1*412f47f9SXin Li// polynomial for approximating e^x 2*412f47f9SXin Li// 3*412f47f9SXin Li// Copyright (c) 2019, Arm Limited. 4*412f47f9SXin Li// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 5*412f47f9SXin Li 6*412f47f9SXin Lideg = 5; // poly degree 7*412f47f9SXin LiN = 128; // table entries 8*412f47f9SXin Lib = log(2)/(2*N); // interval 9*412f47f9SXin Lib = b + b*0x1p-16; // increase interval for non-nearest rounding (TOINT_NARROW) 10*412f47f9SXin Lia = -b; 11*412f47f9SXin Li 12*412f47f9SXin Li// find polynomial with minimal abs error 13*412f47f9SXin Li 14*412f47f9SXin Li// return p that minimizes |exp(x) - poly(x) - x^d*p(x)| 15*412f47f9SXin Liapprox = proc(poly,d) { 16*412f47f9SXin Li return remez(exp(x)-poly(x), deg-d, [a;b], x^d, 1e-10); 17*412f47f9SXin Li}; 18*412f47f9SXin Li 19*412f47f9SXin Li// first 2 coeffs are fixed, iteratively find optimal double prec coeffs 20*412f47f9SXin Lipoly = 1 + x; 21*412f47f9SXin Lifor i from 2 to deg do { 22*412f47f9SXin Li p = roundcoefficients(approx(poly,i), [|D ...|]); 23*412f47f9SXin Li poly = poly + x^i*coeff(p,0); 24*412f47f9SXin Li}; 25*412f47f9SXin Li 26*412f47f9SXin Lidisplay = hexadecimal; 27*412f47f9SXin Liprint("rel error:", accurateinfnorm(1-poly(x)/exp(x), [a;b], 30)); 28*412f47f9SXin Liprint("abs error:", accurateinfnorm(exp(x)-poly(x), [a;b], 30)); 29*412f47f9SXin Liprint("in [",a,b,"]"); 30*412f47f9SXin Li// double interval error for non-nearest rounding 31*412f47f9SXin Liprint("rel2 error:", accurateinfnorm(1-poly(x)/exp(x), [2*a;2*b], 30)); 32*412f47f9SXin Liprint("abs2 error:", accurateinfnorm(exp(x)-poly(x), [2*a;2*b], 30)); 33*412f47f9SXin Liprint("in [",2*a,2*b,"]"); 34*412f47f9SXin Liprint("coeffs:"); 35*412f47f9SXin Lifor i from 0 to deg do coeff(poly,i); 36