e_expf.c revision 218508
167754Smsmith/* e_expf.c -- float version of e_exp.c. 267754Smsmith * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 367754Smsmith */ 467754Smsmith 567754Smsmith/* 667754Smsmith * ==================================================== 7217365Sjkim * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8217365Sjkim * 970243Smsmith * Developed at SunPro, a Sun Microsystems, Inc. business. 1067754Smsmith * Permission to use, copy, modify, and distribute this 11217365Sjkim * software is freely granted, provided that this notice 12217365Sjkim * is preserved. 13217365Sjkim * ==================================================== 14217365Sjkim */ 15217365Sjkim 16217365Sjkim#include <sys/cdefs.h> 17217365Sjkim__FBSDID("$FreeBSD: head/lib/msun/src/e_expf.c 218508 2011-02-10 07:37:29Z das $"); 18217365Sjkim 19217365Sjkim#include "math.h" 20217365Sjkim#include "math_private.h" 21217365Sjkim 22217365Sjkimstatic const float 23217365Sjkimone = 1.0, 24217365SjkimhalF[2] = {0.5,-0.5,}, 2567754Smsmithhuge = 1.0e+30, 26217365Sjkimo_threshold= 8.8721679688e+01, /* 0x42b17180 */ 27217365Sjkimu_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ 28217365Sjkimln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */ 2967754Smsmith -6.9314575195e-01,}, /* 0xbf317200 */ 30217365Sjkimln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */ 31217365Sjkim -1.4286067653e-06,}, /* 0xb5bfbe8e */ 32217365Sjkiminvln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ 33217365Sjkim/* 34217365Sjkim * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]: 35217365Sjkim * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74 36217365Sjkim */ 37217365SjkimP1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */ 38217365SjkimP2 = -2.7667332906e-3; /* -0xb55215.0p-32 */ 39217365Sjkim 40217365Sjkimstatic volatile float twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */ 41217365Sjkim 42217365Sjkimfloat 4367754Smsmith__ieee754_expf(float x) /* default IEEE double exp */ 4467754Smsmith{ 4567754Smsmith float y,hi=0.0,lo=0.0,c,t,twopk; 4667754Smsmith int32_t k=0,xsb; 4780062Smsmith u_int32_t hx; 4867754Smsmith 49193267Sjkim GET_FLOAT_WORD(hx,x); 50167802Sjkim xsb = (hx>>31)&1; /* sign bit of x */ 51167802Sjkim hx &= 0x7fffffff; /* high word of |x| */ 52123315Snjl 53167802Sjkim /* filter out non-finite argument */ 54167802Sjkim if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 55167802Sjkim if(hx>0x7f800000) 56167802Sjkim return x+x; /* NaN */ 57167802Sjkim if(hx==0x7f800000) 58167802Sjkim return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ 59167802Sjkim if(x > o_threshold) return huge*huge; /* overflow */ 60167802Sjkim if(x < u_threshold) return twom100*twom100; /* underflow */ 6167754Smsmith } 62167802Sjkim 63193267Sjkim /* argument reduction */ 64167802Sjkim if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 6567754Smsmith if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 66193267Sjkim hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; 6777424Smsmith } else { 68193267Sjkim k = invln2*x+halF[xsb]; 6991116Smsmith t = k; 70193267Sjkim hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ 71193267Sjkim lo = t*ln2LO[0]; 7291116Smsmith } 73193267Sjkim x = hi - lo; 7491116Smsmith } 7591116Smsmith else if(hx < 0x39000000) { /* when |x|<2**-14 */ 76193267Sjkim if(huge+x>one) return one+x;/* trigger inexact */ 7767754Smsmith } 7867754Smsmith else k = 0; 7967754Smsmith 8067754Smsmith /* x is now in primary range */ 8167754Smsmith t = x*x; 82117521Snjl if(k >= -125) 83117521Snjl SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); 84117521Snjl else 85117521Snjl SET_FLOAT_WORD(twopk,0x3f800000+((k+100)<<23)); 8667754Smsmith c = x - t*(P1+t*P2); 87117521Snjl if(k==0) return one-((x*c)/(c-(float)2.0)-x); 88117521Snjl else y = one-((lo-(x*c)/((float)2.0-c))-hi); 89117521Snjl if(k >= -125) { 90117521Snjl if(k==128) return y*2.0F*0x1p127F; 91117521Snjl return y*twopk; 92117521Snjl } else { 93193267Sjkim return y*twopk*twom100; 94117521Snjl } 95117521Snjl} 96193267Sjkim