Math Library

While the arithmetic and logic operators represent the basic operations that our [[CPU]] can perform, there are many other common math functions that com in handy. Since they are so common, programming languages usually have a math library that provides these functions. Logarithms, trigonometry and random number generation are just of few of the types of functions typically provided.

Math Constants

Math constants provide commonly used mathematical constanst to the highest precesion available. Some of the more useful math constants are summarized below.

Swift Math Constants
Constant	Description
M_E	Euler's constant [[ℯ]], base of the natural logarithm
M_PI	[[Pi]], Ratio of a circle's circumference to its diameter

Math Functions

These most useful math functions are summarized below.

Swift Math Functions
Function	Description
acos(x)	[[Arc cosine]] of x, result is in the range [0,π] [[Radians]]
acosh(x)	[[Arc hyperbolic cosine]] of x
asin(x)	[[Arc sine]] of x, result is in the range [-π/2,π/2] [[Radians]]
asinh(x)	[[Arc hyperbolic sine]] of x
atan(x)	[[Arc tangent]] of x, result is in the range [-π/2,π/2] [[Radians]]
atan2(y,x)	Angle θ from the conversion of [[rectangular coordinates]] (x,y), result is in the range [-π/2,π/2] [[Radians]]
atanh(x)	[[Arc hyperbolic tangent]] of x
ceil(x)	Smallest integer value greater than x
cos(x)	[[Cosine]] of x (in [[Radians]])
cosh(x)	[[Hyperbolic cosine]] of x
exp(x)	[[ℯ]] rasied to the power x, i.e. ℯ^x
fabs(x)	[[Absolute value]] of x
floor(x)	Largest integer less than x
fmax(x,y)	Larger of x and y
fmin(x,y)	Smaller of x and y
log(x)	[[Natural logarithm]] of x
log10(x)	[[Common logarithm]] of x
pow(x,y)	x raised to the power y, i.e. x^y
Double.random(in: 0.0 ..< 1.0)	[[Pseudorandom]] number on the interval [0, 1)
sin(x)	[[Sine]] of x (in [[Radians]])
sqrt(x)	[[Square root]] of x
tan(x)	[[Tangent]] of x (in [[Radians]])
tanh(x)	[[Hyperbolic tangent]] of x

Be sure to add the following import to the top of your program in order to use these math functions and constants.
import Foundation

Math1.swift

#!/usr/bin/env swift;
/******************************************************************************
 * This program demonstrates the math library.
 * 
 * Copyright © 2016 Richard Lesh.  All rights reserved.
 *****************************************************************************/

import Foundation
import Utils

// Begin Main
let a:Double = Double.pi / Double(6)
let b:Double = Double.pi / Double(4)
let c:Double = -a * 2
let d:Double = -b * 2
let e:Double = M_E

print(Utils.format("pi = {0:f}", Double.pi))
print(Utils.format("e = {0:f}", M_E))

// abs, floor, ceil, round, trunc, min, max
print(Utils.format("abs({0:f}) = {1:f}", a, fabs(a)))
print(Utils.format("abs({0:f}) = {1:f}", c, fabs(c)))
print(Utils.format("floor({0:f}) = {1:f}", a, floor(a)))
print(Utils.format("floor({0:f}) = {1:f}", c, floor(c)))
print(Utils.format("ceil({0:f}) = {1:f}", a, ceil(a)))
print(Utils.format("ceil({0:f}) = {1:f}", c, ceil(c)))
print(Utils.format("round({0:f}) = {1:f}", a, round(a)))
print(Utils.format("round({0:f}) = {1:f}", c, round(c)))
print(Utils.format("trunc({0:f}) = {1:f}", a, trunc(a)))
print(Utils.format("trunc({0:f}) = {1:f}", c, trunc(c)))
print(Utils.format("min({0:f}, {1:f}) = {2:f}", a, c, fmin(a, c)))
print(Utils.format("max({0:f}, {1:f}) = {2:f}", a, c, fmax(a, c)))

