Rack/plugins/community/repos/SubmarineFree/manual/AO-list.md

AO-1xx Algorithms

Arithmetical

Display	Code	Description
		Pass-through. X passes across unchanged, Y passes down unchanged
C	c	The value of the selected constant C
X+C	x + c	X added to C
Y+C	y + c	Y added to C
X+Y+C	x + y + c	X and Y added to C
C-X	c - x	X subtracted from C
C-Y	c - y	Y subtracted from C
X-(Y+C)	x - ( y + c )	Y added to C then all subtracted from X
(X+C)-Y	( x + c ) - y	Y subtracted from X and C
Y-(X+C)	y - ( x + c )	X added to C then all subtracted from Y
(Y+C)-X	( y + c ) - x	X subtracted from Y and C
(X⨯Y)+C	( x * y ) + c	X times Y added to C
(X+C)⨯Y	( x + c ) * y	X and C multiplied by Y
X⨯(Y+C)	x * ( y + c )	Y and C multiplied by X
X⨯C	x * c	X times C
Y⨯C	y * c	Y times C
X⨯Y⨯C	x * y * c	X times Y times C
π⨯(X+C)	M_PI * ( x + c )	X and C multiplied by pi
π⨯(Y+C)	M_PI * ( y + c )	Y and C multiplied by pi
τ⨯(X+C)	2 * M_PI * ( x + c )	X and C multiplied by tau
τ⨯(Y+C)	2 * M_PI * ( y + c )	Y and C multiplied by tau
X÷C	x / c	X divided by C
C÷X	c / x	C divided by X
Y÷C	y / c	Y divided by C
C÷Y	c / y	C divided by Y
C+(X÷Y)	c + ( x / y )	C added to X divided by Y
C+(Y÷X)	c + ( y / x )	C added to Y divided by X
X+(Y÷C)	x + ( y / c )	X added to Y divided by C
X+(C÷Y)	x + ( c / y )	X added to C divided by Y
Y+(X÷C)	y + ( x / c )	Y added to X divided by C
Y+(C÷X)	y + ( c / x )	Y added to C divided by X
(X+C)÷Y	( x + c ) / y	X and C divided by Y
X÷(Y+C)	x / ( y + c )	X divided by Y and C
(Y+C)÷X	( y + c ) / x	Y and C divided by X
Y÷(X+C)	y / ( x + c )	Y divided by X and C

Modular

Display	Code	Description
(X+C)%Y	fmodf( x + c , y )	The remainder of X and C divided by Y
(Y+C)%X	fmodf( y + c , x )	The remainder of Y and C divided by X
X%(Y+C)	fmodf( x , y + c )	The remainder of X divided by Y and C
Y%(X+C)	fmodf( y , x + c)	The remainder of Y divided by X and C
X%C	fmodf( x , c )	The remainder of X divided by C
Y%C	fmodf( y , c )	The remainder of Y divided by C

Quadratic

Display	Code	Description
X²+C	x * x + c	X squared added to C
Y²+C	y * y + c	Y squared added to C
(X+C)²	( x + c ) * ( x + c )	X and C squared
(Y+C)²	( y + c ) * ( y + c )	Y and C squared
X²+Y+C	x * x + y + c	X squared added to Y and C
Y²+X+C	y * y + x + c	Y squared added to X and C
X²+CY	x * x + c * y	X squared added to Y multiplied by C
Y²+CX	y * y + c * x	Y squared added to X multiplied by C

Powers

Display	Code	Description
√(X+C)	sqrt( x + c )	The square root of X and C
√(Y+C)	sqrt( y + c )	The square root of Y and C
Cˣ	powf( c , x )	C raised to the power of X
Cʸ	powf( c , y )	C raised to the power of Y
Cˣ⁺ʸ	powf( c , x + y )	C raised to the power of X and Y
Cˣʸ	powf( c , x * y )	C raised to the power of X multiplied by Y
Xᶜ	powf( x , c )	X raised to the power of C
Yᶜ	powf( y , c )	Y raised to the power of C
Xʸ⁺ᶜ	powf( x , y + c )	X raised to the power of Y and C
Yˣ⁺ᶜ	powf( y , x + c )	Y raised to the power of X and C
Xᶜʸ	powf( x , c * y )	X raised to the power of Y multiplied by C
Yᶜˣ	powf( y , c * x )	Y raised to the power of X multiplied by C

Positive values only

Display	Code	Description
|X+C|	abs( x + c )	X Added to C with any minus sign removed
|Y+C|	abs( y + c )	Y added to C with any minus sign removed

