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_j1(x), __ieee754_y1(x) |
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28 * Bessel function of the first and second kinds of order zero. |
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29 * Method -- j1(x): |
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30 * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... |
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31 * 2. Reduce x to |x| since j1(x)=-j1(-x), and |
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32 * for x in (0,2) |
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33 * j1(x) = x/2 + x*z*R0/S0, where z = x*x; |
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34 * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) |
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35 * for x in (2,inf) |
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36 * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) |
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37 * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) |
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38 * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) |
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39 * as follow: |
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40 * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) |
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41 * = 1/sqrt(2) * (sin(x) - cos(x)) |
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42 * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) |
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43 * = -1/sqrt(2) * (sin(x) + cos(x)) |
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44 * (To avoid cancellation, use |
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45 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
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46 * to compute the worse one.) |
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47 * |
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48 * 3 Special cases |
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49 * j1(nan)= nan |
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50 * j1(0) = 0 |
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51 * j1(inf) = 0 |
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52 * |
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53 * Method -- y1(x): |
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54 * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN |
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55 * 2. For x<2. |
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56 * Since |
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57 * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) |
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58 * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. |
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59 * We use the following function to approximate y1, |
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60 * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 |
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61 * where for x in [0,2] (abs err less than 2**-65.89) |
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62 * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 |
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63 * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 |
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64 * Note: For tiny x, 1/x dominate y1 and hence |
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65 * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) |
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66 * 3. For x>=2. |
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67 * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) |
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68 * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) |
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69 * by method mentioned above. |
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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 pone(double), qone(double); |
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76 #else |
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77 static double pone(), qone(); |
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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] */ |
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90 r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ |
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91 r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ |
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92 r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ |
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93 r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ |
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94 s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ |
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95 s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ |
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96 s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ |
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97 s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ |
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98 s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ |
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99 |
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100 static double zero = 0.0; |
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101 |
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102 #ifdef __STDC__ |
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103 double __ieee754_j1(double x) |
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104 #else |
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105 double __ieee754_j1(x) |
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106 double x; |
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107 #endif |
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108 { |
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109 double z, s,c,ss,cc,r,u,v,y; |
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110 int hx,ix; |
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111 |
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112 hx = __HI(x); |
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113 ix = hx&0x7fffffff; |
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114 if(ix>=0x7ff00000) return one/x; |
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115 y = fabs(x); |
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116 if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
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117 s = sin(y); |
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118 c = cos(y); |
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119 ss = -s-c; |
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120 cc = s-c; |
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121 if(ix<0x7fe00000) { /* make sure y+y not overflow */ |
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122 z = cos(y+y); |
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123 if ((s*c)>zero) cc = z/ss; |
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124 else ss = z/cc; |
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125 } |
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126 /* |
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127 * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) |
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128 * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) |
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129 */ |
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130 if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y); |
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131 else { |
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132 u = pone(y); v = qone(y); |
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133 z = invsqrtpi*(u*cc-v*ss)/sqrt(y); |
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134 } |
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135 if(hx<0) return -z; |
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136 else return z; |
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137 } |
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138 if(ix<0x3e400000) { /* |x|<2**-27 */ |
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139 if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ |
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140 } |
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141 z = x*x; |
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142 r = z*(r00+z*(r01+z*(r02+z*r03))); |
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143 s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); |
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144 r *= x; |
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145 return(x*0.5+r/s); |
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146 } |
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147 |
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148 #ifdef __STDC__ |
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149 static const double U0[5] = { |
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150 #else |
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151 static double U0[5] = { |
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152 #endif |
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153 -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ |
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154 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ |
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155 -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ |
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156 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ |
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157 -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ |
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158 }; |
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159 #ifdef __STDC__ |
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160 static const double V0[5] = { |
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161 #else |
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162 static double V0[5] = { |
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163 #endif |
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164 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ |
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165 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ |
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166 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ |
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167 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ |
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168 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ |
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169 }; |
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170 |
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171 #ifdef __STDC__ |
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172 double __ieee754_y1(double x) |
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173 #else |
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174 double __ieee754_y1(x) |
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175 double x; |
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176 #endif |
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177 { |
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178 double z, s,c,ss,cc,u,v; |
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179 int hx,ix,lx; |
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180 |
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181 hx = __HI(x); |
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182 ix = 0x7fffffff&hx; |
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183 lx = __LO(x); |
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184 /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ |
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185 if(ix>=0x7ff00000) return one/(x+x*x); |
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186 if((ix|lx)==0) return -one/zero; |
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187 if(hx<0) return zero/zero; |
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188 if(ix >= 0x40000000) { /* |x| >= 2.0 */ |
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189 s = sin(x); |
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190 c = cos(x); |
