Merge pull request JuliaLang#12498 from wildart/dSFTM-jump

jump function for Mersenne Twister

base/dSFMT.jl

@@ -7,9 +7,22 @@ export DSFMT_state, dsfmt_get_min_array_size, dsfmt_get_idstring,
        dsfmt_fill_array_close_open!, dsfmt_fill_array_close1_open2!,
        win32_SystemFunction036!
 
+"Mersenne Exponent"
+const MEXP = 19937
+"DSFMT internal state array size of N 128-bit integers."
+const N    = floor(Int, ((MEXP - 128) / 104 + 1))
+"""Julia DSFMT state representation size counted in 32-bit integers.
+
+Size: (DSFMT state array of Int128 + 1)*4 + Int32 index + Int32 padding
+"""
+const JN32 = (N+1)*4+1+1
+"Jump polynomial for 10^20 steps for dSFMT with exponent 19937"
+const JPOLY1e21  = "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"
+
 type DSFMT_state
     val::Vector{Int32}
-    DSFMT_state() = new(Array(Int32, 770))
+    DSFMT_state() = new(Array(Int32, JN32))
+    DSFMT_state(val::Vector{Int32}) = new(val)
 end
 
 function dsfmt_get_idstring()
@@ -66,6 +79,76 @@ function dsfmt_fill_array_close_open!(s::DSFMT_state, A::Ptr{Float64}, n::Int)
           s.val, A, n)
 end
 
+# dSFMT jump
+function dsfmt_jump(s::DSFMT_state, jp::AbstractString)
+    index = s.val[end-1]
+    work = zeros(UInt64, JN32>>1)
+    dsfmt = reinterpret(UInt64, copy(s.val))
+    dsfmt[end] = UInt64(N*2)
+
+    for c in jp
+        bits = parse(UInt8,c,16)
+        for j in 1:4
+            (bits & 0x01) != 0x00 && dsfmt_jump_add!(work, dsfmt)
+            bits = bits >> 0x01
+            dsfmt_jump_next_state!(dsfmt)
+        end
+    end
+
+    work[end] = index
+    return DSFMT_state(reinterpret(Int32, work))
+end
+
+function dsfmt_jump_add!(dest::Vector{UInt64}, src::Vector{UInt64})
+    dp = dest[end] >> 1
+    sp = src[end] >> 1
+    diff = ((sp - dp + N) % N)
+    i = 1
+    while i <= N-diff
+        j = i*2-1
+        p = j + diff*2
+        dest[j]   $= src[p]
+        dest[j+1] $= src[p+1]
+        i += 1
+    end
+    while i <= N
+        j = i*2-1
+        p = j + (diff - N)*2
+        dest[j]   $= src[p]
+        dest[j+1] $= src[p+1]
+        i += 1
+    end
+    dest[N*2+1] $= src[N*2+1]
+    dest[N*2+2] $= src[N*2+2]
+    return dest
+end
+
+function dsfmt_jump_next_state!(mts::Vector{UInt64})
+    POS1 = 117
+    SL1  = 19
+    SR   = 12
+    MSK1 = 0x000ffafffffffb3f
+    MSK2 = 0x000ffdfffc90fffd
+
+    idx = (mts[end] >> 1) % N
+
+    a = idx*2+1
+    b = ((idx + POS1) % N)*2+1
+    u = N*2+1
+
+    t0 = mts[a]
+    t1 = mts[a+1]
+    L0 = mts[u]
+    L1 = mts[u+1]
+    mts[u]   = (t0 << SL1) $ (L1 >> 32) $ (L1 << 32) $ mts[b]
+    mts[u+1] = (t1 << SL1) $ (L0 >> 32) $ (L0 << 32) $ mts[b+1]
+    mts[a]   = (mts[u]   >> SR) $ (mts[u]   & MSK1) $ t0
+    mts[a+1] = (mts[u+1] >> SR) $ (mts[u+1] & MSK2) $ t1
+
+    mts[end] = (mts[end] + 2) % (N*2)
+    return mts
+end
+
 ## Windows entropy
 
