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 |
---|---|
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.
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/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. ℯx |
floor(x) | Largest integer less than x |
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. xy |
rand() | [[Pseudorandom]] number on the interval [0, RAND_MAX] |
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 include to the top of your program in order to use these math functions and constants.
#include <cmath>
#include <algorithm>
/****************************************************************************** * This program demonstrates the math library. * * Copyright © 2016 Richard Lesh. All rights reserved. *****************************************************************************/ #include <algorithm> #include <cmath> #include <fmt/format.h> #include <iostream> #include <string> using namespace std; int main(int argc, char **argv) { double const a = M_PI / 6; double const b = M_PI / 4; double const c = -a * 2; double const d = -b * 2; double const e = M_E; cout << fmt::format("pi = {0:f}", M_PI) << endl; cout << fmt::format("e = {0:f}", M_E) << endl; // abs, floor, ceil, round, trunc, min, max cout << fmt::format("abs({0:f}) = {1:f}", a, abs(a)) << endl; cout << fmt::format("abs({0:f}) = {1:f}", c, abs(c)) << endl; cout << fmt::format("floor({0:f}) = {1:f}", a, floor(a)) << endl; cout << fmt::format("floor({0:f}) = {1:f}", c, floor(c)) << endl; cout << fmt::format("ceil({0:f}) = {1:f}", a, ceil(a)) << endl; cout << fmt::format("ceil({0:f}) = {1:f}", c, ceil(c)) << endl; cout << fmt::format("round({0:f}) = {1:f}", a, floor(a + 0.5)) << endl; cout << fmt::format("round({0:f}) = {1:f}", c, floor(c + 0.5)) << endl; cout << fmt::format("trunc({0:f}) = {1:f}", a, trunc(a)) << endl; cout << fmt::format("trunc({0:f}) = {1:f}", c, trunc(c)) << endl; cout << fmt::format("min({0:f}, {1:f}) = {2:f}", a, c, min(a, c)) << endl; cout << fmt::format("max({0:f}, {1:f}) = {2:f}", a, c, max(a, c)) << endl; // sin, cos, tan, atan, atan2, acos, asin cout << fmt::format("sin({0:f}) = {1:f}", a, sin(a)) << endl; cout << fmt::format("sin({0:f}) = {1:f}", b, sin(b)) << endl; cout << fmt::format("sin({0:f}) = {1:f}", c, sin(c)) << endl; cout << fmt::format("sin({0:f}) = {1:f}", d, sin(d)) << endl; cout << fmt::format("cos({0:f}) = {1:f}", a, cos(a)) << endl; cout << fmt::format("cos({0:f}) = {1:f}", b, cos(b)) << endl; cout << fmt::format("cos({0:f}) = {1:f}", c, cos(c)) << endl; cout << fmt::format("cos({0:f}) = {1:f}", d, cos(d)) << endl; cout << fmt::format("tan({0:f}) = {1:f}", a, tan(a)) << endl; cout << fmt::format("tan({0:f}) = {1:f}", b, tan(b)) << endl; cout << fmt::format("tan({0:f}) = {1:f}", c, tan(c)) << endl; cout << fmt::format("asin({0:f}) = {1:f}", sin(a), asin(sin(a))) << endl; cout << fmt::format("asin({0:f}) = {1:f}", sin(b), asin(sin(b))) << endl; cout << fmt::format("asin({0:f}) = {1:f}", sin(c), asin(sin(c))) << endl; cout << fmt::format("asin({0:f}) = {1:f}", sin(d), asin(sin(d))) << endl; cout << fmt::format("acos({0:f}) = {1:f}", cos(a), acos(cos(a))) << endl; cout << fmt::format("acos({0:f}) = {1:f}", cos(b), acos(cos(b))) << endl; cout << fmt::format("acos({0:f}) = {1:f}", cos(c), acos(cos(c))) << endl; cout << fmt::format("acos({0:f}) = {1:f}", cos(d), acos(cos(d))) << endl; cout << fmt::format("atan({0:f}) = {1:f}", tan(a), atan(tan(a))) << endl; cout << fmt::format("atan({0:f}) = {1:f}", tan(b), atan(tan(b))) << endl; cout << fmt::format("atan({0:f}) = {1:f}", tan(c), atan(tan(c))) << endl; // 45 degrees cout << fmt::format("atan2({0:f}, {1:f}) = {2:f}", 1.0, 1.0, atan2(1.0, 1.0)) << endl; // 30 degrees cout << fmt::format("atan2({0:f}, {1:f}) = {2:f}", 1.0, sqrt(3.0), atan2(1.0, sqrt(3.0))) << endl; // sinh, cosh, tanh, atanh, acosh, asinh cout << fmt::format("sinh({0:f}) = {1:f}", a, sinh(a)) << endl; cout << fmt::format("sinh({0:f}) = {1:f}", b, sinh(b)) << endl; cout << fmt::format("sinh({0:f}) = {1:f}", c, sinh(c)) << endl; cout << fmt::format("sinh({0:f}) = {1:f}", d, sinh(d)) << endl; cout << fmt::format("cosh({0:f}) = {1:f}", a, cosh(a)) << endl; cout << fmt::format("cosh({0:f}) = {1:f}", b, cosh(b)) << endl; cout << fmt::format("cosh({0:f}) = {1:f}", c, cosh(c)) << endl; cout << fmt::format("cosh({0:f}) = {1:f}", d, cosh(d)) << endl; cout << fmt::format("tanh({0:f}) = {1:f}", a, tanh(a)) << endl; cout << fmt::format("tanh({0:f}) = {1:f}", b, tanh(b)) << endl; cout << fmt::format("tanh({0:f}) = {1:f}", c, tanh(c)) << endl; cout << fmt::format("tanh({0:f}) = {1:f}", d, tanh(d)) << endl; cout << fmt::format("asinh({0:f}) = {1:f}", sinh(a), asinh(sinh(a))) << endl; cout << fmt::format("asinh({0:f}) = {1:f}", sinh(b), asinh(sinh(b))) << endl; cout << fmt::format("asinh({0:f}) = {1:f}", sinh(c), asinh(sinh(c))) << endl; cout << fmt::format("asinh({0:f}) = {1:f}", sinh(d), asinh(sinh(d))) << endl; cout << fmt::format("acosh({0:f}) = {1:f}", cosh(a), acosh(cosh(a))) << endl; cout << fmt::format("acosh({0:f}) = {1:f}", cosh(b), acosh(cosh(b))) << endl; cout << fmt::format("acosh({0:f}) = {1:f}", cosh(c), acosh(cosh(c))) << endl; cout << fmt::format("acosh({0:f}) = {1:f}", cosh(d), acosh(cosh(d))) << endl; cout << fmt::format("atanh({0:f}) = {1:f}", tanh(a), atanh(tanh(a))) << endl; cout << fmt::format("atanh({0:f}) = {1:f}", tanh(b), atanh(tanh(b))) << endl; cout << fmt::format("atanh({0:f}) = {1:f}", tanh(c), atanh(tanh(c))) << endl; cout << fmt::format("atanh({0:f}) = {1:f}", tanh(d), atanh(tanh(d))) << endl; // log, log10, exp, pow, sqrt cout << fmt::format("log({0:f}) = {1:f}", a, log(a)) << endl; cout << fmt::format("log({0:f}) = {1:f}", b, log(b)) << endl; cout << fmt::format("log({0:f}) = {1:f}", -c, log(-c)) << endl; cout << fmt::format("log({0:f}) = {1:f}", -d, log(-d)) << endl; cout << fmt::format("log({0:f}) = {1:f}", e, log(e)) << endl; cout << fmt::format("log10({0:f}) = {1:f}", a, log10(a)) << endl; cout << fmt::format("log10({0:f}) = {1:f}", b, log10(b)) << endl; cout << fmt::format("log10({0:f}) = {1:f}", -c, log10(-c)) << endl; cout << fmt::format("log10({0:f}) = {1:f}", -d, log10(-d)) << endl; cout << fmt::format("log10({0:f}) = {1:f}", e, log10(e)) << endl; cout << fmt::format("exp({0:f}) = {1:f}", 0.5, exp(0.5)) << endl; cout << fmt::format("exp({0:f}) = {1:f}", 1.0, exp(1.0)) << endl; cout << fmt::format("exp({0:f}) = {1:f}", 2.0, exp(2.0)) << endl; cout << fmt::format("pow({0:f}, {1:f}) = {2:f}", 10.0, 0.5, pow(10.0, 0.5)) << endl; cout << fmt::format("pow({0:f}, {1:f}) = {2:f}", 10.0, 1.0, pow(10.0, 1.0)) << endl; cout << fmt::format("pow({0:f}, {1:f}) = {2:f}", 10.0, 2.0, pow(10.0, 2.0)) << endl; cout << fmt::format("sqrt({0:f}) = {1:f}", 0.5, sqrt(0.5)) << endl; cout << fmt::format("sqrt({0:f}) = {1:f}", 2.0, sqrt(2.0)) << endl; cout << fmt::format("sqrt({0:f}) = {1:f}", 10.0, sqrt(10.0)) << endl; // random numbers cout << fmt::format("random() = {0:f}", rand()/(RAND_MAX + 1.0)) << endl; cout << fmt::format("random() = {0:f}", rand()/(RAND_MAX + 1.0)) << endl; cout << fmt::format("random() = {0:f}", rand()/(RAND_MAX + 1.0)) << endl; return 0; }
