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 * ====================================================
17 static char rcsid[] = "$FreeBSD$";
21 #include "math_private.h"
25 halF[2] = {0.5,-0.5,},
27 twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
28 o_threshold= 8.8721679688e+01, /* 0x42b17180 */
29 u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
30 ln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */
31 -6.9314575195e-01,}, /* 0xbf317200 */
32 ln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */
33 -1.4286067653e-06,}, /* 0xb5bfbe8e */
34 invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
35 P1 = 1.6666667163e-01, /* 0x3e2aaaab */
36 P2 = -2.7777778450e-03, /* 0xbb360b61 */
37 P3 = 6.6137559770e-05, /* 0x388ab355 */
38 P4 = -1.6533901999e-06, /* 0xb5ddea0e */
39 P5 = 4.1381369442e-08; /* 0x3331bb4c */
42 __ieee754_expf(float x) /* default IEEE double exp */
44 float y,hi=0.0,lo=0.0,c,t;
49 xsb = (hx>>31)&1; /* sign bit of x */
50 hx &= 0x7fffffff; /* high word of |x| */
52 /* filter out non-finite argument */
53 if(hx >= 0x42b17218) { /* if |x|>=88.721... */
57 return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
58 if(x > o_threshold) return huge*huge; /* overflow */
59 if(x < u_threshold) return twom100*twom100; /* underflow */
62 /* argument reduction */
63 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
64 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
65 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
67 k = invln2*x+halF[xsb];
69 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
74 else if(hx < 0x31800000) { /* when |x|<2**-28 */
75 if(huge+x>one) return one+x;/* trigger inexact */
79 /* x is now in primary range */
81 c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
82 if(k==0) return one-((x*c)/(c-(float)2.0)-x);
83 else y = one-((lo-(x*c)/((float)2.0-c))-hi);
87 SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
92 SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */