batteries/mathx.lua

--[[
	extra mathematical functions
]]

local mathx = setmetatable({}, {
	__index = math,
})

--wrap v around range [lo, hi)
function mathx.wrap(v, lo, hi)
	return (v - lo) % (hi - lo) + lo
end

--wrap i around the indices of t
function mathx.wrap_index(i, t)
	return math.floor(mathx.wrap(i, 1, #t + 1))
end

--clamp v to range [lo, hi]
function mathx.clamp(v, lo, hi)
	return math.max(lo, math.min(v, hi))
end

--clamp v to range [0, 1]
function mathx.clamp01(v)
	return mathx.clamp(v, 0, 1)
end

--round v to nearest whole, away from zero
function mathx.round(v)
	if v < 0 then
		return math.ceil(v - 0.5)
	end
	return math.floor(v + 0.5)
end

--round v to one-in x
-- (eg x = 2, v rounded to increments of 0.5)
function mathx.to_one_in(v, x)
	return mathx.round(v * x) / x
end

--round v to a given decimal precision
function mathx.to_precision(v, decimal_points)
	return mathx.to_one_in(v, math.pow(10, decimal_points))
end

--0, 1, -1 sign of a scalar
function mathx.sign(v)
	if v < 0 then return -1 end
	if v > 0 then return 1 end
	return 0
end

--linear interpolation between a and b
function mathx.lerp(a, b, t)
	return a * (1.0 - t) + b * t
end

--linear interpolation with a minimum "final step" distance
--useful for making sure dynamic lerps do actually reach their final destination
function mathx.lerp_eps(a, b, t, eps)
	local v = mathx.lerp(a, b, t)
	if math.abs(v - b) < eps then
		v = b
	end
	return v
end

--bilinear interpolation between 4 samples
function mathx.bilerp(a, b, c, d, u, v)
	return math.lerp(
		math.lerp(a, b, u),
		math.lerp(c, d, u),
		v
	)
end

--classic smoothstep
--(only "safe" for 0-1 range)
function mathx.smoothstep(v)
	return v * v * (3 - 2 * v)
end

--classic smootherstep; zero 2nd order derivatives at 0 and 1
--(only safe for 0-1 range)
function mathx.smootherstep(v)
	return v * v * v * (v * (v * 6 - 15) + 10)
end

--todo: various other easing curves

--nan checking
function mathx.isnan(v)
	return v ~= v
end

--prime number stuff
local primes_1k = {
	2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
	73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173,
	179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281,
	283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409,
	419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541,
	547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659,
	661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809,
	811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941,
	947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069,
	1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223,
	1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373,
	1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511,
	1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657,
	1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811,
	1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987,
	1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129,
	2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287,
	2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423,
	2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617,
	2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741,
	2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903,
	2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079,
	3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257,
	3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413,
	3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571,
	3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727,
	3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907,
	3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057,
	4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231,
	4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409,
	4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583,
	4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751,
	4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937,
	4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087,
	5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279,
	5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443,
	5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639,
	5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791,
	5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939,
	5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133,
	6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301,
	6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473,
	6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673,
	6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833,
	6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997,
	7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207,
	7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411,
	7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561,
	7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723,
	7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919,
}

local sparse_primes_1k = {
	2, 3, 5, 11, 19, 37, 59, 79, 109, 151, 191, 239, 293, 367, 431, 499, 571, 653, 733, 853, 1009, 1151, 1301, 1481, 1613,
	1783, 1951, 2113, 2137, 2311, 2477, 2687, 2857, 3079, 3323, 3541, 3853, 4211, 4549, 4933, 5101, 5479, 5843, 6247, 6653,
	6689, 7039, 7307, 7559, 7573, 7919,
}

function mathx.first_above(v, t)
	for _,p in ipairs(t) do
		if p > v then
			return p
		end
	end
	return t[#t]
end

function mathx.next_prime_1k(v)
	return mathx.first_above(v, primes_1k)
end

function mathx.next_prime_1k_sparse(v)
	return mathx.first_above(v, sparse_primes_1k)
end

--angle handling stuff

--superior constant handy for expressing things in turns
mathx.tau = math.pi * 2

--normalise angle onto the interval [-math.pi, math.pi)
--so each angle only has a single value representing it
function mathx.normalise_angle(a)
	return mathx.wrap(a, -math.pi, math.pi)
end

--alias for americans
mathx.normalize_angle = mathx.normalise_angle

--get the normalised difference between two angles
function mathx.angle_difference(a, b)
	a = mathx.normalise_angle(a)
	b = mathx.normalise_angle(b)
	return mathx.normalise_angle(b - a)
end

--mathx.lerp equivalent for angles
function mathx.lerp_angle(a, b, t)
	local dif = mathx.angle_difference(a, b)
	return mathx.normalise_angle(a + dif * t)
end

--mathx.lerp_eps equivalent for angles
function mathx.lerp_angle_eps(a, b, t, eps)
	--short circuit to avoid having to wrap so many angles
	if a == b then
		return a
	end
	--same logic as lerp_eps
	local v = mathx.lerp_angle(a, b, t)
	if math.abs(mathx.angle_difference(v, b)) < eps then
		v = b
	end
	return v
end

--geometric functions standalone/"unpacked" components and multi-return
--consider using vec2 if you need anything complex!

--rotate a point around the origin by an angle
function mathx.rotate(x, y, r)
	local s = math.sin(r)
	local c = math.cos(r)
	return c * x - s * y, s * x + c * y
end

--get the length of a vector from the origin
function mathx.length(x, y)
	return math.sqrt(x * x + y * y)
end

--get the distance between two points
function mathx.distance(x1, y1, x2, y2)
	local dx = x1 - x2
	local dy = y1 - y2
	return mathx.length(dx, dy)
end

return mathx