1 | /* sf_expm1.c -- float version of s_expm1.c. |
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2 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
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3 | */ |
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4 | |
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5 | /* |
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6 | * ==================================================== |
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7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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8 | * |
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9 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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10 | * Permission to use, copy, modify, and distribute this |
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11 | * software is freely granted, provided that this notice |
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12 | * is preserved. |
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13 | * ==================================================== |
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14 | */ |
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15 | |
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16 | #include "fdlibm.h" |
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17 | |
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18 | #ifdef __v810__ |
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19 | #define const |
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20 | #endif |
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21 | |
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22 | #ifdef __STDC__ |
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23 | static const float |
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24 | #else |
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25 | static float |
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26 | #endif |
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27 | one = 1.0, |
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28 | huge = 1.0e+30, |
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29 | tiny = 1.0e-30, |
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30 | ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ |
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31 | ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ |
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32 | invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ |
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33 | /* scaled coefficients related to expm1 */ |
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34 | Q1 = -3.3333335072e-02, /* 0xbd088889 */ |
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35 | Q2 = 1.5873016091e-03, /* 0x3ad00d01 */ |
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36 | Q3 = -7.9365076090e-05, /* 0xb8a670cd */ |
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37 | Q4 = 4.0082177293e-06, /* 0x36867e54 */ |
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38 | Q5 = -2.0109921195e-07; /* 0xb457edbb */ |
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39 | |
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40 | #ifdef __STDC__ |
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41 | float expm1f(float x) |
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42 | #else |
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43 | float expm1f(x) |
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44 | float x; |
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45 | #endif |
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46 | { |
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47 | float y,hi,lo,c,t,e,hxs,hfx,r1; |
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48 | __int32_t k,xsb; |
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49 | __uint32_t hx; |
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50 | |
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51 | GET_FLOAT_WORD(hx,x); |
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52 | xsb = hx&0x80000000; /* sign bit of x */ |
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53 | if(xsb==0) y=x; else y= -x; /* y = |x| */ |
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54 | hx &= 0x7fffffff; /* high word of |x| */ |
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55 | |
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56 | /* filter out huge and non-finite argument */ |
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57 | if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ |
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58 | if(FLT_UWORD_IS_NAN(hx)) |
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59 | return x+x; |
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60 | if(FLT_UWORD_IS_INFINITE(hx)) |
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61 | return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ |
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62 | if(xsb == 0 && hx > FLT_UWORD_LOG_MAX) /* if x>=o_threshold */ |
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63 | return huge*huge; /* overflow */ |
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64 | if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ |
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65 | if(x+tiny<(float)0.0) /* raise inexact */ |
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66 | return tiny-one; /* return -1 */ |
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67 | } |
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68 | } |
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69 | |
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70 | /* argument reduction */ |
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71 | if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ |
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72 | if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ |
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73 | if(xsb==0) |
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74 | {hi = x - ln2_hi; lo = ln2_lo; k = 1;} |
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75 | else |
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76 | {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} |
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77 | } else { |
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78 | k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); |
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79 | t = k; |
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80 | hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ |
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81 | lo = t*ln2_lo; |
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82 | } |
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83 | x = hi - lo; |
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84 | c = (hi-x)-lo; |
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85 | } |
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86 | else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ |
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87 | t = huge+x; /* return x with inexact flags when x!=0 */ |
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88 | return x - (t-(huge+x)); |
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89 | } |
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90 | else k = 0; |
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91 | |
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92 | /* x is now in primary range */ |
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93 | hfx = (float)0.5*x; |
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94 | hxs = x*hfx; |
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95 | r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); |
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96 | t = (float)3.0-r1*hfx; |
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97 | e = hxs*((r1-t)/((float)6.0 - x*t)); |
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98 | if(k==0) return x - (x*e-hxs); /* c is 0 */ |
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99 | else { |
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100 | e = (x*(e-c)-c); |
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101 | e -= hxs; |
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102 | if(k== -1) return (float)0.5*(x-e)-(float)0.5; |
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103 | if(k==1) { |
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104 | if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); |
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105 | else return one+(float)2.0*(x-e); |
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106 | } |
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107 | if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ |
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108 | __int32_t i; |
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109 | y = one-(e-x); |
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110 | GET_FLOAT_WORD(i,y); |
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111 | SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ |
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112 | return y-one; |
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113 | } |
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114 | t = one; |
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115 | if(k<23) { |
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116 | __int32_t i; |
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117 | SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ |
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118 | y = t-(e-x); |
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119 | GET_FLOAT_WORD(i,y); |
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120 | SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ |
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121 | } else { |
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122 | __int32_t i; |
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123 | SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ |
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124 | y = x-(e+t); |
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125 | y += one; |
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126 | GET_FLOAT_WORD(i,y); |
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127 | SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ |
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128 | } |
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129 | } |
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130 | return y; |
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131 | } |
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132 | |
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133 | #ifdef _DOUBLE_IS_32BITS |
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134 | |
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135 | #ifdef __STDC__ |
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136 | double expm1(double x) |
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137 | #else |
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138 | double expm1(x) |
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139 | double x; |
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140 | #endif |
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141 | { |
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142 | return (double) expm1f((float) x); |
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143 | } |
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144 | |
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145 | #endif /* defined(_DOUBLE_IS_32BITS) */ |
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