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| − | --[[
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| | | | |
| − | This module provides a number of basic mathematical operations.
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| − |
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| − | ]]
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| − | local z = {}
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| − |
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| − | -- Generate random number
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| − | function z.random( frame )
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| − | first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil
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| − | second = tonumber(frame.args[2])
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| − |
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| − | if first then -- if NaN or nil, will skip down to final return
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| − | if first <= second then -- could match if both nil, but already checked that first is a number in last line
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| − | return math.random(first, second)
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| − | end
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| − | return math.random(first)
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| − | end
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| − | return math.random()
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| − | end
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| − |
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| − | --[[
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| − | order
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| − |
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| − | Determine order of magnitude of a number
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| − |
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| − | Usage:
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| − | {{#invoke: Math | order | value }}
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| − | ]]
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| − | function z.order(frame)
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| − | local input_string = (frame.args[1] or frame.args.x or '0');
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| − | local input_number;
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| − |
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| − | input_number = z._cleanNumber( frame, input_string );
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| − | if input_number == nil then
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| − | return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>'
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| − | else
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| − | return z._order( input_number )
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| − | end
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| − | end
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| − | function z._order(x)
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| − | if x == 0 then return 0 end
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| − | return math.floor(math.log10(math.abs(x)))
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| − | end
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| − |
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| − | --[[
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| − | precision
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| − |
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| − | Detemines the precision of a number using the string representation
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| − |
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| − | Usage:
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| − | {{ #invoke: Math | precision | value }}
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| − | ]]
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| − | function z.precision( frame )
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| − | local input_string = (frame.args[1] or frame.args.x or '0');
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| − | local trap_fraction = frame.args.check_fraction or false;
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| − | local input_number;
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| − |
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| − | if type( trap_fraction ) == 'string' then
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| − | trap_fraction = trap_fraction:lower();
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| − | if trap_fraction == 'false' or trap_fraction == '0' or
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| − | trap_fraction == 'no' or trap_fraction == '' then
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| − | trap_fraction = false;
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| − | else
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| − | trap_fraction = true;
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| − | end
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| − | end
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| − |
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| − | if trap_fraction then
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| − | local pos = string.find( input_string, '/', 1, true );
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| − | if pos ~= nil then
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| − | if string.find( input_string, '/', pos + 1, true ) == nil then
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| − | local denominator = string.sub( input_string, pos+1, -1 );
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| − | local denom_value = tonumber( denominator );
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| − | if denom_value ~= nil then
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| − | return math.log10(denom_value);
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| − | end
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| − | end
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| − | end
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| − | end
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| − |
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| − | input_number, input_string = z._cleanNumber( frame, input_string );
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| − | if input_string == nil then
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| − | return '<strong class="error">Formatting error: Precision input appears non-numeric</strong>'
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| − | else
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| − | return z._precision( input_string )
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| − | end
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| − | end
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| − | function z._precision( x )
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| − | x = string.upper( x )
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| − |
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| − | local decimal = string.find( x, '.', 1, true )
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| − | local exponent_pos = string.find( x, 'E', 1, true )
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| − | local result = 0;
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| − |
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| − | if exponent_pos ~= nil then
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| − | local exponent = string.sub( x, exponent_pos + 1 )
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| − | x = string.sub( x, 1, exponent_pos - 1 )
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| − | result = result - tonumber( exponent )
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| − | end
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| − |
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| − | if decimal ~= nil then
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| − | result = result + string.len( x ) - decimal
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| − | return result
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| − | end
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| − |
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| − | local pos = string.len( x );
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| − | while x:byte(pos) == string.byte('0') do
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| − | pos = pos - 1
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| − | result = result - 1
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| − | if pos <= 0 then
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| − | return 0
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| − | end
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| − | end
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| − |
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| − | return result
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| − | end
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| − |
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| − | --[[
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| − | max
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| − |
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| − | Finds the maximum argument
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| − |
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| − | Usage:
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| − | {{#invoke:Math| max | value1 | value2 | ... }}
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| − | OR
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| − | {{#invoke:Math| max }}
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| − |
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| − | When used with no arguments, it takes its input from the parent
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| − | frame. Note, any values that do not evaluate to numbers are ignored.
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| − | ]]
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| − | function z.max( frame )
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| − | local args = frame.args;
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| − |
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| − | if args[1] == nil then
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| − | local parent = frame:getParent();
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| − | args = parent.args;
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| − | end
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| − | local max_value = nil;
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| − |
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| − | local i = 1;
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| − | while args[i] ~= nil do
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| − | local val = z._cleanNumber( frame, args[i] );
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| − | if val ~= nil then
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| − | if max_value == nil or val > max_value then
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| − | max_value = val;
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| − | end
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| − | end
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| − | i = i + 1;
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| − | end
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| − |
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| − | return max_value
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| − | end
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| − |
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| − | --[[
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| − | min
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| − |
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| − | Finds the minimum argument
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| − |
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| − | Usage:
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| − | {{#invoke:Math| min | value1 | value2 | ... }}
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| − | OR
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| − | {{#invoke:Math| min }}
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| − |
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| − | When used with no arguments, it takes its input from the parent
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| − | frame. Note, any values that do not evaluate to numbers are ignored.
