# <math.h>

**[<math.h>](https://en.cppreference.com/w/c/header/math)** provides standard math functions: trigonometric, exponential, logarithmic, rounding, and IEEE 754 utilities (`isnan`, `isinf`). Append `f` for float or `l` for long double versions.

Compile with `-lm` to link the math library.

## Example

This example demonstrates basic math functions and special-value checking.

```c
// compile: gcc -o mathexample mathexample.c -lm
// run: ./mathexample
// description: math functions and special value detection

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

int main() {
    printf("sqrt(2) = %.6f\n", sqrt(2.0));
    printf("sin(pi/4) = %.6f\n", sin(M_PI / 4));
    printf("exp(1) = %.6f\n", exp(1.0));
    printf("log(10) = %.6f\n", log(10.0));
    
    double nan_val = 0.0 / 0.0;
    double inf_val = 1.0 / 0.0;
    printf("isnan(nan): %d, isinf(inf): %d\n", isnan(nan_val), isinf(inf_val));
    
    return 0;
}
```

## Common functions

**Root and power**:
- `sqrt(x)`: square root
- `cbrt(x)`: cube root
- `pow(x, y)`: x to power y
- `hypot(x, y)`: sqrt(x² + y²) without overflow

**Exponential and logarithm**:
- `exp(x)`, `exp2(x)`, `exp10(x)`: e^x, 2^x, 10^x
- `expm1(x)`: e^x - 1 (accurate for small x)
- `log(x)`, `log2(x)`, `log10(x)`: natural, base-2, base-10 logarithm
- `log1p(x)`: log(1 + x) (accurate for small x)

**Trigonometric** (argument in radians):
- `sin(x)`, `cos(x)`, `tan(x)`
- `asin(x)`, `acos(x)`, `atan(x)`: inverse (range: -π/2 to π/2)
- `atan2(y, x)`: inverse with quadrant correction

**Hyperbolic**:
- `sinh(x)`, `cosh(x)`, `tanh(x)`
- `asinh(x)`, `acosh(x)`, `atanh(x)`: inverse

**Rounding**:
- `ceil(x)`: round up (smallest integer ≥ x)
- `floor(x)`: round down (largest integer ≤ x)
- `round(x)`: round to nearest integer (0.5 rounds away from zero)
- `trunc(x)`: truncate toward zero
- `nearbyint(x)`: round to nearest using current rounding mode
- `rint(x)`: similar to nearbyint but may raise exception

**Absolute value and remainder**:
- `fabs(x)`: absolute value (floating-point)
- `fmod(x, y)`: floating-point remainder (sign of x)
- `remainder(x, y)`: IEEE remainder (nearest multiple of y)
- `drem(x, y)`: alias for remainder

**Minimum and maximum**:
- `fmin(x, y)`: minimum (NaN-safe: returns non-NaN if possible)
- `fmax(x, y)`: maximum

**Special value checks**:
- `isnan(x)`: check if NaN
- `isinf(x)`: check if infinite
- `isfinite(x)`: check if finite (not NaN or inf)
- `isnormal(x)`: check if normal (not zero, subnormal, inf, or NaN)
- `signbit(x)`: check sign bit

**Constants** (non-standard; require `-D_USE_MATH_DEFINES` or `-D_GNU_SOURCE`):
- `M_PI`: π
- `M_E`: e
- `M_LN2`, `M_LN10`: ln(2), ln(10)
- `M_LOG2E`, `M_LOG10E`: log₂(e), log₁₀(e)
- `M_SQRT2`, `M_SQRT1_2`: √2, 1/√2