v_erfc.sollya

// polynomial for approximating erfc(x)*exp(x*x)
//
// Copyright (c) 2022-2024, 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);