C++ Standard Library`<cmath>`

The C++ standard library provides a wealth of functionality, among which<cmath>is a header file containing mathematical functions, providing many basic mathematical operations and constants.

<cmath>is a header file in the C++ standard library that defines a set of mathematical functions capable of performing basic mathematical operations such as exponentiation, trigonometric functions, logarithms, absolute values, etc.

To use<cmath>For the functions in it, you need to include this header file in your C++ program:

#include <cmath>

Common Functions

<cmath>provides many mathematical functions; here are some commonly used ones.

1. Basic Mathematical Functions

Function	Features	Example
`abs(x)`	Compute an integer`x`'s absolute value	`abs(-5) // 5`
`fabs(x)`	Compute a floating-point number`x`'s absolute value	`fabs(-5.5) // 5.5`
`fmod(x, y)`	Compute`x`divided by`y`the remainder	`fmod(5.3, 2) // 1.3`
`remainder(x, y)`	Compute`x`divided by`y`the remainder	`remainder(5.5, 2) // 1.5`
`fmax(x, y)`	return`x`and`y`the larger value	`fmax(3.5, 4.2) // 4.2`
`fmin(x, y)`	return`x`and`y`the smaller value	`fmin(3.5, 4.2) // 3.5`
`hypot(x, y)`	Compute`sqrt(xx + yy)`	`hypot(3, 4) // 5`

2. Exponential and Logarithmic Functions

Function	Features	Example
`exp(x)`	Compute`e^x`，`e`base of the natural logarithm	`exp(1) // 2.71828...`
`log(x)`	Compute`x`'s natural logarithm	`log(2.71828) // 1`
`log10(x)`	Compute`x`base-10 logarithm of	`log10(100) // 2`
`pow(x, y)`	Compute`x`of`y`power	`pow(2, 3) // 8`
`sqrt(x)`	Compute`x`'s square root	`sqrt(16) // 4`
`cbrt(x)`	Compute`x`'s cube root	`cbrt(27) // 3`
`expm1(x)`	Compute`e^x - 1`	`expm1(1) // 1.71828...`
`log1p(x)`	Compute`log(1 + x)`, suitable for cases where x is close to 0	`log1p(0.00001) // 0.00001`

3. Trigonometric functions

Function	Features	Example
`sin(x)`	Compute`x`sine of,`x`In radians	`sin(3.14159 / 2) // 1`
`cos(x)`	Compute`x`cosine of,`x`In radians	`cos(3.14159) // -1`
`tan(x)`	Compute`x`tangent of,`x`In radians	`tan(0) // 0`
`asin(x)`	Compute`x`arcsine of, returns radians	`asin(1) // 3.14159/2`
`acos(x)`	Compute`x`arccosine of, returns radians	`acos(-1) // 3.14159`
`atan(x)`	Compute`x`arctangent of, returns radians	`atan(1) // 3.14159/4`
`atan2(y, x)`	Compute`y/x`arctangent of, returns radians	`atan2(1, 1) // 3.14159/4`

4. Hyperbolic functions

Function	Features	Example
`sinh(x)`	Compute`x`hyperbolic sine of	`sinh(0) // 0`
`cosh(x)`	Compute`x`hyperbolic cosine of	`cosh(0) // 1`
`tanh(x)`	Compute`x`hyperbolic tangent of	`tanh(1) // 0.7616`
`asinh(x)`	Compute`x`inverse hyperbolic sine of	`asinh(1) // 0.8814`
`acosh(x)`	Compute`x`inverse hyperbolic cosine of,`x` ≥ 1	`acosh(1) // 0`
`atanh(x)`	Compute`x`inverse hyperbolic tangent of,`x`on (-1, 1)	`atanh(0.5) // 0.5493`

