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36 lines
1008 B
36 lines
1008 B
// polynomial for approximating log(1+x)
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//
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// Copyright (c) 2019, Arm Limited.
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// SPDX-License-Identifier: MIT
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deg = 6; // poly degree
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// interval ~= 1/(2*N), where N is the table entries
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a = -0x1.fp-9;
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b = 0x1.fp-9;
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// find log(1+x) polynomial with minimal absolute error
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f = log(1+x);
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// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
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approx = proc(poly,d) {
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return remez(f(x) - poly(x), deg-d, [a;b], x^d, 1e-10);
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};
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// first coeff is fixed, iteratively find optimal double prec coeffs
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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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display = hexadecimal;
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print("abs error:", accurateinfnorm(f(x)-poly(x), [a;b], 30));
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// relative error computation fails if f(0)==0
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// g = f(x)/x = log(1+x)/x; using taylor series
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g = 0;
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for i from 0 to 60 do { g = g + (-x)^i/(i+1); };
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print("rel error:", accurateinfnorm(1-poly(x)/x/g(x), [a;b], 30));
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print("in [",a,b,"]");
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print("coeffs:");
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for i from 0 to deg do coeff(poly,i);
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