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%2Ferfc.html | 75 ++++++++++++++++++++++++++++++++++++ 1 file changed, 75 insertions(+) create mode 100644 devdocs/c/numeric%2Fmath%2Ferfc.html (limited to 'devdocs/c/numeric%2Fmath%2Ferfc.html') diff --git a/devdocs/c/numeric%2Fmath%2Ferfc.html b/devdocs/c/numeric%2Fmath%2Ferfc.html new file mode 100644 index 00000000..cbbc7e72 --- /dev/null +++ b/devdocs/c/numeric%2Fmath%2Ferfc.html @@ -0,0 +1,75 @@ +

erfc, erfcf, erfcl

Defined in header <math.h> 
float       erfcf( float arg );
+		 (1) (since C99) 
double      erfc( double arg );
+		 (2) (since C99) 
long double erfcl( long double arg );
+		 (3) (since C99)
Defined in header <tgmath.h> 
#define erfc( arg )
+		 (4) (since C99)
+1-3) Computes the complementary error function of arg, that is 1.0 - erf(arg), but without loss of precision for large arg.
+4) Type-generic macro: If arg has type long double, erfcl is called. Otherwise, if arg has integer type or the type double, erfc is called. Otherwise, erfcf is called.

Parameters

+ +
arg - floating point value

Return value

If no errors occur, value of the complementary error function of arg, that is \(\frac{2}{\sqrt{\pi} }\int_{arg}^{\infty}{e^{-{t^2} }\mathsf{d}t}\)2/√π∫∞arge-t2dt or \({\small 1-\operatorname{erf}(arg)}\)1-erf(arg), is returned.

If a range error occurs due to underflow, the correct result (after rounding) is returned.

+

Error handling

Errors are reported as specified in math_errhandling.

+

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

+

Notes

For the IEEE-compatible type double, underflow is guaranteed if arg > 26.55.

+

Example

#include <stdio.h>
+#include <math.h>
+ 
+double normalCDF(double x) // Phi(-∞, x) aka N(x)
+{
+    return erfc(-x / sqrt(2)) / 2;
+}
+ 
+int main(void)
+{
+    puts("normal cumulative distribution function:");
+    for(double n = 0; n < 1; n += 0.1)
+        printf("normalCDF(%.2f) %5.2f%%\n", n, 100 * normalCDF(n));
+ 
+    printf("special values:\n"
+           "erfc(-Inf) = %f\n"
+           "erfc(Inf) = %f\n",
+           erfc(-INFINITY),
+           erfc(INFINITY));
+}

Output:

+
normal cumulative distribution function:
+normalCDF(0.00) 50.00%
+normalCDF(0.10) 53.98%
+normalCDF(0.20) 57.93%
+normalCDF(0.30) 61.79%
+normalCDF(0.40) 65.54%
+normalCDF(0.50) 69.15%
+normalCDF(0.60) 72.57%
+normalCDF(0.70) 75.80%
+normalCDF(0.80) 78.81%
+normalCDF(0.90) 81.59%
+normalCDF(1.00) 84.13%
+special values:
+erfc(-Inf) = 2.000000
+erfc(Inf) = 0.000000

References

See also

+ +
+
(C99)(C99)(C99)
 computes error function
(function)
C++ documentation for erfc
+ +
+Weisstein, Eric W. "Erfc." 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/erfc +

+
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