 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ |
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454 }; |
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455 #ifdef __STDC__ |
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456 static const double qS2[6] = { |
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457 #else |
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458 static double qS2[6] = { |
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459 #endif |
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460 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ |
|
461 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ |
|
462 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ |
|
463 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ |
|
464 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ |
|
465 -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ |
|
466 }; |
|
467 |
|
468 #ifdef __STDC__ |
|
469 static double qzero(double x) |
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470 #else |
|
471 static double qzero(x) |
|
472 double x; |
|
473 #endif |
|
474 { |
|
475 #ifdef __STDC__ |
|
476 const double *p=(void*)0,*q=(void*)0; |
|
477 #else |
|
478 double *p,*q; |
|
479 #endif |
|
480 double s,r,z; |
|
481 int ix; |
|
482 ix = 0x7fffffff&__HI(x); |
|
483 if(ix>=0x40200000) {p = qR8; q= qS8;} |
|
484 else if(ix>=0x40122E8B){p = qR5; q= qS5;} |
|
485 else if(ix>=0x4006DB6D){p = qR3; q= qS3;} |
|
486 else if(ix>=0x40000000){p = qR2; q= qS2;} |
|
487 z = one/(x*x); |
|
488 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
|
489 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); |
|
490 return (-.125 + r/s)/x; |
|
491 } |
|