0928368f62
This adds the Arm Optimized Routines (see https://github.com/ARM-software/optimized-routines) source code under the the LLVM license. The version of the code provided in this patch is v20.02 of the Arm Optimized Routines project. This entire contribution is being committed as is even though it does not currently fit the LLVM libc model and does not follow the LLVM coding style. In the near future, implementations from this patch will be moved over to their right place in the LLVM-libc tree. This will be done over many small patches, all of which will go through the normal LLVM code review process. See this libc-dev post for the plan: http://lists.llvm.org/pipermail/libc-dev/2020-March/000044.html Differential revision of the original upload: https://reviews.llvm.org/D75355
39 lines
1.1 KiB
Plaintext
39 lines
1.1 KiB
Plaintext
// 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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