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191 ss = -s-c; |
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192 cc = s-c; |
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193 if(ix<0x7fe00000) { /* make sure x+x not overflow */ |
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194 z = cos(x+x); |
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195 if ((s*c)>zero) cc = z/ss; |
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196 else ss = z/cc; |
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197 } |
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198 /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) |
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199 * where x0 = x-3pi/4 |
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200 * Better formula: |
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201 * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) |
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202 * = 1/sqrt(2) * (sin(x) - cos(x)) |
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203 * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) |
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204 * = -1/sqrt(2) * (cos(x) + sin(x)) |
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205 * To avoid cancellation, use |
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206 * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) |
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207 * to compute the worse one. |
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208 */ |
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209 if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); |
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210 else { |
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211 u = pone(x); v = qone(x); |
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212 z = invsqrtpi*(u*ss+v*cc)/sqrt(x); |
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213 } |
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214 return z; |
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215 } |
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216 if(ix<=0x3c900000) { /* x < 2**-54 */ |
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217 return(-tpi/x); |
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218 } |
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219 z = x*x; |
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220 u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); |
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221 v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); |
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222 return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); |
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223 } |
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224 |
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225 /* For x >= 8, the asymptotic expansions of pone is |
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226 * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. |
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227 * We approximate pone by |
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228 * pone(x) = 1 + (R/S) |
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229 * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 |
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230 * S = 1 + ps0*s^2 + ... + ps4*s^10 |
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231 * and |
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232 * | pone(x)-1-R/S | <= 2 ** ( -60.06) |
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233 */ |
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234 |
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235 #ifdef __STDC__ |
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236 static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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237 #else |
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238 static double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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239 #endif |
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240 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
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241 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ |
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242 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ |
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243 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ |
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244 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ |
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245 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ |
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246 }; |
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247 #ifdef __STDC__ |
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248 static const double ps8[5] = { |
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249 #else |
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250 static double ps8[5] = { |
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251 #endif |
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252 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ |
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253 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ |
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254 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ |
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255 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ |
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256 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ |
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257 }; |
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258 |
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259 #ifdef __STDC__ |
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260 static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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261 #else |
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262 static double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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263 #endif |
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264 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ |
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265 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ |
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266 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ |
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267 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ |
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268 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ |
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269 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ |
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270 }; |
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271 #ifdef __STDC__ |
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272 static const double ps5[5] = { |
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273 #else |
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274 static double ps5[5] = { |
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275 #endif |
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276 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ |
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277 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ |
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278 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ |
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279 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ |
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280 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ |
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281 }; |
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282 |
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283 #ifdef __STDC__ |
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284 static const double pr3[6] = { |
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285 #else |
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286 static double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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287 #endif |
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288 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ |
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289 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ |
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290 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ |
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291 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ |
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292 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ |
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293 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ |
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294 }; |
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295 #ifdef __STDC__ |
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296 static const double ps3[5] = { |
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297 #else |
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298 static double ps3[5] = { |
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299 #endif |
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300 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ |
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301 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ |
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302 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ |
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303 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ |
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304 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ |
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305 }; |
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306 |
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307 #ifdef __STDC__ |
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308 static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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309 #else |
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310 static double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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311 #endif |
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312 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ |
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313 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ |
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314 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ |
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315 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ |
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316 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ |
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317 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ |
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318 }; |
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319 #ifdef __STDC__ |
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320 static const double ps2[5] = { |
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321 #else |
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322 static double ps2[5] = { |
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323 #endif |
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324 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ |
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325 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ |
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326 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ |
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327 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ |
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328 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ |
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329 }; |
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330 |
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331 #ifdef __STDC__ |
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332 static double pone(double x) |
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333 #else |
