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.

Perl Math Constants
Constant	Description
exp(1)	Euler's constant [[ℯ]], base of the natural logarithm
pi	[[π]], Ratio of a circle's circumference to its diameter

Math Functions

These most useful math functions are summarized below.

Perl Math Functions
Function	Description
abs(x)	[[Absolute value]] of x
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,π] [[Radians]]
atanh(x)	[[Arc hyperbolic tangent]] of x
ceil(x)	Smallest integer value greater than or equal to 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
floor(x)	Largest integer less than or equal to x
floor(x+0.5)	Nearest integer to x (round)
log(x)	[[Natural logarithm]] of x
log10(x)	[[Common logarithm]] of x
max(x,y)	Larger of x and y
min(x,y)	Smaller of x and y
pow(x,y)	x raised to the power y, i.e. x^y
rand	[[Pseudorandom]] number on the interval [0,1)
sin(x)	[[Sine]] of x (in [[Radians]])
sinh(x)	[[Hyperbolic sine]] of x
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 use statements to the top of your program in order to use these math functions and constants.
use Math::Trig; use List::Util qw[min max]; use POSIX;

The program below illustrates the use of the floating point math functions.

Math1.pl

#!/usr/bin/env perl
use utf8;
###############################################################################
# This program demonstrates the math library.
# 
# Copyright © 2016 Richard Lesh.  All rights reserved.
###############################################################################

use List::Util qw(min max);
use Math::Trig qw(abs acos acosh asin asinh atan atan2 atanh cosh pi sinh tan tanh);
use POSIX qw(ceil floor log10);
use Utils;
use strict;
use warnings;

MAIN:
{
	my $a = pi() / 6;
	my $b = pi() / 4;
	my $c = -$a * 2;
	my $d = -$b * 2;
	my $e = exp(1.);

	print Utils::messageFormat("pi = \{0:f\}", pi()), "\n";
	print Utils::messageFormat("e = \{0:f\}", exp(1.)), "\n";

# abs, floor, ceil, round, trunc, min, max
	print Utils::messageFormat("abs(\{0:f\}) = \{1:f\}", $a, abs($a)), "\n";
	print Utils::messageFormat("abs(\{0:f\}) = \{1:f\}", $c, abs($c)), "\n";
	print Utils::messageFormat("floor(\{0:f\}) = \{1:f\}", $a, floor($a)), "\n";
	print Utils::messageFormat("floor(\{0:f\}) = \{1:f\}", $c, floor($c)), "\n";
	print Utils::messageFormat("ceil(\{0:f\}) = \{1:f\}", $a, ceil($a)), "\n";
	print Utils::messageFormat("ceil(\{0:f\}) = \{1:f\}", $c, ceil($c)), "\n";
	print Utils::messageFormat("round(\{0:f\}) = \{1:f\}", $a, floor($a + 0.5)), "\n";
	print Utils::messageFormat("round(\{0:f\}) = \{1:f\}", $c, floor($c + 0.5)), "\n";
	print Utils::messageFormat("trunc(\{0:f\}) = \{1:f\}", $a, $a < 0.0 ? ceil($a) : floor($a)), "\n";
	print Utils::messageFormat("trunc(\{0:f\}) = \{1:f\}", $c, $c < 0.0 ? ceil($c) : floor($c)), "\n";
	print Utils::messageFormat("min(\{0:f\}, \{1:f\}) = \{2:f\}", $a, $c, min($a, $c)), "\n";
	print Utils::messageFormat("max(\{0:f\}, \{1:f\}) = \{2:f\}", $a, $c, max($a, $c)), "\n";

