模块:沙盒/a2569875/test1

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local p = {}

function p._init(_math_lib, _to_number)
	local warp_funcs={"factorial","gamma","sec","csc","sech","csch","asec","acsc","asech","acsch","gd","cogd","arcgd",
		"gcd"
	}
	for i=1,#warp_funcs do
		_math_lib[ warp_funcs[i] ] = p['_' .. warp_funcs[i] ]
	end
	math_lib = _math_lib
	to_number = _to_number
	return _math_lib
end
function p._complex_number()
	return p._init(require("Module:Complex Number").cmath.init(), require("Module:Complex Number").cmath.init().toComplexNumber)
end

function p._factorial(cal_z)return p._gamma(to_number(cal_z) + 1)end
function p._sec(cal_z)return math_lib.inverse( math_lib.cos( to_number(cal_z) ) )end
function p._csc(cal_z)return math_lib.inverse( math_lib.sin( to_number(cal_z) ) )end
function p._sech(cal_z)return math_lib.inverse( math_lib.cosh( to_number(cal_z) ) )end
function p._csch(cal_z)return math_lib.inverse( math_lib.sinh( to_number(cal_z) ) )end
function p._asec(cal_z)return  math_lib.acos( math_lib.inverse( to_number(cal_z) ) )end
function p._acsc(cal_z)return  math_lib.asin( math_lib.inverse( to_number(cal_z) ) )end
function p._asech(cal_z)return  math_lib.acosh( math_lib.inverse( to_number(cal_z) ) )end
function p._acsch(cal_z)return  math_lib.asinh( math_lib.inverse( to_number(cal_z) ) )end
function p._gd(cal_z)return math_lib.atan( math_lib.tanh( to_number(cal_z) * 0.5 ) ) * 2 end
function p._arcgd(cal_z)return math_lib.atanh( math_lib.tan( to_number(cal_z) * 0.5 ) ) * 2 end
function p._cogd(cal_z)local x = to_number(cal_z); return - math_lib.sgn( x ) * math_lib.log( math_lib.abs( math_lib.tanh( x * 0.5 ) ) ) 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 = {...}
	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
local Reciprocal_gamma_coeff = {1,0.577215664901532860607,-0.655878071520253881077,-0.0420026350340952355290,0.166538611382291489502,-0.0421977345555443367482,-0.00962197152787697356211,0.00721894324666309954240,-0.00116516759185906511211,-0.000215241674114950972816,0.000128050282388116186153,-0.0000201348547807882386557,-1.25049348214267065735e-6,1.13302723198169588237e-6,-2.05633841697760710345e-7,6.11609510448141581786e-9,5.00200764446922293006e-9,-1.18127457048702014459e-9,1.04342671169110051049e-10,7.78226343990507125405e-12,-3.69680561864220570819e-12,5.10037028745447597902e-13,-2.05832605356650678322e-14,-5.34812253942301798237e-15,1.22677862823826079016e-15,-1.18125930169745876951e-16,1.18669225475160033258e-18,1.41238065531803178156e-18,-2.29874568443537020659e-19,1.71440632192733743338e-20}
local stirling_series_coeff = {1,0.083333333333333333333,0.0034722222222222222222,-0.0026813271604938271605,-0.00022947209362139917695,0.00078403922172006662747,0.000069728137583658577743,-0.00059216643735369388286,-0.000051717909082605921934,0.00083949872067208727999,0.000072048954160200105591,-0.0019144384985654775265, -0.00016251626278391581690}
function p._gamma_high_imag(cal_z)
	local z = to_number(cal_z)
	if z ~= nil and math_lib.abs(math_lib.nonRealPart(z)) > 1 then
		local inv_z = math_lib.inverse(z)
		return math_lib.sqrt((math_lib.pi * 2) * inv_z) * math_lib.pow(z * math_lib.exp(-1) *
			math_lib.sqrt( (z * math_lib.sinh(inv_z) ) + math_lib.inverse(to_number(810) * z * z * z * z * z * z) ),z)
	end
	return nil
end
function p._gamma_morethen_lua_int(cal_z)
	local z = to_number(cal_z) - to_number(1)
	local lua_int_term = 18.1169 --FindRoot[ Factorial[ x ] == 2 ^ 53, {x, 20} ]
	if math_lib.abs(z) > (lua_int_term - 1) or (math_lib.re(z) < 0 and math_lib.abs(math_lib.nonRealPart(z)) > 1 ) then
