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#ifndef lint
| 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#ifndef lint
|
17static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_expf.c 152947 2005-11-30 04:56:49Z bde $";
| 17static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_expf.c 175468 2008-01-18 22:19:04Z das $";
|
18#endif
19
20#include "math.h"
21#include "math_private.h"
22
23static const float
24one = 1.0,
25halF[2] = {0.5,-0.5,},
26huge = 1.0e+30,
| 18#endif
19
20#include "math.h"
21#include "math_private.h"
22
23static const float
24one = 1.0,
25halF[2] = {0.5,-0.5,},
26huge = 1.0e+30,
|
27twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
| |
28o_threshold= 8.8721679688e+01, /* 0x42b17180 */
29u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
30ln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */
31 -6.9314575195e-01,}, /* 0xbf317200 */
32ln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */
33 -1.4286067653e-06,}, /* 0xb5bfbe8e */
34invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
35P1 = 1.6666667163e-01, /* 0x3e2aaaab */
36P2 = -2.7777778450e-03, /* 0xbb360b61 */
37P3 = 6.6137559770e-05, /* 0x388ab355 */
38P4 = -1.6533901999e-06, /* 0xb5ddea0e */
39P5 = 4.1381369442e-08; /* 0x3331bb4c */
40
| 27o_threshold= 8.8721679688e+01, /* 0x42b17180 */
28u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
29ln2HI[2] ={ 6.9314575195e-01, /* 0x3f317200 */
30 -6.9314575195e-01,}, /* 0xbf317200 */
31ln2LO[2] ={ 1.4286067653e-06, /* 0x35bfbe8e */
32 -1.4286067653e-06,}, /* 0xb5bfbe8e */
33invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
34P1 = 1.6666667163e-01, /* 0x3e2aaaab */
35P2 = -2.7777778450e-03, /* 0xbb360b61 */
36P3 = 6.6137559770e-05, /* 0x388ab355 */
37P4 = -1.6533901999e-06, /* 0xb5ddea0e */
38P5 = 4.1381369442e-08; /* 0x3331bb4c */
39
|
| 40static volatile float twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */
41
|
41float
42__ieee754_expf(float x) /* default IEEE double exp */
43{
44 float y,hi=0.0,lo=0.0,c,t;
45 int32_t k=0,xsb;
46 u_int32_t hx;
47
48 GET_FLOAT_WORD(hx,x);
49 xsb = (hx>>31)&1; /* sign bit of x */
50 hx &= 0x7fffffff; /* high word of |x| */
51
52 /* filter out non-finite argument */
53 if(hx >= 0x42b17218) { /* if |x|>=88.721... */
54 if(hx>0x7f800000)
55 return x+x; /* NaN */
56 if(hx==0x7f800000)
57 return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
58 if(x > o_threshold) return huge*huge; /* overflow */
59 if(x < u_threshold) return twom100*twom100; /* underflow */
60 }
61
62 /* argument reduction */
63 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
64 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
65 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
66 } else {
67 k = invln2*x+halF[xsb];
68 t = k;
69 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
70 lo = t*ln2LO[0];
71 }
72 x = hi - lo;
73 }
74 else if(hx < 0x31800000) { /* when |x|<2**-28 */
75 if(huge+x>one) return one+x;/* trigger inexact */
76 }
77 else k = 0;
78
79 /* x is now in primary range */
80 t = x*x;
81 c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
82 if(k==0) return one-((x*c)/(c-(float)2.0)-x);
83 else y = one-((lo-(x*c)/((float)2.0-c))-hi);
84 if(k >= -125) {
85 u_int32_t hy;
86 GET_FLOAT_WORD(hy,y);
87 SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
88 return y;
89 } else {
90 u_int32_t hy;
91 GET_FLOAT_WORD(hy,y);
92 SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
93 return y*twom100;
94 }
95}
| 42float
43__ieee754_expf(float x) /* default IEEE double exp */
44{
45 float y,hi=0.0,lo=0.0,c,t;
46 int32_t k=0,xsb;
47 u_int32_t hx;
48
49 GET_FLOAT_WORD(hx,x);
50 xsb = (hx>>31)&1; /* sign bit of x */
51 hx &= 0x7fffffff; /* high word of |x| */
52
53 /* filter out non-finite argument */
54 if(hx >= 0x42b17218) { /* if |x|>=88.721... */
55 if(hx>0x7f800000)
56 return x+x; /* NaN */
57 if(hx==0x7f800000)
58 return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
59 if(x > o_threshold) return huge*huge; /* overflow */
60 if(x < u_threshold) return twom100*twom100; /* underflow */
61 }
62
63 /* argument reduction */
64 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
65 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
66 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
67 } else {
68 k = invln2*x+halF[xsb];
69 t = k;
70 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
71 lo = t*ln2LO[0];
72 }
73 x = hi - lo;
74 }
75 else if(hx < 0x31800000) { /* when |x|<2**-28 */
76 if(huge+x>one) return one+x;/* trigger inexact */
77 }
78 else k = 0;
79
80 /* x is now in primary range */
81 t = x*x;
82 c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
83 if(k==0) return one-((x*c)/(c-(float)2.0)-x);
84 else y = one-((lo-(x*c)/((float)2.0-c))-hi);
85 if(k >= -125) {
86 u_int32_t hy;
87 GET_FLOAT_WORD(hy,y);
88 SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
89 return y;
90 } else {
91 u_int32_t hy;
92 GET_FLOAT_WORD(hy,y);
93 SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
94 return y*twom100;
95 }
96}
|