Différences entre les versions de « Module:Math »

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(add log10 functionality from module merge)
 
(Page créée avec « --This module provides a number of basic mathematical operations. local z = {} -- Generate random number function z.random( frame ) local first = tonumber(fra... »)
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]]
]]
local z = {}


local yesno, getArgs -- lazily initialized
-- 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])


local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
    if first then -- if NaN or nil, will skip down to final return
local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
        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
Helper functions used to avoid redundant code.
        return math.random(first)
]]
    end 
 
    return math.random()
local function err(msg)
-- Generates wikitext error messages.
return mw.ustring.format('<strong class="error">Formatting error: %s</strong>', msg)
end
 
local function unpackNumberArgs(args)
-- Returns an unpacked list of arguments specified with numerical keys.
local ret = {}
for k, v in pairs(args) do
if type(k) == 'number' then
table.insert(ret, v)
end
end
return unpack(ret)
end
 
local function makeArgArray(...)
-- Makes an array of arguments from a list of arguments that might include nils.
local args = {...} -- Table of arguments. It might contain nils or non-number values, so we can't use ipairs.
local nums = {} -- Stores the numbers of valid numerical arguments.
local ret = {}
for k, v in pairs(args) do
v = p._cleanNumber(v)
if v then
nums[#nums + 1] = k
args[k] = v
end
end
table.sort(nums)
for i, num in ipairs(nums) do
ret[#ret + 1] = args[num]
end
return ret
end
 
local function fold(func, ...)
-- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters,
-- and must return a number as an output. This number is then supplied as input to the next function call.
local vals = makeArgArray(...)
local count = #vals -- The number of valid arguments
if count == 0 then return
-- Exit if we have no valid args, otherwise removing the first arg would cause an error.
nil, 0
end
local ret = table.remove(vals, 1)
for _, val in ipairs(vals) do
ret = func(ret, val)
end
return ret, count
end
 
--[[
Fold arguments by selectively choosing values (func should return when to choose the current "dominant" value).
]]
local function binary_fold(func, ...)
local value = fold((function(a, b) if func(a, b) then return a else return b end end), ...)
return value
end
 
--[[
random
 
Generate a random number
 
Usage:
{{#invoke: Math | random }}
{{#invoke: Math | random | maximum value }}
{{#invoke: Math | random | minimum value | maximum value }}
]]
 
function wrap.random(args)
local first = p._cleanNumber(args[1])
local second = p._cleanNumber(args[2])
return p._random(first, second)
end
 
function p._random(first, second)
math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000))
-- math.random will throw an error if given an explicit nil parameter, so we need to use if statements to check the params.
if first and second then
if first <= second then -- math.random doesn't allow the first number to be greater than the second.
return math.random(first, second)
end
elseif first then
return math.random(first)
else
return math.random()
end
end
end


Ligne 110 : Ligne 26 :


Usage:
Usage:
{{#invoke: Math | order | value }}
    {{#invoke: Math | order | value }}
]]
]]
 
function z.order(frame)
function wrap.order(args)
    local input_string = (frame.args[1] or frame.args.x or '0');
local input_string = (args[1] or args.x or '0');
    local input_number;
local input_number = p._cleanNumber(input_string);
   
if input_number == nil then
    input_number = z._cleanNumber( frame, input_string );
return err('order of magnitude input appears non-numeric')
    if input_number == nil then
else
        return '<strong class="error">Formatting error: Order of magnitude input appears non-numeric</strong>'
return p._order(input_number)
    else
end     
        return z._order( input_number )
    end     
end
end
 
function z._order(x)
function p._order(x)
    if x == 0 then return 0 end
if x == 0 then return 0 end
    return math.floor(math.log10(math.abs(x)))
return math.floor(math.log10(math.abs(x)))
end
end


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Usage:
Usage:
{{ #invoke: Math | precision | value }}
    {{ #invoke: Math | precision | value }}
]]
]]
 
function z.precision( frame )
function wrap.precision(args)
    local input_string = (frame.args[1] or frame.args.x or '0');
local input_string = (args[1] or args.x or '0');
    local trap_fraction = frame.args.check_fraction or false;
local trap_fraction = args.check_fraction;
    local input_number;
local input_number;
   
 
    if type( trap_fraction ) == 'string' then
if not yesno then
        trap_fraction = trap_fraction:lower();
yesno = require('Module:Yesno')
        if trap_fraction == 'false' or trap_fraction == '0' or
end
                trap_fraction == 'no' or trap_fraction == '' then
if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].
            trap_fraction = false;
local pos = string.find(input_string, '/', 1, true);
        else
if pos ~= nil then
            trap_fraction = true;
if string.find(input_string, '/', pos + 1, true) == nil then
        end
local denominator = string.sub(input_string, pos+1, -1);
    end
local denom_value = tonumber(denominator);
   
if denom_value ~= nil then
    if trap_fraction then
return math.log10(denom_value);
        local pos = string.find( input_string, '/', 1, true );
end
        if pos ~= nil then
end                         
            if string.find( input_string, '/', pos + 1, true ) == nil then
end
                local denominator = string.sub( input_string, pos+1, -1 );
end     
                local denom_value = tonumber( denominator );
 
                if denom_value ~= nil then
input_number, input_string = p._cleanNumber(input_string);
                    return math.log10(denom_value);
if input_string == nil then
                end
return err('precision input appears non-numeric')
            end                         
else
        end
return p._precision(input_string)
    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
end
function z._precision( x )   
    x = string.upper( x )


