forked from OSchip/llvm-project
32 lines
951 B
Plaintext
32 lines
951 B
Plaintext
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// polynomial for approximating e^x
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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deg = 4; // poly degree
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N = 128; // table entries
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b = log(2)/(2*N); // interval
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a = -b;
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// find polynomial with minimal abs error
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// return p that minimizes |exp(x) - poly(x) - x^d*p(x)|
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approx = proc(poly,d) {
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return remez(exp(x)-poly(x), deg-d, [a;b], x^d, 1e-10);
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};
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// first 2 coeffs are fixed, iteratively find optimal double prec coeffs
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poly = 1 + 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("rel error:", accurateinfnorm(1-poly(x)/exp(x), [a;b], 30));
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print("abs error:", accurateinfnorm(exp(x)-poly(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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