1 /* origin: FreeBSD /usr/src/lib/msun/src/e_expf.c */
3 * 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 * ====================================================
20 halF[2] = {0.5,-0.5,},
22 o_threshold = 8.8721679688e+01, /* 0x42b17180 */
23 u_threshold = -1.0397208405e+02, /* 0xc2cff1b5 */
24 ln2HI[2] = { 6.9314575195e-01, /* 0x3f317200 */
25 -6.9314575195e-01,},/* 0xbf317200 */
26 ln2LO[2] = { 1.4286067653e-06, /* 0x35bfbe8e */
27 -1.4286067653e-06,},/* 0xb5bfbe8e */
28 invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
30 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
31 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
33 P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */
34 P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */
36 static volatile float twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */
40 float y,hi=0.0,lo=0.0,c,t,twopk;
44 GET_FLOAT_WORD(hx, x);
45 xsb = (hx>>31)&1; /* sign bit of x */
46 hx &= 0x7fffffff; /* high word of |x| */
48 /* filter out non-finite argument */
49 if (hx >= 0x42b17218) { /* if |x|>=88.721... */
50 if (hx > 0x7f800000) /* NaN */
52 if (hx == 0x7f800000) /* exp(+-inf)={inf,0} */
53 return xsb==0 ? x : 0.0;
55 return huge*huge; /* overflow */
57 return twom100*twom100; /* underflow */
60 /* argument reduction */
61 if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
62 if (hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
67 k = invln2*x + halF[xsb];
69 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
72 STRICT_ASSIGN(float, x, hi - lo);
73 } else if(hx < 0x39000000) { /* |x|<2**-14 */
80 /* x is now in primary range */
83 SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23));
85 SET_FLOAT_WORD(twopk, 0x3f800000+((k+100)<<23));
88 return one - ((x*c)/(c - 2.0f) - x);
89 y = one - ((lo - (x*c)/(2.0f - c)) - hi);
91 return y*twopk*twom100;
93 return y*2.0f*0x1p127f;