Pure Programmer
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.
| Constant | Description |
|---|---|
| Math.E | Euler's constant [[ℯ]], base of the natural logarithm |
| Math.PI | [[Pi]], Ratio of a circle's circumference to its diameter |
Math Functions
These most useful math functions are summarized below.
| Function | Description |
|---|---|
| Math.abs(x) | [[Absolute value]] of x |
| Math.acos(x) | [[Arc cosine]] of x, result is in the range [0,π] [[Radians]] |
| Math.acosh(x) | [[Arc hyperbolic cosine]] of x |
| Math.asin(x) | [[Arc sine]] of x, result is in the range [-π/2,π/2] [[Radians]] |
| Math.asinh(x) | [[Arc hyperbolic sine]] of x |
| Math.atan(x) | [[Arc tangent]] of x, result is in the range [-π/2,π/2] [[Radians]] |
| Math.atan2(y,x) | Angle θ from the conversion of [[rectangular coordinates]] (x,y), result is in the range [-π/2,π/2] [[Radians]] |
| Math.atanh(x) | [[Arc hyperbolic tangent]] of x |
| Math.ceil(x) | Smallest integer value greater than x |
| Math.cos(x) | [[Cosine]] of x (in [[Radians]]) |
| Math.exp(x) | [[ℯ]] rasied to the power x, i.e. ℯx |
| Math.floor(x) | Largest integer less than x |
| Math.log(x) | [[Natural logarithm]] of x |
| Math.max(x,y) | Larger of x and y |
| Math.min(x,y) | Smaller of x and y |
| Math.pow(x,y) | x raised to the power y, i.e. xy |
| Math.random() | [[Pseudorandom]] number on the interval [0,1) |
| Math.round(x) | Nearest integer to x |
| Math.sin(x) | [[Sine]] of x (in [[Radians]]) |
| Math.sqrt(x) | [[Square root]] of x |
| Math.tan(x) | [[Tangent]] of x (in [[Radians]]) |
Math1.js
#!/usr/bin/env node;
/******************************************************************************
* This program demonstrates the math library.
*
* Copyright © 2016 Richard Lesh. All rights reserved.
*****************************************************************************/
const Utils = require('./Utils');
const main = async () => {
const a = Math.PI / 6;
const b = Math.PI / 4;
const c = -a * 2;
const d = -b * 2;
const e = Math.E;
console.log(Utils.format("pi = {0:f}", Math.PI));
console.log(Utils.format("e = {0:f}", Math.E));
// abs, floor, ceil, round, trunc, min, max
console.log(Utils.format("abs({0:f}) = {1:f}", a, Math.abs(a)));
console.log(Utils.format("abs({0:f}) = {1:f}", c, Math.abs(c)));
console.log(Utils.format("floor({0:f}) = {1:f}", a, Math.floor(a)));
console.log(Utils.format("floor({0:f}) = {1:f}", c, Math.floor(c)));
console.log(Utils.format("ceil({0:f}) = {1:f}", a, Math.ceil(a)));
console.log(Utils.format("ceil({0:f}) = {1:f}", c, Math.ceil(c)));
console.log(Utils.format("round({0:f}) = {1:f}", a, Math.round(a)));
console.log(Utils.format("round({0:f}) = {1:f}", c, Math.round(c)));
console.log(Utils.format("trunc({0:f}) = {1:f}", a, Math.trunc(a)));
console.log(Utils.format("trunc({0:f}) = {1:f}", c, Math.trunc(c)));
console.log(Utils.format("min({0:f}, {1:f}) = {2:f}", a, c, Math.min(a, c)));
console.log(Utils.format("max({0:f}, {1:f}) = {2:f}", a, c, Math.max(a, c)));
// sin, cos, tan, atan, atan2, acos, asin
