The **`erfcf` function** is defined in the `math.h` header file in C. It takes in a single parameter, a `float` value, and  then computes the *complementary error function* of the given argument, returning a type `float` value. 

The complementary error function in mathematics is defined as follows:

> erfc $z$ = $1- \frac{2}{\sqrt{\pi}}$ $\int_{0}^{arg} e^{-t^2} dt$ 

> = $\frac{2}{\sqrt{\pi}}$ $\int_{arg}^{\infty} e^{-t^2} dt$ 

> The argument to the `erfcf` function serves as the lower limit in the above integral.

The error function is most often used in probability and statistics. It integrates the normal distribution and gives the probability that a normally distributed random variable `Y` (with mean 0 and variance ½) falls into the range `[−x, x]`.

The complementary error function, combined with its series expansion, provides approximate expressions for small and large values of `x`.


> The `erfc` function in mathematics caters to values of all data types. There is a unique function for each data type in C.

The figure below shows the plot of the `erfc` function:


The illustration below shows how `erfcf` function works:

# Declaration

The `erfcf` function is defined as follows:

```C
float erfcf(float arg);
```
It takes in a single value of type `float` and computes its complementary error function. It then returns the answer of type `float`.

# Error Handling

The `erfcf` function returns special values for certain arguments:


|  Special Value | Returned   |
| - | - |
| +INFINITY | +0  |
| -INFINITY | +2  |
| `NAN`| `NAN`|

# Examples

The following code snippet shows how we can use the `erfcf` function:

#include <stdio.h> // Including header file for printf function
#include <math.h>  // Including header file for erfcf function

int main (){

  float param, result;
  param = 1.5;
  result = erfcf(param);
  printf("erfcf (%f) = %f\n", param, result);
  return 0;
}

The following code snippet shows how error handling in the `erfcf` function works:

#include <stdio.h> // Including header file for printf function
#include <math.h>  // Including header file for erfcf function

int main (){

  printf("erfcf (%f) = %f\n", INFINITY, erfcf(INFINITY));
  printf("erfcf (%f) = %f\n", -INFINITY, erfcf(-INFINITY));
  return 0;
}

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What is erfcf in C?

Calculates the complementary error function for a float value, being used in probability and statistics.