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39 lines
1.1 KiB
39 lines
1.1 KiB
4 months ago
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// polynomial for approximating sin(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 = 7; // polynomial degree
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a = -pi/4; // interval
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b = pi/4;
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// find even polynomial with minimal abs error compared to sin(x)/x
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// account for /x
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deg = deg-1;
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// f = sin(x)/x;
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f = 1;
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c = 1;
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for i from 1 to 60 do { c = 2*i*(2*i + 1)*c; f = f + (-1)^i*x^(2*i)/c; };
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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 = 1;
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for i from 1 to deg/2 do {
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p = roundcoefficients(approx(poly,2*i), [|D ...|]);
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poly = poly + x^(2*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)/f(x), [a;b], 30));
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print("abs error:", accurateinfnorm(sin(x)-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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