atan.sollya

// polynomial for approximating atan(x) and atan2(y, x)
//
// Copyright (c) 2022-2024, Arm Limited.
// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception

// atan is odd, so approximate with an odd polynomial:
// x + ax^3 + bx^5 + cx^7 + ...
// We generate a, b, c, ... such that we can approximate atan(x) by:
// x + x^3 * (a + bx^2 + cx^4 + ...)

// Assemble monomials
deg = 20;
mons = [|1,...,deg|];
for i from 0 to deg-1 do mons[i] = mons[i] * 2 + 1;

a = 0x1.0p-1022;
b = 1;

poly = fpminimax(atan(x)-x, mons, [|double ...|], [a;b]);

display = hexadecimal;
print("coeffs:");
for i from 0 to deg-1 do coeff(poly,mons[i]);