math.h - Mathematical Functions

Category: 📂 std/ (C Standard Library)
Header: <math.h>
Scope: C89, C99, C11

The math.h header declares a set of functions to perform common mathematical operations and manipulations on floating-point numbers.

Facilities Overview

Facility Category	Key Symbols	Description
Trigonometric	sin, cos, tan, asin, acos, atan, atan2	Standard angle-based transformations.
Exponential & Log	exp, log, log10, pow, sqrt, cbrt	Power and logarithmic operations.
Rounding & Remainder	ceil, floor, round, trunc, fmod, remainder	Mapping reals to integers or modular arithmetic.
Absolute & Min/Max	fabs, fmax, fmin	Magnitude and value bounds.
Hyperbolic	sinh, cosh, tanh, asinh, acosh, atanh	Hyperbolic angle transformations.

Types & Variables

HUGE_VAL

#define HUGE_VAL (__builtin_huge_val())

Positive double expression representing a very large value, often used to indicate overflow.

INFINITY

#define INFINITY (__builtin_inf())

Constant expression of type float representing positive infinity (C99).

NAN

#define NAN (__builtin_nan(""))

Constant expression of type float representing a quiet NaN (Not a Number) (C99).

Functions

Trigonometric Functions

sin

double sin(double x)

Computes the sine of an angle x (measured in radians).

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double angle = 0.0;
    printf("sin(0) = %f\n", sin(angle)); // Output: sin(0) = 0.000000
    printf("sin(π/2) = %f\n", sin(1.5708)); // Output: sin(π/2) ≈ 1.000000
    return 0;
}

cos

double cos(double x)

Computes the cosine of an angle x (measured in radians).

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double angle = 0.0;
    printf("cos(0) = %f\n", cos(angle)); // Output: cos(0) = 1.000000
    printf("cos(π) = %f\n", cos(3.14159)); // Output: cos(π) ≈ -1.000000
    return 0;
}

tan

double tan(double x)

Computes the tangent of an angle x (measured in radians).

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double angle = 0.7854; // π/4 radians (45 degrees)
    printf("tan(π/4) = %f\n", tan(angle)); // Output: tan(π/4) ≈ 1.000000
    return 0;
}

asin

double asin(double x)

Computes the arc sine of x, returning a value in the range [-π/2, π/2].

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double value = 0.5;
    printf("asin(0.5) = %f radians\n", asin(value)); // Output: ≈ 0.523599 (30°)
    return 0;
}

acos

double acos(double x)

Computes the arc cosine of x, returning a value in the range [0, π].

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double value = 0.5;
    printf("acos(0.5) = %f radians\n", acos(value)); // Output: ≈ 1.047198 (60°)
    return 0;
}

atan

double atan(double x)

Computes the arc tangent of x, returning a value in the range [-π/2, π/2].

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double value = 1.0;
    printf("atan(1.0) = %f radians\n", atan(value)); // Output: ≈ 0.785398 (45°)
    return 0;
}

atan2

double atan2(double y, double x)

Computes the arc tangent of y/x, using the signs of both arguments to determine the correct quadrant. Returns a value in the range [-π, π].

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double y = 1.0, x = 1.0;
    printf("atan2(1, 1) = %f radians\n", atan2(y, x)); // Output: ≈ 0.785398
    printf("atan2(1, -1) = %f radians\n", atan2(1.0, -1.0)); // Output: ≈ 2.356194
    return 0;
}

Exponential & Logarithmic

exp

double exp(double x)

Computes the exponential function e^x.

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double x = 1.0;
    printf("e^1 = %f\n", exp(x)); // Output: e^1 ≈ 2.718282
    printf("e^0 = %f\n", exp(0.0)); // Output: e^0 = 1.000000
    return 0;
}

log

double log(double x)

Computes the natural logarithm (base e) of x.

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double x = 2.718282;
    printf("ln(e) = %f\n", log(x)); // Output: ln(e) ≈ 1.000000
    printf("ln(10) = %f\n", log(10.0)); // Output: ln(10) ≈ 2.302585
    return 0;
}

log10

double log10(double x)

Computes the common logarithm (base 10) of x.

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double x = 100.0;
    printf("log10(100) = %f\n", log10(x)); // Output: log10(100) = 2.000000
    printf("log10(1000) = %f\n", log10(1000.0)); // Output: log10(1000) = 3.000000
    return 0;
}

pow

double pow(double x, double y)

Computes x raised to the power of y (x^y).

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double base = 2.0, exponent = 8.0;
    printf("2^8 = %f\n", pow(base, exponent)); // Output: 2^8 = 256.000000
    printf("3^3 = %f\n", pow(3.0, 3.0)); // Output: 3^3 = 27.000000
    return 0;
}

sqrt

double sqrt(double x)

Computes the square root of x.

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double x = 16.0;
    printf("sqrt(16) = %f\n", sqrt(x)); // Output: sqrt(16) = 4.000000
    printf("sqrt(2) = %f\n", sqrt(2.0)); // Output: sqrt(2) ≈ 1.414214
    return 0;
}

cbrt

double cbrt(double x)

Computes the cube root of x (C99).

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double x = 27.0;
    printf("cbrt(27) = %f\n", cbrt(x)); // Output: cbrt(27) = 3.000000
    printf("cbrt(8) = %f\n", cbrt(8.0)); // Output: cbrt(8) = 2.000000
    return 0;
}

Rounding & Remainder

ceil

double ceil(double x)

Rounds x upward to the nearest integer.

