add: complex numbers

14 files changed, 196 insertions, 12 deletions

diff --git a/examples/tester/main.c b/examples/tester/main.c
deleted file mode 100644
index 9a9428f..0000000
--- a/examples/tester/main.c
+++ /dev/null
@@ -1,9 +0,0 @@
-#include <stdio.h>
-
-#include "psi.h"
-
-int main(void)
-{
-	printf("psi %s\n", psi_version());
-	return 0;
-}
diff --git a/premake5.lua b/premake5.lua
index 8aa81ca..8038a9a 100644
--- a/premake5.lua
+++ b/premake5.lua
@@ -98,13 +98,13 @@ project "tester"
 	setup_c_target()
 
 	files {
-		"examples/tester/**.h",
-		"examples/tester/**.c",
+		"tester/**.h",
+		"tester/**.c",
 	}
 
 	includedirs {
 		"src",
-		"examples/tester",
+		"tester",
 	}
 
 	links "psi"
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);
diff --git a/examples/tester/benchmarks.rs b/tester/benchmarks.rs
index 7aea535..7aea535 100644
--- a/examples/tester/benchmarks.rs
+++ b/tester/benchmarks.rs
diff --git a/examples/tester/clifford.rs b/tester/clifford.rs
index 932a918..932a918 100644
--- a/examples/tester/clifford.rs
+++ b/tester/clifford.rs
diff --git a/examples/tester/common.rs b/tester/common.rs
index 9e576da..9e576da 100644
--- a/examples/tester/common.rs
+++ b/tester/common.rs
diff --git a/examples/tester/custom_gates.rs b/tester/custom_gates.rs
index ffe5c01..ffe5c01 100644
--- a/examples/tester/custom_gates.rs
+++ b/tester/custom_gates.rs
diff --git a/examples/tester/kernels.rs b/tester/kernels.rs
index b42b181..b42b181 100644
--- a/examples/tester/kernels.rs
+++ b/tester/kernels.rs
diff --git a/tester/main.c b/tester/main.c
new file mode 100644
index 0000000..eb629fc
--- /dev/null
+++ b/tester/main.c
@@ -0,0 +1,23 @@
+#include <stdio.h>
+
+#include "maths/complex.h"
+#include "psi.h"
+
+int main(void)
+{
+	printf("psi %s\n", psi_version());
+
+	struct PsiComplex a = psi_new_complex(1.0, 2.0);
+	struct PsiComplex b = psi_new_complex(3.0, -1.0);
+
+	struct PsiComplex sum = psi_add_complex(a, b);
+	struct PsiComplex product = psi_mul_complex(a, b);
+
+	printf("a       = %g + %gi\n", a.real, a.imaginary);
+	printf("b       = %g + %gi\n", b.real, b.imaginary);
+	printf("a + b   = %g + %gi\n", sum.real, sum.imaginary);
+	printf("a * b   = %g + %gi\n", product.real, product.imaginary);
+	printf("|a|     = %g\n", psi_abs_complex(a));
+
+	return 0;
+}
diff --git a/examples/tester/main.rs b/tester/main.rs
index ecebd34..ecebd34 100644
--- a/examples/tester/main.rs
+++ b/tester/main.rs
diff --git a/examples/tester/noise.rs b/tester/noise.rs
index 02a4ba3..02a4ba3 100644
--- a/examples/tester/noise.rs
+++ b/tester/noise.rs
diff --git a/examples/tester/non_clifford.rs b/tester/non_clifford.rs
index 2146fb2..2146fb2 100644
--- a/examples/tester/non_clifford.rs
+++ b/tester/non_clifford.rs
diff --git a/examples/tester/simd.rs b/tester/simd.rs
index e91dc6e..e91dc6e 100644
--- a/examples/tester/simd.rs
+++ b/tester/simd.rs