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424 lines
12 KiB
424 lines
12 KiB
------------------------------------------------------------------------------
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-- Lua SciMark (2010-12-20).
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--
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-- A literal translation of SciMark 2.0a, written in Java and C.
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-- Credits go to the original authors Roldan Pozo and Bruce Miller.
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-- See: http://math.nist.gov/scimark2/
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------------------------------------------------------------------------------
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-- Copyright (C) 2006-2010 Mike Pall. All rights reserved.
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--
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-- Permission is hereby granted, free of charge, to any person obtaining
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-- a copy of this software and associated documentation files (the
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-- "Software"), to deal in the Software without restriction, including
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-- without limitation the rights to use, copy, modify, merge, publish,
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-- distribute, sublicense, and/or sell copies of the Software, and to
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-- permit persons to whom the Software is furnished to do so, subject to
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-- the following conditions:
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--
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-- The above copyright notice and this permission notice shall be
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-- included in all copies or substantial portions of the Software.
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--
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-- THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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-- EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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-- MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
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-- IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
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-- CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
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-- TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
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-- SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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--
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-- [ MIT license: http://www.opensource.org/licenses/mit-license.php ]
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------------------------------------------------------------------------------
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local SCIMARK_VERSION = "2010-12-10"
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local SCIMARK_COPYRIGHT = "Copyright (C) 2006-2010 Mike Pall"
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local MIN_TIME = 2.0
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local RANDOM_SEED = 101009 -- Must be odd.
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local SIZE_SELECT = "small"
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local benchmarks = {
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"FFT", "SOR", "MC", "SPARSE", "LU",
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small = {
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FFT = { 1024 },
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SOR = { 100 },
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MC = { },
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SPARSE = { 1000, 5000 },
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LU = { 100 },
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},
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large = {
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FFT = { 1048576 },
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SOR = { 1000 },
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MC = { },
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SPARSE = { 100000, 1000000 },
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LU = { 1000 },
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},
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}
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local abs, log, sin, floor = math.abs, math.log, math.sin, math.floor
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local pi, clock = math.pi, os.clock
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local format = string.format
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------------------------------------------------------------------------------
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-- Select array type: Lua tables or native (FFI) arrays
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------------------------------------------------------------------------------
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local darray, iarray
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local function array_init()
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if jit and jit.status and jit.status() then
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local ok, ffi = pcall(require, "ffi")
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if ok then
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darray = ffi.typeof("double[?]")
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iarray = ffi.typeof("int[?]")
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return
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end
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end
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function darray(n) return {} end
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iarray = darray
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end
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------------------------------------------------------------------------------
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-- This is a Lagged Fibonacci Pseudo-random Number Generator with
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-- j, k, M = 5, 17, 31. Pretty weak, but same as C/Java SciMark.
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------------------------------------------------------------------------------
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local rand, rand_init
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if jit and jit.status and jit.status() then
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-- LJ2 has bit operations and zero-based arrays (internally).
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local bit = require("bit")
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local band, sar = bit.band, bit.arshift
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function rand_init(seed)
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local Rm, Rj, Ri = iarray(17), 16, 11
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for i=0,16 do Rm[i] = 0 end
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for i=16,0,-1 do
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seed = band(seed*9069, 0x7fffffff)
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Rm[i] = seed
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end
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function rand()
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local i = band(Ri+1, sar(Ri-16, 31))
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local j = band(Rj+1, sar(Rj-16, 31))
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Ri, Rj = i, j
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local k = band(Rm[i] - Rm[j], 0x7fffffff)
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Rm[j] = k
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return k * (1.0/2147483647.0)
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end
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end
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else
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-- Better for standard Lua with one-based arrays and without bit operations.
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function rand_init(seed)
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local Rm, Rj = {}, 1
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for i=1,17 do Rm[i] = 0 end
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for i=17,1,-1 do
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seed = (seed*9069) % (2^31)
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Rm[i] = seed
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end
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function rand()
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local j, m = Rj, Rm
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local h = j - 5
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if h < 1 then h = h + 17 end
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local k = m[h] - m[j]
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if k < 0 then k = k + 2147483647 end
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m[j] = k
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if j < 17 then Rj = j + 1 else Rj = 1 end
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return k * (1.0/2147483647.0)
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end
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end
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end
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local function random_vector(n)
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local v = darray(n+1)
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for x=1,n do v[x] = rand() end
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return v
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end
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local function random_matrix(m, n)
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local a = {}
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for y=1,m do
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local v = darray(n+1)
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a[y] = v
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for x=1,n do v[x] = rand() end
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end
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return a
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end
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------------------------------------------------------------------------------
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-- FFT: Fast Fourier Transform.
