e_expf.c revision 352835 
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#include <sys/cdefs.h>
17__FBSDID("$FreeBSD: stable/11/lib/msun/src/e_expf.c 352835 2019-09-28 08:57:29Z dim $");
18
19#include <float.h>
20
21#include "math.h"
22#include "math_private.h"
23
24static const float
25one	= 1.0,
26halF[2]	= {0.5,-0.5,},
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 */
34/*
35 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
36 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
37 */
38P1 =  1.6666625440e-1,		/*  0xaaaa8f.0p-26 */
39P2 = -2.7667332906e-3;		/* -0xb55215.0p-32 */
40
41static volatile float
42huge	= 1.0e+30,
43twom100 = 7.8886090522e-31;      /* 2**-100=0x0d800000 */
44
45float
46__ieee754_expf(float x)
47{
48	float y,hi=0.0,lo=0.0,c,t,twopk;
49	int32_t k=0,xsb;
50	u_int32_t hx;
51
52	GET_FLOAT_WORD(hx,x);
53	xsb = (hx>>31)&1;		/* sign bit of x */
54	hx &= 0x7fffffff;		/* high word of |x| */
55
56    /* filter out non-finite argument */
57	if(hx >= 0x42b17218) {			/* if |x|>=88.721... */
58	    if(hx>0x7f800000)
59		 return x+x;	 		/* NaN */
60            if(hx==0x7f800000)
61		return (xsb==0)? x:0.0;		/* exp(+-inf)={inf,0} */
62	    if(x > o_threshold) return huge*huge; /* overflow */
63	    if(x < u_threshold) return twom100*twom100; /* underflow */
64	}
65
66    /* argument reduction */
67	if(hx > 0x3eb17218) {		/* if  |x| > 0.5 ln2 */
68	    if(hx < 0x3F851592) {	/* and |x| < 1.5 ln2 */
69		hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
70	    } else {
71		k  = invln2*x+halF[xsb];
72		t  = k;
73		hi = x - t*ln2HI[0];	/* t*ln2HI is exact here */
74		lo = t*ln2LO[0];
75	    }
76	    STRICT_ASSIGN(float, x, hi - lo);
77	}
78	else if(hx < 0x39000000)  {	/* when |x|<2**-14 */
79	    if(huge+x>one) return one+x;/* trigger inexact */
80	}
81	else k = 0;
82
83    /* x is now in primary range */
84	t  = x*x;
85	if(k >= -125)
86	    SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+k))<<23);
87	else
88	    SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+(k+100)))<<23);
89	c  = x - t*(P1+t*P2);
90	if(k==0) 	return one-((x*c)/(c-(float)2.0)-x);
91	else 		y = one-((lo-(x*c)/((float)2.0-c))-hi);
92	if(k >= -125) {
93	    if(k==128) return y*2.0F*0x1p127F;
94	    return y*twopk;
95	} else {
96	    return y*twopk*twom100;
97	}
98}
99