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// polynomial for approximating erfc(x)*exp(x*x)
//
// Copyright (c) 2022-2023, Arm Limited.
// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
deg = 12; // poly degree
itv = parse(__argv[0]);
bounds = [|3.725290298461914e-9,
0.18920711500272103,
0.41421356237309515,
0.681792830507429,
1,
1.378414230005442,
1.8284271247461903,
2.363585661014858,
3,
3.756828460010884,
4.656854249492381,
5.727171322029716,
7,
8.513656920021768,
10.313708498984761,
12.454342644059432,
15,
18.027313840043536,
21.627416997969522,
25.908685288118864,
31|];
a = bounds[itv];
b = bounds[itv + 1];
f = proc(y) {
t = y + a;
return erfc(t) * exp(t*t);
};
poly = fpminimax(f(x), deg, [|double ...|], [0;b-a]);
display = hexadecimal;
print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
print("in [",a,b,"]");
print("coeffs:");
for i from 0 to deg do coeff(poly, i);
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