xref: /llvm-project/libc/AOR_v20.02/math/tools/log_abs.sollya (revision 0928368f623a0f885894f9c3ef1b740b060c0d9c)
1// polynomial for approximating log(1+x)
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6
7deg = 6; // poly degree
8// interval ~= 1/(2*N), where N is the table entries
9a = -0x1.fp-9;
10b =  0x1.fp-9;
11
12// find log(1+x) polynomial with minimal absolute error
13f = log(1+x);
14
15// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
16approx = proc(poly,d) {
17  return remez(f(x) - poly(x), deg-d, [a;b], x^d, 1e-10);
18};
19
20// first coeff is fixed, iteratively find optimal double prec coeffs
21poly = x;
22for i from 2 to deg do {
23  p = roundcoefficients(approx(poly,i), [|D ...|]);
24  poly = poly + x^i*coeff(p,0);
25};
26
27display = hexadecimal;
28print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30));
29// relative error computation fails if f(0)==0
30// g = f(x)/x = log(1+x)/x; using taylor series
31g = 0;
32for i from 0 to 60 do { g = g + (-x)^i/(i+1); };
33print("rel error:", accurateinfnorm(1-poly(x)/x/g(x), [a;b], 30));
34print("in [",a,b,"]");
35print("coeffs:");
36for i from 0 to deg do coeff(poly,i);
37