1// polynomial for approximating 10^x 2// 3// Copyright (c) 2023, Arm Limited. 4// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5 6// exp10f parameters 7deg = 5; // poly degree 8N = 1; // Neon 1, SVE 64 9b = log(2)/(2 * N * log(10)); // interval 10a = -b; 11wp = single; 12 13// exp10 parameters 14//deg = 4; // poly degree - bump to 5 for ~1 ULP 15//N = 128; // table size 16//b = log(2)/(2 * N * log(10)); // interval 17//a = -b; 18//wp = D; 19 20 21// find polynomial with minimal relative error 22 23f = 10^x; 24 25// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)| 26approx = proc(poly,d) { 27 return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10); 28}; 29// return p that minimizes |f(x) - poly(x) - x^d*p(x)| 30approx_abs = proc(poly,d) { 31 return remez(f(x) - poly(x), deg-d, [a;b], x^d, 1e-10); 32}; 33 34// first coeff is fixed, iteratively find optimal double prec coeffs 35poly = 1; 36for i from 1 to deg do { 37 p = roundcoefficients(approx(poly,i), [|wp ...|]); 38// p = roundcoefficients(approx_abs(poly,i), [|wp ...|]); 39 poly = poly + x^i*coeff(p,0); 40}; 41 42display = hexadecimal; 43print("rel error:", accurateinfnorm(1-poly(x)/10^x, [a;b], 30)); 44print("abs error:", accurateinfnorm(10^x-poly(x), [a;b], 30)); 45print("in [",a,b,"]"); 46print("coeffs:"); 47for i from 0 to deg do coeff(poly,i); 48 49log10_2 = round(N * log(10) / log(2), wp, RN); 50log2_10 = log(2) / (N * log(10)); 51log2_10_hi = round(log2_10, wp, RN); 52log2_10_lo = round(log2_10 - log2_10_hi, wp, RN); 53print(log10_2); 54print(log2_10_hi); 55print(log2_10_lo); 56