1 /* e_expf.c -- float version of e_exp.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 */
4
5 /*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
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
12 * is preserved.
13 * ====================================================
14 */
15
16 #include <sys/cdefs.h>
17 __FBSDID("$FreeBSD$");
18
19 #include <float.h>
20
21 #include "math.h"
22 #include "math_private.h"
23
24 static const float
25 one = 1.0,
26 halF[2] = {0.5,-0.5,},
27 o_threshold= 8.8721679688e+01, /* 0x42b17180 */
28 u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
29 ln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */
30 -6.9314575195e-01,}, /* 0xbf317200 */
31 ln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */
32 -1.4286067653e-06,}, /* 0xb5bfbe8e */
33 invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
34 /*
35 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
36 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
37 */
38 P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */
39 P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */
40
41 static volatile float
42 huge = 1.0e+30,
43 twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */
44
45 float
__ieee754_expf(float x)46 __ieee754_expf(float x)
47 {
48 float y,hi=0.0,lo=0.0,c,t,twopk;
49 int32_t k=0,xsb;
50 u_int32_t hx;
51
52 GET_FLOAT_WORD(hx,x);
53 xsb = (hx>>31)&1; /* sign bit of x */
54 hx &= 0x7fffffff; /* high word of |x| */
55
56 /* filter out non-finite argument */
57 if(hx >= 0x42b17218) { /* if |x|>=88.721... */
58 if(hx>0x7f800000)
59 return x+x; /* NaN */
60 if(hx==0x7f800000)
61 return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
62 if(x > o_threshold) return huge*huge; /* overflow */
63 if(x < u_threshold) return twom100*twom100; /* underflow */
64 }
65
66 /* argument reduction */
67 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
68 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
69 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
70 } else {
71 k = invln2*x+halF[xsb];
72 t = k;
73 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
74 lo = t*ln2LO[0];
75 }
76 STRICT_ASSIGN(float, x, hi - lo);
77 }
78 else if(hx < 0x39000000) { /* when |x|<2**-14 */
79 if(huge+x>one) return one+x;/* trigger inexact */
80 }
81 else k = 0;
82
83 /* x is now in primary range */
84 t = x*x;
85 if(k >= -125)
86 SET_FLOAT_WORD(twopk,0x3f800000+(k<<23));
87 else
88 SET_FLOAT_WORD(twopk,0x3f800000+((k+100)<<23));
89 c = x - t*(P1+t*P2);
90 if(k==0) return one-((x*c)/(c-(float)2.0)-x);
91 else y = one-((lo-(x*c)/((float)2.0-c))-hi);
92 if(k >= -125) {
93 if(k==128) return y*2.0F*0x1p127F;
94 return y*twopk;
95 } else {
96 return y*twopk*twom100;
97 }
98 }
99