| /* origin: FreeBSD /usr/src/lib/msun/src/e_expf.c */ |
| /* |
| * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
| */ |
| /* |
| * ==================================================== |
| * 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 "libm.h" |
| |
| static const float |
| half[2] = {0.5,-0.5}, |
| ln2hi = 6.9314575195e-1f, /* 0x3f317200 */ |
| ln2lo = 1.4286067653e-6f, /* 0x35bfbe8e */ |
| invln2 = 1.4426950216e+0f, /* 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-1f, /* 0xaaaa8f.0p-26 */ |
| P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */ |
| |
| float expf(float x) |
| { |
| float_t hi, lo, c, xx, y; |
| int k, sign; |
| uint32_t hx; |
| |
| GET_FLOAT_WORD(hx, x); |
| sign = hx >> 31; /* sign bit of x */ |
| hx &= 0x7fffffff; /* high word of |x| */ |
| |
| /* special cases */ |
| if (hx >= 0x42aeac50) { /* if |x| >= -87.33655f or NaN */ |
| if (hx > 0x7f800000) /* NaN */ |
| return x; |
| if (hx >= 0x42b17218 && !sign) { /* x >= 88.722839f */ |
| /* overflow */ |
| x *= 0x1p127f; |
| return x; |
| } |
| if (sign) { |
| /* underflow */ |
| FORCE_EVAL(-0x1p-149f/x); |
| if (hx >= 0x42cff1b5) /* x <= -103.972084f */ |
| return 0; |
| } |
| } |
| |
| /* argument reduction */ |
| if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ |
| if (hx > 0x3f851592) /* if |x| > 1.5 ln2 */ |
| k = invln2*x + half[sign]; |
| else |
| k = 1 - sign - sign; |
| hi = x - k*ln2hi; /* k*ln2hi is exact here */ |
| lo = k*ln2lo; |
| x = hi - lo; |
| } else if (hx > 0x39000000) { /* |x| > 2**-14 */ |
| k = 0; |
| hi = x; |
| lo = 0; |
| } else { |
| /* raise inexact */ |
| FORCE_EVAL(0x1p127f + x); |
| return 1 + x; |
| } |
| |
| /* x is now in primary range */ |
| xx = x*x; |
| c = x - xx*(P1+xx*P2); |
| y = 1 + (x*c/(2-c) - lo + hi); |
| if (k == 0) |
| return y; |
| return scalbnf(y, k); |
| } |
