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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/double/struve.c
parent22358dd7ce7bb49792204b698f01a6f69b9c8e08 (diff)
uClibc now has a math library. muahahahaha!
-Erik
Diffstat (limited to 'libm/double/struve.c')
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1 files changed, 312 insertions, 0 deletions
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+/* struve.c
+ *
+ * Struve function
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * double v, x, y, struve();
+ *
+ * y = struve( v, x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Computes the Struve function Hv(x) of order v, argument x.
+ * Negative x is rejected unless v is an integer.
+ *
+ * This module also contains the hypergeometric functions 1F2
+ * and 3F0 and a routine for the Bessel function Yv(x) with
+ * noninteger v.
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Not accurately characterized, but spot checked against tables.
+ *
+ */
+
+
+/*
+Cephes Math Library Release 2.81: June, 2000
+Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier
+*/
+#include <math.h>
+#define DEBUG 0
+#ifdef ANSIPROT
+extern double gamma ( double );
+extern double pow ( double, double );
+extern double sqrt ( double );
+extern double yn ( int, double );
+extern double jv ( double, double );
+extern double fabs ( double );
+extern double floor ( double );
+extern double sin ( double );
+extern double cos ( double );
+double yv ( double, double );
+double onef2 (double, double, double, double, double * );
+double threef0 (double, double, double, double, double * );
+#else
+double gamma(), pow(), sqrt(), yn(), yv(), jv(), fabs(), floor();
+double sin(), cos();
+double onef2(), threef0();
+#endif
+static double stop = 1.37e-17;
+extern double MACHEP;
+
+double onef2( a, b, c, x, err )
+double a, b, c, x;
+double *err;
+{
+double n, a0, sum, t;
+double an, bn, cn, max, z;
+
+an = a;
+bn = b;
+cn = c;
+a0 = 1.0;
+sum = 1.0;
+n = 1.0;
+t = 1.0;
+max = 0.0;
+
+do
+ {
+ if( an == 0 )
+ goto done;
+ if( bn == 0 )
+ goto error;
+ if( cn == 0 )
+ goto error;
+ if( (a0 > 1.0e34) || (n > 200) )
+ goto error;
+ a0 *= (an * x) / (bn * cn * n);
+ sum += a0;
+ an += 1.0;
+ bn += 1.0;
+ cn += 1.0;
+ n += 1.0;
+ z = fabs( a0 );
+ if( z > max )
+ max = z;
+ if( sum != 0 )
+ t = fabs( a0 / sum );
+ else
+ t = z;
+ }
+while( t > stop );
+
+done:
+
+*err = fabs( MACHEP*max /sum );
+
+#if DEBUG
+ printf(" onef2 cancellation error %.5E\n", *err );
+#endif
+
+goto xit;
+
+error:
+#if DEBUG
+printf("onef2 does not converge\n");
+#endif
+*err = 1.0e38;
+
+xit:
+
+#if DEBUG
+printf("onef2( %.2E %.2E %.2E %.5E ) = %.3E %.6E\n", a, b, c, x, n, sum);
+#endif
+return(sum);
+}
+
+
+
+
+double threef0( a, b, c, x, err )
+double a, b, c, x;
+double *err;
+{
+double n, a0, sum, t, conv, conv1;
+double an, bn, cn, max, z;
+
+an = a;
+bn = b;
+cn = c;
+a0 = 1.0;
+sum = 1.0;
+n = 1.0;
+t = 1.0;
+max = 0.0;
+conv = 1.0e38;
+conv1 = conv;
+
+do
+ {
+ if( an == 0.0 )
+ goto done;
+ if( bn == 0.0 )
+ goto done;
+ if( cn == 0.0 )
+ goto done;
+ if( (a0 > 1.0e34) || (n > 200) )
+ goto error;
+ a0 *= (an * bn * cn * x) / n;
+ an += 1.0;
+ bn += 1.0;
+ cn += 1.0;
+ n += 1.0;
+ z = fabs( a0 );
+ if( z > max )
+ max = z;
+ if( z >= conv )
+ {
+ if( (z < max) && (z > conv1) )
+ goto done;
+ }
+ conv1 = conv;
+ conv = z;
+ sum += a0;
+ if( sum != 0 )
+ t = fabs( a0 / sum );
+ else
+ t = z;
+ }
+while( t > stop );
+
+done:
+
+t = fabs( MACHEP*max/sum );
+#if DEBUG
+ printf(" threef0 cancellation error %.5E\n", t );
+#endif
+
+max = fabs( conv/sum );
+if( max > t )
+ t = max;
+#if DEBUG
+ printf(" threef0 convergence %.5E\n", max );
+#endif
+
+goto xit;
+
+error:
+#if DEBUG
+printf("threef0 does not converge\n");
+#endif
+t = 1.0e38;
+
+xit:
+
+#if DEBUG
+printf("threef0( %.2E %.2E %.2E %.5E ) = %.3E %.6E\n", a, b, c, x, n, sum);
+#endif
+
+*err = t;
+return(sum);
+}
+
+
+
+
+extern double PI;
+
+double struve( v, x )
+double v, x;
+{
+double y, ya, f, g, h, t;
+double onef2err, threef0err;
+
+f = floor(v);
+if( (v < 0) && ( v-f == 0.5 ) )
+ {
+ y = jv( -v, x );
+ f = 1.0 - f;
+ g = 2.0 * floor(f/2.0);
+ if( g != f )
+ y = -y;
+ return(y);
+ }
+t = 0.25*x*x;
+f = fabs(x);
+g = 1.5 * fabs(v);
+if( (f > 30.0) && (f > g) )
+ {
+ onef2err = 1.0e38;
+ y = 0.0;
+ }
+else
+ {
+ y = onef2( 1.0, 1.5, 1.5+v, -t, &onef2err );
+ }
+
+if( (f < 18.0) || (x < 0.0) )
+ {
+ threef0err = 1.0e38;
+ ya = 0.0;
+ }
+else
+ {
+ ya = threef0( 1.0, 0.5, 0.5-v, -1.0/t, &threef0err );
+ }
+
+f = sqrt( PI );
+h = pow( 0.5*x, v-1.0 );
+
+if( onef2err <= threef0err )
+ {
+ g = gamma( v + 1.5 );
+ y = y * h * t / ( 0.5 * f * g );
+ return(y);
+ }
+else
+ {
+ g = gamma( v + 0.5 );
+ ya = ya * h / ( f * g );
+ ya = ya + yv( v, x );
+ return(ya);
+ }
+}
+
+
+
+
+/* Bessel function of noninteger order
+ */
+
+double yv( v, x )
+double v, x;
+{
+double y, t;
+int n;
+
+y = floor( v );
+if( y == v )
+ {
+ n = v;
+ y = yn( n, x );
+ return( y );
+ }
+t = PI * v;
+y = (cos(t) * jv( v, x ) - jv( -v, x ))/sin(t);
+return( y );
+}
+
+/* Crossover points between ascending series and asymptotic series
+ * for Struve function
+ *
+ * v x
+ *
+ * 0 19.2
+ * 1 18.95
+ * 2 19.15
+ * 3 19.3
+ * 5 19.7
+ * 10 21.35
+ * 20 26.35
+ * 30 32.31
+ * 40 40.0
+ */