e_expf.c revision 176032
12116Sjkh/* e_expf.c -- float version of e_exp.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/e_expf.c 176032 2008-02-06 06:35:21Z bde $"; 182116Sjkh#endif 192116Sjkh 202116Sjkh#include "math.h" 212116Sjkh#include "math_private.h" 222116Sjkh 232116Sjkhstatic const float 242116Sjkhone = 1.0, 252116SjkhhalF[2] = {0.5,-0.5,}, 262116Sjkhhuge = 1.0e+30, 272116Sjkho_threshold= 8.8721679688e+01, /* 0x42b17180 */ 282116Sjkhu_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ 29152947Sbdeln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */ 30152947Sbde -6.9314575195e-01,}, /* 0xbf317200 */ 31152947Sbdeln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */ 32152947Sbde -1.4286067653e-06,}, /* 0xb5bfbe8e */ 332116Sjkhinvln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ 34176032Sbde/* 35176032Sbde * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]: 36176032Sbde * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74 37176032Sbde */ 38176032SbdeP1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */ 39176032SbdeP2 = -2.7667332906e-3; /* -0xb55215.0p-32 */ 402116Sjkh 41175468Sdasstatic volatile float twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */ 42175468Sdas 4397407Salfredfloat 44142369Sdas__ieee754_expf(float x) /* default IEEE double exp */ 452116Sjkh{ 46142369Sdas float y,hi=0.0,lo=0.0,c,t; 4717141Sjkh int32_t k=0,xsb; 482116Sjkh u_int32_t hx; 492116Sjkh 502116Sjkh GET_FLOAT_WORD(hx,x); 512116Sjkh xsb = (hx>>31)&1; /* sign bit of x */ 52142369Sdas hx &= 0x7fffffff; /* high word of |x| */ 532116Sjkh 542116Sjkh /* filter out non-finite argument */ 552116Sjkh if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 562116Sjkh if(hx>0x7f800000) 572116Sjkh return x+x; /* NaN */ 582116Sjkh if(hx==0x7f800000) 592116Sjkh return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ 602116Sjkh if(x > o_threshold) return huge*huge; /* overflow */ 612116Sjkh if(x < u_threshold) return twom100*twom100; /* underflow */ 622116Sjkh } 632116Sjkh 642116Sjkh /* argument reduction */ 658870Srgrimes if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 662116Sjkh if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 67142369Sdas hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; 682116Sjkh } else { 692116Sjkh k = invln2*x+halF[xsb]; 702116Sjkh t = k; 71142369Sdas hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ 72142369Sdas lo = t*ln2LO[0]; 732116Sjkh } 74142369Sdas x = hi - lo; 758870Srgrimes } 762116Sjkh else if(hx < 0x31800000) { /* when |x|<2**-28 */ 772116Sjkh if(huge+x>one) return one+x;/* trigger inexact */ 782116Sjkh } 792116Sjkh else k = 0; 802116Sjkh 812116Sjkh /* x is now in primary range */ 822116Sjkh t = x*x; 83176032Sbde c = x - t*(P1+t*P2); 84142369Sdas if(k==0) return one-((x*c)/(c-(float)2.0)-x); 85142369Sdas else y = one-((lo-(x*c)/((float)2.0-c))-hi); 862116Sjkh if(k >= -125) { 872116Sjkh u_int32_t hy; 882116Sjkh GET_FLOAT_WORD(hy,y); 892116Sjkh SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */ 902116Sjkh return y; 912116Sjkh } else { 922116Sjkh u_int32_t hy; 932116Sjkh GET_FLOAT_WORD(hy,y); 942116Sjkh SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */ 952116Sjkh return y*twom100; 962116Sjkh } 972116Sjkh} 98