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// polynomial for approximating 10^x
//
// Copyright (c) 2023-2024, Arm Limited.
// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
// exp10f parameters
deg = 5; // poly degree
N = 1; // Neon 1, SVE 64
b = log(2)/(2 * N * log(10)); // interval
a = -b;
wp = single;
// exp10 parameters
//deg = 4; // poly degree - bump to 5 for ~1 ULP
//N = 128; // table size
//b = log(2)/(2 * N * log(10)); // interval
//a = -b;
//wp = D;
// find polynomial with minimal relative error
f = 10^x;
// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)|
approx = proc(poly,d) {
return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10);
};
// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
approx_abs = proc(poly,d) {
return remez(f(x) - poly(x), deg-d, [a;b], x^d, 1e-10);
};
// first coeff is fixed, iteratively find optimal double prec coeffs
poly = 1;
for i from 1 to deg do {
p = roundcoefficients(approx(poly,i), [|wp ...|]);
// p = roundcoefficients(approx_abs(poly,i), [|wp ...|]);
poly = poly + x^i*coeff(p,0);
};
display = hexadecimal;
print("rel error:", accurateinfnorm(1-poly(x)/10^x, [a;b], 30));
print("abs error:", accurateinfnorm(10^x-poly(x), [a;b], 30));
print("in [",a,b,"]");
print("coeffs:");
for i from 0 to deg do coeff(poly,i);
log10_2 = round(N * log(10) / log(2), wp, RN);
log2_10 = log(2) / (N * log(10));
log2_10_hi = round(log2_10, wp, RN);
log2_10_lo = round(log2_10 - log2_10_hi, wp, RN);
print(log10_2);
print(log2_10_hi);
print(log2_10_lo);
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