1 /* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.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 * ====================================================
19 o_threshold
= 8.8721679688e+01, /* 0x42b17180 */
20 ln2_hi
= 6.9313812256e-01, /* 0x3f317180 */
21 ln2_lo
= 9.0580006145e-06, /* 0x3717f7d1 */
22 invln2
= 1.4426950216e+00, /* 0x3fb8aa3b */
24 * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
25 * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
26 * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
28 Q1
= -3.3333212137e-2, /* -0x888868.0p-28 */
29 Q2
= 1.5807170421e-3; /* 0xcf3010.0p-33 */
33 float_t y
,hi
,lo
,c
,t
,e
,hxs
,hfx
,r1
,twopk
;
34 union {float f
; uint32_t i
;} u
= {x
};
35 uint32_t hx
= u
.i
& 0x7fffffff;
36 int k
, sign
= u
.i
>> 31;
38 /* filter out huge and non-finite argument */
39 if (hx
>= 0x4195b844) { /* if |x|>=27*ln2 */
40 if (hx
> 0x7f800000) /* NaN */
44 if (x
> o_threshold
) {
50 /* argument reduction */
51 if (hx
> 0x3eb17218) { /* if |x| > 0.5 ln2 */
52 if (hx
< 0x3F851592) { /* and |x| < 1.5 ln2 */
63 k
= invln2
*x
+ (sign
? -0.5f
: 0.5f
);
65 hi
= x
- t
*ln2_hi
; /* t*ln2_hi is exact here */
70 } else if (hx
< 0x33000000) { /* when |x|<2**-25, return x */
77 /* x is now in primary range */
80 r1
= 1.0f
+hxs
*(Q1
+hxs
*Q2
);
82 e
= hxs
*((r1
-t
)/(6.0f
- x
*t
));
83 if (k
== 0) /* c is 0 */
87 /* exp(x) ~ 2^k (x_reduced - e + 1) */
89 return 0.5f
*(x
-e
) - 0.5f
;
92 return -2.0f
*(e
-(x
+0.5f
));
93 return 1.0f
+ 2.0f
*(x
-e
);
95 u
.i
= (0x7f+k
)<<23; /* 2^k */
97 if (k
< 0 || k
> 56) { /* suffice to return exp(x)-1 */
105 u
.i
= (0x7f-k
)<<23; /* 2^-k */
107 y
= (x
-e
+(1-u
.f
))*twopk
;
109 y
= (x
-(e
+u
.f
)+1)*twopk
;