[444] | 1 | |
---|
| 2 | /* @(#)w_j0.c 5.1 93/09/24 */ |
---|
| 3 | /* |
---|
| 4 | * ==================================================== |
---|
| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
---|
| 6 | * |
---|
| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
---|
| 8 | * Permission to use, copy, modify, and distribute this |
---|
| 9 | * software is freely granted, provided that this notice |
---|
| 10 | * is preserved. |
---|
| 11 | * ==================================================== |
---|
| 12 | */ |
---|
| 13 | |
---|
| 14 | /* |
---|
| 15 | FUNCTION |
---|
| 16 | <<jN>>, <<jNf>>, <<yN>>, <<yNf>>---Bessel functions |
---|
| 17 | |
---|
| 18 | INDEX |
---|
| 19 | j0 |
---|
| 20 | INDEX |
---|
| 21 | j0f |
---|
| 22 | INDEX |
---|
| 23 | j1 |
---|
| 24 | INDEX |
---|
| 25 | j1f |
---|
| 26 | INDEX |
---|
| 27 | jn |
---|
| 28 | INDEX |
---|
| 29 | jnf |
---|
| 30 | INDEX |
---|
| 31 | y0 |
---|
| 32 | INDEX |
---|
| 33 | y0f |
---|
| 34 | INDEX |
---|
| 35 | y1 |
---|
| 36 | INDEX |
---|
| 37 | y1f |
---|
| 38 | INDEX |
---|
| 39 | yn |
---|
| 40 | INDEX |
---|
| 41 | ynf |
---|
| 42 | |
---|
| 43 | SYNOPSIS |
---|
| 44 | #include <math.h> |
---|
| 45 | double j0(double <[x]>); |
---|
| 46 | float j0f(float <[x]>); |
---|
| 47 | double j1(double <[x]>); |
---|
| 48 | float j1f(float <[x]>); |
---|
| 49 | double jn(int <[n]>, double <[x]>); |
---|
| 50 | float jnf(int <[n]>, float <[x]>); |
---|
| 51 | double y0(double <[x]>); |
---|
| 52 | float y0f(float <[x]>); |
---|
| 53 | double y1(double <[x]>); |
---|
| 54 | float y1f(float <[x]>); |
---|
| 55 | double yn(int <[n]>, double <[x]>); |
---|
| 56 | float ynf(int <[n]>, float <[x]>); |
---|
| 57 | |
---|
| 58 | DESCRIPTION |
---|
| 59 | The Bessel functions are a family of functions that solve the |
---|
| 60 | differential equation |
---|
| 61 | @ifnottex |
---|
| 62 | . 2 2 2 |
---|
| 63 | . x y'' + xy' + (x - p )y = 0 |
---|
| 64 | @end ifnottex |
---|
| 65 | @tex |
---|
| 66 | $$x^2{d^2y\over dx^2} + x{dy\over dx} + (x^2-p^2)y = 0$$ |
---|
| 67 | @end tex |
---|
| 68 | These functions have many applications in engineering and physics. |
---|
| 69 | |
---|
| 70 | <<jn>> calculates the Bessel function of the first kind of order |
---|
| 71 | <[n]>. <<j0>> and <<j1>> are special cases for order 0 and order |
---|
| 72 | 1 respectively. |
---|
| 73 | |
---|
| 74 | Similarly, <<yn>> calculates the Bessel function of the second kind of |
---|
| 75 | order <[n]>, and <<y0>> and <<y1>> are special cases for order 0 and |
---|
| 76 | 1. |
---|
| 77 | |
---|
| 78 | <<jnf>>, <<j0f>>, <<j1f>>, <<ynf>>, <<y0f>>, and <<y1f>> perform the |
---|
| 79 | same calculations, but on <<float>> rather than <<double>> values. |
---|
| 80 | |
---|
| 81 | RETURNS |
---|
| 82 | The value of each Bessel function at <[x]> is returned. |
---|
| 83 | |
---|
| 84 | PORTABILITY |
---|
| 85 | None of the Bessel functions are in ANSI C. |
---|
| 86 | */ |
---|
| 87 | |
---|
| 88 | /* |
---|
| 89 | * wrapper j0(double x), y0(double x) |
---|
| 90 | */ |
---|
| 91 | |
---|
| 92 | #include "fdlibm.h" |
---|
| 93 | #include <errno.h> |
---|
| 94 | |
---|
| 95 | #ifndef _DOUBLE_IS_32BITS |
