Module:Math: Difference between revisions

    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)
    m>Mr. Stradivarius
    (Undid revision 586591521 by Mr. Stradivarius (talk) reinstate the new version - the problem was limited to two modules, which I will now fix)
    Line 4: Line 4:


    ]]
    ]]
    local z = {}


    -- Generate random number
    local yesno = require('Module:Yesno')
    function z.random( frame )
    local getArgs = require('Module:Arguments').getArgs
        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
    local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
            if first <= second then -- could match if both nil, but already checked that first is a number in last line
    local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
                return math.random(first, second)
     
            end
    --[[
            return math.random(first)
    Helper functions used to avoid redundant code.
        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 26: Line 103:


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


    Line 50: Line 127:


    Usage:
    Usage:
        {{ #invoke: Math | precision | value }}
    {{ #invoke: Math | precision | value }}
    ]]
    ]]
    function z.precision( frame )
     
        local input_string = (frame.args[1] or frame.args.x or '0');
    function wrap.precision(args)
        local trap_fraction = frame.args.check_fraction or false;
    local input_string = (args[1] or args.x or '0');
        local input_number;
    local trap_fraction = args.check_fraction;
       
    local input_number;
        if type( trap_fraction ) == 'string' then
     
            trap_fraction = trap_fraction:lower();
    if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].
            if trap_fraction == 'false' or trap_fraction == '0' or
    local pos = string.find(input_string, '/', 1, true);
                    trap_fraction == 'no' or trap_fraction == '' then
    if pos ~= nil then
                trap_fraction = false;
    if string.find(input_string, '/', pos + 1, true) == nil then
            else
    local denominator = string.sub(input_string, pos+1, -1);
                trap_fraction = true;
    local denom_value = tonumber(denominator);
            end
    if denom_value ~= nil then
        end
    return math.log10(denom_value);
       
    end
        if trap_fraction then
    end                         
            local pos = string.find( input_string, '/', 1, true );
    end
            if pos ~= nil then
    end     
                if string.find( input_string, '/', pos + 1, true ) == nil then
     
                    local denominator = string.sub( input_string, pos+1, -1 );
    input_number, input_string = p._cleanNumber(input_string);
                    local denom_value = tonumber( denominator );
    if input_string == nil then
                    if denom_value ~= nil then
    return err('precision input appears non-numeric')
                        return math.log10(denom_value);
    else
                    end
    return p._precision(input_string)
                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 )


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


    Line 123: Line 195:


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


    When used with no arguments, it takes its input from the parent
    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.max( frame )
     
        local args = frame.args;
    function wrap.max(args)
       
    return p._max(unpackNumberArgs(args))
        if args[1] == nil then
    end
            local parent = frame:getParent();
     
            args = parent.args;
    function p._max(...)
        end
    local function maxOfTwo(a, b)
        local max_value = nil;
    if a > b then
       
    return a
        local i = 1;
    else
        while args[i] ~= nil do
    return b
            local val = z._cleanNumber( frame, args[i] );
    end
            if val ~= nil then
    end
                if max_value == nil or val > max_value then
    local max_value = applyFuncToArgs(maxOfTwo, ...)
                    max_value = val;
    if max_value then
                end
    return max_value
            end      
    end
            i = i + 1;
        end
     
        return max_value
    end
    end


    Line 159: Line 224:


    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 )
     
        local args = frame.args;
    function wrap.min(args)
       
    return p._min(unpackNumberArgs(args))
        if args[1] == nil then
    end
            local parent = frame:getParent();
     
            args = parent.args;
    function p._min(...)
        end
    local function minOfTwo(a, b)
        local min_value = nil;
    if a < b then
       
    return a
        local i = 1;
    else
        while args[i] ~= nil do
    return b
            local val = z._cleanNumber( frame, args[i] );
    end
            if val ~= nil then
    end
                if min_value == nil or val < min_value then
    local min_value = applyFuncToArgs(minOfTwo, ...)
                    min_value = val;
    if min_value then
                end
    return min_value
            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 }}
     
    When used with no arguments, it takes its input from the parent
    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.average( frame )
     
        local args = frame.args;
    function wrap.average(args)
        if args[1] == nil then
    return p._average(unpackNumberArgs(args))
            local parent = frame:getParent();
    end
            args = parent.args;
     
        end
    function p._average(...)
        local sum = 0;
    local function getSum(a, b)
        local count = 0;
    return a + b
    end
        local i = 1;
    local sum, count = applyFuncToArgs(getSum, ...)
        while args[i] ~= nil do
    if not sum then
            local val = z._cleanNumber( frame, args[i] );
    return 0
            if val ~= nil then
    else
                sum = sum + val
    return sum / count
                count = count + 1
    end
            end       
            i = i + 1;
        end
        return (count == 0 and 0 or sum/count)
    end
    end


    Line 230: Line 285:


    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)
     
        local value, precision;
    function wrap.gcd(args)
       
    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 )
     
        local rescale = math.pow( 10, precision );
    function p._gcd(...)
        return math.floor( value * rescale + 0.5 ) / rescale;
    local function findGcd(a, b)
    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 257: Line 371:


    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 );


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


        -- If rounding off, truncate extra digits
    -- Pad with zeros, if needed     
        if precision < current_precision then
    if current_precision < precision then
            value = z._round( value, precision );
    local padding
            current_precision = z._precision( value );
    if current_precision <= 0 then
        end   
    if precision > 0 then
       
    local zero_sep = lang:formatNum(1.1)
        local formatted_num = lang:formatNum( math.abs(value) );
    formatted_num = formatted_num .. zero_sep:sub(2,2)
        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


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


    Line 357: Line 477:
    ]]
    ]]


    function z._cleanNumber( frame, number_string )
    function p._cleanNumber(number_string)
        if number_string == nil or number_string:len() == 0 then
    if type(number_string) == 'number' then
            return nil, nil;
    -- We were passed a number, so we don't need to do any processing.
        end  
    return number_string, tostring(number_string)
       
    elseif type(number_string) ~= 'string' or not number_string:find('%S') then
        -- Attempt basic conversion
    -- We were passed a non-string or a blank string, so exit.
        local number = tonumber( number_string )
    return nil, nil;
       
    end
        -- If failed, attempt to evaluate input as an expression
     
        if number == nil then      
    -- Attempt basic conversion
            local attempt = frame:preprocess( '{{#expr: ' .. number_string .. '}}' );
    local number = tonumber(number_string)
            attempt = tonumber( attempt );
     
            if attempt ~= nil then
    -- If failed, attempt to evaluate input as an expression
                number = attempt;
    if number == nil then
                number_string = tostring( number );
    local frame = mw.getCurrentFrame()
            else
    local attempt = frame:preprocess('{{#expr: ' .. number_string .. '}}')
                number = nil;
    attempt = tonumber(attempt)
                number_string = nil;
    if attempt ~= nil then
            end
    number = attempt
        else
    number_string = tostring(number)
        -- String is valid but may contain padding, clean it.
    else
            number_string = number_string:match( "^%s*(.-)%s*$" );
    number = nil
        end
    number_string = nil
       
    end
        return number, number_string;
    else
    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 z
    return p
    Retrieved from "https://nonbinary.wiki/wiki/Module:Math"