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