1*05a0b428SJohn Marino /* e_expf.c -- float version of e_exp.c.
2*05a0b428SJohn Marino * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3*05a0b428SJohn Marino */
4*05a0b428SJohn Marino
5*05a0b428SJohn Marino /*
6*05a0b428SJohn Marino * ====================================================
7*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8*05a0b428SJohn Marino *
9*05a0b428SJohn Marino * Developed at SunPro, a Sun Microsystems, Inc. business.
10*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
11*05a0b428SJohn Marino * software is freely granted, provided that this notice
12*05a0b428SJohn Marino * is preserved.
13*05a0b428SJohn Marino * ====================================================
14*05a0b428SJohn Marino */
15*05a0b428SJohn Marino
16*05a0b428SJohn Marino #include "math.h"
17*05a0b428SJohn Marino #include "math_private.h"
18*05a0b428SJohn Marino
19*05a0b428SJohn Marino static const volatile float huge = 1.0e+30;
20*05a0b428SJohn Marino
21*05a0b428SJohn Marino static const float
22*05a0b428SJohn Marino one = 1.0,
23*05a0b428SJohn Marino halF[2] = {0.5,-0.5,},
24*05a0b428SJohn Marino twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
25*05a0b428SJohn Marino o_threshold= 8.8721679688e+01, /* 0x42b17180 */
26*05a0b428SJohn Marino u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
27*05a0b428SJohn Marino ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */
28*05a0b428SJohn Marino -6.9313812256e-01,}, /* 0xbf317180 */
29*05a0b428SJohn Marino ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */
30*05a0b428SJohn Marino -9.0580006145e-06,}, /* 0xb717f7d1 */
31*05a0b428SJohn Marino invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
32*05a0b428SJohn Marino P1 = 1.6666667163e-01, /* 0x3e2aaaab */
33*05a0b428SJohn Marino P2 = -2.7777778450e-03, /* 0xbb360b61 */
34*05a0b428SJohn Marino P3 = 6.6137559770e-05, /* 0x388ab355 */
35*05a0b428SJohn Marino P4 = -1.6533901999e-06, /* 0xb5ddea0e */
36*05a0b428SJohn Marino P5 = 4.1381369442e-08; /* 0x3331bb4c */
37*05a0b428SJohn Marino
38*05a0b428SJohn Marino float
expf(float x)39*05a0b428SJohn Marino expf(float x) /* default IEEE double exp */
40*05a0b428SJohn Marino {
41*05a0b428SJohn Marino float y,hi,lo,c,t;
42*05a0b428SJohn Marino int32_t k,xsb;
43*05a0b428SJohn Marino u_int32_t hx;
44*05a0b428SJohn Marino
45*05a0b428SJohn Marino GET_FLOAT_WORD(hx,x);
46*05a0b428SJohn Marino xsb = (hx>>31)&1; /* sign bit of x */
47*05a0b428SJohn Marino hx &= 0x7fffffff; /* high word of |x| */
48*05a0b428SJohn Marino k = 0;
49*05a0b428SJohn Marino
50*05a0b428SJohn Marino /* filter out non-finite argument */
51*05a0b428SJohn Marino if(hx >= 0x42b17218) { /* if |x|>=88.721... */
52*05a0b428SJohn Marino if(hx>0x7f800000)
53*05a0b428SJohn Marino return x+x; /* NaN */
54*05a0b428SJohn Marino if(hx==0x7f800000)
55*05a0b428SJohn Marino return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
56*05a0b428SJohn Marino if(x > o_threshold) return huge*huge; /* overflow */
57*05a0b428SJohn Marino if(x < u_threshold) return twom100*twom100; /* underflow */
58*05a0b428SJohn Marino }
59*05a0b428SJohn Marino
60*05a0b428SJohn Marino /* argument reduction */
61*05a0b428SJohn Marino if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
62*05a0b428SJohn Marino if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
63*05a0b428SJohn Marino hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
64*05a0b428SJohn Marino } else {
65*05a0b428SJohn Marino k = invln2*x+halF[xsb];
66*05a0b428SJohn Marino t = k;
67*05a0b428SJohn Marino hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
68*05a0b428SJohn Marino lo = t*ln2LO[0];
69*05a0b428SJohn Marino }
70*05a0b428SJohn Marino x = hi - lo;
71*05a0b428SJohn Marino }
72*05a0b428SJohn Marino else if(hx < 0x31800000) { /* when |x|<2**-28 */
73*05a0b428SJohn Marino if(huge+x>one) return one+x;/* trigger inexact */
74*05a0b428SJohn Marino }
75*05a0b428SJohn Marino
76*05a0b428SJohn Marino /* x is now in primary range */
77*05a0b428SJohn Marino t = x*x;
78*05a0b428SJohn Marino c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
79*05a0b428SJohn Marino if(k==0) return one-((x*c)/(c-(float)2.0)-x);
80*05a0b428SJohn Marino else y = one-((lo-(x*c)/((float)2.0-c))-hi);
81*05a0b428SJohn Marino if(k >= -125) {
82*05a0b428SJohn Marino u_int32_t hy;
83*05a0b428SJohn Marino GET_FLOAT_WORD(hy,y);
84*05a0b428SJohn Marino SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
85*05a0b428SJohn Marino return y;
86*05a0b428SJohn Marino } else {
87*05a0b428SJohn Marino u_int32_t hy;
88*05a0b428SJohn Marino GET_FLOAT_WORD(hy,y);
89*05a0b428SJohn Marino SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
90*05a0b428SJohn Marino return y*twom100;
91*05a0b428SJohn Marino }
92*05a0b428SJohn Marino }
93