Index

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

Rounding

Display Code Description
⌊X+C⌋ floor(x + c) Round down x and c
⌊Y+C⌋ floor(y + c) Round down y and c
⌊X+Y+C⌋ floor(x + y + c) Round down x and y and c
⌊CX⌋ floor(x * c) Round down x by c
⌊CY⌋ floor(y * c) Round down x by c
⌊CXY⌋ floor(x * y * c) Round down x by y by c
⌈X+C⌉ ceil(x + c) Round up x and c
⌈Y+C⌉ ceil(y + c) Round up y and c
⌈X+Y+C⌉ ceil(x + y + c) Round up x and y and c
⌈CX⌉ ceil(x * c) Round up x by c
⌈CY⌉ ceil(y * c) Round up x by c
⌈CXY⌉ ceil(x * y * c) Round up x by y by c