console.log(Utils.format("sin({0:f}) = {1:f}", a, Math.sin(a)));
console.log(Utils.format("sin({0:f}) = {1:f}", b, Math.sin(b)));
console.log(Utils.format("sin({0:f}) = {1:f}", c, Math.sin(c)));
console.log(Utils.format("sin({0:f}) = {1:f}", d, Math.sin(d)));
console.log(Utils.format("cos({0:f}) = {1:f}", a, Math.cos(a)));
console.log(Utils.format("cos({0:f}) = {1:f}", b, Math.cos(b)));
console.log(Utils.format("cos({0:f}) = {1:f}", c, Math.cos(c)));
console.log(Utils.format("cos({0:f}) = {1:f}", d, Math.cos(d)));
console.log(Utils.format("tan({0:f}) = {1:f}", a, Math.tan(a)));
console.log(Utils.format("tan({0:f}) = {1:f}", b, Math.tan(b)));
console.log(Utils.format("tan({0:f}) = {1:f}", c, Math.tan(c)));
console.log(Utils.format("asin({0:f}) = {1:f}", Math.sin(a), Math.asin(Math.sin(a))));
console.log(Utils.format("asin({0:f}) = {1:f}", Math.sin(b), Math.asin(Math.sin(b))));
console.log(Utils.format("asin({0:f}) = {1:f}", Math.sin(c), Math.asin(Math.sin(c))));
console.log(Utils.format("asin({0:f}) = {1:f}", Math.sin(d), Math.asin(Math.sin(d))));
console.log(Utils.format("acos({0:f}) = {1:f}", Math.cos(a), Math.acos(Math.cos(a))));
console.log(Utils.format("acos({0:f}) = {1:f}", Math.cos(b), Math.acos(Math.cos(b))));
console.log(Utils.format("acos({0:f}) = {1:f}", Math.cos(c), Math.acos(Math.cos(c))));
console.log(Utils.format("acos({0:f}) = {1:f}", Math.cos(d), Math.acos(Math.cos(d))));
console.log(Utils.format("atan({0:f}) = {1:f}", Math.tan(a), Math.atan(Math.tan(a))));
console.log(Utils.format("atan({0:f}) = {1:f}", Math.tan(b), Math.atan(Math.tan(b))));
console.log(Utils.format("atan({0:f}) = {1:f}", Math.tan(c), Math.atan(Math.tan(c))));
// 45 degrees
console.log(Utils.format("atan2({0:f}, {1:f}) = {2:f}", 1.0, 1.0, Math.atan2(1.0, 1.0)));
// 30 degrees
console.log(Utils.format("atan2({0:f}, {1:f}) = {2:f}", 1.0, Math.sqrt(3.0), Math.atan2(1.0, Math.sqrt(3.0))));
// sinh, cosh, tanh, atanh, acosh, asinh
console.log(Utils.format("sinh({0:f}) = {1:f}", a, Math.sinh(a)));
console.log(Utils.format("sinh({0:f}) = {1:f}", b, Math.sinh(b)));
console.log(Utils.format("sinh({0:f}) = {1:f}", c, Math.sinh(c)));
console.log(Utils.format("sinh({0:f}) = {1:f}", d, Math.sinh(d)));
console.log(Utils.format("cosh({0:f}) = {1:f}", a, Math.cosh(a)));
console.log(Utils.format("cosh({0:f}) = {1:f}", b, Math.cosh(b)));
console.log(Utils.format("cosh({0:f}) = {1:f}", c, Math.cosh(c)));
console.log(Utils.format("cosh({0:f}) = {1:f}", d, Math.cosh(d)));
console.log(Utils.format("tanh({0:f}) = {1:f}", a, Math.tanh(a)));
console.log(Utils.format("tanh({0:f}) = {1:f}", b, Math.tanh(b)));
console.log(Utils.format("tanh({0:f}) = {1:f}", c, Math.tanh(c)));
console.log(Utils.format("tanh({0:f}) = {1:f}", d, Math.tanh(d)));
console.log(Utils.format("asinh({0:f}) = {1:f}", Math.sinh(a), Math.asinh(Math.sinh(a))));
console.log(Utils.format("asinh({0:f}) = {1:f}", Math.sinh(b), Math.asinh(Math.sinh(b))));
console.log(Utils.format("asinh({0:f}) = {1:f}", Math.sinh(c), Math.asinh(Math.sinh(c))));
console.log(Utils.format("asinh({0:f}) = {1:f}", Math.sinh(d), Math.asinh(Math.sinh(d))));
