complex.h File Reference

apeNEXT complex functions for nlcc More...

#include <nlibc.h>
#include <math.h>

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Defines

#define _math_setdouble(U, D)

#define _Complex_I   {0., 1.}

#define I   _Complex_I

#define M_PI   3.14159265358979323846

#define M_PI_2   1.57079632679489661923

#define M_PI_4   0.78539816339744830962

#define conj(x)   (~(x))

#define creal(x)   ((x).re)

#define cimag(x)   ((x).im)

#define NAN   (cnan())

#define HUGE_VALD   (cinfty())

Functions

math_inline double cnan (void)

math_inline double cinfty (void)

math_inline complex sincos (double x)

math_inline complex sinhcosh (double x)

math_inline double cabs (complex z)

math_inline double carg (complex z)

math_inline complex cproj (complex z)

math_inline complex cexp (complex z)

math_inline complex clog (complex z)

math_inline complex cpow (complex x, complex y)

math_inline complex csqrt (complex z)

math_inline complex cacosh (complex z)

math_inline complex casinh (complex z)

math_inline complex catanh (complex z)

math_inline complex cacos (complex z)

math_inline complex casin (complex z)

math_inline complex catan (complex z)

math_inline complex ccosh (complex z)

math_inline complex csinh (complex z)

math_inline complex ctanh (complex z)

math_inline complex ccos (complex z)

math_inline complex csin (complex z)

math_inline complex ctan (complex z)

Detailed Description

apeNEXT complex functions for nlcc

NAME: complex.h

SYNOPSIS: #include <complex.h>

DESCRIPTION: The complex.h header file contains the complex functions.
The used data types are defined as double / complex

RETURN VALUE

NOTES

The partial implementations given here are not in the final form!!
Defining the complex variables required the definition or the
regions of the complex-representing variables. We can do this
in different ways:
Using the predefined complex variables in apeNEXT
Redefine these pregiven variables (#pragma)

IMPLEMENTATION for APEnext: possible (complex.h)

VERSION

Id: complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:: K. Huebner, M. Prevot

Definition in file complex.h.

Define Documentation

#define _Complex_I {0., 1.}

Definition at line 120 of file complex.h.

#define _math_setdouble ( U,
D )

Value:
{ \ register union { double d; unsigned i; } u; \ asm("\tatr0h %0 <"#U">" : "=r" (u.i)); D=u.d; \ }
uses: fpclassify(), signbit(), copysign(), fabs() FP_ZERO, FP_NORMAL, FP_INFINITE, FP_NAN,
math_inline double cnan(void) math_inline double cinfty(void)
math_inline complex sincos(double x) (sin_1oct,cos_1oct) math_inline complex sinhcosh(double x) (expm1)
function: uses: double cabs(complex z); (hypot) double carg(complex z); (atan2)
complex cproj(complex z); complex cexp(complex z); (sincos,exp) complex clog(complex z); (log,hypot,atan2) complex cpow(complex x, y); (cexp,clog) complex csqrt(complex z); (sqrt,hypot)
complex cacosh(complex z); (csqrt,clog) complex casinh(complex z); (csqrt,clog) complex catanh(complex z); (log,atan2)
complex cacos(complex z); (cacosh) complex casin(complex z); (casinh) complex catan(complex z); (log,atan2)
complex ccosh(complex z); (sincos,sinhcosh) complex csinh(complex z); (sincos,sinhcosh) complex ctanh(complex z); (sincos,sinhcosh)
complex ccos(complex z); (sincos,sinhcosh) complex csin(complex z); (sincos,sinhcosh) complex ctan(complex z); (sincos,sinhcosh)
Definition at line 115 of file complex.h.
Referenced by acos(), asin(), asin_k(), atan(), atan2(), atan_k(), cbrt(), ceil(), cos(), cos_1oct(), exp(), exp1m(), expm1(), floor(), isqrt(), isqrt2(), log(), log1p(), log2(), sin(), sin_1oct(), sqrt(), sqrt2(), and tan().

#define cimag ( x ) ((x).im)

Definition at line 129 of file complex.h.

#define conj ( x ) (~(x))

Definition at line 127 of file complex.h.

#define creal ( x ) ((x).re)

Definition at line 128 of file complex.h.

#define HUGE_VALD (cinfty())

Definition at line 165 of file complex.h.

#define I _Complex_I

Definition at line 121 of file complex.h.

#define M_PI 3.14159265358979323846

Definition at line 123 of file complex.h.

