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Diffstat (limited to 'pl/math/tools/v_log2f.sollya')
-rw-r--r-- | pl/math/tools/v_log2f.sollya | 38 |
1 files changed, 38 insertions, 0 deletions
diff --git a/pl/math/tools/v_log2f.sollya b/pl/math/tools/v_log2f.sollya new file mode 100644 index 0000000..99e050c --- /dev/null +++ b/pl/math/tools/v_log2f.sollya @@ -0,0 +1,38 @@ +// polynomial used for __v_log2f(x) +// +// Copyright (c) 2022-2023, Arm Limited. +// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + +deg = 9; // poly degree +a = -1/3; +b = 1/3; + +ln2 = evaluate(log(2),0); +invln2 = single(1/ln2); + +// find log2(1+x)/x polynomial with minimal relative error +// (minimal relative error polynomial for log2(1+x) is the same * x) +deg = deg-1; // because of /x + +// f = log2(1+x)/x; using taylor series +f = 0; +for i from 0 to 60 do { f = f + (-x)^i/(i+1); }; +f = f * invln2; + +// 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 = invln2; +for i from 1 to deg do { + p = roundcoefficients(approx(poly,i), [|SG ...|]); + poly = poly + x^i*coeff(p,0); +}; + +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 coeff(poly,i); |