From 82ba818ff456bcd6d56a06226e3f27e98fbb55c3 Mon Sep 17 00:00:00 2001 From: Craig Jennings Date: Thu, 14 Aug 2025 22:58:58 -0500 Subject: removing all downloaded devdocs files --- devdocs/c/numeric%2Fcomplex%2Fcacosh.html | 80 ------------------------------- 1 file changed, 80 deletions(-) delete mode 100644 devdocs/c/numeric%2Fcomplex%2Fcacosh.html (limited to 'devdocs/c/numeric%2Fcomplex%2Fcacosh.html') diff --git a/devdocs/c/numeric%2Fcomplex%2Fcacosh.html b/devdocs/c/numeric%2Fcomplex%2Fcacosh.html deleted file mode 100644 index 9da0e7a1..00000000 --- a/devdocs/c/numeric%2Fcomplex%2Fcacosh.html +++ /dev/null @@ -1,80 +0,0 @@ -

cacoshf, cacosh, cacoshl

Defined in header <complex.h> 
float complex       cacoshf( float complex z );
-		 (1) (since C99) 
double complex      cacosh( double complex z );
-		 (2) (since C99) 
long double complex cacoshl( long double complex z );
-		 (3) (since C99)
Defined in header <tgmath.h> 
#define acosh( z )
-		 (4) (since C99)
-1-3) Computes complex arc hyperbolic cosine of a complex value z with branch cut at values less than 1 along the real axis.
-4) Type-generic macro: If z has type long double complex, cacoshl is called. if z has type double complex, cacosh is called, if z has type float complex, cacoshf is called. If z is real or integer, then the macro invokes the corresponding real function (acoshf, acosh, acoshl). If z is imaginary, then the macro invokes the corresponding complex number version and the return type is complex.

Parameters

- -
z - complex argument

Return value

The complex arc hyperbolic cosine of z in the interval [0; ∞) along the real axis and in the interval [−iπ; +iπ] along the imaginary axis.

-

Error handling and special values

Errors are reported consistent with math_errhandling

-

If the implementation supports IEEE floating-point arithmetic,

-

Notes

Although the C standard names this function "complex arc hyperbolic cosine", the inverse functions of the hyperbolic functions are the area functions. Their argument is the area of a hyperbolic sector, not an arc. The correct name is "complex inverse hyperbolic cosine", and, less common, "complex area hyperbolic cosine".

-

Inverse hyperbolic cosine is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventionally placed at the line segment (-∞,+1) of the real axis.

-

The mathematical definition of the principal value of the inverse hyperbolic cosine is acosh z = ln(z + √z+1 √z-1) For any z, acosh(z) =

-√z-1/√1-z acos(z), or simply i acos(z) in the upper half of the complex plane.

Example

#include <stdio.h>
-#include <complex.h>
- 
-int main(void)
-{
-    double complex z = cacosh(0.5);
-    printf("cacosh(+0.5+0i) = %f%+fi\n", creal(z), cimag(z));
- 
-    double complex z2 = conj(0.5); // or cacosh(CMPLX(0.5, -0.0)) in C11
-    printf("cacosh(+0.5-0i) (the other side of the cut) = %f%+fi\n", creal(z2), cimag(z2));
- 
-    // in upper half-plane, acosh(z) = i*acos(z) 
-    double complex z3 = casinh(1+I);
-    printf("casinh(1+1i) = %f%+fi\n", creal(z3), cimag(z3));
-    double complex z4 = I*casin(1+I);
-    printf("I*asin(1+1i) = %f%+fi\n", creal(z4), cimag(z4));
-}

Output:

-
cacosh(+0.5+0i) = 0.000000-1.047198i
-cacosh(+0.5-0i) (the other side of the cut) = 0.500000-0.000000i
-casinh(1+1i) = 1.061275+0.666239i
-I*asin(1+1i) = -1.061275+0.666239i

References

See also

- - - - - -
-
(C99)(C99)(C99)
 computes the complex arc cosine
(function)
-
(C99)(C99)(C99)
 computes the complex arc hyperbolic sine
(function)
-
(C99)(C99)(C99)
 computes the complex arc hyperbolic tangent
(function)
-
(C99)(C99)(C99)
 computes the complex hyperbolic cosine
(function)
-
(C99)(C99)(C99)
 computes inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x} }\)arcosh(x))
(function)
C++ documentation for acosh
-

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

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