console.log(Utils.format("acosh({0:f}) = {1:f}", Math.cosh(a), Math.acosh(Math.cosh(a))));
console.log(Utils.format("acosh({0:f}) = {1:f}", Math.cosh(b), Math.acosh(Math.cosh(b))));
console.log(Utils.format("acosh({0:f}) = {1:f}", Math.cosh(c), Math.acosh(Math.cosh(c))));
console.log(Utils.format("acosh({0:f}) = {1:f}", Math.cosh(d), Math.acosh(Math.cosh(d))));
console.log(Utils.format("atanh({0:f}) = {1:f}", Math.tanh(a), Math.atanh(Math.tanh(a))));
console.log(Utils.format("atanh({0:f}) = {1:f}", Math.tanh(b), Math.atanh(Math.tanh(b))));
console.log(Utils.format("atanh({0:f}) = {1:f}", Math.tanh(c), Math.atanh(Math.tanh(c))));
console.log(Utils.format("atanh({0:f}) = {1:f}", Math.tanh(d), Math.atanh(Math.tanh(d))));
// log, log10, exp, pow, sqrt
console.log(Utils.format("log({0:f}) = {1:f}", a, Math.log(a)));
console.log(Utils.format("log({0:f}) = {1:f}", b, Math.log(b)));
console.log(Utils.format("log({0:f}) = {1:f}", -c, Math.log(-c)));
console.log(Utils.format("log({0:f}) = {1:f}", -d, Math.log(-d)));
console.log(Utils.format("log({0:f}) = {1:f}", e, Math.log(e)));
console.log(Utils.format("log10({0:f}) = {1:f}", a, Math.log10(a)));
console.log(Utils.format("log10({0:f}) = {1:f}", b, Math.log10(b)));
console.log(Utils.format("log10({0:f}) = {1:f}", -c, Math.log10(-c)));
console.log(Utils.format("log10({0:f}) = {1:f}", -d, Math.log10(-d)));
console.log(Utils.format("log10({0:f}) = {1:f}", e, Math.log10(e)));
console.log(Utils.format("exp({0:f}) = {1:f}", 0.5, Math.exp(0.5)));
console.log(Utils.format("exp({0:f}) = {1:f}", 1.0, Math.exp(1.0)));
console.log(Utils.format("exp({0:f}) = {1:f}", 2.0, Math.exp(2.0)));
console.log(Utils.format("pow({0:f}, {1:f}) = {2:f}", 10.0, 0.5, Math.pow(10.0, 0.5)));
console.log(Utils.format("pow({0:f}, {1:f}) = {2:f}", 10.0, 1.0, Math.pow(10.0, 1.0)));
console.log(Utils.format("pow({0:f}, {1:f}) = {2:f}", 10.0, 2.0, Math.pow(10.0, 2.0)));
console.log(Utils.format("sqrt({0:f}) = {1:f}", 0.5, Math.sqrt(0.5)));
console.log(Utils.format("sqrt({0:f}) = {1:f}", 2.0, Math.sqrt(2.0)));
console.log(Utils.format("sqrt({0:f}) = {1:f}", 10.0, Math.sqrt(10.0)));
// random numbers
console.log(Utils.format("random() = {0:f}", Math.random()));
console.log(Utils.format("random() = {0:f}", Math.random()));
console.log(Utils.format("random() = {0:f}", Math.random()));
}
main().catch( e => { console.error(e) } );
Output
$ node Math1.js
pi = 3.141592653589793
e = 2.718281828459045
abs(0.5235987755982988) = 0.5235987755982988
abs(-1.0471975511965976) = 1.0471975511965976
floor(0.5235987755982988) = 0
floor(-1.0471975511965976) = -2
ceil(0.5235987755982988) = 1
ceil(-1.0471975511965976) = -1
round(0.5235987755982988) = 1
round(-1.0471975511965976) = -1
trunc(0.5235987755982988) = 0
trunc(-1.0471975511965976) = -1
min(0.5235987755982988, -1.0471975511965976) = -1.0471975511965976
max(0.5235987755982988, -1.0471975511965976) = 0.5235987755982988
sin(0.5235987755982988) = 0.49999999999999994
sin(0.7853981633974483) = 0.7071067811865475
