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//# struct extrapolation_table
//# {
//# size_t n;
//# double rlist2[52];
//# size_t nres;
//# double res3la[3];
//# };
#[cfg(not(feature = "std"))]
use crate::float::Float;
pub struct ExtrapolationTable {
/// rlist2\[n\] contains the new element in the first
/// column of the epsilon table
pub n: usize,
/// the vector containing the elements of the two lower
/// diagonals of the triangular epsilon table. the elements
/// are numbered starting at the right^hand corner of the
/// triangle
pub rlist2: [f64; 52],
/// number of calls to the routine
pub nres: usize,
/// the vector containing the last 3 results
pub res3la: [f64; 3],
}
impl ExtrapolationTable {
/// append calculation result.
///
/// size of rlist2 is limited, but when it get full, the contents are
/// shifted and the oldest result are removed from array
#[inline]
pub fn append(&mut self, y: f64) {
let n = self.n;
self.rlist2[n] = y;
self.n += 1;
}
/// the routine determines the limit of a given sequence of
/// approximations, by means of the epsilon algorithm of
/// p. wynn. an estimate of the absolute error is also given.
/// the condensed epsilon table is computed. only those
/// elements needed for the computation of the next diagonal
/// are preserved.
///
/// * `result` - resulting approximation to the integral
/// * `abserr` - estimate of the absolute error computed from
/// result and the 3 previous results
///
pub fn qelg(&mut self, result: &mut f64, abserr: &mut f64) {
//# double *epstab = table->rlist2;
//# double *res3la = table->res3la;
//# const size_t n = table->n - 1;
//#
//# const double current = epstab[n];
//#
//# double absolute = GSL_DBL_MAX;
//# double relative = 5 * GSL_DBL_EPSILON * fabs (current);
//#
//# const size_t newelm = n / 2;
//# const size_t n_orig = n;
//# size_t n_final = n;
//# size_t i;
//#
//# const size_t nres_orig = table->nres;
//#
//# *result = current;
//# *abserr = GSL_DBL_MAX;
let epstab = &mut self.rlist2;
let res3la = &mut self.res3la;
let n = self.n - 1;
let current = unsafe { *epstab.get_unchecked(n) };
let newelm = n / 2;
let n_orig = n;
let mut n_final = n;
let nres_orig = self.nres;
*result = current;
*abserr = core::f64::MAX;
//# if (n < 2)
//# {
//# *result = current;
//# *abserr = GSL_MAX_DBL (absolute, relative);
//# return;
//# }
if n < 2 {
*result = current;
*abserr = core::f64::MAX;
return;
}
unsafe {
//# epstab[n + 2] = epstab[n];
//# epstab[n] = GSL_DBL_MAX;
let mut ep = epstab.as_mut_ptr().add(n);
*ep.add(2) = *ep;
*ep = core::f64::MAX;
for i in 0..newelm {
//# double res = epstab[n - 2 * i + 2];
//# double e0 = epstab[n - 2 * i - 2];
//# double e1 = epstab[n - 2 * i - 1];
//# double e2 = res;
let mut res = *ep.add(2);
let e0 = *ep.sub(2);
let e1 = *ep.sub(1);
let e2 = res;
//# double e1abs = fabs (e1);
//# double delta2 = e2 - e1;
//# double err2 = fabs (delta2);
//# double tol2 = GSL_MAX_DBL (fabs (e2), e1abs) * GSL_DBL_EPSILON;
//# double delta3 = e1 - e0;
//# double err3 = fabs (delta3);
//# double tol3 = GSL_MAX_DBL (e1abs, fabs (e0)) * GSL_DBL_EPSILON;
let elabs = e1.abs();
let delta2 = e2 - e1;
let err2 = delta2.abs();
let tol2 = f64::max(e2.abs(), elabs) * core::f64::EPSILON;
let delta3 = e1 - e0;
let err3 = delta3.abs();
let tol3 = f64::max(elabs, e0.abs()) * core::f64::EPSILON;
//# if (err2 <= tol2 && err3 <= tol3)
//# {
//# /* If e0, e1 and e2 are equal to within machine accuracy,
//# convergence is assumed. */
//# *result = res;
//# absolute = err2 + err3;
//# relative = 5 * GSL_DBL_EPSILON * fabs (res);
//# *abserr = GSL_MAX_DBL (absolute, relative);
//# return;
//# }
if err2 <= tol2 && err3 <= tol3 {
*result = res;
let absolute = err2 + err3;
let relative = 5. * core::f64::EPSILON * res.abs();
*abserr = f64::max(absolute, relative);
return;
}
//# e3 = epstab[n - 2 * i];
//# epstab[n - 2 * i] = e1;
//# delta1 = e1 - e3;
//# err1 = fabs (delta1);
//# tol1 = GSL_MAX_DBL (e1abs, fabs (e3)) * GSL_DBL_EPSILON;
let e3 = *ep;
*ep = e1;
let delta1 = e1 - e3;
let err1 = delta1.abs();
let tol1 = f64::max(elabs, e3.abs()) * core::f64::EPSILON;
//# if (err1 <= tol1 || err2 <= tol2 || err3 <= tol3)
//# {
//# n_final = 2 * i;
//# break;
//# }
//# ss = (1 / delta1 + 1 / delta2) - 1 / delta3;
if err1 <= tol1 || err2 <= tol2 || err3 <= tol3 {
n_final = 2 * i;
break;
}
let ss = (1. / delta1 + 1. / delta2) - 1. / delta3;
// Test to detect irregular behaviour in the table, and
// eventually omit a part of the table by adjusting the value of
// n.
