IEEE double log2 implementation.
authordrepper <drepper>
Wed, 6 Jun 2001 12:48:53 +0000 (12:48 +0000)
committerdrepper <drepper>
Wed, 6 Jun 2001 12:48:53 +0000 (12:48 +0000)
sysdeps/ieee754/dbl-64/e_log2.c [new file with mode: 0644]

diff --git a/sysdeps/ieee754/dbl-64/e_log2.c b/sysdeps/ieee754/dbl-64/e_log2.c
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+/* Adapted for log2 by Ulrich Drepper <drepper@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.
+ * ====================================================
+ */
+
+/* __ieee754_log2(x)
+ * Return the logarithm to base 2 of x
+ *
+ * Method :
+ *   1. Argument Reduction: find k and f such that
+ *                     x = 2^k * (1+f),
+ *        where  sqrt(2)/2 < 1+f < sqrt(2) .
+ *
+ *   2. Approximation of log(1+f).
+ *     Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
+ *              = 2s + 2/3 s**3 + 2/5 s**5 + .....,
+ *              = 2s + s*R
+ *      We use a special Reme algorithm on [0,0.1716] to generate
+ *     a polynomial of degree 14 to approximate R The maximum error
+ *     of this polynomial approximation is bounded by 2**-58.45. In
+ *     other words,
+ *                     2      4      6      8      10      12      14
+ *         R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s
+ *     (the values of Lg1 to Lg7 are listed in the program)
+ *     and
+ *         |      2          14          |     -58.45
+ *         | Lg1*s +...+Lg7*s    -  R(z) | <= 2
+ *         |                             |
+ *     Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
+ *     In order to guarantee error in log below 1ulp, we compute log
+ *     by
+ *             log(1+f) = f - s*(f - R)        (if f is not too large)
+ *             log(1+f) = f - (hfsq - s*(hfsq+R)).     (better accuracy)
+ *
+ *     3. Finally,  log(x) = k + log(1+f).
+ *                         = k+(f-(hfsq-(s*(hfsq+R))))
+ *
+ * Special cases:
+ *     log2(x) is NaN with signal if x < 0 (including -INF) ;
+ *     log2(+INF) is +INF; log(0) is -INF with signal;
+ *     log2(NaN) is that NaN with no signal.
+ *
+ * Constants:
+ * The hexadecimal values are the intended ones for the following
+ * constants. The decimal values may be used, provided that the
+ * compiler will convert from decimal to binary accurately enough
+ * to produce the hexadecimal values shown.
+ */
+
+#include "math.h"
+#include "math_private.h"
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+ln2 = 0.69314718055994530942,
+two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
+Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
+Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
+Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
+Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
+Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
+Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
+Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
+
+#ifdef __STDC__
+static const double zero   =  0.0;
+#else
+static double zero   =  0.0;
+#endif
+
+#ifdef __STDC__
+       double __ieee754_log2(double x)
+#else
+       double __ieee754_log2(x)
+       double x;
+#endif
+{
+       double hfsq,f,s,z,R,w,t1,t2,dk;
+       int32_t k,hx,i,j;
+       u_int32_t lx;
+
+       EXTRACT_WORDS(hx,lx,x);
+
+       k=0;
+       if (hx < 0x00100000) {                  /* x < 2**-1022  */
+           if (((hx&0x7fffffff)|lx)==0)
+               return -two54/(x-x);            /* log(+-0)=-inf */
+           if (hx<0) return (x-x)/(x-x);       /* log(-#) = NaN */
+           k -= 54; x *= two54; /* subnormal number, scale up x */
+           GET_HIGH_WORD(hx,x);
+       }
+       if (hx >= 0x7ff00000) return x+x;
+       k += (hx>>20)-1023;
+       hx &= 0x000fffff;
+       i = (hx+0x95f64)&0x100000;
+       SET_HIGH_WORD(x,hx|(i^0x3ff00000));     /* normalize x or x/2 */
+       k += (i>>20);
+       dk = (double) k;
+       f = x-1.0;
+       if((0x000fffff&(2+hx))<3) {     /* |f| < 2**-20 */
+           if(f==zero) return dk;
+           R = f*f*(0.5-0.33333333333333333*f);
+           return dk-(R-f)/ln2;
+       }
+       s = f/(2.0+f);
+       z = s*s;
+       i = hx-0x6147a;
+       w = z*z;
+       j = 0x6b851-hx;
+       t1= w*(Lg2+w*(Lg4+w*Lg6));
+       t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
+       i |= j;
+       R = t2+t1;
+       if(i>0) {
+           hfsq=0.5*f*f;
+           return dk-((hfsq-(s*(hfsq+R)))-f)/ln2;
+       } else {
+           return dk-((s*(f-R))-f)/ln2;
+       }
+}