s_expm1f.c revision 176082
1/* s_expm1f.c -- float version of s_expm1.c. 2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3 */ 4 5/* 6 * ==================================================== 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16#include <sys/cdefs.h> 17__FBSDID("$FreeBSD: head/lib/msun/src/s_expm1f.c 176082 2008-02-07 09:42:19Z bde $"); 18 19#include "math.h" 20#include "math_private.h" 21 22static const float 23one = 1.0, 24huge = 1.0e+30, 25tiny = 1.0e-30, 26o_threshold = 8.8721679688e+01,/* 0x42b17180 */ 27ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ 28ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ 29invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ 30 /* scaled coefficients related to expm1 */ 31Q1 = -3.3333335072e-02, /* 0xbd088889 */ 32Q2 = 1.5873016091e-03, /* 0x3ad00d01 */ 33Q3 = -7.9365076090e-05, /* 0xb8a670cd */ 34Q4 = 4.0082177293e-06, /* 0x36867e54 */ 35Q5 = -2.0109921195e-07; /* 0xb457edbb */ 36 37float 38expm1f(float x) 39{ 40 float y,hi,lo,c,t,e,hxs,hfx,r1,twopk; 41 int32_t k,xsb; 42 u_int32_t hx; 43 44 GET_FLOAT_WORD(hx,x); 45 xsb = hx&0x80000000; /* sign bit of x */ 46 if(xsb==0) y=x; else y= -x; /* y = |x| */ 47 hx &= 0x7fffffff; /* high word of |x| */ 48 49 /* filter out huge and non-finite argument */ 50 if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ 51 if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 52 if(hx>0x7f800000) 53 return x+x; /* NaN */ 54 if(hx==0x7f800000) 55 return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ 56 if(x > o_threshold) return huge*huge; /* overflow */ 57 } 58 if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ 59 if(x+tiny<(float)0.0) /* raise inexact */ 60 return tiny-one; /* return -1 */ 61 } 62 } 63 64 /* argument reduction */ 65 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 66 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 67 if(xsb==0) 68 {hi = x - ln2_hi; lo = ln2_lo; k = 1;} 69 else 70 {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} 71 } else { 72 k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); 73 t = k; 74 hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ 75 lo = t*ln2_lo; 76 } 77 x = hi - lo; 78 c = (hi-x)-lo; 79 } 80 else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ 81 t = huge+x; /* return x with inexact flags when x!=0 */ 82 return x - (t-(huge+x)); 83 } 84 else k = 0; 85 86 /* x is now in primary range */ 87 hfx = (float)0.5*x; 88 hxs = x*hfx; 89 r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); 90 t = (float)3.0-r1*hfx; 91 e = hxs*((r1-t)/((float)6.0 - x*t)); 92 if(k==0) return x - (x*e-hxs); /* c is 0 */ 93 else { 94 SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); /* 2^k */ 95 e = (x*(e-c)-c); 96 e -= hxs; 97 if(k== -1) return (float)0.5*(x-e)-(float)0.5; 98 if(k==1) 99 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); 100 else return one+(float)2.0*(x-e); 101 if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ 102 y = one-(e-x); 103 if (k == 128) y = y*2.0F*0x1p127F; 104 else y = y*twopk; 105 return y-one; 106 } 107 t = one; 108 if(k<23) { 109 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ 110 y = t-(e-x); 111 y = y*twopk; 112 } else { 113 SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ 114 y = x-(e+t); 115 y += one; 116 y = y*twopk; 117 } 118 } 119 return y; 120} 121