		local sum = 1
		for i = 1, #stirling_series_coeff - 1 do
			local a, n = to_number(z), tonumber(i) local y, k, f = to_number(1), n, to_number(a)
			while k ~= 0 do 
				if k % 2 == 1 then y = y * f end 
				k = math.floor(k / 2); f = f * f
			end
			sum = sum + stirling_series_coeff[i + 1] * math_lib.inverse(y)
		end
		return math_lib.sqrt( (2 * math.pi) * z ) * math_lib.pow( z * math.exp(-1), z ) * sum
	end
	return nil
end
function p._gamma_abs_less1(cal_z)
	local z = to_number(cal_z)
	if math_lib.abs(z) <=1.001 then
		if math_lib.abs(math_lib.nonRealPart(z)) < 1e-14 and ( (math.abs(math_lib.re(z) - 1) < 1e-14) or (math.abs(math_lib.re(z) - 2) < 1e-14) ) then return to_number(1)end
		return math_lib.inverse(p._recigamma_abs_less1(z))
	end
	return nil
end
function p._recigamma_abs_less1(z)
	local result = to_number(0)
	for i=1,#Reciprocal_gamma_coeff do
		result = result + Reciprocal_gamma_coeff[i] * math_lib.pow(z,i)
	end
	return result
end
function p._gamma(cal_z)
	local z = to_number(cal_z)
	if math_lib.abs(math_lib.nonRealPart(z)) < 1e-14 and ((math_lib.re(z) < 0 or math.abs(math_lib.re(z)) < 1e-14)
		and math.abs(math.floor(math_lib.re(z)) - math_lib.re(z)) < 1e-14 ) then return tonumber("nan") end
	local pre_result = p._gamma_morethen_lua_int(z) or p._gamma_high_imag(z) or p._gamma_abs_less1(z)
	if pre_result then return pre_result end
	local real_check = math_lib.re(z)
	local loop_count = math.floor(real_check)
	local start_number, zero_flag = z - loop_count, false
	if math_lib.abs(start_number) <= 1e-14 then start_number = to_number(1);zero_flag = true end
	local result = math_lib.inverse(p._recigamma_abs_less1(start_number))
	if math_lib.abs(math_lib.nonRealPart(z)) < 1e-14 and ((math_lib.re(z) > 1e-14 )and math.abs(math.floor(math_lib.re(z)) - math_lib.re(z)) < 1e-14 ) then result = to_number(1)  end
	local j = to_number(start_number)
	for i=1,math.abs(loop_count) do
		if loop_count > 0 then result = result * j else result = result * math_lib.inverse(j-1) end
		if zero_flag==true and loop_count > 0 then zero_flag=false else if loop_count > 0 then j = j + 1 else j = j - 1 end end
	end
	if math_lib.abs(math_lib.nonRealPart(z)) < 1e-14 and ((math_lib.re(z) > 1e-14 )and math.abs(math.floor(math_lib.re(z)) - math_lib.re(z)) < 1e-14 ) then return math_lib.floor(result) end
	return result
end
function p._gcd(...)
	local function findGcd(a, b)
		local r, oldr = to_number(b), to_number(a)
		while math_lib.abs(r) > 1e-6 do local mod_val = oldr % r oldr, r = to_number(r), mod_val end
		if math_lib.abs(math_lib.nonRealPart(oldr)) < 1e-14 and (math_lib.re(oldr) < 0 ) then oldr = -oldr end
		return oldr
	end
	local result, count = fold(findGcd, ...)
	return result
end

function p.my_test(frame)
    local args
    if frame == mw.getCurrentFrame() then
        -- We're being called via #invoke. The args are passed through to the module
        -- from the template page, so use the args that were passed into the template.
        args = frame.args
    else
        -- We're being called from another module or from the debug console, so assume
        -- the args are passed in directly.
        args = frame
    end
    local get_gobal = mw.getCurrentFrame():getParent()
    if get_gobal then
	    if get_gobal._Template_Add_Count == nil then get_gobal._Template_Add_Count={} end
	    if args[1] or args['1'] then 
	    	get_gobal._Template_Add_Count[(args[1] or args['1'])] = (get_gobal._Template_Add_Count[(args[1] or args['1'])] or 0) + 1
	    end
		return tostring(get_gobal._Template_Add_Count[(args[1] or args['1'])] or '')
	end
	return ''
end

return p