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নতুন নিবন্ধ তৈরি করুন
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    এই মডিউলের জন্য মডিউল:Math/নথি-এ নথিপত্র তৈরি করা হয়ে থাকতে পারে

    --[[
    
    This module provides a number of basic mathematical operations.
    
    ]]
    
    local yesno, getArgs -- lazily initialized
    
    local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.
    local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.
    
    --[[
    Helper functions used to avoid redundant code.
    ]]
    
    local function err(msg)
    	-- Generates wikitext error messages.
    	return mw.ustring.format('<strong class="error">বিন্যাসন ত্রুটি: %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
    
    --[[
    order
    
    Determine order of magnitude of a number
    
    Usage:
    {{#invoke: Math | order | value }}
    ]]
    
    function wrap.order(args)
    	local input_string = (args[1] or args.x or '0');
    	local input_number = p._cleanNumber(input_string);
    	if input_number == nil then
    		return err('মাত্রার ক্রম অ-সাংখ্যিক দেখাচ্ছে')
    	else
    		return p._order(input_number)
    	end
    end
    
    function p._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 wrap.precision(args)
    	local input_string = (args[1] or args.x or '0');
    	local trap_fraction = args.check_fraction;
    	local input_number;
    
    	if not yesno then
    		yesno = require('Module:Yesno')
    	end
    	if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].
    		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 = p._cleanNumber(input_string);
    	if input_string == nil then
    		return err('স্পষ্টতা ইনপুট অ-সাংখ্যিক দেখাচ্ছে')
    	else
    		return p._precision(input_string)
    	end
    end
    
    function p._precision(x)
    	if type(x) == 'number' then
    		x = tostring(x)
    	end
    	x = string.upper(x)
    
    	local decimal = x:find('%.')
    	local exponent_pos = x:find('E')
    	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 | ... }}
    
    Note, any values that do not evaluate to numbers are ignored.
    ]]
    
    function wrap.max(args)
    	return p._max(unpackNumberArgs(args))
    end
    
    function p._max(...)
    	local max_value = binary_fold((function(a, b) return a > b end), ...)
    	if max_value then
    		return max_value
    	end
    end
    
    --[[
    median
    
    Find the median of set of numbers
    
    Usage:
    {{#invoke:Math | median | number1 | number2 | ...}}
    OR
    {{#invoke:Math | median }}
    ]]
    
    function wrap.median(args)
    	return p._median(unpackNumberArgs(args))
    end
    
    function p._median(...)
    	local vals = makeArgArray(...)
    	local count = #vals
    	table.sort(vals)
    
    	if count == 0 then
    		return 0
    	end
    
    	if p._mod(count, 2) == 0 then
    		return (vals[count/2] + vals[count/2+1])/2
    	else
    		return vals[math.ceil(count/2)]
    	end
    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 wrap.min(args)
    	return p._min(unpackNumberArgs(args))
    end
    
    function p._min(...)
    	local min_value = binary_fold((function(a, b) return a < b end), ...)
    	if min_value then
    		return min_value
    	end
    end
    
    --[[
    sum
    
    Finds the sum
    
    Usage:
    {{#invoke:Math| sum | value1 | value2 | ... }}
    OR
    {{#invoke:Math| sum }}
    
    Note, any values that do not evaluate to numbers are ignored.
    ]]
    
    function wrap.sum(args)
    	return p._sum(unpackNumberArgs(args))
    end
    
    function p._sum(...)
    	local sums, count = fold((function(a, b) return a + b end), ...)
    	if not sums then
    		return 0
    	else
    		return sums
    	end
    end
    
    --[[
    average
    
    Finds the average
    
    Usage:
    {{#invoke:Math| average | value1 | value2 | ... }}
    OR
    {{#invoke:Math| average }}
    
    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
    
    --[[
    round
    
    Rounds a number to specified precision
    
    Usage:
    {{#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 | log10 | 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 wrap.gcd(args)
    	return p._gcd(unpackNumberArgs(args))
    end
    
    function p._gcd(...)
    	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 = fold(findGcd, ...)
    	return result
    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 wrap.precision_format(args)
    	local value_string = args[1] or 0
    	local precision = args[2] or 0
    	return p._precision_format(value_string, precision)
    end
    
    function p._precision_format(value_string, precision)
    	-- For access to Mediawiki built-in formatter.
    	local lang = mw.getContentLanguage();
    	local lang_en = mw.getLanguage('en');
    
    	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
    		if order + p._precision(value_string) >= 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 formatted_num_en = lang_en: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_en, '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 .. '.'
    
    				padding = precision
    				if padding > 20 then
    					padding = 20
    				end
    
    				formatted_num = formatted_num .. string.rep('০', padding)
    			end
    		else
    			padding = precision - current_precision
    			if padding > 20 then
    				padding = 20
    			end
    			formatted_num = formatted_num .. string.rep('০', 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>১০<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 p._cleanNumber(number_string)
    	if type(number_string) == 'number' then
    		-- We were passed a number, so we don't need to do any processing.
    		return number_string, tostring(number_string)
    	elseif type(number_string) ~= 'string' or not number_string:find('%S') then
    		-- We were passed a non-string or a blank string, so exit.
    		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 success, result = pcall(mw.ext.ParserFunctions.expr, number_string)
    		if success then
    			number = tonumber(result)
    			number_string = tostring(number)
    		else
    			number = nil
    			number_string = nil
    		end
    	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 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)
    
    কুকিসমূহ আমাদের সেবা প্রদান করতে সহায়তা করে। আমাদের পরিষেবা ব্যবহার করার মাধ্যমে, আপনি আমাদের দ্বারা কুকি ব্যবহারে সম্মত হচ্ছেন।
    আরও তথ্য

    সাম্প্রতিক পরিবর্তন

  • 37.111.194.29 • ৪ মাস আগে
  • 37.111.194.29 • ৪ মাস আগে
  • কুকিসমূহ আমাদের সেবা প্রদান করতে সহায়তা করে। আমাদের পরিষেবা ব্যবহার করার মাধ্যমে, আপনি আমাদের দ্বারা কুকি ব্যবহারে সম্মত হচ্ছেন।
    আরও তথ্য