Maximum and Minimum

Display	Code	Description
min(X+C,Y)	min( x + c, y )	The smaller of X Added to C, or Y
min(X,C)	min( x, c )	The smaller of X or C
min(Y,C)	min( y, c )	The smaller of Y or C
max(X+C,Y)	max( x + c, y )	The larger of X added to C, or Y
max(X,C)	max( x, c )	The larger of X or C
max(Y,C)	max( y, c )	The larger of Y or C

Trigonometric

Display	Code	Description
sin(X+C)	sin( x + c )	The sine of X and C
sin(Y+C)	sin( y + c )	The sine of Y and C
sin(X+Y)	sin( x + y )	The sine of X and Y
sin(CX)	sin( c * x )	The sine of X mulitplied by C
sin(CY)	sin( c * y )	The sine of Y multiplied by C
sin(XY)	sin( x * y )	The sine of X multiplied by Y
cos(X+C)	cos( x + c )	The cosine of X and C
cos(Y+C)	cos( y + c )
cos(X+Y)	cos( x + y )
cos(CX)	cos( c * x )
cos(CY)	cos( c * y )
cos(XY)	cos( x * y )
tan(X+C)	tan( x + c )	The tangent of X and C
tan(Y+C)	tan( y + c )
tan(X+Y)	tan( x + y )
tan(CX)	tan( c * x )
tan(CY)	tan( c * y )
tan(XY)	tan( x * y )
asin(X+C)	asin( x + c )	The arcsine of X and C
asin(Y+C)	asin( y + c )
asin(X+Y)	asin( x + y )
asin(CX)	asin( c * x )
asin(CY)	asin( c * y )
asin(XY)	asin( x * y )
acos(X+C)	acos( x + c )	The arcosine of X and C
acos(Y+C)	acos( y + c )
acos(X+Y)	acos( x + y )
acos(CX)	acos( c * x )
acos(CY)	acos( c * y )
acos(XY)	acos( x * y )
atan(X+C)	atan( x + c )	The arctangent of X and C
atan(Y+C)	atan( y + c )
atan(X+Y)	atan( x + y )
atan(CX)	atan( c * x )
atan(CY)	atan( c * y )
atan(XY)	atan( x * y )

Logarithmic

Display	Code	Description
log(X+C)	log( x + c )	The natural logarithm of X and C
log(Y+C)	log( y + c )	The natural logarithm of Y and C
log₂(X+C)	log2( x + c )	The base-2 logarithm of X and C
log₂(Y+C)	log2( y + c )	The base-2 logarithm of Y and C
log₁₀(X+C)	log10( x + c )	The base-10 logarithm of X and C
log₁₀(Y+C)	log10( y + c )	The base-10 logarithm of Y and C

Exponential

Display	Code	Description
ℯˣ⁺ᶜ	exp( x + c )	e raised to the power of X and C
ℯʸ⁺ᶜ	exp( y + c )	e raised to the power of Y and C
ℯᶜˣ	exp( c * x )	e raised to the power of X multiplied by C
ℯᶜʸ	exp( c * y )	e raised to the power of Y multiplied by C
2ˣ⁺ᶜ	powf( 2, x + c )	2 raised to the power of X and C
2ʸ⁺ᶜ	powf( 2, y + c )	2 raised to the power of Y and C
2ᶜˣ	powf( 2, c * x )	2 raised to the power of X multiplied by C
2ᶜʸ	powf( 2, c * y )	2 raised to the power of Y multiplied by C
10ˣ⁺ᶜ	powf( 10, x + c )	10 raised to the power of X and C
10ʸ⁺ᶜ	powf( 10, y + c )	10 raised to the power of Y and C
10ᶜˣ	powf( 10, c * x )	10 raised to the power of X multiplied by C
10ᶜʸ	powf( 10, c * y )	10 raised to the power of Y multiplied by C

