# 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 XX↣C/0 | (y > x) ? c : 0 || | if YY↣X/0 | (x > y) ? x : 0 | X if X is greater than Y otherwise 0 | | if XX↣X/0 | (y > x) ? x : 0 || | if YY↣Y/0 | (x > y) ? y : 0 || | if XX↣Y/0 | (y > x) ? y : 0 || | if YC↣Y/0 | (x > c) ? y : 0 || | if XX↣Y/0 | (c > x) ? y : 0 || | if CC↣X/0 | (x > c) ? x : 0 || | if XX↣X/0 | (c > x) ? x : 0 || | if CC↣X/Y | (x > c) ? x : y || | if XX↣X/Y | (c > x) ? x : y || | if CC↣X/0 | (y > c) ? x : 0 || | if YY↣X/0 | (c > y) ? x : 0 || | if CC↣Y/0 | (y > c) ? y : 0 || | if YY↣Y/0 | (c > y) ? y : 0 || | if CC↣Y/X | (y > c) ? y : x | Y if Y is greater than C otherwise X | | if YY↣Y/X | (c > y) ? y : x | Y if C is greater than Y otherwise X | | if C