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36 lines
1.1 KiB
36 lines
1.1 KiB
4 months ago
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// polynomial for approximating e^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 = 5; // poly degree
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N = 128; // table entries
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b = log(2)/(2*N); // interval
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b = b + b*0x1p-16; // increase interval for non-nearest rounding (TOINT_NARROW)
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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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// double interval error for non-nearest rounding
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print("rel2 error:", accurateinfnorm(1-poly(x)/exp(x), [2*a;2*b], 30));
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print("abs2 error:", accurateinfnorm(exp(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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