sin(-1.0471975511965976) = -0.8660254037844386
sin(-1.5707963267948966) = -1
cos(0.5235987755982988) = 0.8660254037844387
cos(0.7853981633974483) = 0.7071067811865476
cos(-1.0471975511965976) = 0.5000000000000001
cos(-1.5707963267948966) = 6.123233995736766e-17
tan(0.5235987755982988) = 0.5773502691896257
tan(0.7853981633974483) = 0.9999999999999999
tan(-1.0471975511965976) = -1.7320508075688767
asin(0.49999999999999994) = 0.5235987755982988
asin(0.7071067811865475) = 0.7853981633974482
asin(-0.8660254037844386) = -1.0471975511965976
asin(-1) = -1.5707963267948966
acos(0.8660254037844387) = 0.5235987755982987
acos(0.7071067811865476) = 0.7853981633974483
acos(0.5000000000000001) = 1.0471975511965976
acos(6.123233995736766e-17) = 1.5707963267948966
atan(0.5773502691896257) = 0.5235987755982988
atan(0.9999999999999999) = 0.7853981633974483
atan(-1.7320508075688767) = -1.0471975511965976
atan2(1, 1) = 0.7853981633974483
atan2(1, 1.7320508075688772) = 0.5235987755982989
sinh(0.5235987755982988) = 0.5478534738880397
sinh(0.7853981633974483) = 0.8686709614860095
sinh(-1.0471975511965976) = -1.2493670505239751
sinh(-1.5707963267948966) = -2.3012989023072947
cosh(0.5235987755982988) = 1.1402383210764286
cosh(0.7853981633974483) = 1.3246090892520057
cosh(-1.0471975511965976) = 1.600286857702386
cosh(-1.5707963267948966) = 2.5091784786580567
tanh(0.5235987755982988) = 0.4804727781564516
tanh(0.7853981633974483) = 0.6557942026326724
tanh(-1.0471975511965976) = -0.7807144353592677
tanh(-1.5707963267948966) = -0.9171523356672744
asinh(0.5478534738880397) = 0.5235987755982988
asinh(0.8686709614860095) = 0.7853981633974482
asinh(-1.2493670505239751) = -1.0471975511965976
asinh(-2.3012989023072947) = -1.5707963267948966
acosh(1.1402383210764286) = 0.5235987755982986
acosh(1.3246090892520057) = 0.7853981633974482
acosh(1.600286857702386) = 1.0471975511965976
acosh(2.5091784786580567) = 1.5707963267948966
atanh(0.4804727781564516) = 0.5235987755982989
atanh(0.6557942026326724) = 0.7853981633974483
atanh(-0.7807144353592677) = -1.0471975511965976
atanh(-0.9171523356672744) = -1.570796326794897
log(0.5235987755982988) = -0.6470295833786549
log(0.7853981633974483) = -0.2415644752704905
log(1.0471975511965976) = 0.046117597181290375
log(1.5707963267948966) = 0.4515827052894548
log(2.718281828459045) = 1
log10(0.5235987755982988) = -0.2810013776895098
log10(0.7853981633974483) = -0.10491011863382856
log10(1.0471975511965976) = 0.02002861797447137
log10(1.5707963267948966) = 0.19611987703015263
log10(2.718281828459045) = 0.4342944819032518
exp(0.5) = 1.6487212707001282
exp(1) = 2.718281828459045
exp(2) = 7.38905609893065
pow(10, 0.5) = 3.1622776601683795
pow(10, 1) = 10
pow(10, 2) = 100
sqrt(0.5) = 0.7071067811865476
sqrt(2) = 1.4142135623730951
sqrt(10) = 3.1622776601683795
random() = 0.6589260751563037
random() = 0.12611978183819184
random() = 0.11624939234163323
Math2.js
#!/usr/bin/env node;
/******************************************************************************
* This program demonstrates the math integer functions.
