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 #include "math_private.h"
19 static const volatile float huge
= 1.0e+30;
23 halF
[2] = {0.5,-0.5,},
24 twom100
= 7.8886090522e-31, /* 2**-100=0x0d800000 */
25 o_threshold
= 8.8721679688e+01, /* 0x42b17180 */
26 u_threshold
= -1.0397208405e+02, /* 0xc2cff1b5 */
27 ln2HI
[2] ={ 6.9313812256e-01, /* 0x3f317180 */
28 -6.9313812256e-01,}, /* 0xbf317180 */
29 ln2LO
[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */
30 -9.0580006145e-06,}, /* 0xb717f7d1 */
31 invln2
= 1.4426950216e+00, /* 0x3fb8aa3b */
32 P1
= 1.6666667163e-01, /* 0x3e2aaaab */
33 P2
= -2.7777778450e-03, /* 0xbb360b61 */
34 P3
= 6.6137559770e-05, /* 0x388ab355 */
35 P4
= -1.6533901999e-06, /* 0xb5ddea0e */
36 P5
= 4.1381369442e-08; /* 0x3331bb4c */
39 expf(float x
) /* default IEEE double exp */
46 xsb
= (hx
>>31)&1; /* sign bit of x */
47 hx
&= 0x7fffffff; /* high word of |x| */
50 /* filter out non-finite argument */
51 if(hx
>= 0x42b17218) { /* if |x|>=88.721... */
55 return (xsb
==0)? x
:0.0; /* exp(+-inf)={inf,0} */
56 if(x
> o_threshold
) return huge
*huge
; /* overflow */
57 if(x
< u_threshold
) 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 */
63 hi
= x
-ln2HI
[xsb
]; lo
=ln2LO
[xsb
]; k
= 1-xsb
-xsb
;
65 k
= invln2
*x
+halF
[xsb
];
67 hi
= x
- t
*ln2HI
[0]; /* t*ln2HI is exact here */
72 else if(hx
< 0x31800000) { /* when |x|<2**-28 */
73 if(huge
+x
>one
) return one
+x
;/* trigger inexact */
76 /* x is now in primary range */
78 c
= x
- t
*(P1
+t
*(P2
+t
*(P3
+t
*(P4
+t
*P5
))));
79 if(k
==0) return one
-((x
*c
)/(c
-(float)2.0)-x
);
80 else y
= one
-((lo
-(x
*c
)/((float)2.0-c
))-hi
);
84 SET_FLOAT_WORD(y
,hy
+(k
<<23)); /* add k to y's exponent */
89 SET_FLOAT_WORD(y
,hy
+((k
+100)<<23)); /* add k to y's exponent */