erfc, erfcf, erfcl
Defined in header <math.h>
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(1) | (since C99) |
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(2) | (since C99) |
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(3) | (since C99) |
Defined in header <tgmath.h>
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(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
arg
2 |
√π |
∞
arge-t2t
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),
- If the argument is +∞, +0 is returned
- If the argument is -∞, 2 is returned
- If the argument is NaN, NaN is returned
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));
puts("special values:");
printf("erfc(-Inf) = %f\n", erfc(-INFINITY));
printf("erfc(Inf) = %f\n", 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
C11 standard (ISO/IEC 9899:2011):
- 7.12.8.2 The erfc functions (p: 249-250)
- 7.25 Type-generic math (p: 373-375)
- F.10.5.2 The erfc functions (p: 525)
C99 standard (ISO/IEC 9899:1999):
- 7.12.8.2 The erfc functions (p: 230)
- 7.22 Type-generic math (p: 335-337)
- F.9.5.2 The erfc functions (p: 462)
See also
(C99)(C99)(C99) |
computes error function (function) |
External links
© cppreference.com
Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.
http://en.cppreference.com/w/c/numeric/math/erfc