Reference: math.h

Big idea

<math.h> holds the floating-point maths: roots, powers, rounding, logs, and trigonometry. Almost everything takes and returns double; add f to a name for the float version (sqrtf) and l for long double.

On Linux, link with -lm when you compile by hand: gcc main.c -lm.

Roots and powers

sqrt / cbrt

double sqrt(double x);
double cbrt(double x);

Square root and cube root.

• Gotcha: sqrt of a negative number returns NaN ("not a number"), which then spreads through every calculation it touches.
• Example: sqrt(2) → 1.414214

pow

double pow(double base, double exp);

base to the power exp.

• Gotcha: it's a double — (int) pow(10, 2) is fine for small values, but for integer powers in a loop, multiplying is exact and faster. ^ in C is XOR, not power.
• Example: pow(2, 0.5) → 1.414214

hypot

double hypot(double x, double y);

sqrt(x*x + y*y) without overflowing on big values — distance from the origin.

• Example: hypot(3, 4) → 5

exp / log / log10 / log2

double exp(double x);
double log(double x);     /* natural log, base e */
double log10(double x);
double log2(double x);

• Gotcha: log is the natural log, not base 10. log(0) is minus infinity; log of a negative is NaN.
• Example: log10(1000) → 3

Rounding and absolute value

floor / ceil / round / trunc

double floor(double x);   /* down, towards -infinity */
double ceil(double x);    /* up, towards +infinity */
double round(double x);   /* nearest; halves away from zero */
double trunc(double x);   /* towards zero: drops the fraction */

• Gotcha: they still return a double; cast if you need an int: (int) round(x). A plain (int) cast truncates.

fabs

double fabs(double x);

Absolute value of a double. (abs for ints lives in <stdlib.h>; using it on a double drops the fraction.)

fmod

double fmod(double x, double y);

The remainder of x / y for decimals — % only works on integers.

• Example: fmod(7.5, 2) → 1.5

fmin / fmax

double fmin(double a, double b);
double fmax(double a, double b);

The smaller / larger of two doubles.

Trigonometry

double sin(double x);  double cos(double x);  double tan(double x);
double asin(double x); double acos(double x); double atan(double x);
double atan2(double y, double x);

• Gotcha: angles are in radians, not degrees: radians = degrees * M_PI / 180. M_PI isn't strictly standard; define your own #define PI 3.14159265358979 if it's missing.
• atan2(y, x) gives the angle of the point (x, y) in the right quadrant — prefer it to atan(y / x).
• Example: sin(PI / 6) → 0.5

Special values

• INFINITY, NAN — infinity and not-a-number.
• isnan(x), isinf(x), isfinite(x) — test for them. (x == NAN is always false, even when x is NaN.)
• HUGE_VAL — returned on overflow.

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

#define PI 3.14159265358979

int main(void) {
    printf("%.3f %.1f %.1f\n", sqrt(2), pow(2, 10), cbrt(27));
    printf("%.1f %.1f %.1f %.1f\n", floor(-2.5), ceil(-2.5), round(-2.5), trunc(-2.5));
    printf("%.1f %.1f %.1f\n", fabs(-4.5), fmod(7.5, 2), hypot(5, 12));
    printf("%.1f %.1f\n", log10(1000), log2(8));
    printf("%.2f %.2f\n", sin(PI / 6), cos(0));
    printf("%.1f degrees\n", atan2(1, 1) * 180 / PI);
    printf("%d\n", isnan(sqrt(-1)) != 0);
    return 0;
}

output
1.414 1024.0 3.0
-3.0 -2.0 -3.0 -2.0
4.5 1.5 13.0
3.0 3.0
0.50 1.00
45.0 degrees
1