modlib/math.lua

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-- Localize globals
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local assert, math, math_floor, minetest, modlib_table_reverse, os, string_char, select, setmetatable, table_insert, table_concat
= assert, math, math.floor, minetest, modlib.table.reverse, os, string.char, select, setmetatable, table.insert, table.concat
local inf = math.huge
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-- Set environment
local _ENV = {}
setfenv(1, _ENV)
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-- TODO might be too invasive
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-- Make random random
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math.randomseed(minetest and minetest.get_us_time() or os.time() + os.clock())
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for _ = 1, 100 do math.random() end
negative_nan = 0/0
positive_nan = negative_nan ^ 1
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function sign(number)
if number ~= number then return number end -- nan
if number == 0 then return 0 end
if number < 0 then return -1 end
if number > 0 then return 1 end
end
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function clamp(number, min, max)
return math.min(math.max(number, min), max)
end
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-- Random integer from 0 to 2^53 - 1 (inclusive)
local function _randint()
return math.random(0, 2^27 - 1) * 2^26 + math.random(0, 2^26 - 1)
end
-- Random float from 0 to 1 (exclusive)
local function _randfloat()
return _randint() / (2^53)
end
--+ Increased randomness float random without overflows
--+ `random()`: Random number from `0` to `1` (exclusive)
--+ `random(max)`: Random number from `0` to `max` (exclusive)
--+ `random(min, max)`: Random number from `min` to `max` (exclusive)
function random(...)
local n = select("#", ...)
if n == 0 then
return _randfloat()
end if n == 1 then
local max = ...
return _randfloat() * max
end do assert(n == 2)
local min, max = ...
return min + (max - min) * _randfloat()
end
end
-- Increased randomness integer random
--+ `randint()`: Random integer from `0` to `2^53 - 1` (inclusive)
--+ `randint(max)`: Random integer from `0` to `max` (inclusive)
--+ `randint(min, max)`: Random integer from `min` to `max` (inclusive)
function randint(...)
local n = select("#", ...)
if n == 0 then
return _randint()
end if n == 1 then
local max = ...
return math.floor(_randfloat() * max + 0.5)
end do assert(n == 2)
local min, max = ...
return min + math.floor(_randfloat() * (max - min) + 0.5)
end
end
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log = setmetatable({}, {
__index = function(self, base)
local div = math.log(base)
local function base_log(number)
return math.log(number) / div
end
self[base] = base_log
return base_log
end,
__call = function(_, number, base)
if not base then
return math.log(number)
end
return math.log(number) / math.log(base)
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end
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})
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-- one-based mod
function onemod(number, modulus)
return ((number - 1) % modulus) + 1
end
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function round(number, steps)
steps = steps or 1
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return math_floor(number * steps + 0.5) / steps
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end
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local c0 = ("0"):byte()
local cA = ("A"):byte()
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function default_digit_function(digit)
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if digit <= 9 then return string_char(c0 + digit) end
return string_char(cA + digit - 10)
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end
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default_precision = 10
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-- See https://github.com/appgurueu/Luon/blob/master/index.js#L724
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function tostring(number, base, digit_function, precision)
if number ~= number then
return "nan"
end
if number == inf then
return "inf"
end
if number == -inf then
return "-inf"
end
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digit_function = digit_function or default_digit_function
precision = precision or default_precision
local out = {}
if number < 0 then
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table_insert(out, "-")
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number = -number
end
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-- Rounding
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number = number + base ^ -precision / 2
local digit
while number >= base do
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digit = math_floor(number % base)
table_insert(out, digit_function(digit))
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number = (number - digit) / base
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end
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digit = math_floor(number)
table_insert(out, digit_function(digit))
modlib_table_reverse(out)
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number = number % 1
if number ~= 0 and number >= base ^ -precision then
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table_insert(out, ".")
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while precision >= 0 and number >= base ^ -precision do
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number = number * base
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digit = math_floor(number % base)
table_insert(out, digit_function(digit))
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number = number - digit
precision = precision - 1
end
end
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return table_concat(out)
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end
-- See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/fround#polyfill
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-- Rounds a 64-bit float to a 32-bit float;
-- if the closest 32-bit float is out of bounds,
-- the appropriate infinity is returned.
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function fround(number)
if number == 0 or number ~= number then
return number
end
local sign = 1
if number < 0 then
sign = -1
number = -number
end
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local _, exp = math.frexp(number)
exp = exp - 1 -- we want 2^exponent >= number > 2^(exponent-1)
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local powexp = 2 ^ math.max(-126, math.min(exp, 127))
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local leading = exp <= -127 and 0 or 1 -- subnormal number?
local mantissa = math.floor((number / powexp - leading) * 0x800000 + 0.5)
if
mantissa > 0x800000 -- doesn't fit in mantissa
or (exp >= 127 and mantissa == 0x800000) -- fits if the exponent can be increased
then
return sign * inf
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end
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return sign * powexp * (leading + mantissa / 0x800000)
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end
-- Export environment
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return _ENV