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


--[[
--[[
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Usage:
Usage:
{{#invoke:Math| max | value1 | value2 | ... }}
    {{#invoke:Math| max | value1 | value2 | ... }}
OR
    {{#invoke:Math| max }}


Note, any values that do not evaluate to numbers are ignored.
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 )
function wrap.max(args)
    local args = frame.args;
return p._max(unpackNumberArgs(args))
   
end
    if args[1] == nil then
 
        local parent = frame:getParent();
function p._max(...)
        args = parent.args;
local max_value = binary_fold((function(a, b) return a > b end), ...)
    end
if max_value then
    local max_value = nil;
return max_value
   
end
    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
end


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Usage:
Usage:
{{#invoke:Math| min | value1 | value2 | ... }}
    {{#invoke:Math| min | value1 | value2 | ... }}
OR
OR
{{#invoke:Math| min }}
    {{#invoke:Math| min }}


When used with no arguments, it takes its input from the parent
When used with no arguments, it takes its input from the parent
frame.  Note, any values that do not evaluate to numbers are ignored.
frame.  Note, any values that do not evaluate to numbers are ignored.
]]
]]
 
function z.min( frame )
function wrap.min(args)
    local args = frame.args;
return p._min(unpackNumberArgs(args))
   
end
    if args[1] == nil then
 
        local parent = frame:getParent();
function p._min(...)
        args = parent.args;
local min_value = binary_fold((function(a, b) return a < b end), ...)
    end
if min_value then
    local min_value = nil;
return min_value
   
end
    local i = 1;
end
    while args[i] ~= nil do
 
        local val = z._cleanNumber( frame, args[i] );
--[[
        if val ~= nil then
average
            if min_value == nil or val < min_value then
 
                min_value = val;
Finds the average
            end
 
        end       
Usage:
        i = i + 1;
{{#invoke:Math| average | value1 | value2 | ... }}
    end
OR
 
{{#invoke:Math| average }}
    return min_value
 
Note, any values that do not evaluate to numbers are ignored.
]]
 
function wrap.average(args)
return p._average(unpackNumberArgs(args))
end
 
function p._average(...)
local sum, count = fold((function(a, b) return a + b end), ...)
if not sum then
return 0
else
return sum / count
end
end
end


Ligne 279 : Ligne 195 :


Usage:
Usage:
{{#invoke:Math | round | value | precision }}
    {{#invoke:Math | round | value | precision }}
 
   
--]]
 
function wrap.round(args)
local value = p._cleanNumber(args[1] or args.value or 0)
local precision = p._cleanNumber(args[2] or args.precision or 0)
if value == nil or precision == nil then
return err('round input appears non-numeric')
else
return p._round(value, precision)
end   
end
 
function p._round(value, precision)
local rescale = math.pow(10, precision or 0);
return math.floor(value * rescale + 0.5) / rescale;
end
 
--[[
log10
 
returns the log (base 10) of a number
 
Usage:
{{#invoke:Math | log | x }}
]]
 
function wrap.log10(args)
return math.log10(args[1])
end
 
--[[
mod
 
Implements the modulo operator
 
Usage:
{{#invoke:Math | mod | x | y }}
 
--]]
 
function wrap.mod(args)
local x = p._cleanNumber(args[1])
local y = p._cleanNumber(args[2])
if not x then
return err('first argument to mod appears non-numeric')
elseif not y then
return err('second argument to mod appears non-numeric')
else
return p._mod(x, y)
end   
end
 
function p._mod(x, y)
local ret = x % y
if not (0 <= ret and ret < y) then
ret = 0
end
return ret
end
 
--[[
gcd
 
Calculates the greatest common divisor of multiple numbers
 
Usage:
{{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }}
--]]
--]]
 
function z.round(frame)
function wrap.gcd(args)
    local value, precision;
return p._gcd(unpackNumberArgs(args))
   
    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
end
 
function z._round( value, precision )
function p._gcd(...)
    local rescale = math.pow( 10, precision );
local function findGcd(a, b)
    return math.floor( value * rescale + 0.5 ) / rescale;
local r = b
local oldr = a
while r ~= 0 do
local quotient = math.floor(oldr / r)
oldr, r = r, oldr - quotient * r
end
if oldr < 0 then
oldr = oldr * -1
end
return oldr
end
local result, count = fold(findGcd, ...)
return result
end
end


