tanf.sollya

// polynomial for approximating single precision tan(x)
//
// Copyright (c) 2022-2024, Arm Limited.
// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception

dtype = single;

mthd = 0; // approximate tan
deg = 5; // poly degree

// // Uncomment for cotan
// mthd = 1; // approximate cotan
// deg = 3; // poly degree

// interval bounds
a = 0x1.0p-126;
b = pi / 4;

print("Print some useful constants");
display = hexadecimal!;
if (dtype==double) then { prec = 53!; }
else if (dtype==single) then { prec = 23!; };

print("pi/4");
pi/4;

// Setup precisions (display and computation)
display = decimal!;
prec=128!;
save_prec=prec;

//
// Select function to approximate with Sollya
//
if(mthd==0) then {
  s = "x + x^3 * P(x^2)";
  g = tan(x);
  F = proc(P) { return x + x^3 * P(x^2); };
  f = (g(sqrt(x))-sqrt(x))/(x*sqrt(x));
  init_poly = 0;
  // Display info
  print("Approximate g(x) =", g, "as F(x)=", s, ".");
  poly = fpminimax(f, deg, [|dtype ...|], [a*a;b*b]);
}
else if (mthd==1) then {
  s = "1/x + x * P(x^2)";
  g = 1 / tan(x);
  F = proc(P) { return 1/x + x * P(x^2); };
  f = (g(sqrt(x))-1/sqrt(x))/(sqrt(x));
  init_poly = 0;
  deg_init_poly = -1; // a value such that we actually start by building constant coefficient
  // Display info
  print("Approximate g(x) =", g, "as F(x)=", s, ".");
  // Fpminimax used to minimise absolute error
  approx_fpminimax = proc(func, poly, d) {
    return fpminimax(func - poly / x^-(deg-d), 0, [|dtype|], [a;b], absolute, floating);
  };
  // Optimise all coefficients at once
  poly = fpminimax(f, [|0,...,deg|], [|dtype ...|], [a;b], absolute, floating);
};


//
// Display coefficients in Sollya
//
display = hexadecimal!;
if (dtype==double) then { prec = 53!; }
else if (dtype==single) then { prec = 23!; };
print("_coeffs :_ hex");
for i from 0 to deg do coeff(poly, i);

// Compute errors
display = hexadecimal!;
d_rel_err = dirtyinfnorm(1-F(poly)/g(x), [a;b]);
d_abs_err = dirtyinfnorm(g(x)-F(poly), [a;b]);
print("dirty rel error:", d_rel_err);
print("dirty abs error:", d_abs_err);
print("in [",a,b,"]");