Math
Documentation for this module may be created at ሞድዩል:Math/doc
--[[ This module provides a number of basic mathematical operations. ]] local z = {} -- Generate a random number function z.random(frame) local first = tonumber(frame.args[1]) local second = tonumber(frame.args[2]) local seed = tonumber(frame.args.seed) if seed then math.randomseed(seed * os.time()) -- pseudorandom initialization end if first and second then if first < second then return math.random(first,second) -- integer between [first,second] else return math.random(second,first) end elseif first then if first > 0 then return math.random(first) -- integer between [1,first] else return math.random(first,-1) end else return math.random() -- real number between [0,1) end end --[[ order Determine order of magnitude of a number Usage: {{#invoke: Math | order | }} ]] 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 'Format 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: {{ #invoke: Math | precision | }} ]] 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 'Format 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: {{#invoke:Math| max | | | ... }} or {{#invoke:Math| max }} 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: {{#invoke:Math| min | | | ... }} or {{#invoke:Math| min }} 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 -- Function that counts the number of reported parameters function z.counts( frame ) local result = 0; local Arguments = frame.args; if Arguments[1] == nil then local parent = frame:getParent(); Arguments = parent.args; end local i = 1; while Arguments[i] ~= nil do if Arguments[i] ~= '' then result = result + 1 end i = i + 1; end return result end -- Finds the sum function z.sum( frame ) local result = 0; local Arguments = frame.args; if Arguments[1] == nil then local parent = frame:getParent(); Arguments = parent.args; end local i = 1; while Arguments[i] ~= nil do if Arguments[i] ~= '' then result = result + Arguments[i] end i = i + 1; end return result end --[[ round Rounds a number to specified precision Usage: {{#invoke:Math | round | | }} --]] 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 'Format 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 it according to the rules originally used for {{Template: Rnd}}. The output is a string. Usage: {{#invoke: Math | precision_format | | }} ]] function z.precision_format( frame ) -- To access Mediawiki incorporating 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 ); -- Checks for a non-numeric input if value == nil or precision == nil then return 'Format error: Invalid data to round' end local current_precision = z._precision( value ); local order = z._order( value ); -- Due to rounding effects, it is necessary to limit the returned precision under -- some circumstances, because the terminal digits were reported incorrectly. if order + precision >= 14 then orig_precision = z._precision( value_string ); if order + orig_precision >= 14 then precision = 13 - order; end end -- If rounding, truncate additional 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; -- Uses the appropriate unary minus sign before the default ASCII if value < 0 then sign = '−'; else sign = ''; end -- Handle cases that require 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 necessary 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 -- Uses the appropriate unary minus sign before the default ASCII 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 numeric input. If the input is not a number, it tries to evaluate it as a "parser function" (parser). ]] function z._cleanNumber( frame, number_string ) if number_string == nil or number_string:len() == 0 then return nil, nil; end -- Try the basic conversion local number = tonumber( number_string ) -- If it fails, it tries to evaluate the input as an expression if number == nil then local attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' ); 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