// sin, cos, tan, atan, atan2, acos, asin
print(Utils.format("sin({0:f}) = {1:f}", a, sin(a)))
print(Utils.format("sin({0:f}) = {1:f}", b, sin(b)))
print(Utils.format("sin({0:f}) = {1:f}", c, sin(c)))
print(Utils.format("sin({0:f}) = {1:f}", d, sin(d)))
print(Utils.format("cos({0:f}) = {1:f}", a, cos(a)))
print(Utils.format("cos({0:f}) = {1:f}", b, cos(b)))
print(Utils.format("cos({0:f}) = {1:f}", c, cos(c)))
print(Utils.format("cos({0:f}) = {1:f}", d, cos(d)))
print(Utils.format("tan({0:f}) = {1:f}", a, tan(a)))
print(Utils.format("tan({0:f}) = {1:f}", b, tan(b)))
print(Utils.format("tan({0:f}) = {1:f}", c, tan(c)))
print(Utils.format("asin({0:f}) = {1:f}", sin(a), asin(sin(a))))
print(Utils.format("asin({0:f}) = {1:f}", sin(b), asin(sin(b))))
print(Utils.format("asin({0:f}) = {1:f}", sin(c), asin(sin(c))))
print(Utils.format("asin({0:f}) = {1:f}", sin(d), asin(sin(d))))
print(Utils.format("acos({0:f}) = {1:f}", cos(a), acos(cos(a))))
print(Utils.format("acos({0:f}) = {1:f}", cos(b), acos(cos(b))))
print(Utils.format("acos({0:f}) = {1:f}", cos(c), acos(cos(c))))
print(Utils.format("acos({0:f}) = {1:f}", cos(d), acos(cos(d))))
print(Utils.format("atan({0:f}) = {1:f}", tan(a), atan(tan(a))))
print(Utils.format("atan({0:f}) = {1:f}", tan(b), atan(tan(b))))
print(Utils.format("atan({0:f}) = {1:f}", tan(c), atan(tan(c))))
// 45 degrees
print(Utils.format("atan2({0:f}, {1:f}) = {2:f}", 1.0, 1.0, atan2(1.0, 1.0)))
// 30 degrees
print(Utils.format("atan2({0:f}, {1:f}) = {2:f}", 1.0, sqrt(3.0), atan2(1.0, sqrt(3.0))))

// sinh, cosh, tanh, atanh, acosh, asinh
print(Utils.format("sinh({0:f}) = {1:f}", a, sinh(a)))
print(Utils.format("sinh({0:f}) = {1:f}", b, sinh(b)))
print(Utils.format("sinh({0:f}) = {1:f}", c, sinh(c)))
print(Utils.format("sinh({0:f}) = {1:f}", d, sinh(d)))
print(Utils.format("cosh({0:f}) = {1:f}", a, cosh(a)))
print(Utils.format("cosh({0:f}) = {1:f}", b, cosh(b)))
print(Utils.format("cosh({0:f}) = {1:f}", c, cosh(c)))
print(Utils.format("cosh({0:f}) = {1:f}", d, cosh(d)))
print(Utils.format("tanh({0:f}) = {1:f}", a, tanh(a)))
print(Utils.format("tanh({0:f}) = {1:f}", b, tanh(b)))
print(Utils.format("tanh({0:f}) = {1:f}", c, tanh(c)))
print(Utils.format("tanh({0:f}) = {1:f}", d, tanh(d)))
print(Utils.format("asinh({0:f}) = {1:f}", sinh(a), asinh(sinh(a))))
print(Utils.format("asinh({0:f}) = {1:f}", sinh(b), asinh(sinh(b))))
print(Utils.format("asinh({0:f}) = {1:f}", sinh(c), asinh(sinh(c))))
print(Utils.format("asinh({0:f}) = {1:f}", sinh(d), asinh(sinh(d))))
print(Utils.format("acosh({0:f}) = {1:f}", cosh(a), acosh(cosh(a))))
print(Utils.format("acosh({0:f}) = {1:f}", cosh(b), acosh(cosh(b))))
print(Utils.format("acosh({0:f}) = {1:f}", cosh(c), acosh(cosh(c))))
print(Utils.format("acosh({0:f}) = {1:f}", cosh(d), acosh(cosh(d))))
print(Utils.format("atanh({0:f}) = {1:f}", tanh(a), atanh(tanh(a))))
print(Utils.format("atanh({0:f}) = {1:f}", tanh(b), atanh(tanh(b))))
print(Utils.format("atanh({0:f}) = {1:f}", tanh(c), atanh(tanh(c))))
print(Utils.format("atanh({0:f}) = {1:f}", tanh(d), atanh(tanh(d))))

// log, log10, exp, pow, sqrt
print(Utils.format("log({0:f}) = {1:f}", a, log(a)))
print(Utils.format("log({0:f}) = {1:f}", b, log(b)))
print(Utils.format("log({0:f}) = {1:f}", -c, log(-c)))
print(Utils.format("log({0:f}) = {1:f}", -d, log(-d)))
print(Utils.format("log({0:f}) = {1:f}", e, log(e)))
print(Utils.format("log10({0:f}) = {1:f}", a, log10(a)))
print(Utils.format("log10({0:f}) = {1:f}", b, log10(b)))
print(Utils.format("log10({0:f}) = {1:f}", -c, log10(-c)))
print(Utils.format("log10({0:f}) = {1:f}", -d, log10(-d)))
print(Utils.format("log10({0:f}) = {1:f}", e, log10(e)))
print(Utils.format("exp({0:f}) = {1:f}", 0.5, exp(0.5)))
print(Utils.format("exp({0:f}) = {1:f}", 1.0, exp(1.0)))
print(Utils.format("exp({0:f}) = {1:f}", 2.0, exp(2.0)))
print(Utils.format("pow({0:f}, {1:f}) = {2:f}", 10.0, 0.5, pow(10.0, 0.5)))
print(Utils.format("pow({0:f}, {1:f}) = {2:f}", 10.0, 1.0, pow(10.0, 1.0)))
print(Utils.format("pow({0:f}, {1:f}) = {2:f}", 10.0, 2.0, pow(10.0, 2.0)))
print(Utils.format("sqrt({0:f}) = {1:f}", 0.5, sqrt(0.5)))
print(Utils.format("sqrt({0:f}) = {1:f}", 2.0, sqrt(2.0)))
print(Utils.format("sqrt({0:f}) = {1:f}", 10.0, sqrt(10.0)))

