| |
| /* @(#)w_j0.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 j0(double x), y0(double x) |
| */ |
| |
| #include "fdlibm.h" |
| #include <errno.h> |
| |
| #ifndef _DOUBLE_IS_32BITS |
| |
| #ifdef __STDC__ |
| double j0(double x) /* wrapper j0 */ |
| #else |
| double j0(x) /* wrapper j0 */ |
| double x; |
| #endif |
| { |
| #ifdef _IEEE_LIBM |
| return __ieee754_j0(x); |
| #else |
| struct exception exc; |
| double z = __ieee754_j0(x); |
| if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; |
| if(fabs(x)>X_TLOSS) { |
| /* j0(|x|>X_TLOSS) */ |
| exc.type = TLOSS; |
| exc.name = "j0"; |
| exc.err = 0; |
| exc.arg1 = 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 y0(double x) /* wrapper y0 */ |
| #else |
| double y0(x) /* wrapper y0 */ |
| double x; |
| #endif |
| { |
| #ifdef _IEEE_LIBM |
| return __ieee754_y0(x); |
| #else |
| double z; |
| struct exception exc; |
| z = __ieee754_y0(x); |
| if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; |
| if(x <= 0.0){ |
| #ifndef HUGE_VAL |
| #define HUGE_VAL inf |
| double inf = 0.0; |
| |
| SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ |
| #endif |
| /* y0(0) = -inf or y0(x<0) = NaN */ |
| exc.type = DOMAIN; /* should be SING for IEEE y0(0) */ |
| exc.name = "y0"; |
| exc.err = 0; |
| exc.arg1 = 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) { |
| /* y0(x>X_TLOSS) */ |
| exc.type = TLOSS; |
| exc.name = "y0"; |
| exc.err = 0; |
| exc.arg1 = 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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