diff options
Diffstat (limited to 'pl/math/tools/v_log10.sollya')
-rw-r--r-- | pl/math/tools/v_log10.sollya | 38 |
1 files changed, 38 insertions, 0 deletions
diff --git a/pl/math/tools/v_log10.sollya b/pl/math/tools/v_log10.sollya new file mode 100644 index 0000000..e2df436 --- /dev/null +++ b/pl/math/tools/v_log10.sollya @@ -0,0 +1,38 @@ +// polynomial used for __v_log10(x) +// +// Copyright (c) 2019-2023, Arm Limited. +// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + +deg = 6; // poly degree +a = -0x1.fc1p-9; +b = 0x1.009p-8; + +// find log(1+x)/x polynomial with minimal relative error +// (minimal relative error polynomial for log(1+x) is the same * x) +deg = deg-1; // because of /x + +// f = log(1+x)/x; using taylor series +f = 0; +for i from 0 to 60 do { f = f + (-x)^i/(i+1); }; + +// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)| +approx = proc(poly,d) { + return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10); +}; + +// first coeff is fixed, iteratively find optimal double prec coeffs +poly = 1; +for i from 1 to deg do { + p = roundcoefficients(approx(poly,i), [|D ...|]); + poly = poly + x^i*coeff(p,0); +}; + +// scale coefficients by 1/ln(10) +ln10 = evaluate(log(10),0); +poly = poly/ln10; + +display = hexadecimal; +print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30)); +print("in [",a,b,"]"); +print("coeffs:"); +for i from 0 to deg do double(coeff(poly,i)); |