1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
//
// A rust binding for the GSL library by Guillaume Gomez (guillaume1.gomez@gmail.com)
//
//! Further information about the elliptic integrals can be found in Abramowitz & Stegun, Chapter 17.
/// The Legendre forms of elliptic integrals F(\phi,k), E(\phi,k) and \Pi(\phi,k,n) are defined by,
///
/// F(\phi,k) = \int_0^\phi dt 1/\sqrt((1 - k^2 \sin^2(t)))
///
/// E(\phi,k) = \int_0^\phi dt \sqrt((1 - k^2 \sin^2(t)))
///
/// Pi(\phi,k,n) = \int_0^\phi dt 1/((1 + n \sin^2(t))\sqrt(1 - k^2 \sin^2(t)))
///
/// The complete Legendre forms are denoted by K(k) = F(\pi/2, k) and E(k) = E(\pi/2, k).
///
/// The notation used here is based on Carlson, Numerische Mathematik 33 (1979) 1 and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter m = k^2 and n is replaced by -n.
pub mod legendre {
pub mod complete {
use crate::{types, Value};
use std::mem::MaybeUninit;
/// This routine computes the complete elliptic integral K(k) to the accuracy specified by the mode variable mode.
/// Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
#[doc(alias = "gsl_sf_ellint_Kcomp")]
pub fn ellint_Kcomp(k: f64, mode: crate::Mode) -> f64 {
unsafe { sys::gsl_sf_ellint_Kcomp(k, mode.into()) }
}
/// This routine computes the complete elliptic integral K(k) to the accuracy specified by the mode variable mode.
/// Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
#[doc(alias = "gsl_sf_ellint_Kcomp_e")]
pub fn ellint_Kcomp_e(k: f64, mode: crate::Mode) -> Result<types::Result, Value> {
let mut result = MaybeUninit::<sys::gsl_sf_result>::uninit();
let ret = unsafe { ::sys::gsl_sf_ellint_Kcomp_e(k, mode.into(), result.as_mut_ptr()) };
result_handler!(ret, unsafe { result.assume_init() }.into())
}
/// This routine computes the complete elliptic integral E(k) to the accuracy specified by the mode variable mode.
/// Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
#[doc(alias = "gsl_sf_ellint_Ecomp")]
pub fn ellint_Ecomp(k: f64, mode: crate::Mode) -> f64 {
unsafe { sys::gsl_sf_ellint_Ecomp(k, mode.into()) }
}
/// This routine computes the complete elliptic integral E(k) to the accuracy specified by the mode variable mode.
/// Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
#[doc(alias = "gsl_sf_ellint_Ecomp_e")]
pub fn ellint_Ecomp_e(k: f64, mode: crate::Mode) -> Result<types::Result, Value> {
let mut result = MaybeUninit::<sys::gsl_sf_result>::uninit();
let ret = unsafe { ::sys::gsl_sf_ellint_Ecomp_e(k, mode.into(), result.as_mut_ptr()) };
result_handler!(ret, unsafe { result.assume_init() }.into())
}
/// This routine computes the complete elliptic integral \Pi(k,n) to the accuracy specified by the mode variable mode.
/// Note that Abramowitz & Stegun define this function in terms of the parameters m = k^2 and \sin^2(\alpha) = k^2, with the change of sign n \to -n.
#[doc(alias = "gsl_sf_ellint_Pcomp")]
pub fn ellint_Pcomp(k: f64, n: f64, mode: crate::Mode) -> f64 {
unsafe { sys::gsl_sf_ellint_Pcomp(k, n, mode.into()) }
}
/// This routine computes the complete elliptic integral \Pi(k,n) to the accuracy specified by the mode variable mode.
/// Note that Abramowitz & Stegun define this function in terms of the parameters m = k^2 and \sin^2(\alpha) = k^2, with the change of sign n \to -n.
#[doc(alias = "gsl_sf_ellint_Pcomp_e")]
pub fn ellint_Pcomp_e(k: f64, n: f64, mode: crate::Mode) -> Result<types::Result, Value> {
let mut result = MaybeUninit::<sys::gsl_sf_result>::uninit();
let ret =
unsafe { ::sys::gsl_sf_ellint_Pcomp_e(k, n, mode.into(), result.as_mut_ptr()) };
result_handler!(ret, unsafe { result.assume_init() }.into())
}
}
pub mod incomplete {
use crate::{types, Value};
use std::mem::MaybeUninit;
/// This routine computes the incomplete elliptic integral F(\phi,k) to the accuracy specified by the mode variable mode.
/// Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
#[doc(alias = "gsl_sf_ellint_F")]
pub fn ellint_F(phi: f64, k: f64, mode: crate::Mode) -> f64 {
unsafe { sys::gsl_sf_ellint_F(phi, k, mode.into()) }
}
/// This routine computes the incomplete elliptic integral F(\phi,k) to the accuracy specified by the mode variable mode.
/// Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
#[doc(alias = "gsl_sf_ellint_F_e")]
pub fn ellint_F_e(phi: f64, k: f64, mode: crate::Mode) -> Result<types::Result, Value> {
let mut result = MaybeUninit::<sys::gsl_sf_result>::uninit();
let ret = unsafe { ::sys::gsl_sf_ellint_F_e(phi, k, mode.into(), result.as_mut_ptr()) };
result_handler!(ret, unsafe { result.assume_init() }.into())
}
/// This routine computes the incomplete elliptic integral E(\phi,k) to the accuracy specified by the mode variable mode.
/// Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
#[doc(alias = "gsl_sf_ellint_E")]
pub fn ellint_E(phi: f64, k: f64, mode: crate::Mode) -> f64 {
unsafe { sys::gsl_sf_ellint_E(phi, k, mode.into()) }
}
/// This routine computes the incomplete elliptic integral E(\phi,k) to the accuracy specified by the mode variable mode.
/// Note that Abramowitz & Stegun define this function in terms of the parameter m = k^2.
#[doc(alias = "gsl_sf_ellint_E_e")]
pub fn ellint_E_e(phi: f64, k: f64, mode: crate::Mode) -> Result<types::Result, Value> {
let mut result = MaybeUninit::<sys::gsl_sf_result>::uninit();
let ret = unsafe { ::sys::gsl_sf_ellint_E_e(phi, k, mode.into(), result.as_mut_ptr()) };
result_handler!(ret, unsafe { result.assume_init() }.into())
}
/// This routine computes the incomplete elliptic integral \Pi(\phi,k,n) to the accuracy specified by the mode variable mode.
/// Note that Abramowitz & Stegun define this function in terms of the parameters m = k^2 and \sin^2(\alpha) = k^2, with the change of sign n \to -n.
#[doc(alias = "gsl_sf_ellint_P")]
pub fn ellint_P(phi: f64, k: f64, n: f64, mode: crate::Mode) -> f64 {
unsafe { sys::gsl_sf_ellint_P(phi, k, n, mode.into()) }
}
/// This routine computes the incomplete elliptic integral \Pi(\phi,k,n) to the accuracy specified by the mode variable mode.
/// Note that Abramowitz & Stegun define this function in terms of the parameters m = k^2 and \sin^2(\alpha) = k^2, with the change of sign n \to -n.
#[doc(alias = "gsl_sf_ellint_P_e")]
pub fn ellint_P_e(
phi: f64,
k: f64,
n: f64,
mode: crate::Mode,
) -> Result<types::Result, Value> {
let mut result = MaybeUninit::<sys::gsl_sf_result>::uninit();
let ret =
unsafe { ::sys::gsl_sf_ellint_P_e(phi, k, n, mode.into(), result.as_mut_ptr()) };
result_handler!(ret, unsafe { result.assume_init() }.into())
}
/// This routine computes the incomplete elliptic integral D(\phi,k) which is defined through the Carlson form RD(x,y,z) by the following relation,
///
/// D(\phi,k,n) = (1/3)(\sin(\phi))^3 RD (1-\sin^2(\phi), 1-k^2 \sin^2(\phi), 1).
#[doc(alias = "gsl_sf_ellint_D")]
pub fn ellint_D(phi: f64, k: f64, mode: crate::Mode) -> f64 {
unsafe { sys::gsl_sf_ellint_D(phi, k, mode.into()) }
}
/// This routine computes the incomplete elliptic integral D(\phi,k) which is defined through the Carlson form RD(x,y,z) by the following relation,
///
/// D(\phi,k,n) = (1/3)(\sin(\phi))^3 RD (1-\sin^2(\phi), 1-k^2 \sin^2(\phi), 1).
///
/// The argument n is not used and will be removed in a future release.
