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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/float/igamf.c
parent22358dd7ce7bb49792204b698f01a6f69b9c8e08 (diff)
uClibc now has a math library. muahahahaha!
-Erik
Diffstat (limited to 'libm/float/igamf.c')
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+/* igamf.c
+ *
+ * Incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, x, y, igamf();
+ *
+ * y = igamf( a, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ * x
+ * -
+ * 1 | | -t a-1
+ * igam(a,x) = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * 0
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 20000 7.8e-6 5.9e-7
+ *
+ */
+ /* igamcf()
+ *
+ * Complemented incomplete gamma integral
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * float a, x, y, igamcf();
+ *
+ * y = igamcf( a, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * The function is defined by
+ *
+ *
+ * igamc(a,x) = 1 - igam(a,x)
+ *
+ * inf.
+ * -
+ * 1 | | -t a-1
+ * = ----- | e t dt.
+ * - | |
+ * | (a) -
+ * x
+ *
+ *
+ * In this implementation both arguments must be positive.
+ * The integral is evaluated by either a power series or
+ * continued fraction expansion, depending on the relative
+ * values of a and x.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE 0,30 30000 7.8e-6 5.9e-7
+ *
+ */
+
+/*
+Cephes Math Library Release 2.2: June, 1992
+Copyright 1985, 1987, 1992 by Stephen L. Moshier
+Direct inquiries to 30 Frost Street, Cambridge, MA 02140
+*/
+
+#include <math.h>
+
+/* BIG = 1/MACHEPF */
+#define BIG 16777216.
+
+extern float MACHEPF, MAXLOGF;
+
+#ifdef ANSIC
+float lgamf(float), expf(float), logf(float), igamf(float, float);
+#else
+float lgamf(), expf(), logf(), igamf();
+#endif
+
+#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
+
+
+
+float igamcf( float aa, float xx )
+{
+float a, x, ans, c, yc, ax, y, z;
+float pk, pkm1, pkm2, qk, qkm1, qkm2;
+float r, t;
+static float big = BIG;
+
+a = aa;
+x = xx;
+if( (x <= 0) || ( a <= 0) )
+ return( 1.0 );
+
+if( (x < 1.0) || (x < a) )
+ return( 1.0 - igamf(a,x) );
+
+ax = a * logf(x) - x - lgamf(a);
+if( ax < -MAXLOGF )
+ {
+ mtherr( "igamcf", UNDERFLOW );
+ return( 0.0 );
+ }
+ax = expf(ax);
+
+/* continued fraction */
+y = 1.0 - a;
+z = x + y + 1.0;
+c = 0.0;
+pkm2 = 1.0;
+qkm2 = x;
+pkm1 = x + 1.0;
+qkm1 = z * x;
+ans = pkm1/qkm1;
+
+do
+ {
+ c += 1.0;
+ y += 1.0;
+ z += 2.0;
+ yc = y * c;
+ pk = pkm1 * z - pkm2 * yc;
+ qk = qkm1 * z - qkm2 * yc;
+ if( qk != 0 )
+ {
+ r = pk/qk;
+ t = fabsf( (ans - r)/r );
+ ans = r;
+ }
+ else
+ t = 1.0;
+ pkm2 = pkm1;
+ pkm1 = pk;
+ qkm2 = qkm1;
+ qkm1 = qk;
+ if( fabsf(pk) > big )
+ {
+ pkm2 *= MACHEPF;
+ pkm1 *= MACHEPF;
+ qkm2 *= MACHEPF;
+ qkm1 *= MACHEPF;
+ }
+ }
+while( t > MACHEPF );
+
+return( ans * ax );
+}
+
+
+
+/* left tail of incomplete gamma function:
+ *
+ * inf. k
+ * a -x - x
+ * x e > ----------
+ * - -
+ * k=0 | (a+k+1)
+ *
+ */
+
+float igamf( float aa, float xx )
+{
+float a, x, ans, ax, c, r;
+
+a = aa;
+x = xx;
+if( (x <= 0) || ( a <= 0) )
+ return( 0.0 );
+
+if( (x > 1.0) && (x > a ) )
+ return( 1.0 - igamcf(a,x) );
+
+/* Compute x**a * exp(-x) / gamma(a) */
+ax = a * logf(x) - x - lgamf(a);
+if( ax < -MAXLOGF )
+ {
+ mtherr( "igamf", UNDERFLOW );
+ return( 0.0 );
+ }
+ax = expf(ax);
+
+/* power series */
+r = a;
+c = 1.0;
+ans = 1.0;
+
+do
+ {
+ r += 1.0;
+ c *= x/r;
+ ans += c;
+ }
+while( c/ans > MACHEPF );
+
+return( ans * ax/a );
+}