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
> 0x7f800000) /* NaN */
44 if (hx
>= 0x42b17218 && !sign
) { /* x >= 88.722839f */
51 FORCE_EVAL(-0x1p
-149f
/x
);
52 if (hx
>= 0x42cff1b5) /* x <= -103.972084f */
57 /* argument reduction */
58 if (hx
> 0x3eb17218) { /* if |x| > 0.5 ln2 */
59 if (hx
> 0x3f851592) /* if |x| > 1.5 ln2 */
60 k
= invln2
*x
+ half
[sign
];
63 hi
= x
- k
*ln2hi
; /* k*ln2hi is exact here */
66 } else if (hx
> 0x39000000) { /* |x| > 2**-14 */
72 FORCE_EVAL(0x1p
127f
+ x
);
76 /* x is now in primary range */
78 c
= x
- xx
*(P1
+xx
*P2
);
79 y
= 1 + (x
*c
/(2-c
) - lo
+ hi
);