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/* e_expf.c -- float version of e_exp.c. |
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
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*/ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunPro, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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*/ |
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#include "math.h" |
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#include "math_private.h" |
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static const volatile float huge = 1.0e+30; |
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static const float |
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one = 1.0, |
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halF[2] = {0.5,-0.5,}, |
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twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */ |
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o_threshold= 8.8721679688e+01, /* 0x42b17180 */ |
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u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ |
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ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */ |
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-6.9313812256e-01,}, /* 0xbf317180 */ |
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ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */ |
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-9.0580006145e-06,}, /* 0xb717f7d1 */ |
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invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ |
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P1 = 1.6666667163e-01, /* 0x3e2aaaab */ |
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P2 = -2.7777778450e-03, /* 0xbb360b61 */ |
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P3 = 6.6137559770e-05, /* 0x388ab355 */ |
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P4 = -1.6533901999e-06, /* 0xb5ddea0e */ |
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P5 = 4.1381369442e-08; /* 0x3331bb4c */ |
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float |
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expf(float x) /* default IEEE double exp */ |
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{ |
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float y,hi,lo,c,t; |
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int32_t k,xsb; |
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u_int32_t hx; |
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GET_FLOAT_WORD(hx,x); |
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xsb = (hx>>31)&1; /* sign bit of x */ |
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hx &= 0x7fffffff; /* high word of |x| */ |
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k = 0; |
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/* filter out non-finite argument */ |
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✓✗ |
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if(hx >= 0x42b17218) { /* if |x|>=88.721... */ |
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✗✓ |
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if(hx>0x7f800000) |
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return x+x; /* NaN */ |
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✓✗ |
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if(hx==0x7f800000) |
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return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ |
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if(x > o_threshold) return huge*huge; /* overflow */ |
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if(x < u_threshold) return twom100*twom100; /* underflow */ |
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} |
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/* argument reduction */ |
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if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ |
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if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ |
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hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; |
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} else { |
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k = invln2*x+halF[xsb]; |
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t = k; |
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hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ |
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lo = t*ln2LO[0]; |
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} |
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x = hi - lo; |
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} |
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else if(hx < 0x31800000) { /* when |x|<2**-28 */ |
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if(huge+x>one) return one+x;/* trigger inexact */ |
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} |
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/* x is now in primary range */ |
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t = x*x; |
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c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); |
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if(k==0) return one-((x*c)/(c-(float)2.0)-x); |
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else y = one-((lo-(x*c)/((float)2.0-c))-hi); |
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if(k >= -125) { |
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u_int32_t hy; |
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GET_FLOAT_WORD(hy,y); |
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SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */ |
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return y; |
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} else { |
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u_int32_t hy; |
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GET_FLOAT_WORD(hy,y); |
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SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */ |
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return y*twom100; |
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} |
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} |
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DEF_STD(expf); |