Differences

This shows you the differences between two versions of the page.

--- manual:Calculations [2019/06/18 03:46] – [Operators] peternlewis
+++ manual:Calculations [2025/02/26 02:04] (current) – [Operators] peternlewis
@@ Line 23: / Line 23: @@
 Operators based on precedence from lowest to highest are:
-| Array Separator (`,`) | Allows a text Variable, which has comma separated values, to work somewhat like an Array.\\ Assume `MyKMVariable` contains "value1,value2,value3".\\ Then `MyKMVariable[2]` returns "value2". |
+| Array Separator (`,`) | Allows a text Variable, which has comma separated values, to work somewhat like an Array.\\ Assume `MyKMVariable` contains "12,34,56", then `MyKMVariable[2]` returns "34". |
 | Ternary Operator (`?`) | a=b ? 3 : 4 |
-| Bitwise OR (`|`), Bitwise AND (`&`) and Bitwise XOR | bitwise operators |
+| Bitwise OR (`|`), Bitwise AND (`&`) and Bitwise XOR | bitwise operators, which also act as logical boolean operators for 0 (false) and 1 (true). |
-| Comparison Operators (`<, ≤, =, >, ≥, ≠`) | compare for (in)equality and return 0 or 1 |
+| Comparison Operators (`<, ≤, =, >, ≥, ≠`) | compare for (in)equality and return 0 or 1. |
-| Shift Operators (`≪, ≫`) | shift a number left or right |
+| Shift Operators (`≪, ≫`) | shift a number left or right. |
-| Arithmetic Operators\\   • Add (`+`)\\   • Subtract (`-`)\\   • Multiply (`*`)\\   • Divide (`/`) | A mathematical function that takes two operands and performs a calculation on them. |
+| Arithmetic Addition Operators \\   • Add (`+`)\\   • Subtract (`-`) | Basic mathematical operations. |
-| [Modulo](https://en.wikipedia.org/wiki/Modulo_operation) (`i MOD n`) | The remainder of the division of `i by n`.\\ Both values (`i, n`) must be an integer in Keyboard Maestro.  |
+| Arithmetic Multiplication Operators \\   • Multiply (`*`)\\   • Divide (`/`) | Basic mathematical operations. |
-| Power Operator (`^`) | exponentiation |
+| [Modulo](https://en.wikipedia.org/wiki/Modulo_operation) (`i MOD n`) | The remainder of the division of `i` by `n`.\\ Both values (`i`, `n`) will be treated as integer.\\ `n` must not be 0.\\ The sign of the result is the same as the sign of i.  |
-| Unary Prefix Operators (`√`, `-`, `( )` ) | square root, negation, sub-expressions |
+| Integer division (`i DIV n`) | The integer quotient of the division of `i` by `n`.\\ Both values (`i`, `n`) will be treated as integer.\\ `n` must not be 0.\\ The sign of the result matches the sign of regular division.  |
-| [[:Functions|Functions]] | a large variety of functions |
+| Power Operator (`^`) | exponentiation. |
-| Numbers and Variables or Array Accesses (5,$5A,0x50,8#007,Variable,Variable[5]) | identifiers and values |
+| Unary Prefix Operators (`√`, `-`, `( )` ) | square root, negation, sub-expressions. |
-| Unary Postfix Operators (`!,%,°`)) | factorial, percent, degrees |
+| [[:Functions|Functions]] | a large variety of functions. |
+| Numbers and Variables or Array Accesses (5,$5A,0x50,8#007,Variable,Variable[5]) | identifiers and values. |
+| Unary Postfix Operators (`!,%,°`)) | factorial, percent, degrees. |
-Numbers are in decimal by default, but may use base 16 if they start with `$` or `0x` (eg $5A or 0x5A), or may start with a specific base followed by a `#` (eg 8#007).
+Numbers are in decimal by default, but may use base 16 if they start with `$` or `0x` (eg $5A or 0x5A), or may start with a specific base followed by a `#` (eg 8#007). Numbers may include underscores, for example `1_000_000` or `0xABCD_EF89`.
 [[Variables|Variables]] can be used if they contain numeric expressions, including an *array* of numbers separated by commas, in which case you can use an array index to select the desired number.
-You can use either `=` or `==` (v8+) for testing for equality.
+You can use either `=` or `==` for testing for equality.
 Operators and functions must be in uppercase to minimize conflict with variables.
 ===== Functions =====
 The available functions are listed on the [[/Functions|wiki Functions page]].
-You can insert a function by name by choosing [[Menus#Insert_Function_by_Name|Insert Function by Name]] from the [[Menus#Edit|Edit menu]].