*
* Copyright © 2020 Richard Lesh. All rights reserved.
*****************************************************************************/
const Utils = require('./Utils');
const main = async () => {
const a = 5;
const b = 10;
const c = -2;
// abs, floor, ceil, round, trunc, min, max
console.log(Utils.format("abs({0:d}) = {1:d}", a, Math.abs(a)));
console.log(Utils.format("abs({0:d}) = {1:d}", c, Math.abs(c)));
console.log(Utils.format("min({0:d}, {1:d}) = {2:d}", a, b, Math.min(a, b)));
console.log(Utils.format("max({0:d}, {1:d}) = {2:d}", a, b, Math.max(a, b)));
console.log(Utils.format("min({0:d}, {1:d}) = {2:d}", b, c, Math.min(b, c)));
console.log(Utils.format("max({0:d}, {1:d}) = {2:d}", b, c, Math.max(b, c)));
// random numbers
console.log(Utils.format("random({0:d}) = {1:d}", a, Math.trunc(a * Math.random())));
console.log(Utils.format("random({0:d}) = {1:d}", a, Math.trunc(a * Math.random())));
console.log(Utils.format("random({0:d}) = {1:d}", a, Math.trunc(a * Math.random())));
console.log(Utils.format("random({0:d}) = {1:d}", a, Math.trunc(a * Math.random())));
console.log(Utils.format("random({0:d}) = {1:d}", a, Math.trunc(a * Math.random())));
console.log(Utils.format("random({0:d}) = {1:d}", b, Math.trunc(b * Math.random())));
console.log(Utils.format("random({0:d}) = {1:d}", b, Math.trunc(b * Math.random())));
console.log(Utils.format("random({0:d}) = {1:d}", b, Math.trunc(b * Math.random())));
console.log(Utils.format("random({0:d}) = {1:d}", b, Math.trunc(b * Math.random())));
console.log(Utils.format("random({0:d}) = {1:d}", b, Math.trunc(b * Math.random())));
console.log(Utils.format("random(2) = {0:d}", Math.trunc(2 * Math.random())));
console.log(Utils.format("random(2) = {0:d}", Math.trunc(2 * Math.random())));
console.log(Utils.format("random(2) = {0:d}", Math.trunc(2 * Math.random())));
console.log(Utils.format("random(2) = {0:d}", Math.trunc(2 * Math.random())));
console.log(Utils.format("random(2) = {0:d}", Math.trunc(2 * Math.random())));
console.log(Utils.format("random() = {0:f}", Math.random()));
console.log(Utils.format("random() = {0:f}", Math.random()));
console.log(Utils.format("random() = {0:f}", Math.random()));
console.log(Utils.format("random() = {0:f}", Math.random()));
console.log(Utils.format("random() = {0:f}", Math.random()));
}
main().catch( e => { console.error(e) } );
Output
$ node Math2.js
abs(5) = 5
abs(-2) = 2
min(5, 10) = 5
max(5, 10) = 10
min(10, -2) = -2
max(10, -2) = 10
random(5) = 4
random(5) = 1
random(5) = 2
random(5) = 1
random(5) = 2
random(10) = 4
random(10) = 5
random(10) = 0
random(10) = 9
random(10) = 1
random(2) = 0
random(2) = 0
random(2) = 1
random(2) = 1
random(2) = 1
random() = 0.14052396554971636
random() = 0.7230154864789451
random() = 0.33398566368614135
random() = 0.9815603605536798
random() = 0.06697961682649778
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
- [[JavaScript Language Reference]], Mozilla Developer Network
- [[Mozilla Developer Network]]
- Download [[node.js]]
- [[w3schools.com]]