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--[[
This module provides a number of basic mathematical operations.
]]
local z = {}
-- Generate random number
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])
if first then -- if NaN or nil, will skip down to final return
if first <= second then -- could match if both nil, but already checked that first is a number in last line
return math.random(first, second)
end
return math.random(first)
end
return math.random()
end
--[[
order
Determine order of magnitude of a number
Usage:
{{#invoke: Math | order | value }}
]]
function z.order(frame)
local input_string = (frame.args[1] or frame.args.x or '0');
local input_number;
input_number = z._cleanNumber( frame, input_string );
if input_number == nil then
return '<strong class="error">Ошибка формата данных: нечисловое входное значение при определении десятичной степени</strong>'
else
return z._order( input_number )
end
end
function z._order(x)
if x == 0 then return 0 end
return math.floor(math.log10(math.abs(x)))
end
--[[
precision
Detemines the precision of a number using the string representation
Usage:
{{ #invoke: Math | precision | value }}
]]
function z.precision( frame )
local input_string = (frame.args[1] or frame.args.x or '0');
local trap_fraction = frame.args.check_fraction or false;
local input_number;
if type( trap_fraction ) == 'string' then
trap_fraction = trap_fraction:lower();
if trap_fraction == 'false' or trap_fraction == '0' or
trap_fraction == 'no' or trap_fraction == '' then
trap_fraction = false;
else
trap_fraction = true;
end
end
if trap_fraction then
local pos = string.find( input_string, '/', 1, true );
if pos ~= nil then
if string.find( input_string, '/', pos + 1, true ) == nil then
local denominator = string.sub( input_string, pos+1, -1 );
local denom_value = tonumber( denominator );
if denom_value ~= nil then
return math.log10(denom_value);
end
end
end
end
input_number, input_string = z._cleanNumber( frame, input_string );
if input_string == nil then
return '<strong class="error">Ошибка формата данных: нечисловое входное значение при определении дробной части</strong>'
else
return z._precision( input_string )
end
end
function z._precision( x )
x = string.upper( x )
local decimal = string.find( x, '[.,]', 1 )
local exponent_pos = string.find( x, 'E', 1, true )
local result = 0;
if exponent_pos ~= nil then
local exponent = string.sub( x, exponent_pos + 1 )
x = string.sub( x, 1, exponent_pos - 1 )
result = result - tonumber( exponent )
end
if decimal ~= nil then
result = result + string.len( x ) - decimal
return result
end
local pos = string.len( x );
while x:byte(pos) == string.byte('0') do
pos = pos - 1
result = result - 1
if pos <= 0 then
return 0
end
end
return result
end
--[[
max
Finds the maximum argument
Usage:
{{#invoke:Math| max | value1 | value2 | ... }}
OR
{{#invoke:Math| max }}
When used with no arguments, it takes its input from the parent
frame. Note, any values that do not evaluate to numbers are ignored.
]]
function z.max( frame )
local args = frame.args;
if args[1] == nil then
local parent = frame:getParent();
args = parent.args;
end
local max_value = nil;
local i = 1;
while args[i] ~= nil do
local val = z._cleanNumber( frame, args[i] );
if val ~= nil then
if max_value == nil or val > max_value then
max_value = val;
end
end
i = i + 1;
end
return max_value
end
--[[
min
Finds the minimum argument
Usage:
{{#invoke:Math| min | value1 | value2 | ... }}
OR
{{#invoke:Math| min }}
When used with no arguments, it takes its input from the parent
frame. Note, any values that do not evaluate to numbers are ignored.
