Module:Math : Différence entre versions
(Résumé automatique : blanchiment.) |
m (Pas de variables globales) |
||
(4 révisions intermédiaires par 4 utilisateurs non affichées) | |||
Ligne 1 : | Ligne 1 : | ||
+ | --[[ | ||
+ | This module provides a number of basic mathematical operations. | ||
+ | |||
+ | ]] | ||
+ | local z = {} | ||
+ | |||
+ | -- Generate random number | ||
+ | function z.random( frame ) | ||
+ | local first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil | ||
+ | local 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: | ||
+ | {{#invoke: Math | order | value }} | ||
+ | ]] | ||
+ | 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 '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>' | ||
+ | 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 | value }} | ||
+ | ]] | ||
+ | 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 '<strong class="error">Formatting error: Precision input appears non-numeric</strong>' | ||
+ | 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 | value1 | value2 | ... }} | ||
+ | OR | ||
+ | {{#invoke:Math| max }} | ||
+ | |||
+ | 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: | ||
+ | {{#invoke:Math| min | value1 | value2 | ... }} | ||
+ | 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 | ||
+ | |||
+ | --[[ | ||
+ | round | ||
+ | |||
+ | Rounds a number to specified precision | ||
+ | |||
+ | Usage: | ||
+ | {{#invoke:Math | round | value | precision }} | ||
+ | |||
+ | --]] | ||
+ | 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 '<strong class="error">Formatting error: Round input appears non-numeric</strong>' | ||
+ | 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 {{template:Rnd}}. Output is a string. | ||
+ | |||
+ | Usage: | ||
+ | {{#invoke: Math | precision_format | number | precision }} | ||
+ | ]] | ||
+ | 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 '<strong class="error">Formatting error: invalid input when rounding</strong>' | ||
+ | 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 | ||
+ | local 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 .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>' | ||
+ | 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( '{{#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 |
Version actuelle datée du 15 juin 2015 à 09:51
La documentation pour ce module peut être créée à Module:Math/doc
--[[ This module provides a number of basic mathematical operations. ]] local z = {} -- Generate random number function z.random( frame ) local first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil local 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: {{#invoke: Math | order | value }} ]] 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 '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>' 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 | value }} ]] 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 '<strong class="error">Formatting error: Precision input appears non-numeric</strong>' 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 | value1 | value2 | ... }} OR {{#invoke:Math| max }} 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: {{#invoke:Math| min | value1 | value2 | ... }} 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 --[[ round Rounds a number to specified precision Usage: {{#invoke:Math | round | value | precision }} --]] 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 '<strong class="error">Formatting error: Round input appears non-numeric</strong>' 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 {{template:Rnd}}. Output is a string. Usage: {{#invoke: Math | precision_format | number | precision }} ]] 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 '<strong class="error">Formatting error: invalid input when rounding</strong>' 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 local 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 .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>' 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( '{{#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