Module:Math: Difference between revisions

    m>Mr. Stradivarius
    (add a gcd function per edit request by User:Mxn, add a mod function, alter existing functions to allow access from Lua without calling a frame object, use Module:Arguments to process arguments, p._cleanNumber improvements)
    m>Mr. Stradivarius
    (Undid revision 586573269 by Mr. Stradivarius (talk) the code refactor broke some existing modules - revert for now while I work out the extent of the problem)
    Line 4: Line 4:


    ]]
    ]]
    local z = {}


    local yesno = require('Module:Yesno')
    -- Generate random number
    local getArgs = require('Module:Arguments').getArgs
    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])


    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 applyFuncToArgs(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
     
    --[[
    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


    Line 103: Line 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


    Line 127: Line 50:


    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 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 = trap_fraction:lower();
    local pos = string.find(input_string, '/', 1, true);
            if trap_fraction == 'false' or trap_fraction == '0' or
    if pos ~= nil then
                    trap_fraction == 'no' or trap_fraction == '' then
    if string.find(input_string, '/', pos + 1, true) == nil then
                trap_fraction = false;
    local denominator = string.sub(input_string, pos+1, -1);
            else
    local denom_value = tonumber(denominator);
                trap_fraction = true;
    if denom_value ~= nil then
            end
    return math.log10(denom_value);
        end
    end
       
    end                         
        if trap_fraction then
    end
            local pos = string.find( input_string, '/', 1, true );
    end     
            if pos ~= nil then
     
                if string.find( input_string, '/', pos + 1, true ) == nil then
    input_number, input_string = p._cleanNumber(input_string);
                    local denominator = string.sub( input_string, pos+1, -1 );
    if input_string == nil then
                    local denom_value = tonumber( denominator );
    return err('precision input appears non-numeric')
                    if denom_value ~= nil then
    else
                        return math.log10(denom_value);
    return p._precision(input_string)
                    end
    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
    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


    Line 195: Line 123:


    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 function maxOfTwo(a, b)
        end
    if a > b then
        local max_value = nil;
    return a
       
    else
        local i = 1;
    return b
        while args[i] ~= nil do
    end
            local val = z._cleanNumber( frame, args[i] );
    end
            if val ~= nil then
    local max_value = applyFuncToArgs(maxOfTwo, ...)
                if max_value == nil or val > max_value then
    if max_value then
                    max_value = val;
    return max_value
                end
    end
            end      
            i = i + 1;
        end
     
        return max_value
    end
    end


    Line 224: Line 159:


    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 function minOfTwo(a, b)
        end
    if a < b then
        local min_value = nil;
    return a
       
    else
        local i = 1;
    return b
        while args[i] ~= nil do
    end
            local val = z._cleanNumber( frame, args[i] );
    end
            if val ~= nil then
    local min_value = applyFuncToArgs(minOfTwo, ...)
                if min_value == nil or val < min_value then
    if min_value then
                    min_value = val;
    return min_value
                end
    end
            end      
            i = i + 1;
        end
     
        return min_value
    end
    end


    --[[
    --[[
    average  
    average  
     
    Finds the average
    Finds the average
     
    Usage:
    Usage:
    {{#invoke:Math| average | value1 | value2 | ... }}
        {{#invoke:Math| average | value1 | value2 | ... }}
    OR
    OR
    {{#invoke:Math| average }}
        {{#invoke:Math| average }}
     
    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.average( frame )
    function wrap.average(args)
        local args = frame.args;
    return p._average(unpackNumberArgs(args))
        if args[1] == nil then
    end
            local parent = frame:getParent();
     
            args = parent.args;
    function p._average(...)
        end
    local function getSum(a, b)
        local sum = 0;
    return a + b
        local count = 0;
    end
    local sum, count = applyFuncToArgs(getSum, ...)
        local i = 1;
    if not sum then
        while args[i] ~= nil do
    return 0
            local val = z._cleanNumber( frame, args[i] );
    else
            if val ~= nil then
    return sum / count
                sum = sum + val
    end
                count = count + 1
            end       
            i = i + 1;
        end
        return (count == 0 and 0 or sum/count)
    end
    end


    Line 285: Line 230:


    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
     
    --[[
    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 = applyFuncToArgs(findGcd, ...)
    return result
    end
    end


    Line 371: Line 257:


    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
     
            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 value == nil or precision == nil then
    return err('invalid input when rounding')
    end
     
    local current_precision = p._precision(value)
    local order = p._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 = p._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 = p._round(value, precision)
    current_precision = p._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 rounding off, truncate extra digits
    if current_precision < precision then
        if precision < current_precision then
    local padding
            value = z._round( value, precision );
    if current_precision <= 0 then
            current_precision = z._precision( value );
    if precision > 0 then
        end   
    local zero_sep = lang:formatNum(1.1)
       
    formatted_num = formatted_num .. zero_sep:sub(2,2)
        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
                    padding = precision;
    if padding > 20 then
                    if padding > 20 then
    padding = 20
                        padding = 20;
    end
                    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


    formatted_num = formatted_num .. string.rep('0', padding)
        -- Add exponential notation, if necessary.
    end           
        if order ~= 0 then
    else                 
            -- Use proper unary minus sign rather than ASCII default
    padding = precision - current_precision
            if order < 0 then
    if padding > 20 then
                order = '−' .. lang:formatNum( math.abs(order) );
    padding = 20
            else
    end
                order = lang:formatNum( order );
    formatted_num = formatted_num .. string.rep('0', padding)
            end     
    end
           
    end
            formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
     
        end
    -- Add exponential notation, if necessary.
       
    if order ~= 0 then
        return formatted_num;
    -- 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


    Line 477: Line 357:
    ]]
    ]]


    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 frame = mw.getCurrentFrame()
                number_string = tostring( number );
    local attempt = frame:preprocess('{{#expr: ' .. number_string .. '}}')
            else
    attempt = tonumber(attempt)
                number = nil;
    if attempt ~= nil then
                number_string = nil;
    number = attempt
            end
    number_string = tostring(number)
        else
    else
        -- String is valid but may contain padding, clean it.
    number = nil
            number_string = number_string:match( "^%s*(.-)%s*$" );
    number_string = nil
        end
    end
       
    else
        return number, number_string;
    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.
    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
     
    --[[
    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 function makeWrapper(funcName)
    return function (frame)
    local args = getArgs(frame) -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed.
    return wrap[funcName](args)
    end
    end
     
    for funcName in pairs(wrap) do
    p[funcName] = makeWrapper(funcName)
    end
    end


    return p
    return z
    Retrieved from "https://nonbinary.wiki/wiki/Module:Math"