add: complex numbers

2 files changed, 170 insertions, 0 deletions

diff --git a/src/maths/complex.c b/src/maths/complex.c
new file mode 100644
index 0000000..3115fdd
--- /dev/null
+++ b/src/maths/complex.c
@@ -0,0 +1,142 @@
+#include "maths/complex.h"
+
+#include <math.h>
+
+struct PsiComplex psi_new_complex(double real, double imaginary)
+{
+	return (struct PsiComplex)
+	{
+		real,
+		imaginary,
+	};
+}
+
+struct PsiComplex psi_new_complex_from_real(double real)
+{
+	return (struct PsiComplex)
+	{
+		real,
+		0.0,
+	};
+}
+
+struct PsiComplex psi_conjugate_complex(struct PsiComplex z)
+{
+	return (struct PsiComplex)
+	{
+		z.real,
+		-z.imaginary,
+	};
+}
+
+struct PsiComplex psi_neg_complex(struct PsiComplex z)
+{
+	return (struct PsiComplex)
+	{
+		-z.real,
+		-z.imaginary,
+	};
+}
+
+double psi_phase_complex(struct PsiComplex z)
+{
+	return atan2(z.imaginary, z.real);
+}
+
+double psi_norm2_complex(struct PsiComplex z)
+{
+	return z.real * z.real + z.imaginary * z.imaginary;
+}
+
+double psi_abs_complex(struct PsiComplex z)
+{
+	return sqrt(psi_norm2_complex(z));
+}
+
+struct PsiComplex psi_sqrt_complex(struct PsiComplex z)
+{
+	double r = psi_abs_complex(z);
+	double half_theta = psi_phase_complex(z) / 2.0;
+	double sqrt_r = sqrt(r);
+
+	return (struct PsiComplex)
+	{
+		sqrt_r * cos(half_theta),
+		sqrt_r * sin(half_theta),
+	};
+}
+
+struct PsiComplex psi_add_complex(struct PsiComplex a, struct PsiComplex b)
+{
+	return (struct PsiComplex)
+	{
+		a.real + b.real,
+		a.imaginary + b.imaginary,
+	};
+}
+
+struct PsiComplex psi_sub_complex(struct PsiComplex a, struct PsiComplex b)
+{
+	return (struct PsiComplex)
+	{
+		a.real - b.real,
+		a.imaginary - b.imaginary,
+	};
+}
+
+struct PsiComplex psi_mul_complex(struct PsiComplex a, struct PsiComplex b)
+{
+	// (a + bi)(c + di) = (ac - bd) + (ad + bc)i
+	return (struct PsiComplex)
+	{
+		a.real * b.real - a.imaginary * b.imaginary,
+		a.real * b.imaginary + a.imaginary * b.real,
+	};
+}
+
+struct PsiComplex psi_div_complex(struct PsiComplex a, struct PsiComplex b)
+{
+	// (a + bi) / (c + di) = ((ac + bd) + (bc - ad)i) / (c² + d²)
+	double denom = b.real * b.real + b.imaginary * b.imaginary;
+	return (struct PsiComplex)
+	{
+		(a.real * b.real + a.imaginary * b.imaginary) / denom,
+		(a.imaginary * b.real - a.real * b.imaginary) / denom,
+	};
+}
+
+struct PsiComplex psi_add_complex_real(struct PsiComplex a, double b)
+{
+	return (struct PsiComplex)
+	{
+		a.real + b,
+		a.imaginary,
+	};
+}
+
+struct PsiComplex psi_sub_complex_real(struct PsiComplex a, double b)
+{
+	return (struct PsiComplex)
+	{
+		a.real - b,
+		a.imaginary,
+	};
+}
+
+struct PsiComplex psi_mul_complex_real(struct PsiComplex a, double b)
+{
+	return (struct PsiComplex)
+	{
+		a.real * b,
+		a.imaginary * b,
+	};
+}
+
+struct PsiComplex psi_div_complex_real(struct PsiComplex a, double b)
+{
+	return (struct PsiComplex)
+	{
+		a.real / b,
+		a.imaginary / b,
+	};
+}
diff --git a/src/maths/complex.h b/src/maths/complex.h
new file mode 100644
index 0000000..c94f64a
--- /dev/null
+++ b/src/maths/complex.h
@@ -0,0 +1,28 @@
+#pragma once
+
+struct PsiComplex
+{
+	double real;
+	double imaginary;
+};
+
+struct PsiComplex psi_new_complex(double real, double imaginary);
+struct PsiComplex psi_new_complex_from_real(double real);
+
+struct PsiComplex psi_conjugate_complex(struct PsiComplex z);
+struct PsiComplex psi_neg_complex(struct PsiComplex z);
+
+double psi_phase_complex(struct PsiComplex z);
+double psi_norm2_complex(struct PsiComplex z);
+double psi_abs_complex(struct PsiComplex z);
+struct PsiComplex psi_sqrt_complex(struct PsiComplex z);
+
+struct PsiComplex psi_add_complex(struct PsiComplex a, struct PsiComplex b);
+struct PsiComplex psi_sub_complex(struct PsiComplex a, struct PsiComplex b);
+struct PsiComplex psi_mul_complex(struct PsiComplex a, struct PsiComplex b);
+struct PsiComplex psi_div_complex(struct PsiComplex a, struct PsiComplex b);
+
+struct PsiComplex psi_add_complex_real(struct PsiComplex a, double b);
+struct PsiComplex psi_sub_complex_real(struct PsiComplex a, double b);
+struct PsiComplex psi_mul_complex_real(struct PsiComplex a, double b);
+struct PsiComplex psi_div_complex_real(struct PsiComplex a, double b);