]]
function z.min( frame )
local args = frame.args;
if args[1] == nil then
local parent = frame:getParent();
args = parent.args;
end
local min_value = nil;
local i = 1;
while args[i] ~= nil do
local val = z._cleanNumber( frame, args[i] );
if val ~= nil then
if min_value == nil or val < min_value then
min_value = val;
end
end
i = i + 1;
end
return min_value
end
--[[
round
Rounds a number to specified precision
Usage:
{{#invoke:Math | round | value | precision }}
--]]
function z.round(frame)
local value, precision;
value = z._cleanNumber( frame, frame.args[1] or frame.args.value or 0 );
precision = z._cleanNumber( frame, frame.args[2] or frame.args.precision or 0 );
if value == nil or precision == nil then
return '<strong class="error">Ошибка формата данных: нечисловое входное значение при округлении до целого</strong>'
else
return z._round( value, precision );
end
end
function z._round( value, precision )
local rescale = math.pow( 10, precision );
return math.floor( value * rescale + 0.5 ) / rescale;
end
--[[
precision_format
Rounds a number to the specified precision and formats according to rules
originally used for {{template:Rnd}}. Output is a string.
Usage:
{{#invoke: Math | precision_format | number | precision }}
]]
function z.precision_format(args)
local value_string = args[1] or 0
local precision = args[2] or 0
return z._precision_format(value_string, precision)
end
function z._precision_format(value_string, precision)
-- For access to Mediawiki built-in formatter.
local lang = mw.getContentLanguage();
local value
value, value_string = z._cleanNumber(value_string)
precision = z._cleanNumber(precision)
-- Check for non-numeric input
if value == nil or precision == nil then
return '<strong class="error">Ошибка формата данных: нечисловое входное значение при округлении с заданной точностью</strong>'
end
local current_precision = z._precision(value)
local order = z._order(value)
-- Due to round-off effects it is neccesary to limit the returned precision under
-- some circumstances because the terminal digits will be inaccurately reported.
if order + precision >= 14 then
orig_precision = z._precision(value_string)
if order + orig_precision >= 14 then
precision = 13 - order;
end
end
-- If rounding off, truncate extra digits
if precision < current_precision then
value = z._round(value, precision)
current_precision = z._precision(value)
end
local formatted_num = lang:formatNum(math.abs(value))
local sign
-- Use proper unary minus sign rather than ASCII default
if value < 0 then
sign = '−'
else
sign = ''
end
-- Handle cases requiring scientific notation
if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 9 then
value = value * math.pow(10, -order)
current_precision = current_precision + order
precision = precision + order
formatted_num = lang:formatNum(math.abs(value))
else
order = 0;
end
formatted_num = sign .. formatted_num
-- Pad with zeros, if needed
if current_precision < precision then
local padding
if current_precision <= 0 then
if precision > 0 then
local zero_sep = lang:formatNum(1.1)
formatted_num = formatted_num .. zero_sep:sub(2,2)
padding = precision
if padding > 20 then
padding = 20
end
formatted_num = formatted_num .. string.rep('0', padding)
end
else
padding = precision - current_precision
if padding > 20 then
padding = 20
end
formatted_num = formatted_num .. string.rep('0', padding)
end
end
-- Add exponential notation, if necessary.
if order ~= 0 then
-- Use proper unary minus sign rather than ASCII default
if order < 0 then
order = '−' .. lang:formatNum(math.abs(order))
else
order = lang:formatNum(order)
end
formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
end
return formatted_num
end
--[[
Helper function that interprets the input numerically. If the
input does not appear to be a number, attempts evaluating it as
a parser functions expression.
]]
function z._cleanNumber( frame, number_string )
if number_string == nil or number_string:len() == 0 then
return nil, nil;
end
-- Attempt basic conversion
local number = tonumber( number_string )
-- If failed, attempt to evaluate input as an expression
if number == nil then
local attempt = frame:callParserFunction( '#expr', number_string );
attempt = tonumber( attempt );
if attempt ~= nil then
number = attempt;
number_string = tostring( number );
else
number = nil;
number_string = nil;
end
else
-- String is valid but may contain padding, clean it.
