author | William Roberts <williamr@symbian.org> |
Thu, 22 Jul 2010 16:48:56 +0100 | |
branch | GCC_SURGE |
changeset 45 | 4b03adbd26ca |
parent 0 | e4d67989cc36 |
permissions | -rw-r--r-- |
0
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/*-------------------------------------------------------------------- |
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*© Portions copyright (c) 2006 Nokia Corporation. All rights reserved. |
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*-------------------------------------------------------------------- |
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*/ |
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/* e_jnf.c -- float version of e_jn.c. |
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
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*/ |
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|
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunPro, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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*/ |
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#ifndef __SYMBIAN32__ |
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#ifndef lint |
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static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_jnf.c,v 1.8 2002/05/28 18:15:04 alfred Exp $"; |
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#endif |
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#endif //__SYMBIAN32__ |
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|
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#include <math.h> |
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#include "math_private.h" |
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|
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|
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static const float |
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#ifndef __SYMBIAN32__ |
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invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ |
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#endif //__SYMBIAN32__ |
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two = 2.0000000000e+00, /* 0x40000000 */ |
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one = 1.0000000000e+00; /* 0x3F800000 */ |
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|
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static const float zero = 0.0000000000e+00; |
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|
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EXPORT_C |
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float |
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__ieee754_jnf(int n, float x) |
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{ |
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int32_t i,hx,ix, sgn; |
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float a, b, temp, di; |
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float z, w; |
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|
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/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) |
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* Thus, J(-n,x) = J(n,-x) |
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*/ |
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GET_FLOAT_WORD(hx,x); |
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ix = 0x7fffffff&hx; |
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/* if J(n,NaN) is NaN */ |
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if(ix>0x7f800000) return x+x; |
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if(n<0){ |
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n = -n; |
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x = -x; |
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hx ^= 0x80000000; |
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} |
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if(n==0) return(__ieee754_j0f(x)); |
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if(n==1) return(__ieee754_j1f(x)); |
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sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ |
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x = fabsf(x); |
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if(ix==0||ix>=0x7f800000) /* if x is 0 or inf */ |
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b = zero; |
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else if((float)n<=x) { |
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/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ |
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a = __ieee754_j0f(x); |
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b = __ieee754_j1f(x); |
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for(i=1;i<n;i++){ |
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temp = b; |
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b = b*((float)(i+i)/x) - a; /* avoid underflow */ |
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a = temp; |
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} |
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} else { |
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if(ix<0x30800000) { /* x < 2**-29 */ |
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/* x is tiny, return the first Taylor expansion of J(n,x) |
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* J(n,x) = 1/n!*(x/2)^n - ... |
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*/ |
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if(n>33) /* underflow */ |
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b = zero; |
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else { |
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temp = x*(float)0.5; b = temp; |
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for (a=one,i=2;i<=n;i++) { |
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a *= (float)i; /* a = n! */ |
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b *= temp; /* b = (x/2)^n */ |
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} |
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b = b/a; |
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} |
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} else { |
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/* use backward recurrence */ |
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/* x x^2 x^2 |
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* J(n,x)/J(n-1,x) = ---- ------ ------ ..... |
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* 2n - 2(n+1) - 2(n+2) |
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* |
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* 1 1 1 |
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* (for large x) = ---- ------ ------ ..... |
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* 2n 2(n+1) 2(n+2) |
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* -- - ------ - ------ - |
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* x x x |
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* |
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* Let w = 2n/x and h=2/x, then the above quotient |
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* is equal to the continued fraction: |
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102 |
* 1 |
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103 |
* = ----------------------- |
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104 |
* 1 |
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105 |
* w - ----------------- |
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106 |
* 1 |
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107 |
* w+h - --------- |
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108 |
* w+2h - ... |
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109 |
* |