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334 static double pone(x) |
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335 double x; |
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336 #endif |
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337 { |
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338 #ifdef __STDC__ |
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339 const double *p=(void*)0,*q=(void*)0; |
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340 #else |
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341 double *p,*q; |
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342 #endif |
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343 double z,r,s; |
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344 int ix; |
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345 ix = 0x7fffffff&__HI(x); |
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346 if(ix>=0x40200000) {p = pr8; q= ps8;} |
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347 else if(ix>=0x40122E8B){p = pr5; q= ps5;} |
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348 else if(ix>=0x4006DB6D){p = pr3; q= ps3;} |
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349 else if(ix>=0x40000000){p = pr2; q= ps2;} |
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350 z = one/(x*x); |
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351 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
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352 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); |
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353 return one+ r/s; |
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354 } |
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355 |
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356 |
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357 /* For x >= 8, the asymptotic expansions of qone is |
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358 * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. |
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359 * We approximate pone by |
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360 * qone(x) = s*(0.375 + (R/S)) |
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361 * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 |
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362 * S = 1 + qs1*s^2 + ... + qs6*s^12 |
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363 * and |
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364 * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) |
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365 */ |
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366 |
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367 #ifdef __STDC__ |
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368 static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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369 #else |
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370 static double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ |
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371 #endif |
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372 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
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373 -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ |
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374 -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ |
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375 -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ |
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376 -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ |
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377 -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ |
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378 }; |
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379 #ifdef __STDC__ |
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380 static const double qs8[6] = { |
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381 #else |
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382 static double qs8[6] = { |
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383 #endif |
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384 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ |
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385 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ |
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386 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ |
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387 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ |
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388 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ |
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389 -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ |
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390 }; |
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391 |
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392 #ifdef __STDC__ |
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393 static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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394 #else |
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395 static double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ |
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396 #endif |
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397 -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ |
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398 -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ |
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399 -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ |
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400 -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ |
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401 -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ |
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402 -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ |
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403 }; |
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404 #ifdef __STDC__ |
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405 static const double qs5[6] = { |
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406 #else |
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407 static double qs5[6] = { |
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408 #endif |
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409 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ |
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410 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ |
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411 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ |
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412 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ |
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413 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ |
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414 -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ |
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415 }; |
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416 |
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417 #ifdef __STDC__ |
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418 static const double qr3[6] = { |
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419 #else |
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420 static double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ |
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421 #endif |
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422 -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ |
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423 -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ |
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424 -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ |
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425 -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ |
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426 -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ |
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427 -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ |
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428 }; |
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429 #ifdef __STDC__ |
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430 static const double qs3[6] = { |
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431 #else |
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432 static double qs3[6] = { |
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433 #endif |
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434 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ |
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435 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ |
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436 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ |
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437 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ |
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438 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ |
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439 -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ |
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440 }; |
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441 |
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442 #ifdef __STDC__ |
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443 static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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444 #else |
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445 static double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ |
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446 #endif |
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447 -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ |
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448 -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ |
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449 -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ |
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450 -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ |
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451 -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ |
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452 -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ |
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453 }; |
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454 #ifdef __STDC__ |
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455 static const double qs2[6] = { |
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456 #else |
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457 static double qs2[6] = { |
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458 #endif |
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459 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ |
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460 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ |
|
461 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ |
|
462 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ |
|
463 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ |
|
464 -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ |
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465 }; |
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466 |
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467 #ifdef __STDC__ |
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468 static double qone(double x) |
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469 #else |
|
470 static double qone(x) |
|
471 double x; |
|
472 #endif |
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473 { |
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474 #ifdef __STDC__ |
|
475 const double *p=(void*)0,*q=(void*)0; |
|
476 #else |
|
477 double *p,*q; |
|
478 #endif |
|
479 double s,r,z; |
|
480 int ix; |
|
481 ix = 0x7fffffff&__HI(x); |
|
482 if(ix>=0x40200000) {p = qr8; q= qs8;} |
|
483 else if(ix>=0x40122E8B){p = qr5; q= qs5;} |
|
484 else if(ix>=0x4006DB6D){p = qr3; q= qs3;} |
|
485 else if(ix>=0x40000000){p = qr2; q= qs2;} |
|
486 z = one/(x*x); |
|
487 r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); |
|
488 s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); |
|
489 return (.375 + r/s)/x; |
|
490 } |
|