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: src/lib/msun/src/e_expf.c,v 1.16 2011/10/21 06:26:38 das Exp $";
21 #include "math_private.h"
25 halF
[2] = {0.5,-0.5,},
26 o_threshold
= 8.8721679688e+01, /* 0x42b17180 */
27 u_threshold
= -1.0397208405e+02, /* 0xc2cff1b5 */
28 ln2HI
[2] ={ 6.9314575195e-01, /* 0x3f317200 */
29 -6.9314575195e-01,}, /* 0xbf317200 */
30 ln2LO
[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */
31 -1.4286067653e-06,}, /* 0xb5bfbe8e */
32 invln2
= 1.4426950216e+00, /* 0x3fb8aa3b */
34 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
35 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
37 P1
= 1.6666625440e-1, /* 0xaaaa8f.0p-26 */
38 P2
= -2.7667332906e-3; /* -0xb55215.0p-32 */
40 static const volatile float
41 huge
__attribute__ ((__section__(".rodata"))) = 1.0e+30,
42 twom100
__attribute__ ((__section__(".rodata"))) = 7.8886090522e-31; /* 2**-100=0x0d800000 */
45 __ieee754_expf(float x
) /* default IEEE double exp */
47 float y
,hi
=0.0,lo
=0.0,c
,t
,twopk
;
52 xsb
= (hx
>>31)&1; /* sign bit of x */
53 hx
&= 0x7fffffff; /* high word of |x| */
55 /* filter out non-finite argument */
56 if(hx
>= 0x42b17218) { /* if |x|>=88.721... */
60 return (xsb
==0)? x
:0.0; /* exp(+-inf)={inf,0} */
61 if(x
> o_threshold
) return huge
*huge
; /* overflow */
62 if(x
< u_threshold
) return twom100
*twom100
; /* underflow */
65 /* argument reduction */
66 if(hx
> 0x3eb17218) { /* if |x| > 0.5 ln2 */
67 if(hx
< 0x3F851592) { /* and |x| < 1.5 ln2 */
68 hi
= x
-ln2HI
[xsb
]; lo
=ln2LO
[xsb
]; k
= 1-xsb
-xsb
;
70 k
= invln2
*x
+halF
[xsb
];
72 hi
= x
- t
*ln2HI
[0]; /* t*ln2HI is exact here */
75 STRICT_ASSIGN(float, x
, hi
- lo
);
77 else if(hx
< 0x39000000) { /* when |x|<2**-14 */
78 if(huge
+x
>one
) return one
+x
;/* trigger inexact */
82 /* x is now in primary range */
85 SET_FLOAT_WORD(twopk
,0x3f800000+(k
<<23));
87 SET_FLOAT_WORD(twopk
,0x3f800000+((k
+100)<<23));
89 if(k
==0) return one
-((x
*c
)/(c
-(float)2.0)-x
);
90 else y
= one
-((lo
-(x
*c
)/((float)2.0-c
))-hi
);
92 if(k
==128) return y
*2.0F
*0x1p
127F
;
95 return y
*twopk
*twom100
;