#define M_PI_2 1.57079632679489661923

Definition at line 124 of file complex.h.

#define M_PI_4 0.78539816339744830962

Definition at line 125 of file complex.h.

#define NAN (cnan())

Definition at line 149 of file complex.h.

Function Documentation

math_inline double cabs ( complex z )

NAME
cabs() - complex absolute value

SYNOPSIS
#include <complex.h>
double cabs(complex)

DESCRIPTION
The cabs() function computes the absolute value of argument (also called norm, modulus, or magnitude).

RETURN VALUE
The cabs() functio returns the absolute value

NOTES
z = (x) + j(y) cabs(z) = hypot(x,y)

IMPLEMENTATION for APEnext: implem (cabs)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex cacos ( complex z )

NAME
cacos - arc cosine

SYNOPSIS
#include <complex.h>
complex cacos(complex)

DESCRIPTION
The cacos() function computes complex double precision arc cosine of complex, with branch cuts outside the interval [-1, +1] along the real axis.

RETURN VALUE
The cacos() function returns the complex arc cosine value, in the range of a strip mathematically unbounded along the imaginary axis and in the interval [0,pi] along the real axis.

NOTES
z = (x) + j(y) cacos(z) = (PI/2, 0) - casin(z) (old version) cacos(z) = (+/-) j*cacosh(z)

IMPLEMENTATION for APEnext: implem (cacos)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex cacosh ( complex z )

NAME
cacosh - complex arc hyperbolic cosine

SYNOPSIS
#include <complex.h>
complex cacosh(complex)

DESCRIPTION
The cacosh() function computes the complex arc hyperbolic cosine, with a branch cut at values less than 1 along the real axis.

RETURN VALUE
The cacosh() function returns the complex arc hyperbolic cosine value, in the range of a half-strip of non-negative values along the real axis and in the interval [-i pi, +i pi] along the imaginary axis.

NOTES
z = (x) + j(y) cacosh(z) = clog(z+csqrt(~z*z-1.0))

IMPLEMENTATION for APEnext: implem (cacosh)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline double carg ( complex z )

NAME
carg() - double argument

SYNOPSIS
#include <complex.h>
double carg(complex)

DESCRIPTION
The carg() function computes the argument (also called phase angle), with a branch cut along the negative real axis

RETURN VALUE
The carg() function returns the value of the argument in the interval [-pi, +pi].

NOTES
z = (x) + j(y) carg(z) = atan2(y,x)

IMPLEMENTATION for APEnext: implem (carg)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex casin ( complex z )

NAME
casin - arc sine

SYNOPSIS
#include <complex.h>
complex casin(complex)

DESCRIPTION
The casin() function computes complex double precision arc sine of the complex, with branch cuts outside the interval [-1, +1] along the real axis.

RETURN VALUE
The casin() function returns the complex arc sine value, in the range of a strip mathematically unbounded along the imaginary axis and in the interval [-pi/2, +pi/2] along the real axis.

NOTES
z = (x) + j(y) casin(z) = -j*casinh(j*z)

IMPLEMENTATION for APEnext: implem (casin)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex casinh ( complex z )

NAME
casinh - complex arc hyperbolic sine

SYNOPSIS
#include <complex.h>
complex casinh(complex)

DESCRIPTION
The casinh() function computes the complex arc hyperbolic sine, with a branch cut at values less than 1 along the real axis.

RETURN VALUE
The casinh() function returns the complex arc hyperbolic cosine value, in the range of a half-strip of non-negative values along the real axis and in the interval [-i pi, +i pi] along the imaginary axis.

NOTES
z = (x) + j(y) casinh(z) = clog(z+csqrt(~z*z+1))

IMPLEMENTATION for APEnext: implem (casinh)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex catan ( complex z )

NAME
catan - arc tangent

SYNOPSIS
#include <complex.h>
complex catan(complex)

DESCRIPTION
The catan() function computes complex double precision arc tangent of the complex, with branch cuts outside the interval [-i, +i] along the imaginary axis.

RETURN VALUE
The catan() function returns the complex arc tangent value, in the range of a strip mathematically unbounded along the imaginary axis and in the interval [-pi/2, +pi/2] along the real axis.

