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Diffstat (limited to 'libm/double/struve.c')
| -rw-r--r-- | libm/double/struve.c | 312 |
1 files changed, 312 insertions, 0 deletions
diff --git a/libm/double/struve.c b/libm/double/struve.c new file mode 100644 index 000000000..fabf0735e --- /dev/null +++ b/libm/double/struve.c @@ -0,0 +1,312 @@ +/* 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 + */ |