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Usage:
Usage:
{{#invoke: Math | precision_format | number | precision }}
    {{#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 );


function wrap.precision_format(args)
    local order = z._order( value );
local value_string = args[1] or 0
   
local precision = args[2] or 0
    -- Due to round-off effects it is neccesary to limit the returned precision under
return p._precision_format(value_string, precision)
    -- some circumstances because the terminal digits will be inaccurately reported.
end
    if order + precision >= 14 then
 
        local orig_precision = z._precision( value_string );
function p._precision_format(value_string, precision)
        if order + orig_precision >= 14 then
-- For access to Mediawiki built-in formatter.
            precision = 13 - order;       
local lang = mw.getContentLanguage();
        end       
 
    end
local value
value, value_string = p._cleanNumber(value_string)
precision = p._cleanNumber(precision)


-- Check for non-numeric input
    -- If rounding off, truncate extra digits
if value == nil or precision == nil then
    if precision < current_precision then
return err('invalid input when rounding')
        value = z._round( value, precision );
end
        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);


local current_precision = p._precision(value)
                padding = precision;
local order = p._order(value)
                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


-- Due to round-off effects it is neccesary to limit the returned precision under
    -- Add exponential notation, if necessary.
-- some circumstances because the terminal digits will be inaccurately reported.
    if order ~= 0 then
if order + precision >= 14 then
        -- Use proper unary minus sign rather than ASCII default
orig_precision = p._precision(value_string)
        if order < 0 then
if order + orig_precision >= 14 then
            order = '−' .. lang:formatNum( math.abs(order) );
precision = 13 - order;       
        else
end       
            order = lang:formatNum( order );
end
        end     
 
       
-- If rounding off, truncate extra digits
        formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
if precision < current_precision then
    end
value = p._round(value, precision)
   
current_precision = p._precision(value)
    return formatted_num;
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
end


Ligne 484 : Ligne 322 :
]]
]]


function p._cleanNumber(number_string)
function z._cleanNumber( frame, number_string )
if type(number_string) == 'number' then
    if number_string == nil or number_string:len() == 0 then
-- We were passed a number, so we don't need to do any processing.
        return nil, nil;
return number_string, tostring(number_string)
    end  
elseif type(number_string) ~= 'string' or not number_string:find('%S') then
   
-- We were passed a non-string or a blank string, so exit.
    -- Attempt basic conversion
return nil, nil;
    local number = tonumber( number_string )
end
   
 
    -- If failed, attempt to evaluate input as an expression
-- Attempt basic conversion
    if number == nil then      
local number = tonumber(number_string)
        local attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' );
 
        attempt = tonumber( attempt );
-- If failed, attempt to evaluate input as an expression
        if attempt ~= nil then
if number == nil then
            number = attempt;
local success, result = pcall(mw.ext.ParserFunctions.expr, number_string)
            number_string = tostring( number );
if success then
        else
number = tonumber(result)
            number = nil;
number_string = tostring(number)
            number_string = nil;
else
        end
number = nil
    else
number_string = nil
    -- String is valid but may contain padding, clean it.
end
        number_string = number_string:match( "^%s*(.-)%s*$" );
else
    end
number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it.
   
number_string = number_string:match("^%+(.*)$") or number_string -- Trim any leading + signs.
    return number, number_string;
if number_string:find('^%-?0[xX]') then
-- Number is using 0xnnn notation to indicate base 16; use the number that Lua detected instead.
number_string = tostring(number)
end
end
 
return number, number_string
end
end


--[[
return z
Wrapper function that does basic argument processing. This ensures that all functions from #invoke can use either the current
frame or the parent frame, and it also trims whitespace for all arguments and removes blank arguments.
]]
 
local mt = { __index = function(t, k)
return function(frame)
if not getArgs then
getArgs = require('Module:Arguments').getArgs
end
return wrap[k](getArgs(frame))  -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed.
end
end }
 
return setmetatable(p, mt)

Version du 16 septembre 2018 à 16:16

--[[

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: 

   Formatting error: Order of magnitude input appears non-numeric

]] 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: 

   Formatting error: Precision input appears non-numeric

]] 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: 

   0

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: 

   0

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: 

   Formatting error: Round input appears non-numeric

--]] 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 Formatting error: invalid input when rounding . Output is a string.

Usage: 

   Formatting error: invalid input when rounding

]] 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
       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 .. '×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( 'Erreur d’expression : caractère de ponctuation « ' » non reconnu.' );
       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

Récupérée de « https://wiki.froce.fr//index.php?title=Module:Math&oldid=356 »