local function ud_floor(x) return x-x:mod(1) end
local function ud_floor(x) return x:idiv(1) end -- Alternative. Faster for userdatas smaller than ~270 elements.
local function ud_round(x)
  x += 0.5
  return x-x:mod(1)
end
local function ud_ceil(x) return (0-x):mod(1)-x end
local function ud_abs(x) return x:max(0-x) end
local function ud_sign(x) return x/(x:max(0-x)) end -- Not zero-safe.
local function ud_positive(x) return x:max(0)/x end -- Not zero-safe.
local function ud_negative(x) return x:min(0)/x end -- Not zero-safe.
local function ud_tern(c,a,b) return a*c+b*(1-c) end

local function sum(x)
  return vec(0):add(x,true,0,0,1,1,0,#x)[0]
end
local function prod(x)
  return vec(1):mul(x,true,0,0,1,1,0,#x)[0]
end

-- If you have a matrix with a vector in each row, and you'd like to get their dot products
-- with a single vector, you can do so like this:
local function dot_all(v,m)
  return m:matmul(v:transpose())
end

-- luchak discovered this prefix sum operation.
local function psum(v)
  return v:add(v,true,0,1,1,1,1,#v-1)
end
-- which is useful for creating a linear sequence with a specific slope.
-- v[n] = init+n*step
local function linstep(v,init,step)
  return v:copy(step,true):copy(init,true,0,0,1):add(v,true,0,1,1,1,1,#v-1)
end