#[doc(alias = "gsl_sf_ellint_D_e")]
pub fn ellint_D_e(phi: f64, k: f64, mode: crate::Mode) -> Result<types::Result, Value> {
let mut result = MaybeUninit::<sys::gsl_sf_result>::uninit();
let ret = unsafe { ::sys::gsl_sf_ellint_D_e(phi, k, mode.into(), result.as_mut_ptr()) };
result_handler!(ret, unsafe { result.assume_init() }.into())
}
}
}
/// The Carlson symmetric forms of elliptical integrals RC(x,y), RD(x,y,z), RF(x,y,z) and RJ(x,y,z,p) are defined by,
///
/// RC(x,y) = 1/2 \int_0^\infty dt (t+x)^(-1/2) (t+y)^(-1)
///
/// RD(x,y,z) = 3/2 \int_0^\infty dt (t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-3/2)
///
/// RF(x,y,z) = 1/2 \int_0^\infty dt (t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2)
///
/// RJ(x,y,z,p) = 3/2 \int_0^\infty dt
/// (t+x)^(-1/2) (t+y)^(-1/2) (t+z)^(-1/2) (t+p)^(-1)
pub mod carlson {
use crate::{types, Value};
use std::mem::MaybeUninit;
/// This routine computes the incomplete elliptic integral RC(x,y) to the accuracy specified by the mode variable mode.
#[doc(alias = "gsl_sf_ellint_RC")]
pub fn ellint_RC(x: f64, y: f64, mode: crate::Mode) -> f64 {
unsafe { sys::gsl_sf_ellint_RC(x, y, mode.into()) }
}
/// This routine computes the incomplete elliptic integral RC(x,y) to the accuracy specified by the mode variable mode.
#[doc(alias = "gsl_sf_ellint_RC_e")]
pub fn ellint_RC_e(x: f64, y: f64, mode: crate::Mode) -> Result<types::Result, Value> {
let mut result = MaybeUninit::<sys::gsl_sf_result>::uninit();
let ret = unsafe { ::sys::gsl_sf_ellint_RC_e(x, y, mode.into(), result.as_mut_ptr()) };
result_handler!(ret, unsafe { result.assume_init() }.into())
}
/// This routine computes the incomplete elliptic integral RD(x,y,z) to the accuracy specified by the mode variable mode.
#[doc(alias = "gsl_sf_ellint_RD")]
pub fn ellint_RD(x: f64, y: f64, z: f64, mode: crate::Mode) -> f64 {
unsafe { sys::gsl_sf_ellint_RD(x, y, z, mode.into()) }
}
/// This routine computes the incomplete elliptic integral RD(x,y,z) to the accuracy specified by the mode variable mode.
#[doc(alias = "gsl_sf_ellint_RD_e")]
pub fn ellint_RD_e(x: f64, y: f64, z: f64, mode: crate::Mode) -> Result<types::Result, Value> {
let mut result = MaybeUninit::<sys::gsl_sf_result>::uninit();
let ret = unsafe { ::sys::gsl_sf_ellint_RD_e(x, y, z, mode.into(), result.as_mut_ptr()) };
result_handler!(ret, unsafe { result.assume_init() }.into())
}
/// This routine computes the incomplete elliptic integral RF(x,y,z) to the accuracy specified by the mode variable mode.
#[doc(alias = "gsl_sf_ellint_RF")]
pub fn ellint_RF(x: f64, y: f64, z: f64, mode: crate::Mode) -> f64 {
unsafe { sys::gsl_sf_ellint_RF(x, y, z, mode.into()) }
}
/// This routine computes the incomplete elliptic integral RF(x,y,z) to the accuracy specified by the mode variable mode.
#[doc(alias = "gsl_sf_ellint_RF_e")]
pub fn ellint_RF_e(x: f64, y: f64, z: f64, mode: crate::Mode) -> Result<types::Result, Value> {
let mut result = MaybeUninit::<sys::gsl_sf_result>::uninit();
let ret = unsafe { ::sys::gsl_sf_ellint_RF_e(x, y, z, mode.into(), result.as_mut_ptr()) };
result_handler!(ret, unsafe { result.assume_init() }.into())
}
/// This routine computes the incomplete elliptic integral RJ(x,y,z,p) to the accuracy specified by the mode variable mode.
#[doc(alias = "gsl_sf_ellint_RJ")]
pub fn ellint_RJ(x: f64, y: f64, z: f64, p: f64, mode: crate::Mode) -> f64 {
unsafe { sys::gsl_sf_ellint_RJ(x, y, z, p, mode.into()) }
}
/// This routine computes the incomplete elliptic integral RJ(x,y,z,p) to the accuracy specified by the mode variable mode.
#[doc(alias = "gsl_sf_ellint_RJ_e")]
pub fn ellint_RJ_e(
x: f64,
y: f64,
z: f64,
p: f64,
mode: crate::Mode,
) -> Result<types::Result, Value> {
let mut result = MaybeUninit::<sys::gsl_sf_result>::uninit();
let ret =
unsafe { ::sys::gsl_sf_ellint_RJ_e(x, y, z, p, mode.into(), result.as_mut_ptr()) };
result_handler!(ret, unsafe { result.assume_init() }.into())
}
}