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 16176451Sdas#include <sys/cdefs.h> 17176451Sdas__FBSDID("$FreeBSD$"); 182116Sjkh 19226596Sdas#include <float.h> 20226596Sdas 212116Sjkh#include "math.h" 222116Sjkh#include "math_private.h" 232116Sjkh 242116Sjkhstatic const float 252116Sjkhone = 1.0, 262116SjkhhalF[2] = {0.5,-0.5,}, 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 41251024Sdasstatic volatile float 42251024Sdashuge = 1.0e+30, 43251024Sdastwom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */ 44175468Sdas 4597407Salfredfloat 46226596Sdas__ieee754_expf(float x) 472116Sjkh{ 48176074Sbde float y,hi=0.0,lo=0.0,c,t,twopk; 4917141Sjkh int32_t k=0,xsb; 502116Sjkh u_int32_t hx; 512116Sjkh 522116Sjkh GET_FLOAT_WORD(hx,x); 532116Sjkh xsb = (hx>>31)&1; /* sign bit of x */ 54142369Sdas hx &= 0x7fffffff; /* high word of |x| */ 552116Sjkh 562116Sjkh /* filter out non-finite argument */ 572116Sjkh if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 582116Sjkh if(hx>0x7f800000) 592116Sjkh return x+x; /* NaN */ 602116Sjkh if(hx==0x7f800000) 612116Sjkh return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ 622116Sjkh if(x > o_threshold) return huge*huge; /* overflow */ 632116Sjkh if(x < u_threshold) return twom100*twom100; /* underflow */ 642116Sjkh } 652116Sjkh 662116Sjkh /* argument reduction */ 678870Srgrimes if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 682116Sjkh if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 69142369Sdas hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; 702116Sjkh } else { 712116Sjkh k = invln2*x+halF[xsb]; 722116Sjkh t = k; 73142369Sdas hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ 74142369Sdas lo = t*ln2LO[0]; 752116Sjkh } 76226596Sdas STRICT_ASSIGN(float, x, hi - lo); 778870Srgrimes } 78218508Sdas else if(hx < 0x39000000) { /* when |x|<2**-14 */ 792116Sjkh if(huge+x>one) return one+x;/* trigger inexact */ 802116Sjkh } 812116Sjkh else k = 0; 822116Sjkh 832116Sjkh /* x is now in primary range */ 842116Sjkh t = x*x; 85176074Sbde if(k >= -125) 86176074Sbde SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); 87176074Sbde else 88176074Sbde SET_FLOAT_WORD(twopk,0x3f800000+((k+100)<<23)); 89176032Sbde c = x - t*(P1+t*P2); 90142369Sdas if(k==0) return one-((x*c)/(c-(float)2.0)-x); 91142369Sdas else y = one-((lo-(x*c)/((float)2.0-c))-hi); 922116Sjkh if(k >= -125) { 93176074Sbde if(k==128) return y*2.0F*0x1p127F; 94176074Sbde return y*twopk; 952116Sjkh } else { 96176074Sbde return y*twopk*twom100; 972116Sjkh } 982116Sjkh} 99