s_expm1f.c revision 97413
12116Sjkh/* s_expm1f.c -- float version of s_expm1.c. 22116Sjkh * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 32116Sjkh */ 42116Sjkh 52116Sjkh/* 62116Sjkh * ==================================================== 72116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 82116Sjkh * 92116Sjkh * Developed at SunPro, a Sun Microsystems, Inc. business. 102116Sjkh * Permission to use, copy, modify, and distribute this 118870Srgrimes * software is freely granted, provided that this notice 122116Sjkh * is preserved. 132116Sjkh * ==================================================== 142116Sjkh */ 152116Sjkh 162116Sjkh#ifndef lint 1750476Speterstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/s_expm1f.c 97413 2002-05-28 18:15:04Z alfred $"; 182116Sjkh#endif 192116Sjkh 202116Sjkh#include "math.h" 212116Sjkh#include "math_private.h" 222116Sjkh 232116Sjkhstatic const float 242116Sjkhone = 1.0, 252116Sjkhhuge = 1.0e+30, 262116Sjkhtiny = 1.0e-30, 272116Sjkho_threshold = 8.8721679688e+01,/* 0x42b17180 */ 282116Sjkhln2_hi = 6.9313812256e-01,/* 0x3f317180 */ 292116Sjkhln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ 302116Sjkhinvln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ 312116Sjkh /* scaled coefficients related to expm1 */ 322116SjkhQ1 = -3.3333335072e-02, /* 0xbd088889 */ 332116SjkhQ2 = 1.5873016091e-03, /* 0x3ad00d01 */ 342116SjkhQ3 = -7.9365076090e-05, /* 0xb8a670cd */ 352116SjkhQ4 = 4.0082177293e-06, /* 0x36867e54 */ 362116SjkhQ5 = -2.0109921195e-07; /* 0xb457edbb */ 372116Sjkh 3897413Salfredfloat 3997413Salfredexpm1f(float x) 402116Sjkh{ 412116Sjkh float y,hi,lo,c,t,e,hxs,hfx,r1; 422116Sjkh int32_t k,xsb; 432116Sjkh u_int32_t hx; 442116Sjkh 452116Sjkh GET_FLOAT_WORD(hx,x); 462116Sjkh xsb = hx&0x80000000; /* sign bit of x */ 472116Sjkh if(xsb==0) y=x; else y= -x; /* y = |x| */ 482116Sjkh hx &= 0x7fffffff; /* high word of |x| */ 492116Sjkh 502116Sjkh /* filter out huge and non-finite argument */ 512116Sjkh if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ 522116Sjkh if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 532116Sjkh if(hx>0x7f800000) 542116Sjkh return x+x; /* NaN */ 552116Sjkh if(hx==0x7f800000) 562116Sjkh return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ 572116Sjkh if(x > o_threshold) return huge*huge; /* overflow */ 582116Sjkh } 592116Sjkh if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ 602116Sjkh if(x+tiny<(float)0.0) /* raise inexact */ 612116Sjkh return tiny-one; /* return -1 */ 622116Sjkh } 632116Sjkh } 642116Sjkh 652116Sjkh /* argument reduction */ 668870Srgrimes if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 672116Sjkh if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 682116Sjkh if(xsb==0) 692116Sjkh {hi = x - ln2_hi; lo = ln2_lo; k = 1;} 702116Sjkh else 712116Sjkh {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} 722116Sjkh } else { 732116Sjkh k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); 742116Sjkh t = k; 752116Sjkh hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ 762116Sjkh lo = t*ln2_lo; 772116Sjkh } 782116Sjkh x = hi - lo; 792116Sjkh c = (hi-x)-lo; 808870Srgrimes } 812116Sjkh else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ 822116Sjkh t = huge+x; /* return x with inexact flags when x!=0 */ 838870Srgrimes return x - (t-(huge+x)); 842116Sjkh } 852116Sjkh else k = 0; 862116Sjkh 872116Sjkh /* x is now in primary range */ 882116Sjkh hfx = (float)0.5*x; 892116Sjkh hxs = x*hfx; 902116Sjkh r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); 912116Sjkh t = (float)3.0-r1*hfx; 922116Sjkh e = hxs*((r1-t)/((float)6.0 - x*t)); 932116Sjkh if(k==0) return x - (x*e-hxs); /* c is 0 */ 942116Sjkh else { 952116Sjkh e = (x*(e-c)-c); 962116Sjkh e -= hxs; 972116Sjkh if(k== -1) return (float)0.5*(x-e)-(float)0.5; 988870Srgrimes if(k==1) 992116Sjkh if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); 1002116Sjkh else return one+(float)2.0*(x-e); 1012116Sjkh if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ 1022116Sjkh int32_t i; 1032116Sjkh y = one-(e-x); 1042116Sjkh GET_FLOAT_WORD(i,y); 1052116Sjkh SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ 1062116Sjkh return y-one; 1072116Sjkh } 1082116Sjkh t = one; 1092116Sjkh if(k<23) { 1102116Sjkh int32_t i; 1112116Sjkh SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ 1122116Sjkh y = t-(e-x); 1132116Sjkh GET_FLOAT_WORD(i,y); 1142116Sjkh SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ 1152116Sjkh } else { 1162116Sjkh int32_t i; 1172116Sjkh SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ 1182116Sjkh y = x-(e+t); 1192116Sjkh y += one; 1202116Sjkh GET_FLOAT_WORD(i,y); 1212116Sjkh SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ 1222116Sjkh } 1232116Sjkh } 1242116Sjkh return y; 1252116Sjkh} 126