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| Rev | Author | Line No. | Line |
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| 2 | pj | 1 | /* s_expm1f.c -- float version of s_expm1.c. |
| 2 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
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| 3 | */ |
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| 4 | |||
| 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 | |||
| 16 | #ifndef lint |
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| 17 | static char rcsid[] = "$\Id: s_expm1f.c,v 1.2 1995/05/30 05:49:34 rgrimes Exp $"; |
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| 18 | #endif |
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| 19 | |||
| 20 | #include "math.h" |
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| 21 | #include "math_private.h" |
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| 22 | |||
| 23 | #ifdef __STDC__ |
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| 24 | static const float |
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| 25 | #else |
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| 26 | static float |
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| 27 | #endif |
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| 28 | one = 1.0, |
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| 29 | huge = 1.0e+30, |
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| 30 | tiny = 1.0e-30, |
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| 31 | o_threshold = 8.8721679688e+01,/* 0x42b17180 */ |
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| 32 | ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ |
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| 33 | ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ |
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| 34 | invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ |
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| 35 | /* scaled coefficients related to expm1 */ |
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| 36 | Q1 = -3.3333335072e-02, /* 0xbd088889 */ |
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| 37 | Q2 = 1.5873016091e-03, /* 0x3ad00d01 */ |
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| 38 | Q3 = -7.9365076090e-05, /* 0xb8a670cd */ |
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| 39 | Q4 = 4.0082177293e-06, /* 0x36867e54 */ |
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| 40 | Q5 = -2.0109921195e-07; /* 0xb457edbb */ |
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| 41 | |||
| 42 | #ifdef __STDC__ |
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| 43 | float expm1f(float x) |
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| 44 | #else |
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| 45 | float expm1f(x) |
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| 46 | float x; |
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| 47 | #endif |
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| 48 | { |
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| 49 | float y,hi,lo,c,t,e,hxs,hfx,r1; |
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| 50 | int32_t k,xsb; |
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| 51 | u_int32_t hx; |
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| 52 | |||
| 53 | GET_FLOAT_WORD(hx,x); |
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| 54 | xsb = hx&0x80000000; /* sign bit of x */ |
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| 55 | if(xsb==0) y=x; else y= -x; /* y = |x| */ |
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| 56 | hx &= 0x7fffffff; /* high word of |x| */ |
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| 57 | |||
| 58 | /* filter out huge and non-finite argument */ |
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| 59 | if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ |
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| 60 | if(hx >= 0x42b17218) { /* if |x|>=88.721... */ |
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| 61 | if(hx>0x7f800000) |
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| 62 | return x+x; /* NaN */ |
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| 63 | if(hx==0x7f800000) |
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| 64 | return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ |
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| 65 | if(x > o_threshold) return huge*huge; /* overflow */ |
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| 66 | } |
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| 67 | if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ |
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| 68 | if(x+tiny<(float)0.0) /* raise inexact */ |
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| 69 | return tiny-one; /* return -1 */ |
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| 70 | } |
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| 71 | } |
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| 72 | |||
| 73 | /* argument reduction */ |
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| 74 | if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ |
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| 75 | if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ |
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| 76 | if(xsb==0) |
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| 77 | {hi = x - ln2_hi; lo = ln2_lo; k = 1;} |
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| 78 | else |
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| 79 | {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} |
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| 80 | } else { |
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| 81 | k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); |
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| 82 | t = k; |
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| 83 | hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ |
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| 84 | lo = t*ln2_lo; |
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| 85 | } |
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| 86 | x = hi - lo; |
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| 87 | c = (hi-x)-lo; |
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| 88 | } |
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| 89 | else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ |
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| 90 | t = huge+x; /* return x with inexact flags when x!=0 */ |
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| 91 | return x - (t-(huge+x)); |
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| 92 | } |
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| 93 | else k = 0; |
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| 94 | |||
| 95 | /* x is now in primary range */ |
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| 96 | hfx = (float)0.5*x; |
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| 97 | hxs = x*hfx; |
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| 98 | r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); |
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| 99 | t = (float)3.0-r1*hfx; |
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| 100 | e = hxs*((r1-t)/((float)6.0 - x*t)); |
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| 101 | if(k==0) return x - (x*e-hxs); /* c is 0 */ |
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| 102 | else { |
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| 103 | e = (x*(e-c)-c); |
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| 104 | e -= hxs; |
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| 105 | if(k== -1) return (float)0.5*(x-e)-(float)0.5; |
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| 106 | if(k==1) |
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| 107 | if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); |
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| 108 | else return one+(float)2.0*(x-e); |
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| 109 | if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ |
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| 110 | int32_t i; |
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| 111 | y = one-(e-x); |
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| 112 | GET_FLOAT_WORD(i,y); |
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| 113 | SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ |
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| 114 | return y-one; |
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| 115 | } |
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| 116 | t = one; |
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| 117 | if(k<23) { |
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| 118 | int32_t i; |
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| 119 | SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ |
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| 120 | y = t-(e-x); |
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| 121 | GET_FLOAT_WORD(i,y); |
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| 122 | SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ |
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| 123 | } else { |
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| 124 | int32_t i; |
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| 125 | SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ |
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| 126 | y = x-(e+t); |
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| 127 | y += one; |
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| 128 | GET_FLOAT_WORD(i,y); |
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| 129 | SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ |
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| 130 | } |
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| 131 | } |
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| 132 | return y; |
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| 133 | } |