//# if (fabs (ss * e1) <= 0.0001)
//# {
//# n_final = 2 * i;
//# break;
//# }
if (ss * e1).abs() <= 0.0001 {
n_final = 2 * i;
break;
}
// Compute a new element and eventually adjust the value of
// result.
//# res = e1 + 1 / ss;
//# epstab[n - 2 * i] = res;
res = e1 + 1. / ss;
*ep = res;
//# {
//# const double error = err2 + fabs (res - e2) + err3;
//# if (error <= *abserr)
//# {
//# *abserr = error;
//# *result = res;
//# }
//# }
let error = err2 + (res - e2).abs() + err3;
if error <= *abserr {
*abserr = error;
*result = res;
}
ep = ep.sub(2);
}
// shift table
//# const size_t limexp = 50 - 1;
//# if (n_final == limexp)
//# {
//# n_final = 2 * (limexp / 2);
//# }
const LIMEXP: usize = 50 - 1;
if n_final == LIMEXP {
n_final = 2 * (LIMEXP / 2);
}
//# if (n_orig % 2 == 1)
//# {
//# for (i = 0; i <= newelm; i++)
//# {
//# epstab[1 + i * 2] = epstab[i * 2 + 3];
//# }
//# }
//# else
//# {
//# for (i = 0; i <= newelm; i++)
//# {
//# epstab[i * 2] = epstab[i * 2 + 2];
//# }
//# }
let mut ep = if n_orig & 1 == 1 {
epstab.as_mut_ptr().add(1)
} else {
epstab.as_mut_ptr()
};
let ep_end = ep.add(newelm * 2);
while ep <= ep_end {
*ep = *ep.add(2);
ep = ep.add(2);
}
//# if (n_orig != n_final)
//# {
//# for (i = 0; i <= n_final; i++)
//# {
//# epstab[i] = epstab[n_orig - n_final + i];
//# }
//# }
//# table->n = n_final + 1;
if n_orig != n_final {
core::ptr::copy(
epstab.as_ptr().add(n_orig - n_final),
epstab.as_mut_ptr(),
n_final + 1,
);
}
self.n = n_final + 1;
//# if (nres_orig < 3)
//# {
//# res3la[nres_orig] = *result;
//# *abserr = GSL_DBL_MAX;
//# }
//# else
//# { /* Compute error estimate */
//# *abserr = (fabs (*result - res3la[2]) + fabs (*result - res3la[1])
//# + fabs (*result - res3la[0]));
//# res3la[0] = res3la[1];
//# res3la[1] = res3la[2];
//# res3la[2] = *result;
//# }
if let Some(res) = res3la.get_mut(nres_orig) {
*res = *result;
*abserr = core::f64::MAX;
} else {
/* Compute error estimate */
*abserr = (*result - res3la[2]).abs()
+ (*result - res3la[1]).abs()
+ (*result - res3la[0]).abs();
/* append result at the tail of res3la */
res3la[0] = res3la[1];
res3la[1] = res3la[2];
res3la[2] = *result;
}
}
// In QUADPACK the variable table->nres is incremented at the top of
// qelg, so it increases on every call. This leads to the array
// res3la being accessed when its elements are still undefined, so I
// have moved the update to this point so that its value more
// useful.
//# table->nres = nres_orig + 1;
//# *abserr = GSL_MAX_DBL (*abserr, 5 * GSL_DBL_EPSILON * fabs (*result));
self.nres = nres_orig + 1;
*abserr = f64::max(*abserr, 5. * core::f64::EPSILON * result.abs());
}
}
impl Default for ExtrapolationTable {
#[inline]
fn default() -> Self {
Self {
n: 0,
rlist2: [0f64; 52],
nres: 0,
res3la: [0f64; 3],
}
}
}