NOTES
z = (x) + j(y) catan(z) = -j/2 * log( (j+z) / (j-z) ) catan(z) = 0.5 * atan(2*x,1-(x^2)-(y^2)) + j*0.25*(log((x^2)+(y+1)^2) - log((x^2)+(y-1)^2))

IMPLEMENTATION for APEnext: implem (catan)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex catanh ( complex z )

NAME
catanh - complex arc hyperbolic tangent

SYNOPSIS
#include <complex.h>
complex catanh(complex)

DESCRIPTION
The catanh() function computes the complex arc hyperbolic tangent, with a branch cuts outside the interval [-1, +1] along the real axis.

RETURN VALUE
catanh() function returns the complex arc hyperbolic tangent value, in the range of a strip mathematically unbounded along the real axis and in the interval [-i pi/2, +i pi/2] along the imaginary axis.

NOTES
z = (x) + j(y) catanh(z) = 0.5 * clog((1+z)/(1-z)) catanh(z) = 0.25 * (log( (y^2)+(1+x)^2 ) - log( (y^2)+(1-x)^2 )) + j * 0.5 * atan(2*y,(1-(x^2)-(y^2))

IMPLEMENTATION for APEnext: implem (catanh)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex ccos ( complex z )

NAME
ccos - complex cosine

SYNOPSIS
#include <complex.h>
complex ccos(complex)

DESCRIPTION
The ccos() function computes complex double precision cosine complex argument

RETURN VALUE
The ccos() function returns the complex cosine value.

NOTES
z =(x) + j(y) ccos(z) = ccosh(j*z)

IMPLEMENTATION for APEnext: implem (ccos)

VERSION

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex ccosh ( complex z )

NAME
ccosh - complex hyperbolic cosine

SYNOPSIS
#include <complex.h>
complex ccosh(complex)

DESCRIPTION
The ccosh() function computes the complex hyperbolic cosine

RETURN VALUE
The ccosh() function returnes complex hyperbolic cosine value

NOTES
z = (x) + j(y) ccosh(z) = cosh(x) * cos(y) + j * sinh(x) * sin(y)

IMPLEMENTATION for APEnext: implem (ccosh)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex cexp ( complex z )

NAME
cexp() - exponential function

SYNOPSIS
#include <complex.h>
complex cexp(complex)

DESCRIPTION
cexp() computes the complex exponent, defined as e^(argument).

RETURN VALUE
The cexp() function returnes complex exponential of argument

NOTES
z = (x) + j(y) cexp(z) = exp(x) * (cos(y) + j*sin(y))

IMPLEMENTATION for APEnext: implem (cexp)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline double cinfty ( void )

math_inline complex clog ( complex z )

NAME
clog() - complex natural logarithm

SYNOPSIS
#include <complex.h>
complex clog(complex)

DESCRIPTION
clog() computes the complex natural (base e) logarithm of argument, with a branch cut along the negative real axis.

RETURN VALUE
The clog() function returns the complex natural logarithm value, in the range of a strip mathematically unbounded along the real axis and in the interval [-i pi, +i pi] along the imaginary axis.

NOTES
z = (x) + j(y) clog(z) = log(hypot(x,y)) + j*atan2(y,x)

IMPLEMENTATION for APEnext: implem (clog)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline double cnan ( void )

math_inline complex cpow ( complex x,

complex y

)

NAME
cpow() - complex power

SYNOPSIS
#include <complex.h>
complex cpow(complex x, complex y)

DESCRIPTION
cpow() computes the complex power function x to the power of y, with a branch cut for the first parameter along the negative real axis.

RETURN VALUE
The cpow() function return complex power function value

NOTES
z = (x) + j(y) cpow(x,y) = cexp(y*clog(x))

IMPLEMENTATION for APEnext: implem (cpow)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex cproj ( complex z )

NAME
cproj() - complex projection function

SYNOPSIS
#include <complex.h>
complex cproj(complex)

DESCRIPTION
Double precision complex of the projection of the double complex argument

RETURN VALUE
The cproj() function computes a projection of z onto the Riemann sphere: Argument projects to argument, except that all complex infinities (even those with one infinite part and one NaN part) project to positive infinity on the real axis. If argument has an infinite part, then cproj(argument) shall be equivalent to: INFINITY + I * copysign(0.0, cimag(argument))

NOTES
z = (x) + j(y) cproj(z) = (2.0 * z) / (~z*z + 1.0)

IMPLEMENTATION for APEnext: implem (cproj)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex csin ( complex z )

NAME
csin - complex sine

SYNOPSIS
#include <complex.h>
complex csin(complex)

DESCRIPTION
The csin() function computes complex double precision sine complex argument

RETURN VALUE
The csin() function returns the complex sine value.

