abs

1 import std.math: approxEqual;
2 // f(x) = |x|, f'(x) = signum(x)
3 auto x = dual(2.0, 1.0);
4 auto result = abs(x);
5 assert(approxEqual(result.re, 2.0)); // f(2) = 2
6 assert(approxEqual(result.du, 1.0)); // f'(2) = 1
7 
8 x = dual(-2.0, 1.0);
9 result = abs(x);
10 assert(approxEqual(result.re, 2.0)); // f(-2) = 2
11 assert(approxEqual(result.du, -1.0)); // f'(-2) = -1
12 
13 // because floating point numbers have -0 and +0 f'(x) is defined for x = 0
14 x = dual(0.0, 1.0);
15 result = abs(x);
16 assert(approxEqual(result.du, 1.0));
17 x = dual(-0.0, 1.0);
18 result = abs(x);
19 assert(approxEqual(result.du, -1.0));