function "*" (Left, Right : Interval) return Interval
Multiplies two intervals
First interval operand
Second interval operand
Result based on sign combinations of operands @see IEEE 1788-2015 Section 8.2 "arithmetic operations" @see IEEE 1788.1-2017 Section 10.8.3 "multiplication"
function "+" (Right : Interval) return Interval
Unary plus operator (identity function)
The interval to operate on
The same interval unchanged @see IEEE 1788-2015 Section 8.2 "arithmetic operations" @see IEEE 1788.1-2017 Section 10.8.1 "unary plus"
function "+" (Left, Right : Interval) return Interval
Adds two intervals
First interval operand
Second interval operand
[Left.Lower + Right.Lower, Left.Upper + Right.Upper] @see IEEE 1788-2015 Section 8.2 "arithmetic operations" @see IEEE 1788.1-2017 Section 10.8.1 "addition"
function "-" (Right : Interval) return Interval
Unary minus operator (negation)
The interval to negate
[-Right.Upper, -Right.Lower] @see IEEE 1788-2015 Section 8.2 "arithmetic operations" @see IEEE 1788.1-2017 Section 10.8.2 "negation"
function "-" (Left, Right : Interval) return Interval
Subtracts two intervals
First interval operand
Second interval operand
[Left.Lower - Right.Upper, Left.Upper - Right.Lower] @see IEEE 1788-2015 Section 8.2 "arithmetic operations" @see IEEE 1788.1-2017 Section 10.8.2 "subtraction"
function "/" (Left, Right : Interval) return Interval
Divides two intervals
First interval operand
Second interval operand
Result based on sign combinations of operands
if Right contains zero @see IEEE 1788-2015 Section 8.2 "arithmetic operations" @see IEEE 1788.1-2017 Section 10.8.4 "division"
function "<" (Left, Right : Interval) return Boolean
Tests if one interval is strictly less than another
First interval to compare
Second interval to compare
True if Left's upper bound is less than Right's lower bound @see IEEE 1788-2015 Section 7.2 "set relations" @see IEEE 1788.1-2017 Section 10.7.2 "less than"
function "<=" (Left, Right : Interval) return Boolean
Tests if one interval is less than or equal to another
First interval to compare
Second interval to compare
True if Left's upper bound <= Right's lower bound @see IEEE 1788-2015 Section 7.2 "set relations" @see IEEE 1788.1-2017 Section 10.7.2 "less than or equal"
function "=" (Left, Right : Interval) return Boolean
Tests if two intervals are equal
First interval to compare
Second interval to compare
True if both intervals have equal bounds @see IEEE 1788-2015 Section 7.2 "set relations" @see IEEE 1788.1-2017 Section 10.7.1 "equality"
function ">" (Left, Right : Interval) return Boolean
Tests if one interval is greater than another
First interval to compare
Second interval to compare
True if Left's lower bound is greater than Right's upper bound @see IEEE 1788-2015 Section 7.2 "set relations" @see IEEE 1788.1-2017 Section 10.7.3 "greater than"
function ">=" (Left, Right : Interval) return Boolean
Tests if one interval is greater than or equal to another
First interval to compare
Second interval to compare
True if Left's lower bound >= Right's upper bound @see IEEE 1788-2015 Section 7.2 "set relations" @see IEEE 1788.1-2017 Section 10.7.3 "greater than or equal"
function "abs" (Right : Interval) return Interval
Returns the absolute value of an interval
The interval to take the absolute value of
Interval containing absolute values of all points in Right @see IEEE 1788-2015 Section 8.3 "absolute value" @see IEEE 1788.1-2017 Section 10.9.1 "absolute value"
function Entire return Interval
Returns an interval containing all representable values of type T Creates an interval spanning the entire range of type T
An interval [T'First,T'Last] representing the complete range @see IEEE 1788-2015 Section 6.3 "interval literals" @see IEEE 1788.1-2017 Section 10.5.1 "entire"
function Hull (Left, Right : Interval) return Interval
Creates the smallest interval containing two given intervals
First interval to include
Second interval to include
The smallest interval containing both input intervals @see IEEE 1788-2015 Section 7.3 "convex hull" @see IEEE 1788.1-2017 Section 10.6.2 "hull"
function Hull (Right : IntervalElements) return Interval
Creates smallest interval containing the union of all input intervals
Array of intervals to combine into single interval
Smallest interval containing all input intervals
function Hull (Left, Right : T) return Interval
Creates the smallest interval containing two given values
First value to include
Second value to include
The smallest interval containing both input values @see IEEE 1788-2015 Section 7.3 "convex hull" @see IEEE 1788.1-2017 Section 10.6.2 "hull"
function Hull (Right : TElements) return Interval
Computes the smallest interval containing all numbers in the array
Array of numbers to enclose in interval
Interval [a,b] containing all elements of Right
function Max (Left, Right : T) return T
Returns the maximum of two values
First value to compare
Second value to compare
The larger of the two input values @see IEEE 1788-2015 Section 8.5 "min/max operations" @see IEEE 1788.1-2017 Section 10.11.2 "maximum"
function Min (Left, Right : T) return T
Returns the minimum of two values
First value to compare
Second value to compare
The smaller of the two input values @see IEEE 1788-2015 Section 8.5 "min/max operations" @see IEEE 1788.1-2017 Section 10.11.1 "minimum"
function Sgn (Right : T) return Sign
Returns the sign of a value
The value to determine the sign of
-1 for negative, 0 for zero, 1 for positive @see IEEE 1788-2015 Section 8.4 "sign operations" @see IEEE 1788.1-2017 Section 10.10.1 "sign"
function To_Interval (Right : T) return Interval
Creates an interval [x,x] containing a single point
The value to be enclosed in the interval
A degenerate interval [Right,Right] @see IEEE 1788-2015 Section 6.3 "interval literals" @see IEEE 1788.1-2017 Section 10.5.2 "point intervals"
function To_Interval (Lower_Bound, Upper_Bound : T) return Interval
Creates an interval from explicit bounds
The lower bound of the interval
The upper bound of the interval
An interval [Lower_Bound,Upper_Bound] @see IEEE 1788-2015 Section 6.3 "interval literals" @see IEEE 1788.1-2017 Section 10.5.3 "bounded intervals"
function To_String (Right : Interval) return String
Converts an interval to its string representation
The interval to convert
A string "[lower,upper]" representing the interval