# sin, cos, tan, atan, atan2, acos, asin
	print Utils::messageFormat("sin(\{0:f\}) = \{1:f\}", $a, sin($a)), "\n";
	print Utils::messageFormat("sin(\{0:f\}) = \{1:f\}", $b, sin($b)), "\n";
	print Utils::messageFormat("sin(\{0:f\}) = \{1:f\}", $c, sin($c)), "\n";
	print Utils::messageFormat("sin(\{0:f\}) = \{1:f\}", $d, sin($d)), "\n";
	print Utils::messageFormat("cos(\{0:f\}) = \{1:f\}", $a, cos($a)), "\n";
	print Utils::messageFormat("cos(\{0:f\}) = \{1:f\}", $b, cos($b)), "\n";
	print Utils::messageFormat("cos(\{0:f\}) = \{1:f\}", $c, cos($c)), "\n";
	print Utils::messageFormat("cos(\{0:f\}) = \{1:f\}", $d, cos($d)), "\n";
	print Utils::messageFormat("tan(\{0:f\}) = \{1:f\}", $a, tan($a)), "\n";
	print Utils::messageFormat("tan(\{0:f\}) = \{1:f\}", $b, tan($b)), "\n";
	print Utils::messageFormat("tan(\{0:f\}) = \{1:f\}", $c, tan($c)), "\n";
	print Utils::messageFormat("asin(\{0:f\}) = \{1:f\}", sin($a), asin(sin($a))), "\n";
	print Utils::messageFormat("asin(\{0:f\}) = \{1:f\}", sin($b), asin(sin($b))), "\n";
	print Utils::messageFormat("asin(\{0:f\}) = \{1:f\}", sin($c), asin(sin($c))), "\n";
	print Utils::messageFormat("asin(\{0:f\}) = \{1:f\}", sin($d), asin(sin($d))), "\n";
	print Utils::messageFormat("acos(\{0:f\}) = \{1:f\}", cos($a), acos(cos($a))), "\n";
	print Utils::messageFormat("acos(\{0:f\}) = \{1:f\}", cos($b), acos(cos($b))), "\n";
	print Utils::messageFormat("acos(\{0:f\}) = \{1:f\}", cos($c), acos(cos($c))), "\n";
	print Utils::messageFormat("acos(\{0:f\}) = \{1:f\}", cos($d), acos(cos($d))), "\n";
	print Utils::messageFormat("atan(\{0:f\}) = \{1:f\}", tan($a), atan(tan($a))), "\n";
	print Utils::messageFormat("atan(\{0:f\}) = \{1:f\}", tan($b), atan(tan($b))), "\n";
	print Utils::messageFormat("atan(\{0:f\}) = \{1:f\}", tan($c), atan(tan($c))), "\n";
# 45 degrees
	print Utils::messageFormat("atan2(\{0:f\}, \{1:f\}) = \{2:f\}", 1.0, 1.0, atan2(1.0, 1.0)), "\n";
# 30 degrees
	print Utils::messageFormat("atan2(\{0:f\}, \{1:f\}) = \{2:f\}", 1.0, sqrt(3.0), atan2(1.0, sqrt(3.0))), "\n";

# sinh, cosh, tanh, atanh, acosh, asinh
	print Utils::messageFormat("sinh(\{0:f\}) = \{1:f\}", $a, sinh($a)), "\n";
	print Utils::messageFormat("sinh(\{0:f\}) = \{1:f\}", $b, sinh($b)), "\n";
	print Utils::messageFormat("sinh(\{0:f\}) = \{1:f\}", $c, sinh($c)), "\n";
	print Utils::messageFormat("sinh(\{0:f\}) = \{1:f\}", $d, sinh($d)), "\n";
	print Utils::messageFormat("cosh(\{0:f\}) = \{1:f\}", $a, cosh($a)), "\n";
	print Utils::messageFormat("cosh(\{0:f\}) = \{1:f\}", $b, cosh($b)), "\n";
	print Utils::messageFormat("cosh(\{0:f\}) = \{1:f\}", $c, cosh($c)), "\n";
	print Utils::messageFormat("cosh(\{0:f\}) = \{1:f\}", $d, cosh($d)), "\n";
	print Utils::messageFormat("tanh(\{0:f\}) = \{1:f\}", $a, tanh($a)), "\n";
	print Utils::messageFormat("tanh(\{0:f\}) = \{1:f\}", $b, tanh($b)), "\n";
	print Utils::messageFormat("tanh(\{0:f\}) = \{1:f\}", $c, tanh($c)), "\n";
	print Utils::messageFormat("tanh(\{0:f\}) = \{1:f\}", $d, tanh($d)), "\n";
	print Utils::messageFormat("asinh(\{0:f\}) = \{1:f\}", sinh($a), asinh(sinh($a))), "\n";
	print Utils::messageFormat("asinh(\{0:f\}) = \{1:f\}", sinh($b), asinh(sinh($b))), "\n";
	print Utils::messageFormat("asinh(\{0:f\}) = \{1:f\}", sinh($c), asinh(sinh($c))), "\n";
	print Utils::messageFormat("asinh(\{0:f\}) = \{1:f\}", sinh($d), asinh(sinh($d))), "\n";
	print Utils::messageFormat("acosh(\{0:f\}) = \{1:f\}", cosh($a), acosh(cosh($a))), "\n";
	print Utils::messageFormat("acosh(\{0:f\}) = \{1:f\}", cosh($b), acosh(cosh($b))), "\n";
	print Utils::messageFormat("acosh(\{0:f\}) = \{1:f\}", cosh($c), acosh(cosh($c))), "\n";
	print Utils::messageFormat("acosh(\{0:f\}) = \{1:f\}", cosh($d), acosh(cosh($d))), "\n";
	print Utils::messageFormat("atanh(\{0:f\}) = \{1:f\}", tanh($a), atanh(tanh($a))), "\n";
	print Utils::messageFormat("atanh(\{0:f\}) = \{1:f\}", tanh($b), atanh(tanh($b))), "\n";
	print Utils::messageFormat("atanh(\{0:f\}) = \{1:f\}", tanh($c), atanh(tanh($c))), "\n";
	print Utils::messageFormat("atanh(\{0:f\}) = \{1:f\}", tanh($d), atanh(tanh($d))), "\n";