---|
| 96 | |
---|
| 97 | #ifdef __STDC__ |
---|
| 98 | double j0(double x) /* wrapper j0 */ |
---|
| 99 | #else |
---|
| 100 | double j0(x) /* wrapper j0 */ |
---|
| 101 | double x; |
---|
| 102 | #endif |
---|
| 103 | { |
---|
| 104 | #ifdef _IEEE_LIBM |
---|
| 105 | return __ieee754_j0(x); |
---|
| 106 | #else |
---|
| 107 | struct exception exc; |
---|
| 108 | double z = __ieee754_j0(x); |
---|
| 109 | if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; |
---|
| 110 | if(fabs(x)>X_TLOSS) { |
---|
| 111 | /* j0(|x|>X_TLOSS) */ |
---|
| 112 | exc.type = TLOSS; |
---|
| 113 | exc.name = "j0"; |
---|
| 114 | exc.err = 0; |
---|
| 115 | exc.arg1 = exc.arg2 = x; |
---|
| 116 | exc.retval = 0.0; |
---|
| 117 | if (_LIB_VERSION == _POSIX_) |
---|
| 118 | errno = ERANGE; |
---|
| 119 | else if (!matherr(&exc)) { |
---|
| 120 | errno = ERANGE; |
---|
| 121 | } |
---|
| 122 | if (exc.err != 0) |
---|
| 123 | errno = exc.err; |
---|
| 124 | return exc.retval; |
---|
| 125 | } else |
---|
| 126 | return z; |
---|
| 127 | #endif |
---|
| 128 | } |
---|
| 129 | |
---|
| 130 | #ifdef __STDC__ |
---|
| 131 | double y0(double x) /* wrapper y0 */ |
---|
| 132 | #else |
---|
| 133 | double y0(x) /* wrapper y0 */ |
---|
| 134 | double x; |
---|
| 135 | #endif |
---|
| 136 | { |
---|
| 137 | #ifdef _IEEE_LIBM |
---|
| 138 | return __ieee754_y0(x); |
---|
| 139 | #else |
---|
| 140 | double z; |
---|
| 141 | struct exception exc; |
---|
| 142 | z = __ieee754_y0(x); |
---|
| 143 | if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; |
---|
| 144 | if(x <= 0.0){ |
---|
| 145 | #ifndef HUGE_VAL |
---|
| 146 | #define HUGE_VAL inf |
---|
| 147 | double inf = 0.0; |
---|
| 148 | |
---|
| 149 | SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ |
---|
| 150 | #endif |
---|
| 151 | /* y0(0) = -inf or y0(x<0) = NaN */ |
---|
| 152 | exc.type = DOMAIN; /* should be SING for IEEE y0(0) */ |
---|
| 153 | exc.name = "y0"; |
---|
| 154 | exc.err = 0; |
---|
| 155 | exc.arg1 = exc.arg2 = x; |
---|
| 156 | if (_LIB_VERSION == _SVID_) |
---|
| 157 | exc.retval = -HUGE; |
---|
| 158 | else |
---|
| 159 | exc.retval = -HUGE_VAL; |
---|
| 160 | if (_LIB_VERSION == _POSIX_) |
---|
| 161 | errno = EDOM; |
---|
| 162 | else if (!matherr(&exc)) { |
---|
| 163 | errno = EDOM; |
---|
| 164 | } |
---|
| 165 | if (exc.err != 0) |
---|
| 166 | errno = exc.err; |
---|
| 167 | return exc.retval; |
---|
| 168 | } |
---|
| 169 | if(x>X_TLOSS) { |
---|
| 170 | /* y0(x>X_TLOSS) */ |
---|
| 171 | exc.type = TLOSS; |
---|
| 172 | exc.name = "y0"; |
---|
| 173 | exc.err = 0; |
---|
| 174 | exc.arg1 = exc.arg2 = x; |
---|
| 175 | exc.retval = 0.0; |
---|
| 176 | if (_LIB_VERSION == _POSIX_) |
---|
| 177 | errno = ERANGE; |
---|
| 178 | else if (!matherr(&exc)) { |
---|
| 179 | errno = ERANGE; |
---|
| 180 | } |
---|
| 181 | if (exc.err != 0) |
---|
| 182 | errno = exc.err; |
---|
| 183 | return exc.retval; |
---|
| 184 | } else |
---|
| 185 | return z; |
---|
| 186 | #endif |
---|
| 187 | } |
---|
| 188 | |
---|
| 189 | #endif /* defined(_DOUBLE_IS_32BITS) */ |
---|
| 190 | |
---|
| 191 | |
---|
| 192 | |
---|
| 193 | |
---|
| 194 | |
---|
| 195 | |
---|
| 196 | |
---|