abs

import std.math: approxEqual;
// f(x) = |x|, f'(x) = signum(x)
auto x = dual(2.0, 1.0);
auto result = abs(x);
assert(approxEqual(result.re, 2.0)); // f(2) = 2
assert(approxEqual(result.du, 1.0)); // f'(2) = 1

x = dual(-2.0, 1.0);
result = abs(x);
assert(approxEqual(result.re, 2.0)); // f(-2) = 2
assert(approxEqual(result.du, -1.0)); // f'(-2) = -1

// because floating point numbers have -0 and +0 f'(x) is defined for x = 0
x = dual(0.0, 1.0);
result = abs(x);
assert(approxEqual(result.du, 1.0));
x = dual(-0.0, 1.0);
result = abs(x);
assert(approxEqual(result.du, -1.0));