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[/] [openrisc/] [trunk/] [gnu-src/] [newlib-1.18.0/] [newlib/] [libm/] [mathfp/] [w_jn.c] - Rev 307
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/* @(#)w_jn.c 5.1 93/09/24 */ /* * ==================================================== * 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. * ==================================================== */ /* FUNCTION <<jN>>, <<jNf>>, <<yN>>, <<yNf>>---Bessel functions INDEX j0 INDEX j0f INDEX j1 INDEX j1f INDEX jn INDEX jnf INDEX y0 INDEX y0f INDEX y1 INDEX y1f INDEX yn INDEX ynf ANSI_SYNOPSIS #include <math.h> double j0(double <[x]>); float j0f(float <[x]>); double j1(double <[x]>); float j1f(float <[x]>); double jn(int <[n]>, double <[x]>); float jnf(int <[n]>, float <[x]>); double y0(double <[x]>); float y0f(float <[x]>); double y1(double <[x]>); float y1f(float <[x]>); double yn(int <[n]>, double <[x]>); float ynf(int <[n]>, float <[x]>); TRAD_SYNOPSIS #include <math.h> double j0(<[x]>) double <[x]>; float j0f(<[x]>) float <[x]>; double j1(<[x]>) double <[x]>; float j1f(<[x]>) float <[x]>; double jn(<[n]>, <[x]>) int <[n]>; double <[x]>; float jnf(<[n]>, <[x]>) int <[n]>; float <[x]>; double y0(<[x]>) double <[x]>; float y0f(<[x]>) float <[x]>; double y1(<[x]>) double <[x]>; float y1f(<[x]>) float <[x]>; double yn(<[n]>, <[x]>) int <[n]>; double <[x]>; float ynf(<[n]>, <[x]>) int <[n]>; float <[x]>; DESCRIPTION The Bessel functions are a family of functions that solve the differential equation @ifnottex . 2 2 2 . x y'' + xy' + (x - p )y = 0 @end ifnottex @tex $$x^2{d^2y\over dx^2} + x{dy\over dx} + (x^2-p^2)y = 0$$ @end tex These functions have many applications in engineering and physics. <<jn>> calculates the Bessel function of the first kind of order <[n]>. <<j0>> and <<j1>> are special cases for order 0 and order 1 respectively. Similarly, <<yn>> calculates the Bessel function of the second kind of order <[n]>, and <<y0>> and <<y1>> are special cases for order 0 and 1. <<jnf>>, <<j0f>>, <<j1f>>, <<ynf>>, <<y0f>>, and <<y1f>> perform the same calculations, but on <<float>> rather than <<double>> values. RETURNS The value of each Bessel function at <[x]> is returned. PORTABILITY None of the Bessel functions are in ANSI C. */ /* * wrapper jn(int n, double x), yn(int n, double x) * floating point Bessel's function of the 1st and 2nd kind * of order n * * Special cases: * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. * Note 2. About jn(n,x), yn(n,x) * For n=0, j0(x) is called, * for n=1, j1(x) is called, * for n<x, forward recursion us used starting * from values of j0(x) and j1(x). * for n>x, a continued fraction approximation to * j(n,x)/j(n-1,x) is evaluated and then backward * recursion is used starting from a supposed value * for j(n,x). The resulting value of j(0,x) is * compared with the actual value to correct the * supposed value of j(n,x). * * yn(n,x) is similar in all respects, except * that forward recursion is used for all * values of n>1. * */ #include "fdlibm.h" #include <errno.h> #ifndef _DOUBLE_IS_32BITS #ifdef __STDC__ double jn(int n, double x) /* wrapper jn */ #else double jn(n,x) /* wrapper jn */ double x; int n; #endif { #ifdef _IEEE_LIBM return jn(n,x); #else double z; struct exception exc; z = jn(n,x); if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; if(fabs(x)>X_TLOSS) { /* jn(|x|>X_TLOSS) */ exc.type = TLOSS; exc.name = "jn"; exc.err = 0; exc.arg1 = n; exc.arg2 = x; exc.retval = 0.0; if (_LIB_VERSION == _POSIX_) errno = ERANGE; else if (!matherr(&exc)) { errno = ERANGE; } if (exc.err != 0) errno = exc.err; return exc.retval; } else return z; #endif } #ifdef __STDC__ double yn(int n, double x) /* wrapper yn */ #else double yn(n,x) /* wrapper yn */ double x; int n; #endif { #ifdef _IEEE_LIBM return yn(n,x); #else double z; struct exception exc; z = yn(n,x); if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; if(x <= 0.0){ /* yn(n,0) = -inf or yn(x<0) = NaN */ #ifndef HUGE_VAL #define HUGE_VAL inf double inf = 0.0; SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ #endif exc.type = DOMAIN; /* should be SING for IEEE */ exc.name = "yn"; exc.err = 0; exc.arg1 = n; exc.arg2 = x; if (_LIB_VERSION == _SVID_) exc.retval = -HUGE; else exc.retval = -HUGE_VAL; if (_LIB_VERSION == _POSIX_) errno = EDOM; else if (!matherr(&exc)) { errno = EDOM; } if (exc.err != 0) errno = exc.err; return exc.retval; } if(x>X_TLOSS) { /* yn(x>X_TLOSS) */ exc.type = TLOSS; exc.name = "yn"; exc.err = 0; exc.arg1 = n; exc.arg2 = x; exc.retval = 0.0; if (_LIB_VERSION == _POSIX_) errno = ERANGE; else if (!matherr(&exc)) { errno = ERANGE; } if (exc.err != 0) errno = exc.err; return exc.retval; } else return z; #endif } #endif /* defined(_DOUBLE_IS_32BITS) */
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