math: basic complex number support with tests

vlib/math/complex.v

@@ -0,0 +1,93 @@
+// Copyright (c) 2019 Alexander Medvednikov. All rights reserved.
+// Use of this source code is governed by an MIT license
+// that can be found in the LICENSE file.
+
+module math
+
+struct Complex {
+	re f64
+	im f64
+}
+
+pub fn complex(re f64,im f64) Complex {
+	return Complex{re,im}
+}
+
+// To String method
+pub fn (c Complex) str() string { 
+	mut out := '$c.re'
+	out += if c.im >= 0 {
+		'+$c.im'
+	}
+	else {
+		'$c.im'
+	}
+	out += 'i'
+	return out
+}
+
+// Complex Addition c1 + c2
+pub fn (c1 Complex) + (c2 Complex) Complex {
+	return Complex{c1.re+c2.re,c1.im+c2.im}
+}
+
+// Complex Substraction c1 - c2
+pub fn (c1 Complex) - (c2 Complex) Complex {
+	return Complex{c1.re-c2.re,c1.im-c2.im}
+}
+
+// Complex Multiplication c1 * c2
+// Currently Not Supported
+// pub fn (c1 Complex) * (c2 Complex) Complex {
+// 	return Complex{
+// 		(c1.re * c2.re) + ((c1.im * c2.im) * -1), 
+// 		(c1.re * c2.im) + (c1.im * c2.re)
+// 	}
+// }
+
+// Complex Division c1 / c2
+// Currently Not Supported
+// pub fn (c1 Complex) / (c2 Complex) Complex {
+// 	denom := (c2.re * c2.re) + (c2.im * c2.im)
+// 	return Complex { 
+// 		((c1.re * c2.re) + ((c1.im * -c2.im) * -1))/denom, 
+// 		((c1.re * -c2.im) + (c1.im * c2.re))/denom
+// 	}
+// }
+
+// Complex Addition c1.add(c2)
+pub fn (c1 Complex) add(c2 Complex) Complex {
+	return c1 + c2
+}
+
+// Complex Subtraction c1.subtract(c2)
+pub fn (c1 Complex) subtract(c2 Complex) Complex {
+	return c1 - c2
+}
+
+// Complex Multiplication c1.multiply(c2)
+pub fn (c1 Complex) multiply(c2 Complex) Complex {
+	return Complex{
+		(c1.re * c2.re) + ((c1.im * c2.im) * -1), 
+		(c1.re * c2.im) + (c1.im * c2.re)
+	}
+}
+
+// Complex Division c1.divide(c2)
+pub fn (c1 Complex) divide(c2 Complex) Complex {
+	denom := (c2.re * c2.re) + (c2.im * c2.im)
+	return Complex { 
+		((c1.re * c2.re) + ((c1.im * -c2.im) * -1))/denom, 
+		((c1.re * -c2.im) + (c1.im * c2.re))/denom
+	}
+}
+
+// Complex Conjugate
+pub fn (c1 Complex) conjugate() Complex{
+	return Complex{c1.re,-c1.im}
+}
+
+// Complex Equals
+pub fn (c1 Complex) equals(c2 Complex) bool {
+	return (c1.re == c2.re) && (c1.im == c2.im)
+}

vlib/math/complex_test.v

@@ -0,0 +1,104 @@
+import math
+
+// Tests are based on and verified from practice examples of Khan Academy 
+// https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers
+
+fn test_complex_addition() {
+	mut c1 := math.complex(0,-10)
+	mut c2 := math.complex(-40,8)
+	mut result := c1 + c2
+	assert result.equals(math.complex(-40,-2))
+	c1 = math.complex(-71,2)
+	c2 = math.complex(88,-12)
+	result = c1 + c2
+	assert result.equals(math.complex(17,-10))
+	c1 = math.complex(0,-30)
+	c2 = math.complex(52,-30)
+	result = c1 + c2
+	assert result.equals(math.complex(52,-60))
+	c1 = math.complex(12,-9)
+	c2 = math.complex(32,-6)
+	result = c1 + c2
+	assert result.equals(math.complex(44,-15))
+}
+
+fn test_complex_subtraction() {
+	mut c1 := math.complex(-8,0)
+	mut c2 := math.complex(6,30)
+	mut result := c1 - c2
+	assert result.equals(math.complex(-14,-30))
+	c1 = math.complex(-19,7)
+	c2 = math.complex(29,32)
+	result = c1 - c2
+	assert result.equals(math.complex(-48,-25))
+	c1 = math.complex(12,0)
+	c2 = math.complex(23,13)
+	result = c1 - c2
+	assert result.equals(math.complex(-11,-13))
+	c1 = math.complex(-14,3)
+	c2 = math.complex(0,14)
+	result = c1 - c2
+	assert result.equals(math.complex(-14,-11))
+}
+
+fn test_complex_multiplication() {
+	mut c1 := math.complex(1,2)
+	mut c2 := math.complex(1,-4)
+	mut result := c1.multiply(c2)
+	assert result.equals(math.complex(9,-2))
+	c1 = math.complex(-4,-4)
+	c2 = math.complex(-5,-3)
+	result = c1.multiply(c2)
+	assert result.equals(math.complex(8,32))
+	c1 = math.complex(4,4)
+	c2 = math.complex(-2,-5)
+	result = c1.multiply(c2)
+	assert result.equals(math.complex(12,-28))
+	c1 = math.complex(2,-2)
+	c2 = math.complex(4,-4)
+	result = c1.multiply(c2)
+	assert result.equals(math.complex(0,-16))
+}
+
+fn test_complex_division() {
+	mut c1 := math.complex(-9,-6)
+	mut c2 := math.complex(-3,-2)
+	mut result := c1.divide(c2)
+	assert result.equals(math.complex(3,0))
+	c1 = math.complex(-23,11)
+	c2 = math.complex(5,1)
+	result = c1.divide(c2)
+	assert result.equals(math.complex(-4,3))
+	c1 = math.complex(8,-2)
+	c2 = math.complex(-4,1)
+	result = c1.divide(c2)
+	assert result.equals(math.complex(-2,0))
+	c1 = math.complex(11,24)
+	c2 = math.complex(-4,-1)
+	result = c1.divide(c2)
+	assert result.equals(math.complex(-4,-5))
+}
+
+fn test_complex_conjugate() {
+	mut c1 := math.complex(0,8)
+	mut result := c1.conjugate()
+	assert result.equals(math.complex(0,-8))
+	c1 = math.complex(7,3)
+	result = c1.conjugate()
+	assert result.equals(math.complex(7,-3))
+	c1 = math.complex(2,2)
+	result = c1.conjugate()
+	assert result.equals(math.complex(2,-2))
+	c1 = math.complex(7,0)
+	result = c1.conjugate()
+	assert result.equals(math.complex(7,0))
+}
+
+fn test_complex_equals() {
+	mut c1 := math.complex(0,8)
+	mut c2 := math.complex(0,8)
+	assert c1.equals(c2)
+	c1 = math.complex(-3,19)
+	c2 = math.complex(-3,19)
+	assert c1.equals(c2)
+}