| // polynomial for approximating log(1+x) in double precision |
| // |
| // Copyright (c) 2022-2023, Arm Limited. |
| // SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception |
| |
| deg = 20; |
| |
| a = sqrt(2)/2-1; |
| b = sqrt(2)-1; |
| |
| f = proc(y) { |
| return log(1+y); |
| }; |
| |
| approx = proc(poly, d) { |
| return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10); |
| }; |
| |
| poly = x; |
| for i from 2 to deg do { |
| p = roundcoefficients(approx(poly,i), [|D ...|]); |
| poly = poly + x^i*coeff(p,0); |
| }; |
| |
| |
| print("coeffs:"); |
| display = hexadecimal; |
| for i from 2 to deg do coeff(poly,i); |
| print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); |
| print("in [",a,b,"]"); |