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authorRich Felker <dalias@aerifal.cx>2011-02-12 00:22:29 -0500
committerRich Felker <dalias@aerifal.cx>2011-02-12 00:22:29 -0500
commit0b44a0315b47dd8eced9f3b7f31580cf14bbfc01 (patch)
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initial check-in, version 0.5.0v0.5.0
Diffstat (limited to 'src/math/e_expf.c')
-rw-r--r--src/math/e_expf.c91
1 files changed, 91 insertions, 0 deletions
diff --git a/src/math/e_expf.c b/src/math/e_expf.c
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+/* 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 <math.h>
+#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;
+ }
+}