number_string = mw.text.trim(number_string)
end
return number, number_string;
end
local function roman(i)
local w, t, val, let = {}, {
{1000, "M"},
{900, "CM"},
{500, "D"},
{400, "CD"},
{100, "C"},
{90, "XC"},
{50, "L"},
{40, "XL"},
{10, "X"},
{9, "IX"},
{5, "V"},
{4, "IV"},
{1, "I"}
}
for n, v in ipairs(t) do
val, let = unpack(v)
w[n]=string.rep(let,i/val)
i=i % val
end
return table.concat(w)
end
function z.Roman(frame) -- Преобразует числа от 1 до 4999999 в римские
local function try_tonumber(a)
return math.floor(tonumber(a) or error('\''.. a ..'\' не является числом.'));
end
local str = frame.args[1] or '';
if str == '' then -- пустой параметр
return str;
end
local r, N = pcall(try_tonumber, str); -- попытка преобразовать в число
if r then
if N<1 or N>=5e6 then
return frame.args[2] or 'N/A'
end
local R=N%5000
N=(N-R)/1000
return (N>0 and table.concat{'<span style="text-decoration:overline;">',roman(N),'</span>'} or '')..roman(R)
else
return '<strong class="error">' .. N .. '</strong>'; -- вывод ошибки
end
end
--[[
Выводит числа прописью на русском
]]
function z.Russian(frame)
local str = frame.args[1] or '';
if str == '' then
return '';
end
local number = tonumber( str, 10 )
local lang = mw.getLanguage( 'ru' )
local zero = 'ноль'
local ones = { 'один', 'два', 'три', 'четыре', 'пять', 'шесть',
'семь', 'восемь', 'девять', 'десять', 'одиннадцать', 'двенадцать',
'тринадцать', 'четырнадцать', 'пятнадцать', 'шестнадцать', 'семнадцать',
'восемнадцать', 'девятнадцать' }
local tens = { '', 'двадцать', 'тридцать', 'сорок', 'пятьдесят',
'шестьдесят', 'семьдесят', 'восемьдесят', 'девяносто' }
local hundreds = { 'сто', 'двести', 'триста', 'четыреста', 'пятьсот',
'шестьсот', 'семьсот', 'восемьсот', 'девятьсот' }
local unitsPlural = {
{ '', '', '' },
{ 'тысяча', 'тысячи', 'тысяч' },
{ 'миллион', 'миллиона', 'миллионов' },
{ 'миллиард', 'миллиарда', 'миллиардов' },
{ 'триллион', 'триллиона', 'триллионов' },
}
local out = ''
local outMinus = ''
if ( number < 0 ) then
outMinus = 'минус '
number = math.abs( number )
end
local tripletPos = 0
while ( number > 0 ) do
local triplet = number % 1000
number = math.floor( number / 1000 )
tripletPos = tripletPos + 1
if ( tripletPos > 5 ) then
return ''
end
local tripletStr = ''
local tripletUnit = ''
if ( triplet > 0 ) then
local unitPlural = unitsPlural[ tripletPos ]
tripletUnit = lang:plural( triplet, unitPlural[1], unitPlural[2], unitPlural[3] )
end
if ( triplet >= 100 ) then
tripletStr = hundreds[ math.floor( triplet / 100 ) ]
triplet = triplet % 100
end
if ( triplet >= 20 ) then
tripletStr = tripletStr .. ' ' .. tens[ math.floor( triplet / 10 ) ]
triplet = triplet % 10
end
if ( triplet >= 1 ) then
tripletStr = tripletStr .. ' ' .. ones[ triplet ]
end
-- две тысячи
if ( tripletPos == 2 ) then
tripletStr = mw.ustring.gsub( tripletStr, 'один$', 'одна' )
tripletStr = mw.ustring.gsub( tripletStr, 'два$', 'две' )
end
out = tripletStr .. ' ' .. tripletUnit .. ' ' .. out
end
if ( out == '' ) then
out = zero
end
out = outMinus .. out
out = mw.ustring.gsub( out, ' +', ' ' )
out = mw.text.trim ( out )
return out
end
return z
This module provides a number of basic mathematical operations.