// random numbers
print(Utils.format("random() = {0:f}", Double.random(in: 0.0 ..< 1.0)))
print(Utils.format("random() = {0:f}", Double.random(in: 0.0 ..< 1.0)))
print(Utils.format("random() = {0:f}", Double.random(in: 0.0 ..< 1.0)))

exit(EXIT_SUCCESS)

Output

$ swiftc Math1.swift -I . -L . -lUtils error: link command failed with exit code 1 (use -v to see invocation) ld: library not found for -lUtils clang: error: linker command failed with exit code 1 (use -v to see invocation)

Math2.swift

#!/usr/bin/env swift;
/******************************************************************************
 * This program demonstrates the math integer functions.
 * 
 * Copyright © 2020 Richard Lesh.  All rights reserved.
 *****************************************************************************/

import Foundation
import Utils

// Begin Main
let a:Int = 5
let b:Int = 10
let c:Int = -2

// abs, floor, ceil, round, trunc, min, max
print(Utils.format("abs({0:d}) = {1:d}", a, abs(a)))
print(Utils.format("abs({0:d}) = {1:d}", c, abs(c)))
print(Utils.format("min({0:d}, {1:d}) = {2:d}", a, b, min(a, b)))
print(Utils.format("max({0:d}, {1:d}) = {2:d}", a, b, max(a, b)))
print(Utils.format("min({0:d}, {1:d}) = {2:d}", b, c, min(b, c)))
print(Utils.format("max({0:d}, {1:d}) = {2:d}", b, c, max(b, c)))

// random numbers
print(Utils.format("random({0:d}) = {1:d}", a, Int.random(in: 0..<a)))
print(Utils.format("random({0:d}) = {1:d}", a, Int.random(in: 0..<a)))
print(Utils.format("random({0:d}) = {1:d}", a, Int.random(in: 0..<a)))
print(Utils.format("random({0:d}) = {1:d}", a, Int.random(in: 0..<a)))
print(Utils.format("random({0:d}) = {1:d}", a, Int.random(in: 0..<a)))
print(Utils.format("random({0:d}) = {1:d}", b, Int.random(in: 0..<b)))
print(Utils.format("random({0:d}) = {1:d}", b, Int.random(in: 0..<b)))
print(Utils.format("random({0:d}) = {1:d}", b, Int.random(in: 0..<b)))
print(Utils.format("random({0:d}) = {1:d}", b, Int.random(in: 0..<b)))
print(Utils.format("random({0:d}) = {1:d}", b, Int.random(in: 0..<b)))
print(Utils.format("random(2) = {0:d}", Int.random(in: 0..<2)))
print(Utils.format("random(2) = {0:d}", Int.random(in: 0..<2)))
print(Utils.format("random(2) = {0:d}", Int.random(in: 0..<2)))
print(Utils.format("random(2) = {0:d}", Int.random(in: 0..<2)))
print(Utils.format("random(2) = {0:d}", Int.random(in: 0..<2)))
print(Utils.format("random() = {0:f}", Double.random(in: 0.0 ..< 1.0)))
print(Utils.format("random() = {0:f}", Double.random(in: 0.0 ..< 1.0)))
print(Utils.format("random() = {0:f}", Double.random(in: 0.0 ..< 1.0)))
print(Utils.format("random() = {0:f}", Double.random(in: 0.0 ..< 1.0)))
print(Utils.format("random() = {0:f}", Double.random(in: 0.0 ..< 1.0)))

exit(EXIT_SUCCESS)

Output

$ swiftc Math2.swift -I . -L . -lUtils error: link command failed with exit code 1 (use -v to see invocation) ld: library not found for -lUtils clang: error: linker command failed with exit code 1 (use -v to see invocation)

Random Numbers

Explain how to generate uniform random numbers, int and fp.

Questions

{{Write an expression that yields √5.}}
{{Write an expression that yields ³√5.}}
{{Write an expression that yields the secant of π/4.}}
{{Write an expression that yields log₁₆ 100.}}

Projects

More ★'s indicate higher difficulty level.

References

[[Swift Community]]
[[Swift Language Guide]]
[[Swift Language Reference]]
[[Swift Programming Language]], Apple Inc.
[[Swift Doc]]
[[We Heart Swift]]
[[Swift Cookbook]]
[[Swift Playground]]
[[Swift at TutorialsPoint]]
[[Hacking with Swift]]