Module:Math

--[[

This module provides a number of basic mathematical operations.

]] local z = {}

-- Generate random number function z.random( frame ) first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil second = tonumber(frame.args[2])

if first then -- if NaN or nil, will skip down to final return if first <= second then -- could match if both nil, but already checked that first is a number in last line return math.random(first, second) end return math.random(first) end return math.random end

--[[ order

Determine order of magnitude of a number

Usage: ]] function z.order(frame) local input_string = (frame.args[1] or frame.args.x or '0'); local input_number; input_number = z._cleanNumber( frame, input_string ); if input_number == nil then return ' Formatting error: Order of magnitude input appears non-numeric ' else return z._order( input_number ) end end function z._order(x) if x == 0 then return 0 end return math.floor(math.log10(math.abs(x))) end

--[[ precision

Detemines the precision of a number using the string representation

Usage: ]] function z.precision( frame ) local input_string = (frame.args[1] or frame.args.x or '0'); local trap_fraction = frame.args.check_fraction or false; local input_number; if type( trap_fraction ) == 'string' then trap_fraction = trap_fraction:lower; if trap_fraction == 'false' or trap_fraction == '0' or               trap_fraction == 'no' or trap_fraction == '' then trap_fraction = false; else trap_fraction = true; end end if trap_fraction then local pos = string.find( input_string, '/', 1, true ); if pos ~= nil then if string.find( input_string, '/', pos + 1, true ) == nil then local denominator = string.sub( input_string, pos+1, -1 ); local denom_value = tonumber( denominator ); if denom_value ~= nil then return math.log10(denom_value); end end end end input_number, input_string = z._cleanNumber( frame, input_string ); if input_string == nil then return ' Formatting error: Precision input appears non-numeric ' else return z._precision( input_string ) end end function z._precision( x ) x = string.upper( x )

local decimal = string.find( x, '.', 1, true ) local exponent_pos = string.find( x, 'E', 1, true ) local result = 0; if exponent_pos ~= nil then local exponent = string.sub( x, exponent_pos + 1 ) x = string.sub( x, 1, exponent_pos - 1 ) result = result - tonumber( exponent ) end if decimal ~= nil then result = result + string.len( x ) - decimal return result end local pos = string.len( x ); while x:byte(pos) == string.byte('0') do       pos = pos - 1 result = result - 1 if pos <= 0 then return 0 end end return result end

--[[ max

Finds the maximum argument

Usage: OR

When used with no arguments, it takes its input from the parent frame. Note, any values that do not evaluate to numbers are ignored. ]] function z.max( frame ) local args = frame.args; if args[1] == nil then local parent = frame:getParent; args = parent.args; end local max_value = nil; local i = 1; while args[i] ~= nil do       local val = z._cleanNumber( frame, args[i] ); if val ~= nil then if max_value == nil or val > max_value then max_value = val; end end i = i + 1; end return max_value end

--[[ min

Finds the minimum argument

Usage: OR

When used with no arguments, it takes its input from the parent frame. Note, any values that do not evaluate to numbers are ignored. ]] function z.min( frame ) local args = frame.args; if args[1] == nil then local parent = frame:getParent; args = parent.args; end local min_value = nil; local i = 1; while args[i] ~= nil do       local val = z._cleanNumber( frame, args[i] ); if val ~= nil then if min_value == nil or val < min_value then min_value = val; end end i = i + 1; end return min_value end

--[[ round

Rounds a number to specified precision

Usage: --]] function z.round(frame) local value, precision; value = z._cleanNumber( frame, frame.args[1] or frame.args.value or 0 ); precision = z._cleanNumber( frame, frame.args[2] or frame.args.precision or 0 ); if value == nil or precision == nil then return ' Formatting error: Round input appears non-numeric ' else return z._round( value, precision ); end end function z._round( value, precision ) local rescale = math.pow( 10, precision ); return math.floor( value * rescale + 0.5 ) / rescale; end

--[[ precision_format

Rounds a number to the specified precision and formats according to rules originally used for. Output is a string.

Usage: ]] function z.precision_format( frame ) -- For access to Mediawiki built-in formatter. local lang = mw.getContentLanguage; local value_string, value, precision; value, value_string = z._cleanNumber( frame, frame.args[1] or 0 ); precision = z._cleanNumber( frame, frame.args[2] or 0 ); -- Check for non-numeric input if value == nil or precision == nil then return ' Formatting error: invalid input when rounding ' end local current_precision = z._precision( value );

local order = z._order( value ); -- Due to round-off effects it is neccesary to limit the returned precision under -- some circumstances because the terminal digits will be inaccurately reported. if order + precision >= 14 then orig_precision = z._precision( value_string ); if order + orig_precision >= 14 then precision = 13 - order; end end

-- If rounding off, truncate extra digits if precision < current_precision then value = z._round( value, precision ); current_precision = z._precision( value ); end local formatted_num = lang:formatNum( math.abs(value) ); local sign; -- Use proper unary minus sign rather than ASCII default if value < 0 then sign = '−'; else sign = ''; end -- Handle cases requiring scientific notation if string.find( formatted_num, 'E', 1, true ) ~= nil or math.abs(order) >= 9 then value = value * math.pow( 10, -order ); current_precision = current_precision + order; precision = precision + order; formatted_num = lang:formatNum( math.abs(value) ); else order = 0; end formatted_num = sign .. formatted_num; -- Pad with zeros, if needed if current_precision < precision then local padding; if current_precision <= 0 then if precision > 0 then local zero_sep = lang:formatNum( 1.1 ); formatted_num = formatted_num .. zero_sep:sub(2,2);

padding = precision; if padding > 20 then padding = 20; end formatted_num = formatted_num .. string.rep( '0', padding ); end else padding = precision - current_precision if padding > 20 then padding = 20; end formatted_num = formatted_num .. string.rep( '0', padding ); end end

-- Add exponential notation, if necessary. if order ~= 0 then -- Use proper unary minus sign rather than ASCII default if order < 0 then order = '−' .. lang:formatNum( math.abs(order) ); else order = lang:formatNum( order ); end formatted_num = formatted_num .. ' × 10' .. order .. ''   end return formatted_num; end

-- Helper function that interprets the input numerically. If the input does not appear to be a number, attempts evaluating it as a parser functions expression.

function z._cleanNumber( frame, number_string ) if number_string == nil or number_string:len == 0 then return nil, nil; end -- Attempt basic conversion local number = tonumber( number_string ) -- If failed, attempt to evaluate input as an expression if number == nil then local attempt = frame:preprocess( '' ); attempt = tonumber( attempt ); if attempt ~= nil then number = attempt; number_string = tostring( number ); else number = nil; number_string = nil; end else -- String is valid but may contain padding, clean it. number_string = number_string:match( "^%s*(.-)%s*$" ); end return number, number_string; end

return z