 @windows_only begin

base/docs/helpdb.jl

@@ -16377,3 +16377,14 @@ If ``pkg`` is installed, return the installed version number, otherwise return `
 """
 Pkg.installed
 
+doc"""
+```rst
+::
+           randjump(r::MersenneTwister, jumps, [jumppoly]) -> Vector{MersenneTwister}
+
+Create an array of the size ``jumps`` of initialized ``MersenneTwister`` RNG objects where the first RNG object given as a parameter and following ``MersenneTwister`` RNGs in the array initialized such that a state of the RNG object in the array would be moved forward (without generating numbers) from a previous RNG object array element on a particular number of steps encoded by the jump polynomial ``jumppoly``.
+
+Default jump polynomial moves forward ``MersenneTwister`` RNG state on 10^20 steps.
+```
+"""
+randjump

base/exports.jl

@@ -918,6 +918,7 @@ export
     randexp,
     srand,
     bitrand,
+    randjump,
 
 # bigfloat & precision
     precision,

base/random.jl

@@ -15,7 +15,7 @@ export srand,
        shuffle,shuffle!,
        randperm, randcycle,
        AbstractRNG, RNG, MersenneTwister, RandomDevice,
-       GLOBAL_RNG
+       GLOBAL_RNG, randjump
 
 
 abstract AbstractRNG
@@ -71,8 +71,8 @@ type MersenneTwister <: AbstractRNG
     idx::Int
     seed::Vector{UInt32}
 
-    MersenneTwister(seed) = srand(new(DSFMT_state(), Array(Float64, MTCacheLength)),
-                                  seed)
+    MersenneTwister(state::DSFMT_state, seed) = new(state, Array(Float64, MTCacheLength), MTCacheLength, seed)
+    MersenneTwister(seed) = srand(new(DSFMT_state(), Array(Float64, MTCacheLength)), seed)
     MersenneTwister() = MersenneTwister(0)
 end
 
@@ -114,6 +114,17 @@ function srand(r::MersenneTwister, seed::Vector{UInt32})
     return r
 end
 
+# MersenneTwister jump
+function randjump(mt::MersenneTwister, jumps::Integer, jumppoly::AbstractString)
+    mts = MersenneTwister[]
+    push!(mts, mt)
+    for i in 1:jumps-1
+        cmt = mts[end]
+        push!(mts, MersenneTwister(dSFMT.dsfmt_jump(cmt.state, jumppoly),  cmt.seed))
+    end
+    return mts
+end
+randjump(r::MersenneTwister, jumps::Integer) = randjump(r, jumps, dSFMT.JPOLY1e21)
 
 ## initialization
 

doc/stdlib/numbers.rst

@@ -569,3 +569,6 @@ As ``BigInt`` represents unbounded integers, the interval must be specified (e.g
 
    Fill the array A with random numbers following the exponential distribution (with scale 1).
 
+.. function:: randjump(rng, jumps)
+
+   Create an array of the size ``jumps`` of initialized ``MersenneTwister`` RNG objects where the first RNG object given as a parameter and following ``MersenneTwister`` RNGs in the array initialized such that a state of the RNG object in the array would be moved forward (without generating numbers) from a previous RNG object array element on a particular number of steps encoded by the jump polynomial ``jumppoly``.

