blob: 6824f991a38737456f37e14139f546baccada141 [file] [log] [blame]
Andrew Rossignolcf10b662016-09-07 14:17:47 -07001/* ef_exp.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#include "fdlibm.h"
17
18#ifdef __v810__
19#define const
20#endif
21
22#ifdef __STDC__
23static const float
24#else
25static float
26#endif
27one = 1.0,
28halF[2] = {0.5,-0.5,},
29huge = 1.0e+30,
30twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
31ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */
32 -6.9313812256e-01,}, /* 0xbf317180 */
33ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */
34 -9.0580006145e-06,}, /* 0xb717f7d1 */
35invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
36P1 = 1.6666667163e-01, /* 0x3e2aaaab */
37P2 = -2.7777778450e-03, /* 0xbb360b61 */
38P3 = 6.6137559770e-05, /* 0x388ab355 */
39P4 = -1.6533901999e-06, /* 0xb5ddea0e */
40P5 = 4.1381369442e-08; /* 0x3331bb4c */
41
42#ifdef __STDC__
43 float __ieee754_expf(float x) /* default IEEE double exp */
44#else
45 float __ieee754_expf(x) /* default IEEE double exp */
46 float x;
47#endif
48{
49 float y,hi,lo,c,t;
50 __int32_t k = 0,xsb,sx;
51 __uint32_t hx;
52
53 GET_FLOAT_WORD(sx,x);
54 xsb = (sx>>31)&1; /* sign bit of x */
55 hx = sx & 0x7fffffff; /* high word of |x| */
56
57 /* filter out non-finite argument */
58 if(FLT_UWORD_IS_NAN(hx))
59 return x+x; /* NaN */
60 if(FLT_UWORD_IS_INFINITE(hx))
61 return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
62 if(sx > FLT_UWORD_LOG_MAX)
63 return huge*huge; /* overflow */
64 if(sx < 0 && hx > FLT_UWORD_LOG_MIN)
65 return twom100*twom100; /* underflow */
66
67 /* argument reduction */
68 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
69 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
70 hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
71 } else {
72 k = invln2*x+halF[xsb];
73 t = k;
74 hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
75 lo = t*ln2LO[0];
76 }
77 x = hi - lo;
78 }
79 else if(hx < 0x31800000) { /* when |x|<2**-28 */
80 if(huge+x>one) return one+x;/* trigger inexact */
81 }
82
83 /* x is now in primary range */
84 t = x*x;
85 c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
86 if(k==0) return one-((x*c)/(c-(float)2.0)-x);
87 else y = one-((lo-(x*c)/((float)2.0-c))-hi);
88 if(k >= -125) {
89 __uint32_t hy;
90 GET_FLOAT_WORD(hy,y);
91 SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
92 return y;
93 } else {
94 __uint32_t hy;
95 GET_FLOAT_WORD(hy,y);
96 SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
97 return y*twom100;
98 }
99}