NOTES
z = (x) + j(y) csin(z) = cosh(y) * sin(x) + j * sinh(y) * cos(x)

IMPLEMENTATION for APEnext: implem (csin)

VERSION

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex csinh ( complex z )

NAME
csinh - complex hyperbolic sine

SYNOPSIS
#include <complex.h>
complex csinh(complex)

DESCRIPTION
The csinh() function computes the complex hyperbolic sine

RETURN VALUE
The csinh() function returnes complex hyperbolic sine value

NOTES
z = (x) + j(y) csinh(z) = sinh(x) * cos(y) + j * cosh(x) * sin(y)

IMPLEMENTATION for APEnext: impelm (csinh)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex csqrt ( complex z )

NAME
csqrt() - square root

SYNOPSIS
#include <complex.h>
complex csqrt(complex)

DESCRIPTION
csqrt() computes complex double precision square root of argument, with a branch cut along the negative real axis.

RETURN VALUE
The sqrt() function returns the complex square root value, in the range of the right half-plane (including the imaginary axis)

NOTES
z = (x) + j(y) csqrt(z) = sqrt(0.5*(cabs(z)+x)) + j*(y/abs(y))*sqrt(0.5*(cabs(z)-x))
r = sqrt(0.5 * (abs(x) + cabs(z)) q = (0.5 * y) / r where(x >= 0) csqrt(z) = r + j*q where(x < 0 && y >= 0) csqrt(z) = q + j*r where(x < 0 && y < 0) csqrt(z) = -q + j*r

IMPLEMENTATION for APEnext: implem (csqrt)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex ctan ( complex z )

NAME
ctan - complex tangent

SYNOPSIS
#include <complex.h>
complex ctan(complex)

DESCRIPTION
The ctan() function computes complex double precision tangent of complex argument

RETURN VALUE
The ctan() function returns the complex tangent value.

NOTES
z = (x) + j(y) ctan(z) = (sin(2*x) + j*sinh(2*y)) / (cos(2*x) + cosh(2*y)) when (CCOS(z) = 0 + j0) ctan(z)= MAX_POS_DBLF + j0 else ctan (z) = CSIN(z) / CCOS(z)

IMPLEMENTATION for APEnext: implem (ctan)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex ctanh ( complex z )

NAME
ctanh - complex hyperbolic tangent

SYNOPSIS
#include <complex.h>
complex ctanh(complex)

DESCRIPTION
The ctanh() function computes the complex hyperbolic tangent

RETURN VALUE
The ctanh() function returnes complex hyperbolic tangent value

NOTES
z = (x) + j(y) ctanh(z) = (sinh(2*x) + j * sin(2*y)) / (cosh(2*x) + cos(2*y))

IMPLEMENTATION for APEnext: implem (ctanh)

VERSION

Id
complex.h,v 1.31 2005/11/10 19:28:30 morinl Exp

ISO/IEC 9899:1999 (E) Standard

Author:
K. Huebner, M. Prevot

math_inline complex sincos ( double x )

math_inline complex sinhcosh ( double x )

Generated on Fri Jul 14 10:51:37 2006 for nlibc by

1.3.5


Defines
#define	_math_setdouble(U, D)
#define	_Complex_I {0., 1.}
#define	I _Complex_I
#define	M_PI 3.14159265358979323846
#define	M_PI_2 1.57079632679489661923
#define	M_PI_4 0.78539816339744830962
#define	conj(x) (~(x))
#define	creal(x) ((x).re)
#define	cimag(x) ((x).im)
#define	NAN (cnan())
#define	HUGE_VALD (cinfty())
Functions
math_inline double	cnan (void)
math_inline double	cinfty (void)
math_inline complex	sincos (double x)
math_inline complex	sinhcosh (double x)
math_inline double	cabs (complex z)
math_inline double	carg (complex z)
math_inline complex	cproj (complex z)
math_inline complex	cexp (complex z)
math_inline complex	clog (complex z)
math_inline complex	cpow (complex x, complex y)
math_inline complex	csqrt (complex z)
math_inline complex	cacosh (complex z)
math_inline complex	casinh (complex z)
math_inline complex	catanh (complex z)
math_inline complex	cacos (complex z)
math_inline complex	casin (complex z)
math_inline complex	catan (complex z)
math_inline complex	ccosh (complex z)
math_inline complex	csinh (complex z)
math_inline complex	ctanh (complex z)
math_inline complex	ccos (complex z)
math_inline complex	csin (complex z)
math_inline complex	ctan (complex z)