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------------------------------------------------------------------------------
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local function fft_bitreverse(v, n)
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local j = 0
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for i=0,2*n-4,2 do
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if i < j then
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v[i+1], v[i+2], v[j+1], v[j+2] = v[j+1], v[j+2], v[i+1], v[i+2]
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end
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local k = n
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while k <= j do j = j - k; k = k / 2 end
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j = j + k
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end
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end
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local function fft_transform(v, n, dir)
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if n <= 1 then return end
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fft_bitreverse(v, n)
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local dual = 1
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repeat
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local dual2 = 2*dual
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for i=1,2*n-1,2*dual2 do
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local j = i+dual2
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local ir, ii = v[i], v[i+1]
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local jr, ji = v[j], v[j+1]
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v[j], v[j+1] = ir - jr, ii - ji
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v[i], v[i+1] = ir + jr, ii + ji
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end
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local theta = dir * pi / dual
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local s, s2 = sin(theta), 2.0 * sin(theta * 0.5)^2
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local wr, wi = 1.0, 0.0
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for a=3,dual2-1,2 do
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wr, wi = wr - s*wi - s2*wr, wi + s*wr - s2*wi
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for i=a,a+2*(n-dual2),2*dual2 do
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local j = i+dual2
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local jr, ji = v[j], v[j+1]
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local dr, di = wr*jr - wi*ji, wr*ji + wi*jr
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local ir, ii = v[i], v[i+1]
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v[j], v[j+1] = ir - dr, ii - di
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v[i], v[i+1] = ir + dr, ii + di
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end
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end
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dual = dual2
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until dual >= n
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end
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function benchmarks.FFT(n)
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local l2n = log(n)/log(2)
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if l2n % 1 ~= 0 then
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io.stderr:write("Error: FFT data length is not a power of 2\n")
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os.exit(1)
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end
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local v = random_vector(n*2)
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return function(cycles)
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local norm = 1.0 / n
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for p=1,cycles do
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fft_transform(v, n, -1)
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fft_transform(v, n, 1)
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for i=1,n*2 do v[i] = v[i] * norm end
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end
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return ((5*n-2)*l2n + 2*(n+1)) * cycles
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end
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end
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------------------------------------------------------------------------------
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-- SOR: Jacobi Successive Over-Relaxation.
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------------------------------------------------------------------------------
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local function sor_run(mat, m, n, cycles, omega)
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local om4, om1 = omega*0.25, 1.0-omega
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m = m - 1
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n = n - 1
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for i=1,cycles do
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for y=2,m do
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local v, vp, vn = mat[y], mat[y-1], mat[y+1]
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for x=2,n do
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v[x] = om4*((vp[x]+vn[x])+(v[x-1]+v[x+1])) + om1*v[x]
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end
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end
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end
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end
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function benchmarks.SOR(n)
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local mat = random_matrix(n, n)
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return function(cycles)
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sor_run(mat, n, n, cycles, 1.25)
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return (n-1)*(n-1)*cycles*6
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end
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end
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------------------------------------------------------------------------------
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-- MC: Monte Carlo Integration.
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------------------------------------------------------------------------------
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local function mc_integrate(cycles)
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local under_curve = 0
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local rand = rand
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for i=1,cycles do
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local x = rand()
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local y = rand()
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if x*x + y*y <= 1.0 then under_curve = under_curve + 1 end
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end
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return (under_curve/cycles) * 4
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end
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function benchmarks.MC()
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return function(cycles)
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local res = mc_integrate(cycles)
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assert(math.sqrt(cycles)*math.abs(res-math.pi) < 5.0, "bad MC result")
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return cycles * 4 -- Way off, but same as SciMark in C/Java.
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end
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end
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------------------------------------------------------------------------------
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-- Sparse Matrix Multiplication.
