Mathematical Operations

Mathematical Operations
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Temporal addition

{number,tnumber} + {number,tnumber} → tnumber

SELECT tint '[2@2001-01-01, 2@2001-01-04)' + 1;
-- [3@2001-01-01, 3@2001-01-04)
SELECT tfloat '[2@2001-01-01, 2@2001-01-04)' + tfloat '[1@2001-01-01, 4@2001-01-04)';
-- [3@2001-01-01, 6@2001-01-04)
SELECT tfloat '[1@2001-01-01, 4@2001-01-04)' +
  tfloat '{[1@2001-01-01, 2@2001-01-02), [1@2001-01-02, 2@2001-01-04)}';
-- {[2@2001-01-01, 4@2001-01-04), [3@2001-01-02, 6@2001-01-04)}

Temporal subtraction

{number,tnumber} - {number,tnumber} → tnumber

SELECT tint '[1@2001-01-01, 1@2001-01-04)' - tint '[2@2001-01-03, 2@2001-01-05)';
-- [-1@2001-01-03, -1@2001-01-04)
SELECT tfloat '[3@2001-01-01, 6@2001-01-04)' - tfloat '[2@2001-01-01, 2@2001-01-04)';
-- [1@2001-01-01, 4@2001-01-04)

Temporal multiplication

{number,tnumber} * {number,tnumber} → tnumber

SELECT tint '[1@2001-01-01, 4@2001-01-04]' * 2;
-- [2@2001-01-01, 8@2001-01-04]
SELECT tfloat '[1@2001-01-01, 4@2001-01-04)' * tfloat '[2@2001-01-01, 2@2001-01-04)';
-- [2@2001-01-01, 8@2001-01-04)
SELECT tfloat '[1@2001-01-01, 3@2001-01-03)' * '[3@2001-01-01, 1@2001-01-03)'
-- {[3@2001-01-01, 4@2001-01-02, 3@2001-01-03)}

Temporal division

{number,tnumber} / {number,tnumber} → tnumber

The function will raise an error if the denominator will ever be equal to zero during the common timespan of the arguments.

SELECT 2 / tfloat '[1@2001-01-01, 3@2001-01-04)';
-- [2@2001-01-01, 0.666666666666667@2001-01-04)
SELECT tfloat '[1@2001-01-01, 5@2001-01-05)' / tfloat '[5@2001-01-01, 1@2001-01-05)';
-- {[0.2@2001-01-01, 1@2001-01-03,2001-01-03, 5@2001-01-03,2001-01-05)}
SELECT 2 / tfloat '[-1@2001-01-01, 1@2001-01-02]';
-- ERROR:  Division by zero
SELECT tfloat '[-1@2001-01-04, 1@2001-01-05]' / tfloat '[-1@2001-01-01, 1@2001-01-05]';
-- [-2@2001-01-04, 1@2001-01-05]

Return the absolute value of the temporal number

abs(tnumber) → tnumber

SELECT abs(tfloat '[1@2001-01-01, -1@2001-01-03, 1@2001-01-05]');
-- [1@2001-01-01, 0@2001-01-02, 1@2001-01-03, 0@2001-01-04, 1@2001-01-05]
SELECT abs(tint '[1@2001-01-01, -1@2001-01-03, 1@2001-01-05]');
-- [1@2001-01-01, 1@2001-01-05]

Return the value difference between consecutive instants of the temporal number

deltaValue(tnumber) → tnumber

SELECT deltaValue(tint '[1@2001-01-01, 2@2001-01-02, 1@2001-01-03]');
-- [1@2001-01-01, -1@2001-01-02, -1@2001-01-03)
SELECT deltaValue(tfloat '{[1.5@2001-01-01, 2@2001-01-02, 1@2001-01-03],
  [2@2001-01-04, 2@2001-01-05]}');
/* Interp=Step;{[0.5@2001-01-01, -1@2001-01-02, -1@2001-01-03),
  [0@2001-01-04, 0@2001-01-05)} */

Round up or down to the neareast integer

floor(tfloat) → tfloat

ceil(tfloat) → tfloat

SELECT floor(tfloat '[0.5@2001-01-01, 1.5@2001-01-02]');
-- [0@2001-01-01, 1@2001-01-02]
SELECT ceil(tfloat '[0.5@2001-01-01, 0.6@2001-01-02, 0.7@2001-01-03]');
-- [1@2001-01-01, 1@2001-01-03]

Round to a number of decimal places

round(tfloat,integer=0) → tfloat

SELECT round(tfloat '[0.785398163397448@2001-01-01, 2.356194490192345@2001-01-02]', 2);
-- [0.79@2001-01-01, 2.36@2001-01-02]

Convert to degrees or radians

degrees({float,tfloat},normalize=false) → tfloat

radians(tfloat) → tfloat

The additional parameter in the degrees function can be used to normalize the values between 0 and 360 degrees.

SELECT degrees(pi() * 5);
-- 900
SELECT degrees(pi() * 5, true);
-- 180
SELECT round(degrees(tfloat '[0.785398163397448@2001-01-01, 2.356194490192345@2001-01-02]'));
-- [45@2001-01-01, 135@2001-01-02]
SELECT radians(tfloat '[45@2001-01-01, 135@2001-01-02]');
-- [0.785398163397448@2001-01-01, 2.356194490192345@2001-01-02]

Return the derivative over time of the temporal float in units per second

derivative(tfloat) → tfloat

The temporal float must have linear interpolation

SELECT derivative(tfloat '{[0@2001-01-01, 10@2001-01-02, 5@2001-01-03],
  [1@2001-01-04, 0@2001-01-05]}') * 3600 * 24;
/* Interp=Step;{[-10@2001-01-01, 5@2001-01-02, 5@2001-01-03],
  [1@2001-01-04, 1@2001-01-05]} */
SELECT derivative(tfloat 'Interp=Step;[0@2001-01-01, 10@2001-01-02, 5@2001-01-03]');
-- ERROR:  The temporal value must have linear interpolation