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| − | ]]
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| − | function z.min( frame )
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| − | local args = frame.args;
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| − |
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| − | if args[1] == nil then
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| − | local parent = frame:getParent();
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| − | args = parent.args;
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| − | end
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| − | local min_value = nil;
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| − |
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| − | local i = 1;
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| − | while args[i] ~= nil do
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| − | local val = z._cleanNumber( frame, args[i] );
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| − | if val ~= nil then
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| − | if min_value == nil or val < min_value then
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| − | min_value = val;
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| − | end
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| − | end
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| − | i = i + 1;
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| − | end
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| − |
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| − | return min_value
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| − | end
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| − |
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| − | --[[
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| − | round
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| − |
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| − | Rounds a number to specified precision
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| − |
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| − | Usage:
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| − | {{#invoke:Math | round | value | precision }}
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| − |
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| − | --]]
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| − | function z.round(frame)
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| − | local value, precision;
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| − |
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| − | value = z._cleanNumber( frame, frame.args[1] or frame.args.value or 0 );
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| − | precision = z._cleanNumber( frame, frame.args[2] or frame.args.precision or 0 );
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| − |
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| − | if value == nil or precision == nil then
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| − | return '<strong class="error">Formatting error: Round input appears non-numeric</strong>'
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| − | else
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| − | return z._round( value, precision );
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| − | end
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| − | end
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| − | function z._round( value, precision )
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| − | local rescale = math.pow( 10, precision );
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| − | return math.floor( value * rescale + 0.5 ) / rescale;
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| − | end
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| − |
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| − | --[[
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| − | precision_format
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| − |
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| − | Rounds a number to the specified precision and formats according to rules
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| − | originally used for {{template:Rnd}}. Output is a string.
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| − |
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| − | Usage:
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| − | {{#invoke: Math | precision_format | number | precision }}
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| − | ]]
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| − | function z.precision_format( frame )
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| − | -- For access to Mediawiki built-in formatter.
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| − | local lang = mw.getContentLanguage();
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| − |
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| − | local value_string, value, precision;
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| − | value, value_string = z._cleanNumber( frame, frame.args[1] or 0 );
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| − | precision = z._cleanNumber( frame, frame.args[2] or 0 );
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| − |
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| − | -- Check for non-numeric input
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| − | if value == nil or precision == nil then
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| − | return '<strong class="error">Formatting error: invalid input when rounding</strong>'
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| − | end
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| − |
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| − | local current_precision = z._precision( value );
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| − |
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| − | local order = z._order( value );
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| − |
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| − | -- Due to round-off effects it is neccesary to limit the returned precision under
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| − | -- some circumstances because the terminal digits will be inaccurately reported.
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| − | if order + precision >= 14 then
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| − | orig_precision = z._precision( value_string );
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| − | if order + orig_precision >= 14 then
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| − | precision = 13 - order;
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| − | end
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| − | end
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| − |
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| − | -- If rounding off, truncate extra digits
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| − | if precision < current_precision then
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| − | value = z._round( value, precision );
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| − | current_precision = z._precision( value );
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| − | end
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| − |
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| − | local formatted_num = lang:formatNum( math.abs(value) );
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| − | local sign;
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| − |
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| − | -- Use proper unary minus sign rather than ASCII default
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| − | if value < 0 then
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| − | sign = '−';
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| − | else
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| − | sign = '';
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| − | end
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| − |
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| − | -- Handle cases requiring scientific notation
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| − | if string.find( formatted_num, 'E', 1, true ) ~= nil or math.abs(order) >= 9 then
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| − | value = value * math.pow( 10, -order );
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| − | current_precision = current_precision + order;
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| − | precision = precision + order;
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| − | formatted_num = lang:formatNum( math.abs(value) );
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| − | else
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| − | order = 0;
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| − | end
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| − | formatted_num = sign .. formatted_num;
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| − |
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| − | -- Pad with zeros, if needed
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| − | if current_precision < precision then
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| − | local padding;
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| − | if current_precision <= 0 then
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| − | if precision > 0 then
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| − | local zero_sep = lang:formatNum( 1.1 );
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| − | formatted_num = formatted_num .. zero_sep:sub(2,2);
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| − |
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| − | padding = precision;
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| − | if padding > 20 then
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| − | padding = 20;
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| − | end
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| − |
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| − | formatted_num = formatted_num .. string.rep( '0', padding );
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| − | end
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| − | else
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| − | padding = precision - current_precision
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| − | if padding > 20 then
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| − | padding = 20;
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| − | end
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| − | formatted_num = formatted_num .. string.rep( '0', padding );
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| − | end
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| − | end
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| − |
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| − | -- Add exponential notation, if necessary.
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| − | if order ~= 0 then
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| − | -- Use proper unary minus sign rather than ASCII default
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| − | if order < 0 then
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| − | order = '−' .. lang:formatNum( math.abs(order) );
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| − | else
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| − | order = lang:formatNum( order );
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| − | end
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| − |
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| − | formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
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| − | end
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| − |
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| − | return formatted_num;
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| − | end
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| − |
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| − | --[[
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| − | Helper function that interprets the input numerically. If the
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| − | input does not appear to be a number, attempts evaluating it as
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| − | a parser functions expression.
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| − | ]]
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| − |
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| − | function z._cleanNumber( frame, number_string )
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| − | if number_string == nil or number_string:len() == 0 then
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| − | return nil, nil;
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| − | end
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| − |
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| − | -- Attempt basic conversion
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| − | local number = tonumber( number_string )
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| − |
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| − | -- If failed, attempt to evaluate input as an expression
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| − | if number == nil then
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| − | local attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' );
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| − | attempt = tonumber( attempt );
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| − | if attempt ~= nil then
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| − | number = attempt;
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| − | number_string = tostring( number );
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| − | else
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| − | number = nil;
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| − | number_string = nil;
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| − | end
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| − | else
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| − | -- String is valid but may contain padding, clean it.
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| − | number_string = number_string:match( "^%s*(.-)%s*$" );
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| − | end
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| − |
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| − | return number, number_string;
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| − | end
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| − |
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| − | return z
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