Conditional

Display	Code	Description
if X>0↣Y/C	(x > 0) ? y : c	Y if X is greater than 0 otherwise C
if X<0↣Y/C	(x < 0) ? y : c	Y if X is less than 0 otherwise C
if X=0↣Y/C	(x == 0) ? y : c	Y if X is 0 otherwise C
if X>0↣C/Y	(x > 0) ? c : y	C if X is greater than 0 otherwise Y
if X<0↣C/Y	(x < 0) ? c : y	C if X is less that 0 otherwise Y
if X=0↣C/Y	(x == 0) ? c : y	C if X is 0 otherwise Y
if X>0↣1/0	(x > 0) ? 1 : 0	1 if X is greater than 0 otherwise 0
if X<0↣1/0	(x < 0) ? 1 : 0
if X=0↣1/0	(x == 0) ? 1 : 0
if X>0↣X/C	(x > 0) ? x : c	X if X is greater than 0 otherwise C
if X<0↣X/C	(x < 0) ? x : c
if X=0↣X/C	(x == 0) ? x : c
if X>0↣C/X	(x > 0) ? c : x	C if X is greater than 0 otherwise X
if X<0↣C/X	(x < 0) ? c : x
if X=0↣C/X	(x == 0) ? c : x
if Y>0↣X/C	(y > 0) ? x : c	X if Y is greater than 0 otherwise C
if Y<0↣X/C	(y < 0) ? x : c
if Y=0↣X/C	(y == 0) ? x : c
if Y>0↣C/X	(y > 0) ? c : x	C if Y is greater than 0 otherwise X
if Y<0↣C/X	(y < 0) ? c : x
if Y=0↣C/X	(y == 0) ? c : x
if Y>0↣1/0	(y > 0) ? 1 : 0
if Y<0↣1/0	(y < 0) ? 1 : 0
if Y=0↣1/0	(y == 0) ? 1 : 0
if Y>0↣Y/C	(y > 0) ? y : c
if Y<0↣Y/C	(y < 0) ? y : c
if Y=0↣Y/C	(y == 0) ? y : c
if Y>0↣C/Y	(y > 0) ? c : y
if Y<0↣C/Y	(y < 0) ? c : y
if Y=0↣C/Y	(y == 0) ? c : y
if X>Y↣C/0	(x > y) ? c : 0	C if X is greater than Y otherwise 0
if X<Y↣C/0	(x < y) ? c : 0
if X=Y↣C/0	(x == y) ? c : 0
if Y>X↣C/0	(y > x) ? c : 0
if Y<X↣C/0	(y < x) ? c : 0
if X>Y↣X/0	(x > y) ? x : 0	X if X is greater than Y otherwise 0
if X<Y↣X/0	(x < y) ? x : 0
if X=Y↣X/0	(x == y) ? x : 0
if Y>X↣X/0	(y > x) ? x : 0
if Y<X↣X/0	(y < x) ? x : 0
if X>Y↣Y/0	(x > y) ? y : 0
if X<Y↣Y/0	(x < y) ? y : 0
if X=Y↣Y/0	(x == y) ? y : 0
if Y>X↣Y/0	(y > x) ? y : 0
if Y<X↣Y/0	(y < x) ? y : 0
if X>C↣Y/0	(x > c) ? y : 0
if X<C↣Y/0	(x < c) ? y : 0
if X=C↣Y/0	(x == c) ? y : 0
if C>X↣Y/0	(c > x) ? y : 0
if C<X↣Y/0	(c < x) ? y : 0
if X>C↣X/0	(x > c) ? x : 0
if X<C↣X/0	(x < c) ? x : 0
if X=C↣X/0	(x == c) ? x : 0
if C>X↣X/0	(c > x) ? x : 0
if C<X↣X/0	(c < x) ? x : 0
if X>C↣X/Y	(x > c) ? x : y
if X<C↣X/Y	(x < c) ? x : y
if X=C↣X/Y	(x == c) ? x : y
if C>X↣X/Y	(c > x) ? x : y
if C<X↣X/Y	(c < x) ? x : y
if Y>C↣X/0	(y > c) ? x : 0
if Y<C↣X/0	(y < c) ? x : 0
if Y=C↣X/0	(y == c) ? x : 0
if C>Y↣X/0	(c > y) ? x : 0
if C<Y↣X/0	(c < y) ? x : 0
if Y>C↣Y/0	(y > c) ? y : 0
if Y<C↣Y/0	(y < c) ? y : 0
if Y=C↣Y/0	(y == c) ? y : 0
if C>Y↣Y/0	(c > y) ? y : 0
if C<Y↣Y/0	(c < y) ? y : 0
if Y>C↣Y/X	(y > c) ? y : x	Y if Y is greater than C otherwise X
if Y<C↣Y/X	(y < c) ? y : x	Y if Y is less than C otherwise X
if Y=C↣Y/X	(y == c) ? y : x	Y if Y is C otherwise X
if C>Y↣Y/X	(c > y) ? y : x	Y if C is greater than Y otherwise X
if C<Y↣Y/X	(c < y) ? y : x	Y if C is less than Y otherwise X