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110 |
* To determine how many terms needed, let |
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111 |
* Q(0) = w, Q(1) = w(w+h) - 1, |
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* Q(k) = (w+k*h)*Q(k-1) - Q(k-2), |
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113 |
* When Q(k) > 1e4 good for single |
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114 |
* When Q(k) > 1e9 good for double |
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115 |
* When Q(k) > 1e17 good for quadruple |
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116 |
*/ |
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117 |
/* determine k */ |
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118 |
float t,v; |
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119 |
float q0,q1,h,tmp; int32_t k,m; |
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120 |
w = (n+n)/(float)x; h = (float)2.0/(float)x; |
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121 |
q0 = w; z = w+h; q1 = w*z - (float)1.0; k=1; |
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122 |
while(q1<(float)1.0e9) { |
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123 |
k += 1; z += h; |
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tmp = z*q1 - q0; |
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q0 = q1; |
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q1 = tmp; |
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127 |
} |
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128 |
m = n+n; |
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129 |
for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); |
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130 |
a = t; |
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131 |
b = one; |
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132 |
/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) |
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133 |
* Hence, if n*(log(2n/x)) > ... |
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134 |
* single 8.8722839355e+01 |
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* double 7.09782712893383973096e+02 |
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136 |
* long double 1.1356523406294143949491931077970765006170e+04 |
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137 |
* then recurrent value may overflow and the result is |
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138 |
* likely underflow to zero |
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139 |
*/ |
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140 |
tmp = n; |
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141 |
v = two/x; |
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142 |
tmp = tmp*__ieee754_logf(fabsf(v*tmp)); |
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143 |
if(tmp<(float)8.8721679688e+01) { |
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144 |
for(i=n-1,di=(float)(i+i);i>0;i--){ |
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145 |
temp = b; |
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146 |
b *= di; |
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147 |
b = b/x - a; |
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148 |
a = temp; |
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149 |
di -= two; |
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150 |
} |
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151 |
} else { |
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152 |
for(i=n-1,di=(float)(i+i);i>0;i--){ |
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153 |
temp = b; |
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154 |
b *= di; |
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155 |
b = b/x - a; |
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156 |
a = temp; |
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157 |
di -= two; |
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158 |
/* scale b to avoid spurious overflow */ |
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159 |
if(b>(float)1e10) { |
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160 |
a /= b; |
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161 |
t /= b; |
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162 |
b = one; |
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163 |
} |
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164 |
} |
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165 |
} |
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166 |
b = (t*__ieee754_j0f(x)/b); |
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167 |
} |
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168 |
} |
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169 |
if(sgn==1) return -b; else return b; |
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170 |
} |
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171 |
|
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172 |
EXPORT_C float |
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173 |
__ieee754_ynf(int n, float x) |
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174 |
{ |
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175 |
int32_t i,hx,ix,ib; |
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176 |
int32_t sign; |
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177 |
float a, b, temp; |
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178 |
|
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179 |
GET_FLOAT_WORD(hx,x); |
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180 |
ix = 0x7fffffff&hx; |
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181 |
/* if Y(n,NaN) is NaN */ |
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182 |
if(ix>0x7f800000) return x+x; |
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183 |
#ifdef __SYMBIAN32__ |
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184 |
if(hx<0) return -one/zero; |
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185 |
#else |
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186 |
if(hx<0) return zero/zero; |
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187 |
#endif //__SYMBIAN32__ |
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188 |
|
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189 |
sign = 1; |
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190 |
if(n<0){ |
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191 |
n = -n; |
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192 |
sign = 1 - ((n&1)<<1); |
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193 |
} |
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194 |
if(n==0) return(__ieee754_y0f(x)); |
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195 |
if(n==1) return(sign*__ieee754_y1f(x)); |
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196 |
if(ix==0x7f800000) return zero; |
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197 |
|
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198 |
a = __ieee754_y0f(x); |
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199 |
b = __ieee754_y1f(x); |
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200 |
/* quit if b is -inf */ |
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201 |
GET_FLOAT_WORD(ib,b); |
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202 |
for(i=1;i<n&&ib!=0xff800000;i++){ |
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203 |
temp = b; |
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204 |
b = ((float)(i+i)/x)*b - a; |
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205 |
GET_FLOAT_WORD(ib,b); |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
206 |
a = temp; |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
207 |
} |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
208 |
if(sign>0) return b; else return -b; |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
209 |
} |