]]
local z = {}
-- Generate random number
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])
if first then -- if NaN or nil, will skip down to final return
if first <= second then -- could match if both nil, but already checked that first is a number in last line
return math.random(first, second)
end
return math.random(first)
end
return math.random()
end
--[[
order
Determine order of magnitude of a number
Usage:
{{#invoke: Math | order | value }}
]]
function z.order(frame)
local input_string = (frame.args[1] or frame.args.x or '0');
local input_number;
input_number = z._cleanNumber( frame, input_string );
if input_number == nil then
return '<strong class="error">Ошибка формата данных: нечисловое входное значение при определении десятичной степени</strong>'
else
return z._order( input_number )
end
end
function z._order(x)
if x == 0 then return 0 end
return math.floor(math.log10(math.abs(x)))
end
--[[
precision
Detemines the precision of a number using the string representation
Usage:
{{ #invoke: Math | precision | value }}
]]
function z.precision( frame )
local input_string = (frame.args[1] or frame.args.x or '0');
local trap_fraction = frame.args.check_fraction or false;
local input_number;
if type( trap_fraction ) == 'string' then
trap_fraction = trap_fraction:lower();
if trap_fraction == 'false' or trap_fraction == '0' or
trap_fraction == 'no' or trap_fraction == '' then
trap_fraction = false;
else
trap_fraction = true;
end
end
if trap_fraction then
local pos = string.find( input_string, '/', 1, true );
if pos ~= nil then
if string.find( input_string, '/', pos + 1, true ) == nil then
local denominator = string.sub( input_string, pos+1, -1 );
local denom_value = tonumber( denominator );
if denom_value ~= nil then
return math.log10(denom_value);
end
end
end
end
input_number, input_string = z._cleanNumber( frame, input_string );
if input_string == nil then
return '<strong class="error">Ошибка формата данных: нечисловое входное значение при определении дробной части</strong>'
else
return z._precision( input_string )
end
end
function z._precision( x )
x = string.upper( x )
local decimal = string.find( x, '[.,]', 1 )
local exponent_pos = string.find( x, 'E', 1, true )
local result = 0;
if exponent_pos ~= nil then
local exponent = string.sub( x, exponent_pos + 1 )
x = string.sub( x, 1, exponent_pos - 1 )
result = result - tonumber( exponent )
end
if decimal ~= nil then
result = result + string.len( x ) - decimal
return result
end
local pos = string.len( x );
while x:byte(pos) == string.byte('0') do
pos = pos - 1
result = result - 1
if pos <= 0 then
return 0
end
end
return result
end
--[[
max
Finds the maximum argument
Usage:
{{#invoke:Math| max | value1 | value2 | ... }}
OR
{{#invoke:Math| max }}
When used with no arguments, it takes its input from the parent
frame. Note, any values that do not evaluate to numbers are ignored.
]]
function z.max( frame )
local args = frame.args;
if args[1] == nil then
local parent = frame:getParent();
args = parent.args;
end
local max_value = nil;
local i = 1;
while args[i] ~= nil do
local val = z._cleanNumber( frame, args[i] );
if val ~= nil then
if max_value == nil or val > max_value then
max_value = val;
end
end
i = i + 1;
end
return max_value
end
--[[
min
Finds the minimum argument
Usage:
{{#invoke:Math| min | value1 | value2 | ... }}
OR
{{#invoke:Math| min }}
When used with no arguments, it takes its input from the parent
frame. Note, any values that do not evaluate to numbers are ignored.