+You can insert a function by name by choosing from the [[Menus#Insert_Function|Edit ➤ Insert Function menu]] or choosing the [[Menus#Insert_Function_by_Name|Edit ➤ Insert Function by Name menu]].
 ===== Variables =====
-In numeric calculation fields, Variable Names are used without the `%` that are used in text token fields.  Do not try to use tokens (like `%Variable%MyVar%`) in numeric calculation fields, just use MyVar by itself. The variable must contain a valid numeric value, or an expression (v8+) that evaluates to a valid numeric value.  So for example, if MyVar contains a text value of `2*3`, then the calculation `4*MyVar` will return 24.
+In numeric calculation fields, Variable Names are used without the `%` that are used in text token fields.  Do not try to use tokens (like `%Variable%MyVar%`) in numeric calculation fields, just use MyVar by itself. The variable must contain a valid numeric value, or an expression that evaluates to a valid numeric value.  So for example, if MyVar contains a text value of `2*3`, then the calculation `4*MyVar` will return 24.
-===== Screen Coordinates =====
-Keyboard Maestro refers to screen coordinates as two or four comma separated numbers in the text of a Keyboard Maestro Variable (which is always a string).
-  * Screen object points, like the left,top position of a window, have two values, like 12,34
-  * Screen object rectangles, like the frame of a window, have four values 12,34,56,78 (with a fifth value for fuzz in some instances).
-  * You can reference these values by position in the string, as it the Variable were an array:
-  * For example:
-if the Variable `myWindow` is "12,34,56,78"
-then all of these forms of reference will provide a value of 34 in a Calculation field:
-    * myWindow[2]
-    * myWindow.y
-    * myWindow.Top
 ===== Variable Array Access =====
@@ Line 74: / Line 64: @@
 Indices are 1-based, so MyVar[1] is the first element.  If the index is 0, the size of the array is returned (so MyVar[0] would be `6`).  If the index is less than zero, the array is indexed from the end (so MyVar[-5] would be `20`).
-===== Variable Dot Notation =====
+===== Screen Coordinates and Dot Notation =====
+Keyboard Maestro refers to screen coordinates as two or four comma separated numbers in the text of a Keyboard Maestro Variable (which is always a string).
+Screen object points, like the left,top position of a window, have two values, like 12,34.
+Screen object rectangles, like the frame of a window, have four values 12,34,56,78 (with a fifth value for fuzz in some instances).
 In a Calculation field you can reference the numbers in a Keyboard Maestro Variable (which is always a string) using dot notation:
@@ Line 89: / Line 85: @@
 | Variable.MidX | the horizontal middle of a rectangle |
 | Variable.MidY | the vertical middle of a rectangle |
+For example if the Variable `myWindow` is "12,34,56,78" then all of these forms of reference will provide a value of 34 in a Calculation field:
+    * myWindow[2]
+    * myWindow.y
+    * myWindow.Top
 The Variable Name and Dot reference are case insensitive.
 ===== Text Fields =====
@@ Line 99: / Line 101: @@
 However in a text field, since any text is allowed, you must use percent encoded tokens to indicate where more processing is required.  You can include a variable in the text by using the [[token:Variable|%Variable%]] token, or you can use a calculation by using the [[token:Calculate|%Calculate%]] token, or any number of other [[:Tokens|Tokens]].
-    The result is %Calculate%3 * Count + 7%.
+    The result is %Calculate% 3 * Count + 7 %.
-===== Examples of Variable Data Reference =====
+===== Examples of Variable Array Reference =====
-** Macro Actions**\\
+=== Macro Actions ===
-{{:manual:window-frame-example-actions-km-7.3.png?nolink|}}
-**Example Results**\\
+{{ window-frame-example-actions.png?nolink&584x592 | Window Frame Example Actions }}
-{{:manual:window-frame-example-results-km-7.3.png?nolink|}}
-Some example expressions might be:
+=== Example Results ===
+{{ window-frame-example-results.png?nolink&487x495 | Window Frame Example Results }}
+===== Example Expressions =====
 <code>
 Amount in Dollars * 100
 MJD() > 55928
-NOW() > TIME(2012,3,23,12,2,1)
+NOW() > TIME(2023,3,23,12,2,1)
-DOW(TIME(2012,4,4)) = 4
+DOW(TIME(2023,4,4)) = 4
 Radius*SIN(20°),Radius*COS(20°)
 Window Frame[1]+Window Frame[3]/2,Window Frame.MidY
@@ Line 122: / Line 126: @@
 </code>
----
-**KeyWords:**  MOD, Modulo