| /* e_expf.c -- float version of e_exp.c. |
| * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected]. |
| */ |
| |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| #include <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| #include <float.h> |
| |
| #include "math.h" |
| #include <math_private.h> |
| |
| static const float |
| one = 1.0, |
| halF[2] = {0.5,-0.5,}, |
| o_threshold= 8.8721679688e+01, /* 0x42b17180 */ |
| u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ |
| ln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */ |
| -6.9314575195e-01,}, /* 0xbf317200 */ |
| ln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */ |
| -1.4286067653e-06,}, /* 0xb5bfbe8e */ |
| invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ |
| /* |
| * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]: |
| * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74 |
| */ |
| P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */ |
| P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */ |
| |
| static volatile float |
| huge = 1.0e+30, |
| twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */ |
| |
| float |
| __ieee754_expf(float x) |
| { |
| float y,hi=0.0,lo=0.0,c,t,twopk; |
| int32_t k=0,xsb; |
| u_int32_t hx; |
| |
| GET_FLOAT_WORD(hx,x); |
| xsb = (hx>>31)&1; /* sign bit of x */ |
| hx &= 0x7fffffff; /* high word of |x| */ |
| |
| /* filter out non-finite argument */ |
| if(hx >= 0x42b17218) { /* if |x|>=88.721... */ |
| if(hx>0x7f800000) |
| return x+x; /* NaN */ |
| if(hx==0x7f800000) |
| return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ |
| if(x > o_threshold) return huge*huge; /* overflow */ |
| if(x < u_threshold) return twom100*twom100; /* underflow */ |
| } |
| |
| /* argument reduction */ |
| if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ |
| if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ |
| hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; |
| } else { |
| k = invln2*x+halF[xsb]; |
| t = k; |
| hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ |
| lo = t*ln2LO[0]; |
| } |
| STRICT_ASSIGN(float, x, hi - lo); |
| } |
| else if(hx < 0x39000000) { /* when |x|<2**-14 */ |
| if(huge+x>one) return one+x;/* trigger inexact */ |
| } |
| else k = 0; |
| |
| /* x is now in primary range */ |
| t = x*x; |
| if(k >= -125) |
| SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); |
| else |
| SET_FLOAT_WORD(twopk,0x3f800000+((k+100)<<23)); |
| c = x - t*(P1+t*P2); |
| if(k==0) return one-((x*c)/(c-(float)2.0)-x); |
| else y = one-((lo-(x*c)/((float)2.0-c))-hi); |
| if(k >= -125) { |
| if(k==128) return y*2.0F*0x1p127F; |
| return y*twopk; |
| } else { |
| return y*twopk*twom100; |
| } |
| } |
