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
50 lines
1.5 KiB
Plaintext
50 lines
1.5 KiB
Plaintext
// polynomial for approximating 2^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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// exp2f parameters
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deg = 3; // poly degree
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N = 32; // table entries
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b = 1/(2*N); // interval
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a = -b;
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//// exp2 parameters
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//deg = 5; // poly degree
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//N = 128; // table entries
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//b = 1/(2*N); // interval
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//a = -b;
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// find polynomial with minimal relative error
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f = 2^x;
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// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)|
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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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// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
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approx_abs = 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 do {
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p = roundcoefficients(approx(poly,i), [|D ...|]);
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// p = roundcoefficients(approx_abs(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)/2^x, [a;b], 30));
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print("abs error:", accurateinfnorm(2^x-poly(x), [a;b], 30));
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print("in [",a,b,"]");
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// double interval error for non-nearest rounding:
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print("rel2 error:", accurateinfnorm(1-poly(x)/2^x, [2*a;2*b], 30));
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print("abs2 error:", accurateinfnorm(2^x-poly(x), [2*a;2*b], 30));
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print("in [",2*a,2*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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