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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 __FBSDID("$FreeBSD$");
     18 
     19 #include <float.h>
     20 
     21 #include "math.h"
     22 #include "math_private.h"
     23 
     24 static const float
     25 one	= 1.0,
     26 halF[2]	= {0.5,-0.5,},
     27 o_threshold=  8.8721679688e+01,  /* 0x42b17180 */
     28 u_threshold= -1.0397208405e+02,  /* 0xc2cff1b5 */
     29 ln2HI[2]   ={ 6.9314575195e-01,		/* 0x3f317200 */
     30 	     -6.9314575195e-01,},	/* 0xbf317200 */
     31 ln2LO[2]   ={ 1.4286067653e-06,  	/* 0x35bfbe8e */
     32 	     -1.4286067653e-06,},	/* 0xb5bfbe8e */
     33 invln2 =  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  */
     38 P1 =  1.6666625440e-1,		/*  0xaaaa8f.0p-26 */
     39 P2 = -2.7667332906e-3;		/* -0xb55215.0p-32 */
     40 
     41 static volatile float
     42 huge	= 1.0e+30,
     43 twom100 = 7.8886090522e-31;      /* 2**-100=0x0d800000 */
     44 
     45 float
     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,0x3f800000+(k<<23));
     87 	else
     88 	    SET_FLOAT_WORD(twopk,0x3f800000+((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