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Annotation of src/lib/libm/src/e_expf.c, Revision 1.9

1.1       jtc         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
1.8       simonb     11:  * software is freely granted, provided that this notice
1.1       jtc        12:  * is preserved.
                     13:  * ====================================================
                     14:  */
                     15:
1.7       lukem      16: #include <sys/cdefs.h>
1.3       jtc        17: #if defined(LIBM_SCCS) && !defined(lint)
1.9     ! wiz        18: __RCSID("$NetBSD: e_expf.c,v 1.8 1999/07/02 15:37:39 simonb Exp $");
1.1       jtc        19: #endif
                     20:
                     21: #include "math.h"
                     22: #include "math_private.h"
                     23:
1.6       phil       24: static const float huge = 1.0e+30;
1.4       jtc        25:
1.1       jtc        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:
1.9     ! wiz        43: float
        !            44: __ieee754_expf(float x)        /* default IEEE double exp */
1.1       jtc        45: {
                     46:        float y,hi,lo,c,t;
1.2       jtc        47:        int32_t k,xsb;
                     48:        u_int32_t hx;
1.1       jtc        49:
1.7       lukem      50:        hi = lo = 0;
                     51:        k = 0;
1.1       jtc        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 */
1.8       simonb     67:        if(hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
1.1       jtc        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;
1.8       simonb     77:        }
1.1       jtc        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))));
1.8       simonb     86:        if(k==0)        return one-((x*c)/(c-(float)2.0)-x);
1.1       jtc        87:        else            y = one-((lo-(x*c)/((float)2.0-c))-hi);
                     88:        if(k >= -125) {
1.2       jtc        89:            u_int32_t hy;
1.1       jtc        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 {
1.2       jtc        94:            u_int32_t hy;
1.1       jtc        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: }