# log, log10, exp, pow, sqrt
	print Utils::messageFormat("log(\{0:f\}) = \{1:f\}", $a, log($a)), "\n";
	print Utils::messageFormat("log(\{0:f\}) = \{1:f\}", $b, log($b)), "\n";
	print Utils::messageFormat("log(\{0:f\}) = \{1:f\}", -$c, log(-$c)), "\n";
	print Utils::messageFormat("log(\{0:f\}) = \{1:f\}", -$d, log(-$d)), "\n";
	print Utils::messageFormat("log(\{0:f\}) = \{1:f\}", $e, log($e)), "\n";
	print Utils::messageFormat("log10(\{0:f\}) = \{1:f\}", $a, log10($a)), "\n";
	print Utils::messageFormat("log10(\{0:f\}) = \{1:f\}", $b, log10($b)), "\n";
	print Utils::messageFormat("log10(\{0:f\}) = \{1:f\}", -$c, log10(-$c)), "\n";
	print Utils::messageFormat("log10(\{0:f\}) = \{1:f\}", -$d, log10(-$d)), "\n";
	print Utils::messageFormat("log10(\{0:f\}) = \{1:f\}", $e, log10($e)), "\n";
	print Utils::messageFormat("exp(\{0:f\}) = \{1:f\}", 0.5, exp(0.5)), "\n";
	print Utils::messageFormat("exp(\{0:f\}) = \{1:f\}", 1.0, exp(1.0)), "\n";
	print Utils::messageFormat("exp(\{0:f\}) = \{1:f\}", 2.0, exp(2.0)), "\n";
	print Utils::messageFormat("pow(\{0:f\}, \{1:f\}) = \{2:f\}", 10.0, 0.5, ((10.0) ** (0.5))), "\n";
	print Utils::messageFormat("pow(\{0:f\}, \{1:f\}) = \{2:f\}", 10.0, 1.0, ((10.0) ** (1.0))), "\n";
	print Utils::messageFormat("pow(\{0:f\}, \{1:f\}) = \{2:f\}", 10.0, 2.0, ((10.0) ** (2.0))), "\n";
	print Utils::messageFormat("sqrt(\{0:f\}) = \{1:f\}", 0.5, sqrt(0.5)), "\n";
	print Utils::messageFormat("sqrt(\{0:f\}) = \{1:f\}", 2.0, sqrt(2.0)), "\n";
	print Utils::messageFormat("sqrt(\{0:f\}) = \{1:f\}", 10.0, sqrt(10.0)), "\n";

# random numbers
	print Utils::messageFormat("random() = \{0:f\}", rand()), "\n";
	print Utils::messageFormat("random() = \{0:f\}", rand()), "\n";
	print Utils::messageFormat("random() = \{0:f\}", rand()), "\n";
}

Output

$ perl Math1.pl "abs" is not exported by the Math::Trig module "atan2" is not exported by the Math::Trig module "pow" is not exported by the Math::Trig module "rand" is not exported by the Math::Trig module Can't continue after import errors at Math1.pl line 10. BEGIN failed--compilation aborted at Math1.pl line 10.

