immutable class CPXD < $CPX_NUMBER{FLTD,CPXD},$FMT

---

Ancestors

$FMT	$CPX_NUMBER{_,_}	$NFE{_}	$IS_EQ
$STR	$NIL	$IS_NIL	CPX{_}

---

Public

Readable Attributes

attr re,im:T; .. Included as im

****	Real and imaginary parts.

attr re,im:T; .. Included as re

****	Real and imaginary parts.

Writable Attributes

attr re,im:T; .. Included as im

****	Real and imaginary parts.

attr re,im:T; .. Included as re

****	Real and imaginary parts.

Features

abs: SAME .. Included as abs

****	For conformance with $NFE

abs_squared:T .. Included as abs_squared

****	The square of the absolute magnitude of self.

absolute:T .. Included as absolute

****	The absolute magnitude of self. Cannot overload abs From Numerical Recipes in C, 2nd ed. p. 949.

acos:SAME .. Included as acos

****	-i log(z + sqrt(1-z^2)) better to use: (pi/2)-asin(z) Steele p. 305.***

acosh:SAME .. Included as acosh

****	log(z+(z+1)sqrt((z-1)/(z+1))) Steele p. 308***

asin:SAME .. Included as asin

****	-i log(iz + sqrt(1-z^2)) Steele p. 305.***

asinh:SAME .. Included as asinh

****	log(z+sqrt(1+z^2)) Steele p. 308***

atan:SAME .. Included as atan

****	(log(1+i*y)-log(1-i*y))/(2*i) Steele p. 307.***

atanh:SAME .. Included as atanh

****	log((1+z)sqrt(1/(1-z^2))) Steele p. 308***

cis(f:T):SAME .. Included as cis

****	Ignores self, e^i*f=cos f + i sin f . Steele p. 304.

conjugate:SAME .. Included as conjugate

****	The complex conjugate of self.

cos:SAME .. Included as cos

cosh:SAME .. Included as cosh

****	(e^z+e^(-z))/2 Steele p. 308***

create(f: FLT): SAME .. Included as create

create(f: FLTD): SAME .. Included as create

create(re,im:T):SAME .. Included as create

****	A complex number with real part `re' and imaginary part `im'.

create(i: INT): SAME .. Included as create

create_from_polar(mag,phase:T):SAME .. Included as create_from_polar

****	A complex number with magnitude `mag' and phase `phase'.

create_real(x:T):SAME .. Included as create_real

cube:SAME .. Included as cube

****	Self cubed

cube_root:SAME .. Included as cube_root

****	The cube root of self. preliminary, but working.

div(c:SAME):SAME .. Included as div

****	The ratio of self and `c'. From Numerical Recipes in C, 2nd ed. p. 949.

div(f:T):SAME .. Included as div

****	Self div the floating point f.

exp:SAME .. Included as exp

****	The complex exponential `e^self'.

fmt( fmt: STR ): STR

is_eq(c: SAME): BOOL .. Included as is_eq

****	Return true if the two numbers are equal

is_eq(arg: $OB): BOOL .. Included as is_eq

is_nil:BOOL .. Included as is_nil

****	Return true if self is nil

is_within(r:T,c:SAME):BOOL .. Included as is_within

****	self is within a circle around c with radius r

log:SAME .. Included as log

****	The complex logarithm. The chosen branch is `log |z| + i phase(z)'. Same convention as Steele, p. 302.

magnitude:T .. Included as magnitude

****	The absolute magnitude of self.

magnitude_squared:T .. Included as magnitude_squared

****	The square of the absolute magnitude of self.

maxval: SAME .. Included as maxval

****	Maximum values of real and imaginary part

minus(c:SAME):SAME .. Included as minus

****	The difference of self and `c'.

negate:SAME .. Included as negate

****	The additive inverse of self.

nil:SAME .. Included as nil

****	Return a nil valued complex number with real and imaginary parts both nil

one: SAME .. Included as one

****	A unit value (real part=1, imaginary part=0)

phase:T .. Included as phase

****	The angle part of the polar represenation of self. `-pi < res <= pi'. Also get "-pi" from a negative real part and a "-0.0" imaginary part. They say 0+0i should be +0, 0-0i should be -0, -0+0i should be +pi, and -0-0i should be -pi. Same convention as Steele, p. 303.

plus(c:SAME):SAME .. Included as plus

****	The sum of self and `c'.

pow(c:SAME):SAME .. Included as pow

****	self^c = exp(c*log(self))

reciprocal:SAME .. Included as reciprocal

****	The multiplicative inverse of self.

sign:SAME .. Included as sign

****	If not zero, a number with same phase as self but unit magnitude. If it is, then returns self. Steele, p. 304***

sin:SAME .. Included as sin

sinh:SAME .. Included as sinh

****	(e^z-e^(-z))/2 Steele p. 308***

sqrt:SAME .. Included as sqrt

****	The square root of self. From Numerical Recipes in C, 2nd ed. p. 949. Steele, p. 302 chooses the branch cut by `e^((log z)/2)'

square:SAME .. Included as square

****	Self squared

str:STR .. Included as str

****	A string representation of self of the form "1.02+3.23i".

tan:SAME .. Included as tan

tanh:SAME .. Included as tanh

****	(e^z-e^(-z))/(e^z+e^(-z)) Steele p. 308***

times(c:SAME):SAME .. Included as times

****	The product of self and `c'.

times(f:T):SAME .. Included as times

****	Self times the floating point c.

zero: SAME .. Included as zero

****	A zero valued complex number

---

The Sather Home Page

---