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      1 /* e_expf.c -- float version of e_exp.c.
      2  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian (at) 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 #if defined(LIBM_SCCS) && !defined(lint)
     18 __RCSID("$NetBSD: e_expf.c,v 1.9 2002/05/26 22:01:49 wiz Exp $");
     19 #endif
     20 
     21 #include "math.h"
     22 #include "math_private.h"
     23 
     24 static const float huge = 1.0e+30;
     25 
     26 static const float
     27 one	= 1.0,
     28 halF[2]	= {0.5,-0.5,},
     29 twom100 = 7.8886090522e-31,      /* 2**-100=0x0d800000 */
     30 o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
     31 u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
     32 ln2HI[2]   ={ 6.9313812256e-01,		/* 0x3f317180 */
     33 	     -6.9313812256e-01,},	/* 0xbf317180 */
     34 ln2LO[2]   ={ 9.0580006145e-06,  	/* 0x3717f7d1 */
     35 	     -9.0580006145e-06,},	/* 0xb717f7d1 */
     36 invln2 =  1.4426950216e+00, 		/* 0x3fb8aa3b */
     37 P1   =  1.6666667163e-01, /* 0x3e2aaaab */
     38 P2   = -2.7777778450e-03, /* 0xbb360b61 */
     39 P3   =  6.6137559770e-05, /* 0x388ab355 */
     40 P4   = -1.6533901999e-06, /* 0xb5ddea0e */
     41 P5   =  4.1381369442e-08; /* 0x3331bb4c */
     42 
     43 float
     44 __ieee754_expf(float x)	/* default IEEE double exp */
     45 {
     46 	float y,hi,lo,c,t;
     47 	int32_t k,xsb;
     48 	u_int32_t hx;
     49 
     50 	hi = lo = 0;
     51 	k = 0;
     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 	    x  = hi - lo;
     77 	}
     78 	else if(hx < 0x31800000)  {	/* when |x|<2**-28 */
     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 	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 	    u_int32_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 	    u_int32_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 }
    100