From 754bbf7a25a8dda49b5d08ef0d0443bbf5af0e36 Mon Sep 17 00:00:00 2001 From: Craig Jennings Date: Sun, 7 Apr 2024 13:41:34 -0500 Subject: new repository --- devdocs/c/numeric%2Fmath%2Ferf.html | 69 +++++++++++++++++++++++++++++++++++++ 1 file changed, 69 insertions(+) create mode 100644 devdocs/c/numeric%2Fmath%2Ferf.html (limited to 'devdocs/c/numeric%2Fmath%2Ferf.html') diff --git a/devdocs/c/numeric%2Fmath%2Ferf.html b/devdocs/c/numeric%2Fmath%2Ferf.html new file mode 100644 index 00000000..a4223e04 --- /dev/null +++ b/devdocs/c/numeric%2Fmath%2Ferf.html @@ -0,0 +1,69 @@ +

erf, erff, erfl

Defined in header <math.h> 
float       erff( float arg );
+		 (1) (since C99) 
double      erf( double arg );
+		 (2) (since C99) 
long double erfl( long double arg );
+		 (3) (since C99)
Defined in header <tgmath.h> 
#define erf( arg )
+		 (4) (since C99)
+1-3) Computes the error function of arg.
+4) Type-generic macro: If arg has type long double, erfl is called. Otherwise, if arg has integer type or the type double, erf is called. Otherwise, erff is called.

Parameters

+ +
arg - floating point value

Return value

If no errors occur, value of the error function of arg, that is \(\frac{2}{\sqrt{\pi} }\int_{0}^{arg}{e^{-{t^2} }\mathsf{d}t}\)2/√π∫arg0e-t2dt, is returned. If a range error occurs due to underflow, the correct result (after rounding), that is \(\frac{2\cdot arg}{\sqrt{\pi} }\)2*arg/√π, is returned.

Error handling

Errors are reported as specified in math_errhandling.

+

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

+

Notes

Underflow is guaranteed if |arg| < DBL_MIN*(sqrt(π)/2). \(\operatorname{erf}(\frac{x}{\sigma \sqrt{2} })\)erf(

+x/σ√2) is the probability that a measurement whose errors are subject to a normal distribution with standard deviation \(\sigma\)σ is less than \(x\)x away from the mean value.

Example

#include <math.h>
+#include <stdio.h>
+ 
+double phi(double x1, double x2)
+{
+    return (erf(x2 / sqrt(2)) - erf(x1 / sqrt(2))) / 2;
+}
+ 
+int main(void)
+{
+    puts("normal variate probabilities:");
+    for (int n = -4; n < 4; ++n)
+        printf("[%2d:%2d]: %5.2f%%\n", n, n + 1, 100 * phi(n, n + 1));
+ 
+    puts("special values:");
+    printf("erf(-0) = %f\n", erf(-0.0));
+    printf("erf(Inf) = %f\n", erf(INFINITY));
+}

Output:

+
normal variate probabilities:
+[-4:-3]:  0.13%
+[-3:-2]:  2.14%
+[-2:-1]: 13.59%
+[-1: 0]: 34.13%
+[ 0: 1]: 34.13%
+[ 1: 2]: 13.59%
+[ 2: 3]:  2.14%
+[ 3: 4]:  0.13%
+special values:
+erf(-0) = -0.000000
+erf(Inf) = 1.000000

References

See also

+ +
+
(C99)(C99)(C99)
 computes complementary error function
(function)
C++ documentation for erf
+ +
+Weisstein, Eric W. "Erf." From MathWorld — A Wolfram Web Resource.
+

+ © cppreference.com
Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.
+ https://en.cppreference.com/w/c/numeric/math/erf +

+
-- cgit v1.2.3