Output
/****************************************************************************** * This program demonstrates the math integer functions. * * Copyright © 2020 Richard Lesh. All rights reserved. *****************************************************************************/ #include <algorithm> #include <cmath> #include <ctime> #include <fmt/format.h> #include <iostream> #include <string> using namespace std; int main(int argc, char **argv) { int const a = 5; int const b = 10; int const c = -2; // abs, floor, ceil, round, trunc, min, max cout << fmt::format("abs({0:d}) = {1:d}", a, abs(a)) << endl; cout << fmt::format("abs({0:d}) = {1:d}", c, abs(c)) << endl; cout << fmt::format("min({0:d}, {1:d}) = {2:d}", a, b, min(a, b)) << endl; cout << fmt::format("max({0:d}, {1:d}) = {2:d}", a, b, max(a, b)) << endl; cout << fmt::format("min({0:d}, {1:d}) = {2:d}", b, c, min(b, c)) << endl; cout << fmt::format("max({0:d}, {1:d}) = {2:d}", b, c, max(b, c)) << endl; // random numbers srand(time(0)); cout << fmt::format("random({0:d}) = {1:d}", a, int(a * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random({0:d}) = {1:d}", a, int(a * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random({0:d}) = {1:d}", a, int(a * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random({0:d}) = {1:d}", a, int(a * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random({0:d}) = {1:d}", a, int(a * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random({0:d}) = {1:d}", b, int(b * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random({0:d}) = {1:d}", b, int(b * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random({0:d}) = {1:d}", b, int(b * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random({0:d}) = {1:d}", b, int(b * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random({0:d}) = {1:d}", b, int(b * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random(2) = {0:d}", int(2 * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random(2) = {0:d}", int(2 * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random(2) = {0:d}", int(2 * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random(2) = {0:d}", int(2 * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random(2) = {0:d}", int(2 * (rand()/(RAND_MAX + 1.0)))) << endl; cout << fmt::format("random() = {0:f}", rand()/(RAND_MAX + 1.0)) << endl; cout << fmt::format("random() = {0:f}", rand()/(RAND_MAX + 1.0)) << endl; cout << fmt::format("random() = {0:f}", rand()/(RAND_MAX + 1.0)) << endl; cout << fmt::format("random() = {0:f}", rand()/(RAND_MAX + 1.0)) << endl; cout << fmt::format("random() = {0:f}", rand()/(RAND_MAX + 1.0)) << endl; return 0; }
Output
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
-
[[C++ Programming Language]], 4th Edition, Bjarne Stroustrup, Addison-Wesley, 2013, ISBN 978-0321563842.
- [[C++ Language Reference]]
- [[cplusplus.com]]
- [[Cprogramming.com]]