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// polynomial for approximating asinf(x)
//
// Copyright (c) 2023-2024, Arm Limited.
// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
f = asin(x);
dtype = single;
a = 0x1p-24;
b = 0.25;
deg = 4;
backward = proc(poly, d) {
return d + d ^ 3 * poly(d * d);
};
forward = proc(f, d) {
return (f(sqrt(d))-sqrt(d))/(d*sqrt(d));
};
approx = proc(poly, d) {
return remez(1 - poly(x) / forward(f, x), deg - d, [a;b], x^d/forward(f, x), 1e-16);
};
poly = 0;
for i from 0 to deg do {
i;
p = roundcoefficients(approx(poly,i), [|dtype ...|]);
poly = poly + x^i*coeff(p,0);
};
display = hexadecimal!;
print("rel error:", accurateinfnorm(1-backward(poly, x)/f(x), [a;b], 30));
print("in [", a, b, "]");
for i from 0 to deg do print(coeff(poly, i));
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