test/random.jl

@@ -358,3 +358,24 @@ let mta = MersenneTwister(42), mtb = MersenneTwister(42)
     @test sprand(mta,1,1,0.9) == sprand(mtb,1,1,0.9)
     @test sprand(mta,10,10,0.3) == sprand(mtb,10,10,0.3)
 end
+
+# test PRNG jump
+let mta = MersenneTwister(seed), mtb = MersenneTwister(seed)
+    step = 25000*2
+    size = 4
+    jump25000  = "35931a4947eeab70a9abbfaca4a79cfcf2610a35a586c6f4e4bdfa826d538cbfb0432c37321fcec4f6c98de3df06685087032988b0ad9a2144562aa82e06f2f6f256b5b412c524e35383a894da7b04e142c4156290585186d8fc06d3141a778220c2519a851b5a9e5947a3f745b71804631988825e21dba40392ff4c036b30d2d013b45e2be94b5e130a9c6424d2e82f48c855c81bd10757fdb5a91e23e9e312e430514ea31631d8897b4cf26eb39b37be0c92706e5637d4b34c1e4046b741e455df195cb512e8e0f8d578175a3da5e00d7ce247d9b92042b1b515d01f7f89fe661ebccb06dfb77bc0fbb99806921b472ccce58f2166ac058d9cf427ad7d74986e60a56d2fee0a8b680e466a8ea4e508a76c058b6f97b99c9aa5b10297b1a1bd6a8e80f3a79e008fa55a4a8915fbdec78b6b117ad67e195311fe79fc084c33f6db546f5b7602d010fa8b830e3f1b00cef00ee16840178fc7e9aa5f1cee625d43de8488bf6c8bd379ea6f97c55c7a9ee091477a23533d5e52e194bd9d4e17b02a64a2736feb3779fabd5777e448ffee0f2d4b38a8e7441822b882fc6df0bde8541e85c0c78a05936cff0c88a50980b7a84971fba3650991fe2cba425ac4b4289e7b06ce2cfabfcc8a553201e8c74b45e4ae74b6d054e37af95e6fd55e029b7c526b85ecfb3be8db670218ee3dda7b2a54ab1ed26eefe4cd1d2a9c589a6e94d0aa3ebe29e40e616aa0b731061c3d6e247ec610024a1a97b7adb7919308b0fb5dd5d51a58aa2f55d77b88037de7c1a74823c96cb09d22dd7f90dba14eefdcffaab34d323c829f24742f6f6b32b0724a26ae4a81130a8a275d30c21e6245fa27cf26d606a49bccba2980697c32d9efe583c4ee2140569025c4f044d744bc40cec1660d9e4d2de3a4de83bae4f0a9fdb34ef4509b2b4e6c37967a485a52d69d1573bb826bc64c966de9c792b7c2f07b645c56a29381911a98928e48516f246a55bcaa78f3c7d1c30127df5f06ba0a2d6a5e54605a20e60fab30c01a9472cb610ca0ef2418a985af00c7e47539111bf539dd554297d0374a7ff627d879600595b442c8dcffcffa3bbb07e5c7882ff0858142be4deac448698f0917fe2b7a9b686a9df1fa929f06a51aff992a6ee0b0605f8b34b87600cfa0af2475333b78625ce1520c793dc5080218247b4e41bbd7d9dab163470fe17a3d2622cdce979cc5565b0bc04eabaf656f21fa072a18ab33c656b665248ef20321407fef263b1c67316f2c6f236951990099e42d4614d8e08b27aa89d9f4548fa321d4b381d2da04fd7f17d6b9a68adfd0e4427196d25dcad869f8a155c6242f7d072baa5e7405ceb65dfaa3eb864bfe679a17df34273fde5037befe9ed5391b932cee271f59128c61ab3f0fc3f7cf8ff051fbda8382c64579efddd494c79850c56bda73bcd39c20c2820d191995b3335253c3b0ac8f5e5373f40c228886e6c526c2c249a5304578ba2a80f591c34ca1eaa84d6cc9399cf3f1207e61c4acada647e4e87ad5fba84aeeff6b6881d35bda77c74384fc5e279a0f495d509bc882c2b8bc790651a6d7a4ecba23a3f05111e1d8be37c03439fbd484668ceab69a52b7d519b169cbbcf634ee5e3bf78a5f8771f95fea03f2cb889e116a9f5de3abeacb8e42475fb5d022484b02d11f1e406332e0a773098fc4f0baa57cda2863c554f291d4eb74e63e4b3d44b0ed156bff1820003d407a3aaa9e6dfaa226ba7ef2fd0eff90a5482926f47f24f67019edccb6fd329eef30b5fb2125276aa1fe75a702b32c907ab133c72a74e77e0a5eb48fc5176b9d65b75b0038e1a9ed74ec2a3dcd2348fa54256f082abc01a301bacef7380f20ee0411c08a35dafdaae9f9fc123448da28626ffcc654e9d522bc8b8776b13a3310f7eeb4d27290ef4cbc7492fbcb5409d455748a8a1f087430cf5e6f453e2caa0c5343fcf4374cc38bead49941d8ab59b4d5181716c238aa88dbf1c4a2da3a9a9b9435d5ee1d51d27b0655a4308c1252aaf633cd8f44a351ffc8cec65de0b7e4e2556100e2ae9bc511044351109a6254b2d387b1a72c768f43fa7be6b93806e323b55c3e7925ed627dc708fde0954b299b1ca33bb7fbe33e0f9e4ce5b4f26efaf8e5b9507ada4f8658998eb7167afbd4482ee47cc60f4039d6a77c1fb126033bfc2e7c6162ff7561f22e263325c53a014a4ac9390fe6fab5d433c1e9896fe561f22fc8290f3f4560b676f3dfbfd1fe605343a0685349241b83a28d61cc0292d1f638a36d3d87bfa9f72f9df1cfe90692dfda5bd5e698362f5316984cbe73a132a801acbca76b5f5c23d98a217f2159b6cbbcdf8f52d23ea24c9471a31562a651b20e05cd0300ee500a450cfdaa4d2d83f7e7e27f8b7c793cf80f8067dadef77e49a64c373b97bac4dd472e5145072c73d0fdd68d9646c8a8ed9aec6c40bc915ae44ae27391ca0f1a4d2cb1c3d097be614e6eba807f4549d769a5872f268ccf770f2682d844490348f0b6a0d2b51aadbb5523cf708b66f9928eed12b35a39cf42d283b29f5283e1c8ba1f73457af17b14cdfdf9a85b0589acf1f9504e46b0bab8be848dac5673587035b99f56c41d3195bbba1616b149a22193cfb760d6bf2d84861653cd21be9a2d33187cb25d47fbecdd4626d1d97202f460a39b7128cadb77ddf682feca61fb6de0290df598a565a6361a91d76c0c685046489ed4cb1dcc4f1cea849c12dc4a3d38d3010567f387590532b78927e92f0b718c84e882b3df071a78a011d0fd56d4101dcb009914a16a781b240a6fb2440c72b0ffb365be9d3459d114e665a0d35d7b8bd280101d85d1211d939ba0b15ab528c4f9dd2b001172561d211671b96873010ae3c2b8317f773d735698914228764b831423ae19dd4bbb008b9f1bd1e3ebdd626e629a46a9dd70bdd4bb30e2279e83c12bbbead6479b5f9980b1a9c785395520703a9367d931b45c1566c9d314b1745cafc6d0667cc9bc94d0c53a960c829eb09b768ab6bb2133e4fea1d939f3d3f8e1237210cf3577c830f0493073dc1d189abf27402b8b31b7c172c43dbf331a0828adfe737380e763d0ab0bfaaf94ec04830f94380a83718f340c4eeb20d7eb22b94613be84a9ed332ab364efff6cb37eec35d186185cca725e7a748f6bdb427604fb1628d49a7424a5a62a2e930fe142b035503af332fe748d5e63591b9ac54071ca843d5e474a48837de8b80387f3269ab50d2fd99c08c971e015d13fa02c7c315922ce58bdacbf8ee48827851a61fca59882d7eadcce3166dfe012aa9ec849e698e776a4d384f4755b506a222636942a81bbbffa1ff47e4d81fe68120aebcfd1a7e0000fd0cffdc44e1f0cd69ea2b4936564c78af51fed1cc8e34f0b46d6330b4b50ddee09335b7b0be0bc9f7f8e48415e15d08f811653d21bc6dd152742b086caadcc6dff5e27b40da42c2f1ebf3dd2bd51c418718e499859239317fcab10892eadf1c0ebf7a4246bce4cce3617193032f3e41b977dc8650298ac39631c527460364effea0f0bfd043df72ead0406aba1bcd636d65d7b89979eb8e1";
+
+    mts = randjump(mta, size, jump25000)
+    @test length(mts) == 4
+
+    tmp = zeros(Float64, size*step)
+    for j in 1:step
+        for k in 1:size
+            tmp[j + (k-1) * step] = rand(mts[k], Float64)
+        end
+    end
+
+    for j in 1:(size * step)
+        @test rand(mtb, Float64) == tmp[j]
+    end
+end