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 ln2hi = 6.9314575195e-1f, /* 0x3f317200 */
21 ln2lo = 1.4286067653e-6f, /* 0x35bfbe8e */
22 invln2 = 1.4426950216e+0f, /* 0x3fb8aa3b */
24 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
25 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
27 P1 = 1.6666625440e-1f, /* 0xaaaa8f.0p-26 */
28 P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
32 float_t hi, lo, c, xx, y;
36 GET_FLOAT_WORD(hx, x);
37 sign = hx >> 31; /* sign bit of x */
38 hx &= 0x7fffffff; /* high word of |x| */
41 if (hx >= 0x42aeac50) { /* if |x| >= -87.33655f or NaN */
42 if (hx >= 0x42b17218 && !sign) { /* x >= 88.722839f */
49 FORCE_EVAL(-0x1p-149f/x);
50 if (hx >= 0x42cff1b5) /* x <= -103.972084f */
55 /* argument reduction */
56 if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
57 if (hx > 0x3f851592) /* if |x| > 1.5 ln2 */
58 k = invln2*x + half[sign];
61 hi = x - k*ln2hi; /* k*ln2hi is exact here */
64 } else if (hx > 0x39000000) { /* |x| > 2**-14 */
70 FORCE_EVAL(0x1p127f + x);
74 /* x is now in primary range */
76 c = x - xx*(P1+xx*P2);
77 y = 1 + (x*c/(2-c) - lo + hi);