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authorEric Andersen <andersen@codepoet.org>2001-05-10 00:40:28 +0000
committerEric Andersen <andersen@codepoet.org>2001-05-10 00:40:28 +0000
commit1077fa4d772832f77a677ce7fb7c2d513b959e3f (patch)
tree579bee13fb0b58d2800206366ec2caecbb15f3fc /libm/ldouble/powil.c
parent22358dd7ce7bb49792204b698f01a6f69b9c8e08 (diff)
uClibc now has a math library. muahahahaha!
-Erik
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+/* powil.c
+ *
+ * Real raised to integer power, long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, powil();
+ * int n;
+ *
+ * y = powil( x, n );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns argument x raised to the nth power.
+ * The routine efficiently decomposes n as a sum of powers of
+ * two. The desired power is a product of two-to-the-kth
+ * powers of x. Thus to compute the 32767 power of x requires
+ * 28 multiplications instead of 32767 multiplications.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ *
+ * Relative error:
+ * arithmetic x domain n domain # trials peak rms
+ * IEEE .001,1000 -1022,1023 50000 4.3e-17 7.8e-18
+ * IEEE 1,2 -1022,1023 20000 3.9e-17 7.6e-18
+ * IEEE .99,1.01 0,8700 10000 3.6e-16 7.2e-17
+ *
+ * Returns MAXNUM on overflow, zero on underflow.
+ *
+ */
+
+/* powil.c */
+
+/*
+Cephes Math Library Release 2.2: December, 1990
+Copyright 1984, 1990 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+extern long double MAXNUML, MAXLOGL, MINLOGL;
+extern long double LOGE2L;
+#ifdef ANSIPROT
+extern long double frexpl ( long double, int * );
+#else
+long double frexpl();
+#endif
+
+long double powil( x, nn )
+long double x;
+int nn;
+{
+long double w, y;
+long double s;
+int n, e, sign, asign, lx;
+
+if( x == 0.0L )
+ {
+ if( nn == 0 )
+ return( 1.0L );
+ else if( nn < 0 )
+ return( MAXNUML );
+ else
+ return( 0.0L );
+ }
+
+if( nn == 0 )
+ return( 1.0L );
+
+
+if( x < 0.0L )
+ {
+ asign = -1;
+ x = -x;
+ }
+else
+ asign = 0;
+
+
+if( nn < 0 )
+ {
+ sign = -1;
+ n = -nn;
+ }
+else
+ {
+ sign = 1;
+ n = nn;
+ }
+
+/* Overflow detection */
+
+/* Calculate approximate logarithm of answer */
+s = x;
+s = frexpl( s, &lx );
+e = (lx - 1)*n;
+if( (e == 0) || (e > 64) || (e < -64) )
+ {
+ s = (s - 7.0710678118654752e-1L) / (s + 7.0710678118654752e-1L);
+ s = (2.9142135623730950L * s - 0.5L + lx) * nn * LOGE2L;
+ }
+else
+ {
+ s = LOGE2L * e;
+ }
+
+if( s > MAXLOGL )
+ {
+ mtherr( "powil", OVERFLOW );
+ y = MAXNUML;
+ goto done;
+ }
+
+if( s < MINLOGL )
+ {
+ mtherr( "powil", UNDERFLOW );
+ return(0.0L);
+ }
+/* Handle tiny denormal answer, but with less accuracy
+ * since roundoff error in 1.0/x will be amplified.
+ * The precise demarcation should be the gradual underflow threshold.
+ */
+if( s < (-MAXLOGL+2.0L) )
+ {
+ x = 1.0L/x;
+ sign = -sign;
+ }
+
+/* First bit of the power */
+if( n & 1 )
+ y = x;
+
+else
+ {
+ y = 1.0L;
+ asign = 0;
+ }
+
+w = x;
+n >>= 1;
+while( n )
+ {
+ w = w * w; /* arg to the 2-to-the-kth power */
+ if( n & 1 ) /* if that bit is set, then include in product */
+ y *= w;
+ n >>= 1;
+ }
+
+
+done:
+
+if( asign )
+ y = -y; /* odd power of negative number */
+if( sign < 0 )
+ y = 1.0L/y;
+return(y);
+}