You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
39 lines
1.1 KiB
39 lines
1.1 KiB
// polynomial for approximating sin(x)
|
|
//
|
|
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
|
|
// See https://llvm.org/LICENSE.txt for license information.
|
|
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
|
|
|
|
deg = 7; // polynomial degree
|
|
a = -pi/4; // interval
|
|
b = pi/4;
|
|
|
|
// find even polynomial with minimal abs error compared to sin(x)/x
|
|
|
|
// account for /x
|
|
deg = deg-1;
|
|
|
|
// f = sin(x)/x;
|
|
f = 1;
|
|
c = 1;
|
|
for i from 1 to 60 do { c = 2*i*(2*i + 1)*c; f = f + (-1)^i*x^(2*i)/c; };
|
|
|
|
// return p that minimizes |f(x) - poly(x) - x^d*p(x)|
|
|
approx = 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/2 do {
|
|
p = roundcoefficients(approx(poly,2*i), [|D ...|]);
|
|
poly = poly + x^(2*i)*coeff(p,0);
|
|
};
|
|
|
|
display = hexadecimal;
|
|
print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
|
|
print("abs error:", accurateinfnorm(sin(x)-x*poly(x), [a;b], 30));
|
|
print("in [",a,b,"]");
|
|
print("coeffs:");
|
|
for i from 0 to deg do coeff(poly,i);
|