5. Rounding and Floating-Point Operations

Function	Features	Example
`ceil(x)`	Returns not less than`x`the smallest integer	`ceil(2.3) // 3`
`floor(x)`	Returns not greater than`x`the largest integer	`floor(2.3) // 2`
`trunc(x)`	Returns the integer value with the fractional part removed	`trunc(2.8) // 2`
`round(x)`	Returns the nearest integer after rounding	`round(2.5) // 3`
`lround(x)`	Returns rounded to`long`Type	`lround(2.5) // 3`
`llround(x)`	Returns rounded to`long long`Type	`llround(2.5) // 3`
`nearbyint(x)`	returns rounding to the nearest integer (but does not raise floating-point exceptions)	`nearbyint(2.5) // 2`
`rint(x)`	returns rounding to an integer according to the current rounding mode	`rint(2.5) // 3`
`modf(x, &intpart)`	will`x`Separate the integer and fractional parts of	`modf(2.3, &intpart)`

6. Floating-Point Checks

Function	Features	Example
`isfinite(x)`	Checks`x`whether it is a finite value (not infinity or NaN)	`isfinite(3.0) // true`
`isinf(x)`	Checks`x`whether it is infinity	`isinf(1.0 / 0.0) // true`
`isnan(x)`	Checks`x`whether it is NaN	`isnan(0.0 / 0.0) // true`
`isnormal(x)`	Checks`x`Whether it is a normal non-zero floating-point number	`isnormal(1.0) // true`
`signbit(x)`	Checks`x`whether the sign is negative	`signbit(-5.3) // true`

Example

Below is an example using<cmath>A simple example of , demonstrating how to compute the square root, sine, and absolute value of a number.

Example 1

#include <iostream>
#include <cmath> // include the <cmath> header file

int main() {
double num = 9.0;
double root = sqrt(num); // calculate square root
double sinValue = sin(M_PI / 2); // Calculate the sine value, M_PI is an approximation of π
double absValue = abs(-5.0); // Calculate the absolute value

std::cout << "The square root of " << num << " is " << root << std::endl;
std::cout << "The sine of " << M_PI / 2 << " is " << sinValue << std::endl;
std::cout << "The absolute value of -5.0 is " << absValue << std::endl;

return 0;
}

Output:

The square root of 9 is 3
The sine of 1.570796 is 1
The absolute value of -5 is 5

Example 2

#include <iostream>
#include <cmath>

int main() {
// Basic mathematical operations
std::cout << "abs(-5) = " << abs(-5) << std::endl;
std::cout << "fmod(5.3, 2) = " << fmod(5.3, 2) << std::endl;

// Exponential and logarithmic functions
std::cout << "exp(1) = " << exp(1) << std::endl;
std::cout << "log(2.71828) = " << log(2.71828) << std::endl;
std::cout << "pow(2, 3) = " << pow(2, 3) << std::endl;

// Trigonometric functions
std::cout << "sin(3.14159 / 2) = " << sin(3.14159 / 2) << std::endl;
std::cout << "cos(3.14159) = " << cos(3.14159) << std::endl;

// Rounding functions
std::cout << "ceil(2.3) = " << ceil(2.3) << std::endl;
std::cout << "floor(2.3) = " << floor(2.3) << std::endl;

// Floating-point checks
double x = 1.0 / 0.0;
if (isinf(x)) {
std::cout << "x is infinite" << std::endl;
}

return 0;
}

Notes

<cmath>Functions in typically acceptfloatordoubletype arguments and return results of the corresponding type. Forlong doubletype, you can use<cmath>functions in , but you need to add after the function namelsuffix, for examplesqrtl。
Certain functions, such aspowandlog, you can pass integers as arguments, but the result is still a floating-point number.
<cmath>functions in may throw exceptions, for example whensqrtWhen the argument of the function is negative, it throwsstd::domain_erroran exception.

<cmath>is a very useful header file in the C++ standard library. It provides many basic mathematical functions that can help developers perform mathematical operations when writing programs.

C++ Standard Library<cmath>