xref: /aosp_15_r20/external/arm-optimized-routines/pl/math/tools/atan.sollya (revision 412f47f9e737e10ed5cc46ec6a8d7fa2264f8a14)
1*412f47f9SXin Li// polynomial for approximating atan(x) and atan2(y, x)
2*412f47f9SXin Li//
3*412f47f9SXin Li// Copyright (c) 2022-2023, Arm Limited.
4*412f47f9SXin Li// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
5*412f47f9SXin Li
6*412f47f9SXin Li// atan is odd, so approximate with an odd polynomial:
7*412f47f9SXin Li// x + ax^3 + bx^5 + cx^7 + ...
8*412f47f9SXin Li// We generate a, b, c, ... such that we can approximate atan(x) by:
9*412f47f9SXin Li// x + x^3 * (a + bx^2 + cx^4 + ...)
10*412f47f9SXin Li
11*412f47f9SXin Li// Assemble monomials
12*412f47f9SXin Lideg = 20;
13*412f47f9SXin Limons = [|1,...,deg|];
14*412f47f9SXin Lifor i from 0 to deg-1 do mons[i] = mons[i] * 2 + 1;
15*412f47f9SXin Li
16*412f47f9SXin Lia = 0x1.0p-1022;
17*412f47f9SXin Lib = 1;
18*412f47f9SXin Li
19*412f47f9SXin Lipoly = fpminimax(atan(x)-x, mons, [|double ...|], [a;b]);
20*412f47f9SXin Li
21*412f47f9SXin Lidisplay = hexadecimal;
22*412f47f9SXin Liprint("coeffs:");
23*412f47f9SXin Lifor i from 0 to deg-1 do coeff(poly,mons[i]);
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