The program below illustrates the use of the integer math and random number functions.

Math2.pl

#!/usr/bin/env perl
use utf8;
###############################################################################
# This program demonstrates the math integer functions.
# 
# Copyright © 2020 Richard Lesh.  All rights reserved.
###############################################################################

use List::Util qw(min max);
use Utils;
use strict;
use warnings;

MAIN:
{
	my $a = 5;
	my $b = 10;
	my $c = -2;

# abs, floor, ceil, round, trunc, min, max
	print Utils::messageFormat("abs(\{0:d\}) = \{1:d\}", $a, abs($a)), "\n";
	print Utils::messageFormat("abs(\{0:d\}) = \{1:d\}", $c, abs($c)), "\n";
	print Utils::messageFormat("min(\{0:d\}, \{1:d\}) = \{2:d\}", $a, $b, min($a, $b)), "\n";
	print Utils::messageFormat("max(\{0:d\}, \{1:d\}) = \{2:d\}", $a, $b, max($a, $b)), "\n";
	print Utils::messageFormat("min(\{0:d\}, \{1:d\}) = \{2:d\}", $b, $c, min($b, $c)), "\n";
	print Utils::messageFormat("max(\{0:d\}, \{1:d\}) = \{2:d\}", $b, $c, max($b, $c)), "\n";

# random numbers
	print Utils::messageFormat("random(\{0:d\}) = \{1:d\}", $a, int(rand($a))), "\n";
	print Utils::messageFormat("random(\{0:d\}) = \{1:d\}", $a, int(rand($a))), "\n";
	print Utils::messageFormat("random(\{0:d\}) = \{1:d\}", $a, int(rand($a))), "\n";
	print Utils::messageFormat("random(\{0:d\}) = \{1:d\}", $a, int(rand($a))), "\n";
	print Utils::messageFormat("random(\{0:d\}) = \{1:d\}", $a, int(rand($a))), "\n";
	print Utils::messageFormat("random(\{0:d\}) = \{1:d\}", $b, int(rand($b))), "\n";
	print Utils::messageFormat("random(\{0:d\}) = \{1:d\}", $b, int(rand($b))), "\n";
	print Utils::messageFormat("random(\{0:d\}) = \{1:d\}", $b, int(rand($b))), "\n";
	print Utils::messageFormat("random(\{0:d\}) = \{1:d\}", $b, int(rand($b))), "\n";
	print Utils::messageFormat("random(\{0:d\}) = \{1:d\}", $b, int(rand($b))), "\n";
	print Utils::messageFormat("random(2) = \{0:d\}", int(rand(2))), "\n";
	print Utils::messageFormat("random(2) = \{0:d\}", int(rand(2))), "\n";
	print Utils::messageFormat("random(2) = \{0:d\}", int(rand(2))), "\n";
	print Utils::messageFormat("random(2) = \{0:d\}", int(rand(2))), "\n";
	print Utils::messageFormat("random(2) = \{0:d\}", int(rand(2))), "\n";
	print Utils::messageFormat("random() = \{0:f\}", rand()), "\n";
	print Utils::messageFormat("random() = \{0:f\}", rand()), "\n";
	print Utils::messageFormat("random() = \{0:f\}", rand()), "\n";
	print Utils::messageFormat("random() = \{0:f\}", rand()), "\n";
	print Utils::messageFormat("random() = \{0:f\}", rand()), "\n";
}

Output

$ perl Math2.pl "abs" is not exported by the Math::Trig module "rand" is not exported by the Math::Trig module Can't continue after import errors at Math2.pl line 10. BEGIN failed--compilation aborted at Math2.pl line 10.

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

[[Perl Language Reference]]
[[Comprehensive Perl Archive Network (CPAN)]]
[[Beginning Perl]], Simon Cozens
[[Perl Monks Tutorials]]