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Diffstat (limited to 'math/tools/v_exp.sollya')
-rw-r--r-- | math/tools/v_exp.sollya | 30 |
1 files changed, 30 insertions, 0 deletions
diff --git a/math/tools/v_exp.sollya b/math/tools/v_exp.sollya new file mode 100644 index 0000000..c0abb63 --- /dev/null +++ b/math/tools/v_exp.sollya @@ -0,0 +1,30 @@ +// polynomial for approximating e^x +// +// Copyright (c) 2019, Arm Limited. +// SPDX-License-Identifier: MIT + +deg = 4; // poly degree +N = 128; // table entries +b = log(2)/(2*N); // interval +a = -b; + +// find polynomial with minimal abs error + +// return p that minimizes |exp(x) - poly(x) - x^d*p(x)| +approx = proc(poly,d) { + return remez(exp(x)-poly(x), deg-d, [a;b], x^d, 1e-10); +}; + +// first 2 coeffs are fixed, iteratively find optimal double prec coeffs +poly = 1 + x; +for i from 2 to deg do { + p = roundcoefficients(approx(poly,i), [|D ...|]); + poly = poly + x^i*coeff(p,0); +}; + +display = hexadecimal; +print("rel error:", accurateinfnorm(1-poly(x)/exp(x), [a;b], 30)); +print("abs error:", accurateinfnorm(exp(x)-poly(x), [a;b], 30)); +print("in [",a,b,"]"); +print("coeffs:"); +for i from 0 to deg do coeff(poly,i); |