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path: root/src/math/e_expf.c
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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 /* e_expf.c -- float version of e_exp.c. * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== */ #include #include "math_private.h" static const float one = 1.0, halF[2] = {0.5,-0.5,}, huge = 1.0e+30, twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */ o_threshold= 8.8721679688e+01, /* 0x42b17180 */ u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */ -6.9313812256e-01,}, /* 0xbf317180 */ ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */ -9.0580006145e-06,}, /* 0xb717f7d1 */ invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ P1 = 1.6666667163e-01, /* 0x3e2aaaab */ P2 = -2.7777778450e-03, /* 0xbb360b61 */ P3 = 6.6137559770e-05, /* 0x388ab355 */ P4 = -1.6533901999e-06, /* 0xb5ddea0e */ P5 = 4.1381369442e-08; /* 0x3331bb4c */ float expf(float x) /* default IEEE double exp */ { float y,hi=0.0,lo=0.0,c,t; int32_t k=0,xsb; uint32_t hx; GET_FLOAT_WORD(hx,x); xsb = (hx>>31)&1; /* sign bit of x */ hx &= 0x7fffffff; /* high word of |x| */ /* filter out non-finite argument */ if(hx >= 0x42b17218) { /* if |x|>=88.721... */ if(hx>0x7f800000) return x+x; /* NaN */ if(hx==0x7f800000) return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ if(x > o_threshold) return huge*huge; /* overflow */ if(x < u_threshold) return twom100*twom100; /* underflow */ } /* argument reduction */ if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; } else { k = invln2*x+halF[xsb]; t = k; hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ lo = t*ln2LO[0]; } x = hi - lo; } else if(hx < 0x31800000) { /* when |x|<2**-28 */ if(huge+x>one) return one+x;/* trigger inexact */ } else k = 0; /* x is now in primary range */ t = x*x; c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); if(k==0) return one-((x*c)/(c-(float)2.0)-x); else y = one-((lo-(x*c)/((float)2.0-c))-hi); if(k >= -125) { uint32_t hy; GET_FLOAT_WORD(hy,y); SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */ return y; } else { uint32_t hy; GET_FLOAT_WORD(hy,y); SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */ return y*twom100; } }