]]
function z.min( frame )
local args = frame.args;
if args[1] == nil then
local parent = frame:getParent();
args = parent.args;
end
local min_value = nil;
local i = 1;
while args[i] ~= nil do
local val = z._cleanNumber( frame, args[i] );
if val ~= nil then
if min_value == nil or val < min_value then
min_value = val;
end
end
i = i + 1;
end
return min_value
end
--[[
round
Rounds a number to specified precision
Usage:
{{#invoke:Math | round | value | precision }}
--]]
function z.round(frame)
local value, precision;
value = z._cleanNumber( frame, frame.args[1] or frame.args.value or 0 );
precision = z._cleanNumber( frame, frame.args[2] or frame.args.precision or 0 );
if value == nil or precision == nil then
return '<strong class="error">Ошибка формата данных: нечисловое входное значение при округлении до целого</strong>'
else
return z._round( value, precision );
end
end
function z._round( value, precision )
local rescale = math.pow( 10, precision );
return math.floor( value * rescale + 0.5 ) / rescale;
end
--[[
precision_format
Rounds a number to the specified precision and formats according to rules
originally used for {{template:Rnd}}. Output is a string.
Usage:
{{#invoke: Math | precision_format | number | precision }}
]]
function z.precision_format(args)
local value_string = args[1] or 0
local precision = args[2] or 0
return z._precision_format(value_string, precision)
end
function z._precision_format(value_string, precision)
-- For access to Mediawiki built-in formatter.
local lang = mw.getContentLanguage();
local value
value, value_string = z._cleanNumber(value_string)
precision = z._cleanNumber(precision)
-- Check for non-numeric input
if value == nil or precision == nil then
return '<strong class="error">Ошибка формата данных: нечисловое входное значение при округлении с заданной точностью</strong>'
end
local current_precision = z._precision(value)
local order = z._order(value)
-- Due to round-off effects it is neccesary to limit the returned precision under
-- some circumstances because the terminal digits will be inaccurately reported.
if order + precision >= 14 then
orig_precision = z._precision(value_string)
if order + orig_precision >= 14 then
precision = 13 - order;
end
end
-- If rounding off, truncate extra digits
if precision < current_precision then
value = z._round(value, precision)
current_precision = z._precision(value)
end
local formatted_num = lang:formatNum(math.abs(value))
local sign
-- Use proper unary minus sign rather than ASCII default
if value < 0 then
sign = '−'
else
sign = ''
end
-- Handle cases requiring scientific notation
if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 9 then
value = value * math.pow(10, -order)
current_precision = current_precision + order
precision = precision + order
formatted_num = lang:formatNum(math.abs(value))
else
order = 0;
end
formatted_num = sign .. formatted_num
-- Pad with zeros, if needed
if current_precision < precision then
local padding
if current_precision <= 0 then
if precision > 0 then
local zero_sep = lang:formatNum(1.1)
formatted_num = formatted_num .. zero_sep:sub(2,2)
padding = precision
if padding > 20 then
padding = 20
end
formatted_num = formatted_num .. string.rep('0', padding)
end
else
padding = precision - current_precision
if padding > 20 then
padding = 20
end
formatted_num = formatted_num .. string.rep('0', padding)
end
end
-- Add exponential notation, if necessary.
if order ~= 0 then
-- Use proper unary minus sign rather than ASCII default
if order < 0 then
order = '−' .. lang:formatNum(math.abs(order))
else
order = lang:formatNum(order)
end
formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'
end
return formatted_num
end
--[[
Helper function that interprets the input numerically. If the
input does not appear to be a number, attempts evaluating it as
a parser functions expression.
]]
function z._cleanNumber( frame, number_string )
if number_string == nil or number_string:len() == 0 then
return nil, nil;
end
-- Attempt basic conversion
local number = tonumber( number_string )
-- If failed, attempt to evaluate input as an expression
if number == nil then
local attempt = frame:callParserFunction( '#expr', number_string );
attempt = tonumber( attempt );
if attempt ~= nil then
number = attempt;
number_string = tostring( number );
else
number = nil;
number_string = nil;
end
else
-- String is valid but may contain padding, clean it.
