Complex.h: Difference between revisions

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{{merge#redirect to|[[C mathematical operations|discuss=Talk:math.h#Single page for C mathematical functions|date=OctoberFunction 2011}}overview]]

{{lowercase|title=complex.h}}

{{C Standard library}}

'''complex.h''' is a [[header file]] in the [[C standard library|standard library]] of the [[C programming language]] that defines functionality for [[complex arithmetic]].<ref name="SUS">{{man|bd|complex.h|SUS|complex arithmetic}}</ref> These functions use the built-in type <code>complex</code> which was introduced with the [[C99]] revision of C.

This header should not be confused with the [[C++ standard library]] header <code>&lt;complex&gt;</code>, which implements complex numbers in a completely different way (as a template class, <code>complex&lt;T&gt;</code>).

== Macro ==

Universal macro:

* complex - alias of _Complex

* _Complex_I - constant, which has type "const float _Complex" and value of imaginary unit I, I*I=-1

Defined only for `C99 Annex G`-compatible compiler modes - native support of imaginary types (it is very rare because Annex G is mathematically incorrect<ref>[http://books.google.com/books?id=PmNVAAAAMAAJ&q=C99+Annex+G& Dr. Dobb's journal: software tools for the professional programmer, Volume 27] "many results in Annex G are pure invention and mathematically incorrect"</ref>):

* imaginary - alias of _Imaginary

* _Imaginary_I Expands to a constant expression of type const float _Imaginary with the value of the imaginary unit.

Universal alias of I:

* I - alias of _Imaginary_I if it is defined else - alias of _Complex_I

Application may undefine complex, imaginary, and I macros if they interfere with internal values.

==Functions==

Each function declared in <code>complex.h</code> has three versions, each of which works with a different floating-point type (<code>double</code>, <code>float</code> and <code>long{{nbsp}}double</code>). Only the <code>double</code> version of each function is listed here; to use the <code>float</code> (or <code>long{{nbsp}}double</code>) version, append an <code>f</code> (or an <code>l<code>, respectively) to the function's name.

Note that all angles are in [[radian]]s.

{| class="wikitable"

|-

|<code>double {{spaces|7}} cabs(double complex); || [[Absolute value#Complex numbers|Absolute value]]

|-

|<code>double complex cacos(double complex);</code> || Complex [[inverse cosine]]

|-

|<code>double complex cacosh(double complex);</code> || Complex [[inverse hyperbolic cosine]]

|-

|<code>double {{spaces|7}} carg(double complex);</code> || [[arg (mathematics)|Complex argument]]

|-

|<code>double complex casin(double complex);</code> || Complex [[inverse sine]]

|-

|<code>double complex casinh(double complex);</code> || Complex [[inverse hyperbolic sine]]

|-

|<code>double complex catan(double complex);</code> || Complex [[inverse tangent]]

|-

|<code>double complex catanh(double complex);</code> || Complex [[inverse hyperbolic tangent]]

|-

|<code>double complex ccos(double complex);</code> || Complex [[cosine]]

|-

|<code>double complex ccosh(double complex);</code> || Complex [[hyperbolic cosine]]

|-

|<code>double complex cexp(double complex);</code> || Complex [[Exponential function|exponential]]

|-

|<code>double {{spaces|7}} cimag(double complex);</code> || [[Imaginary part]] of complex number

|-

|<code>double complex clog(double complex);</code> || Complex [[logarithm]]

|-

|<code>double complex conj(double complex);</code> || [[Complex conjugate]]

|-

|<code>double complex cpow(double complex, double complex);</code> || Complex [[exponentiation|power]]

|-

|<code>double complex cproj(double complex);</code> || Complex projection{{ref label|cproj|A|A}}

|-

|<code>double {{spaces|7}} creal(double complex);</code> || [[Real part]] of complex number

|-

|<code>double complex csin(double complex);</code> || Complex [[sine]]

|-

|<code>double complex csinh(double complex);</code> || Complex [[hyperbolic sine]]

|-

|<code>double complex csqrt(double complex);</code> || Complex [[square root]]

|-

|<code>double complex ctan(double complex);</code> || Complex [[tangent (trigonometric function)|tangent]]

|-

|<code>double complex ctanh(double complex);</code> || Complex [[hyperbolic tangent]]

|-

|}

:{{note label|cproj|A|A}} cproj(''z'') projects the complex number ''z'' onto the [[Riemann sphere]]; the result is ''z'' itself, except complex infinities are mapped to positive infinity on the real axis.<ref>{{man|sh|cproj|SUS|complex projection function}}</ref>

==References==

<references />

[[Category:C standard library headers]]

[[es:Complex.h]]

[[pt:Complex.h]]

[[ru:Complex.h]]

[[uk:Complex.h]]