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------------------------------------------------------------------------------
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local function sparse_mult(n, cycles, vy, val, row, col, vx)
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for p=1,cycles do
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for r=1,n do
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local sum = 0
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for i=row[r],row[r+1]-1 do sum = sum + vx[col[i]] * val[i] end
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vy[r] = sum
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end
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end
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end
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function benchmarks.SPARSE(n, nz)
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local nr = floor(nz/n)
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local anz = nr*n
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local vx = random_vector(n)
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local val = random_vector(anz)
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local vy, col, row = darray(n+1), iarray(nz+1), iarray(n+2)
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row[1] = 1
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for r=1,n do
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local step = floor(r/nr)
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if step < 1 then step = 1 end
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local rr = row[r]
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row[r+1] = rr+nr
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for i=0,nr-1 do col[rr+i] = 1+i*step end
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end
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return function(cycles)
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sparse_mult(n, cycles, vy, val, row, col, vx)
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return anz*cycles*2
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end
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end
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------------------------------------------------------------------------------
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-- LU: Dense Matrix Factorization.
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------------------------------------------------------------------------------
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local function lu_factor(a, pivot, m, n)
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local min_m_n = m < n and m or n
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for j=1,min_m_n do
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local jp, t = j, abs(a[j][j])
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for i=j+1,m do
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local ab = abs(a[i][j])
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if ab > t then
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jp = i
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t = ab
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end
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end
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pivot[j] = jp
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if a[jp][j] == 0 then error("zero pivot") end
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if jp ~= j then a[j], a[jp] = a[jp], a[j] end
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if j < m then
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local recp = 1.0 / a[j][j]
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for k=j+1,m do
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local v = a[k]
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v[j] = v[j] * recp
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end
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end
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if j < min_m_n then
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for i=j+1,m do
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local vi, vj = a[i], a[j]
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local eij = vi[j]
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for k=j+1,n do vi[k] = vi[k] - eij * vj[k] end
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end
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end
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end
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end
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local function matrix_alloc(m, n)
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local a = {}
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for y=1,m do a[y] = darray(n+1) end
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return a
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end
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local function matrix_copy(dst, src, m, n)
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for y=1,m do
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local vd, vs = dst[y], src[y]
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for x=1,n do vd[x] = vs[x] end
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end
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end
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function benchmarks.LU(n)
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local mat = random_matrix(n, n)
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local tmp = matrix_alloc(n, n)
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local pivot = iarray(n+1)
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return function(cycles)
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for i=1,cycles do
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matrix_copy(tmp, mat, n, n)
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lu_factor(tmp, pivot, n, n)
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end
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return 2.0/3.0*n*n*n*cycles
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end
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end
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------------------------------------------------------------------------------
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-- Main program.
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------------------------------------------------------------------------------
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local function printf(...)
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io.write(format(...))
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end
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local function fmtparams(p1, p2)
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if p2 then return format("[%d, %d]", p1, p2)
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elseif p1 then return format("[%d]", p1) end
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return ""
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end
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local function measure(min_time, name, ...)
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array_init()
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rand_init(RANDOM_SEED)
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local run = benchmarks[name](...)
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local cycles = 1
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repeat
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local tm = clock()
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local flops = run(cycles, ...)
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tm = clock() - tm
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if tm >= min_time then
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local res = flops / tm * 1.0e-6
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local p1, p2 = ...
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printf("%-7s %8.2f %s\n", name, res, fmtparams(...))
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return res
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end
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cycles = cycles * 2
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until false
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end
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local unpack = table.unpack or unpack
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printf("Lua SciMark %s based on SciMark 2.0a. %s.\n\n",
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SCIMARK_VERSION, SCIMARK_COPYRIGHT)
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while arg and arg[1] do
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local a = table.remove(arg, 1)
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if a == "-noffi" then
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package.preload.ffi = nil
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elseif a == "-small" then
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SIZE_SELECT = "small"
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elseif a == "-large" then
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SIZE_SELECT = "large"
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elseif benchmarks[a] then
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local p = benchmarks[SIZE_SELECT][a]
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measure(MIN_TIME, a, tonumber(arg[1]) or p[1], tonumber(arg[2]) or p[2])
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return
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else
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printf("Usage: scimark [-noffi] [-small|-large] [BENCH params...]\n\n")
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printf("BENCH -small -large\n")
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printf("---------------------------------------\n")
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for _,name in ipairs(benchmarks) do
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printf("%-7s %-13s %s\n", name,
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fmtparams(unpack(benchmarks.small[name])),
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fmtparams(unpack(benchmarks.large[name])))
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end
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printf("\n")
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os.exit(1)
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end
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end
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local params = benchmarks[SIZE_SELECT]
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local sum = 0
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for _,name in ipairs(benchmarks) do
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sum = sum + measure(MIN_TIME, name, unpack(params[name]))
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end
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printf("\nSciMark %8.2f [%s problem sizes]\n", sum / #benchmarks, SIZE_SELECT)
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io.flush()
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