number_string = mw.text.trim(number_string)
end
return number, number_string;
end
local function roman(i)
local w, t, val, let = {}, {
{1000, "M"},
{900, "CM"},
{500, "D"},
{400, "CD"},
{100, "C"},
{90, "XC"},
{50, "L"},
{40, "XL"},
{10, "X"},
{9, "IX"},
{5, "V"},
{4, "IV"},
{1, "I"}
}
for n, v in ipairs(t) do
val, let = unpack(v)
w[n]=string.rep(let,i/val)
i=i % val
end
return table.concat(w)
end
function z.Roman(frame) -- Преобразует числа от 1 до 4999999 в римские
local function try_tonumber(a)
return math.floor(tonumber(a) or error('\''.. a ..'\' не является числом.'));
end
local str = frame.args[1] or '';
if str == '' then -- пустой параметр
return str;
end
local r, N = pcall(try_tonumber, str); -- попытка преобразовать в число
if r then
if N<1 or N>=5e6 then
return frame.args[2] or 'N/A'
end
local R=N%5000
N=(N-R)/1000
return (N>0 and table.concat{'<span style="text-decoration:overline;">',roman(N),'</span>'} or '')..roman(R)
else
return '<strong class="error">' .. N .. '</strong>'; -- вывод ошибки
end
end
--[[
Выводит числа прописью на русском
]]
function z.Russian(frame)
local str = frame.args[1] or '';
if str == '' then
return '';
end
local number = tonumber( str, 10 )
local lang = mw.getLanguage( 'ru' )
local zero = 'ноль'
local ones = { 'один', 'два', 'три', 'четыре', 'пять', 'шесть',
'семь', 'восемь', 'девять', 'десять', 'одиннадцать', 'двенадцать',
'тринадцать', 'четырнадцать', 'пятнадцать', 'шестнадцать', 'семнадцать',
'восемнадцать', 'девятнадцать' }
local tens = { '', 'двадцать', 'тридцать', 'сорок', 'пятьдесят',
'шестьдесят', 'семьдесят', 'восемьдесят', 'девяносто' }
local hundreds = { 'сто', 'двести', 'триста', 'четыреста', 'пятьсот',
'шестьсот', 'семьсот', 'восемьсот', 'девятьсот' }
local unitsPlural = {
{ '', '', '' },
{ 'тысяча', 'тысячи', 'тысяч' },
{ 'миллион', 'миллиона', 'миллионов' },
{ 'миллиард', 'миллиарда', 'миллиардов' },
{ 'триллион', 'триллиона', 'триллионов' },
}
local out = ''
local outMinus = ''
if ( number < 0 ) then
outMinus = 'минус '
number = math.abs( number )
end
local tripletPos = 0
while ( number > 0 ) do
local triplet = number % 1000
number = math.floor( number / 1000 )
tripletPos = tripletPos + 1
if ( tripletPos > 5 ) then
return ''
end
local tripletStr = ''
local tripletUnit = ''
if ( triplet > 0 ) then
local unitPlural = unitsPlural[ tripletPos ]
tripletUnit = lang:plural( triplet, unitPlural[1], unitPlural[2], unitPlural[3] )
end
if ( triplet >= 100 ) then
tripletStr = hundreds[ math.floor( triplet / 100 ) ]
triplet = triplet % 100
end
if ( triplet >= 20 ) then
tripletStr = tripletStr .. ' ' .. tens[ math.floor( triplet / 10 ) ]
triplet = triplet % 10
end
if ( triplet >= 1 ) then
tripletStr = tripletStr .. ' ' .. ones[ triplet ]
end
-- две тысячи
if ( tripletPos == 2 ) then
tripletStr = mw.ustring.gsub( tripletStr, 'один$', 'одна' )
tripletStr = mw.ustring.gsub( tripletStr, 'два$', 'две' )
end
out = tripletStr .. ' ' .. tripletUnit .. ' ' .. out
end
if ( out == '' ) then
out = zero
end
out = outMinus .. out
out = mw.ustring.gsub( out, ' +', ' ' )
out = mw.text.trim ( out )
return out
end
return z
