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 142181 2005-02-21 17:44:57Z das $";
| 17static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_expf.c 142369 2005-02-24 06:32:13Z 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,
27twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
28o_threshold= 8.8721679688e+01, /* 0x42b17180 */
29u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
| 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] ={ 6.9313812256e-01, /* 0x3f317180 */
31 -6.9313812256e-01,}, /* 0xbf317180 */
32ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */
33 -9.0580006145e-06,}, /* 0xb717f7d1 */
|
30invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
31P1 = 1.6666667163e-01, /* 0x3e2aaaab */
32P2 = -2.7777778450e-03, /* 0xbb360b61 */
33P3 = 6.6137559770e-05, /* 0x388ab355 */
34P4 = -1.6533901999e-06, /* 0xb5ddea0e */
35P5 = 4.1381369442e-08; /* 0x3331bb4c */
| 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 */
|
36double ln2[2] = { 6.93147180369123816490e-01, -6.93147180369123816490e-01 };
| |
37
38float
| 40
41float
|
39__ieee754_expf(float x) /* IEEE float exp */
| 42__ieee754_expf(float x) /* default IEEE double exp */
|
40{
| 43{
|
41 float y,c,t;
| 44 float y,hi=0.0,lo=0.0,c,t;
|
42 int32_t k=0,xsb;
43 u_int32_t hx;
44
45 GET_FLOAT_WORD(hx,x);
46 xsb = (hx>>31)&1; /* sign bit of x */
| 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 */
|
47 hx &= 0x7fffffff; /* |x| */
| 50 hx &= 0x7fffffff; /* high word of |x| */
|
48
49 /* filter out non-finite argument */
50 if(hx >= 0x42b17218) { /* if |x|>=88.721... */
51 if(hx>0x7f800000)
52 return x+x; /* NaN */
53 if(hx==0x7f800000)
54 return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
55 if(x > o_threshold) return huge*huge; /* overflow */
56 if(x < u_threshold) return twom100*twom100; /* underflow */
57 }
58
59 /* argument reduction */
60 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
61 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
| 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 */
|
62 x = x-ln2[xsb]; k = 1-xsb-xsb;
| 65 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
|
63 } else {
64 k = invln2*x+halF[xsb];
65 t = k;
| 66 } else {
67 k = invln2*x+halF[xsb];
68 t = k;
|
66 x = x - t*ln2[0];
| 69 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
70 lo = t*ln2LO[0];
|
67 }
| 71 }
|
| 72 x = hi - lo;
|
68 }
69 else if(hx < 0x31800000) { /* when |x|<2**-28 */
70 if(huge+x>one) return one+x;/* trigger inexact */
71 }
72 else k = 0;
73
74 /* x is now in primary range */
75 t = x*x;
76 c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
| 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))));
|
77 y = one-(((double)x*c)/(c-2.0)-x);
78 if(k==0) return y;
| 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);
|
79 if(k >= -125) {
80 u_int32_t hy;
81 GET_FLOAT_WORD(hy,y);
82 SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
83 return y;
84 } else {
85 u_int32_t hy;
86 GET_FLOAT_WORD(hy,y);
87 SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
88 return y*twom100;
89 }
90}
| 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}
|