1 /* e_expf.c -- float version of e_exp.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
13 * ====================================================
16 #include <sys/cdefs.h>
17 __FBSDID("$FreeBSD$");
20 #include "math_private.h"
24 halF[2] = {0.5,-0.5,},
26 o_threshold= 8.8721679688e+01, /* 0x42b17180 */
27 u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
28 ln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */
29 -6.9314575195e-01,}, /* 0xbf317200 */
30 ln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */
31 -1.4286067653e-06,}, /* 0xb5bfbe8e */
32 invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
34 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
35 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
37 P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */
38 P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */
40 static volatile float twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */
43 __ieee754_expf(float x) /* default IEEE double exp */
45 float y,hi=0.0,lo=0.0,c,t,twopk;
50 xsb = (hx>>31)&1; /* sign bit of x */
51 hx &= 0x7fffffff; /* high word of |x| */
53 /* filter out non-finite argument */
54 if(hx >= 0x42b17218) { /* if |x|>=88.721... */
58 return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
59 if(x > o_threshold) return huge*huge; /* overflow */
60 if(x < u_threshold) return twom100*twom100; /* underflow */
63 /* argument reduction */
64 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
65 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
66 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
68 k = invln2*x+halF[xsb];
70 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
75 else if(hx < 0x39000000) { /* when |x|<2**-14 */
76 if(huge+x>one) return one+x;/* trigger inexact */
80 /* x is now in primary range */
83 SET_FLOAT_WORD(twopk,0x3f800000+(k<<23));
85 SET_FLOAT_WORD(twopk,0x3f800000+((k+100)<<23));
87 if(k==0) return one-((x*c)/(c-(float)2.0)-x);
88 else y = one-((lo-(x*c)/((float)2.0-c))-hi);
90 if(k==128) return y*2.0F*0x1p127F;
93 return y*twopk*twom100;