| 1 | /* e_expf.c -- float version of e_exp.c.
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| 2 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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| 3 | */
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| 4 |
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| 5 | /*
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| 6 | * ====================================================
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| 7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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| 8 | *
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| 9 | * Developed at SunPro, a Sun Microsystems, Inc. business.
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| 10 | * Permission to use, copy, modify, and distribute this
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| 11 | * software is freely granted, provided that this notice
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| 12 | * is preserved.
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| 13 | * ====================================================
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| 14 | */
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| 15 |
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| 16 | #ifndef lint
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| 17 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_expf.c,v 1.9 2005/02/24 06:32:13 das Exp $";
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| 18 | #endif
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| 19 |
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| 20 | #include "math.h"
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| 21 | #include "math_private.h"
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| 22 |
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| 23 | static const float
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| 24 | one = 1.0,
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| 25 | halF[2] = {0.5,-0.5,},
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| 26 | huge = 1.0e+30,
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| 27 | twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
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| 28 | o_threshold= 8.8721679688e+01, /* 0x42b17180 */
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| 29 | u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
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| 30 | ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */
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| 31 | -6.9313812256e-01,}, /* 0xbf317180 */
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| 32 | ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */
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| 33 | -9.0580006145e-06,}, /* 0xb717f7d1 */
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| 34 | invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
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| 35 | P1 = 1.6666667163e-01, /* 0x3e2aaaab */
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| 36 | P2 = -2.7777778450e-03, /* 0xbb360b61 */
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| 37 | P3 = 6.6137559770e-05, /* 0x388ab355 */
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| 38 | P4 = -1.6533901999e-06, /* 0xb5ddea0e */
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| 39 | P5 = 4.1381369442e-08; /* 0x3331bb4c */
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| 40 |
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| 41 | float
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| 42 | __ieee754_expf(float x) /* default IEEE double exp */
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| 43 | {
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| 44 | float y,hi=0.0,lo=0.0,c,t;
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| 45 | int32_t k=0,xsb;
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| 46 | u_int32_t hx;
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| 47 |
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| 48 | GET_FLOAT_WORD(hx,x);
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| 49 | xsb = (hx>>31)&1; /* sign bit of x */
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| 50 | hx &= 0x7fffffff; /* high word of |x| */
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| 51 |
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| 52 | /* filter out non-finite argument */
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| 53 | if(hx >= 0x42b17218) { /* if |x|>=88.721... */
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| 54 | if(hx>0x7f800000)
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| 55 | return x+x; /* NaN */
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| 56 | if(hx==0x7f800000)
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| 57 | return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
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| 58 | if(x > o_threshold) return huge*huge; /* overflow */
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| 59 | if(x < u_threshold) return twom100*twom100; /* underflow */
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| 60 | }
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| 61 |
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| 62 | /* argument reduction */
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| 63 | if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
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| 64 | if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
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| 65 | hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
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| 66 | } else {
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| 67 | k = invln2*x+halF[xsb];
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| 68 | t = k;
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| 69 | hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
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| 70 | lo = t*ln2LO[0];
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| 71 | }
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| 72 | x = hi - lo;
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| 73 | }
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| 74 | else if(hx < 0x31800000) { /* when |x|<2**-28 */
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| 75 | if(huge+x>one) return one+x;/* trigger inexact */
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| 76 | }
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| 77 | else k = 0;
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| 78 |
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| 79 | /* x is now in primary range */
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| 80 | t = x*x;
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| 81 | c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
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| 82 | if(k==0) return one-((x*c)/(c-(float)2.0)-x);
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| 83 | else y = one-((lo-(x*c)/((float)2.0-c))-hi);
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| 84 | if(k >= -125) {
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| 85 | u_int32_t hy;
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| 86 | GET_FLOAT_WORD(hy,y);
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| 87 | SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
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| 88 | return y;
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| 89 | } else {
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| 90 | u_int32_t hy;
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| 91 | GET_FLOAT_WORD(hy,y);
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| 92 | SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
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| 93 | return y*twom100;
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| 94 | }
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| 95 | }
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