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    printf("ceil(2.3) = %f\n", ceil(2.3)); // Output: ceil(2.3) = 3.000000
    printf("ceil(-2.3) = %f\n", ceil(-2.3)); // Output: ceil(-2.3) = -2.000000
    return 0;
}

floor

double floor(double x)

Rounds x downward to the nearest integer.

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    printf("floor(2.7) = %f\n", floor(2.7)); // Output: floor(2.7) = 2.000000
    printf("floor(-2.3) = %f\n", floor(-2.3)); // Output: floor(-2.3) = -3.000000
    return 0;
}

round

double round(double x)

Rounds x to the nearest integer value (C99).

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    printf("round(2.3) = %f\n", round(2.3)); // Output: round(2.3) = 2.000000
    printf("round(2.7) = %f\n", round(2.7)); // Output: round(2.7) = 3.000000
    return 0;
}

trunc

double trunc(double x)

Rounds x toward zero, removing the fractional part (C99).

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    printf("trunc(2.7) = %f\n", trunc(2.7)); // Output: trunc(2.7) = 2.000000
    printf("trunc(-2.7) = %f\n", trunc(-2.7)); // Output: trunc(-2.7) = -2.000000
    return 0;
}

fmod

double fmod(double x, double y)

Computes the floating-point remainder of x/y.

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double x = 7.5, y = 2.0;
    printf("fmod(7.5, 2.0) = %f\n", fmod(x, y)); // Output: fmod(7.5, 2.0) = 1.500000
    printf("fmod(10.0, 3.0) = %f\n", fmod(10.0, 3.0)); // Output: fmod(10.0, 3.0) = 1.000000
    return 0;
}

remainder

double remainder(double x, double y)

Computes the IEEE remainder of x/y (C99).

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double x = 10.0, y = 3.0;
    printf("remainder(10.0, 3.0) = %f\n", remainder(x, y)); // Output: ≈ 1.000000
    return 0;
}

Absolute Value & Min/Max

fabs

double fabs(double x)

Computes the absolute value of x.

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    printf("fabs(-5.5) = %f\n", fabs(-5.5)); // Output: fabs(-5.5) = 5.500000
    printf("fabs(5.5) = %f\n", fabs(5.5)); // Output: fabs(5.5) = 5.500000
    return 0;
}

fmax

double fmax(double x, double y)

Returns the larger of two floating-point values (C99).

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    printf("fmax(3.5, 2.1) = %f\n", fmax(3.5, 2.1)); // Output: fmax(3.5, 2.1) = 3.500000
    printf("fmax(-1.0, -5.0) = %f\n", fmax(-1.0, -5.0)); // Output: fmax(-1.0, -5.0) = -1.000000
    return 0;
}

fmin

double fmin(double x, double y)

Returns the smaller of two floating-point values (C99).

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    printf("fmin(3.5, 2.1) = %f\n", fmin(3.5, 2.1)); // Output: fmin(3.5, 2.1) = 2.100000
    printf("fmin(-1.0, -5.0) = %f\n", fmin(-1.0, -5.0)); // Output: fmin(-1.0, -5.0) = -5.000000
    return 0;
}

Hyperbolic Functions

sinh

double sinh(double x)

Computes the hyperbolic sine of x.

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double x = 1.0;
    printf("sinh(1.0) = %f\n", sinh(x)); // Output: sinh(1.0) ≈ 1.175201
    return 0;
}

cosh

double cosh(double x)

Computes the hyperbolic cosine of x.

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double x = 1.0;
    printf("cosh(1.0) = %f\n", cosh(x)); // Output: cosh(1.0) ≈ 1.543081
    return 0;
}

tanh

double tanh(double x)

Computes the hyperbolic tangent of x.

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double x = 1.0;
    printf("tanh(1.0) = %f\n", tanh(x)); // Output: tanh(1.0) ≈ 0.761594
    return 0;
}

asinh

double asinh(double x)

Computes the inverse hyperbolic sine of x (C99).

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double x = 1.0;
    printf("asinh(1.0) = %f\n", asinh(x)); // Output: asinh(1.0) ≈ 0.881374
    return 0;
}

acosh

double acosh(double x)

Computes the inverse hyperbolic cosine of x (C99).

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double x = 2.0;
    printf("acosh(2.0) = %f\n", acosh(x)); // Output: acosh(2.0) ≈ 1.316958
    return 0;
}

atanh

double atanh(double x)

Computes the inverse hyperbolic tangent of x (C99).

Example

#include <math.h>
#include <stdio.h>

int main(void) {
    double x = 0.5;
    printf("atanh(0.5) = %f\n", atanh(x)); // Output: atanh(0.5) ≈ 0.549306
    return 0;
}

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math.h - Mathematical Functions

Facilities Overview

Types & Variables

HUGE_VAL

INFINITY

NAN

Functions

Trigonometric Functions

sin

cos

tan

asin

acos

atan

atan2

Exponential & Logarithmic

exp

log

log10

pow

sqrt

cbrt

Rounding & Remainder

ceil

floor

round

trunc

fmod

remainder

Absolute Value & Min/Max

fabs

fmax

fmin

Hyperbolic Functions

sinh

cosh

tanh

asinh

acosh

atanh