Notebooks · lib/randla/philox

Philox4x32-10, the counter-based generator behind every randla sketch

A counter-based generator maps a counter and a key to random bits with no state in between: the bits for entry 7,000 of a sketch are computed directly from the number 7,000, without drawing the 6,999 before it. That is what lets randla build a sketching operator on the fly, one block of entries at a time, and give the same operator in the interpreter, in C and in wasm, and in any order of evaluation (Salmon, Moraes, Dror and Shaw, "Parallel random numbers: as easy as 1, 2, 3", SC11). RandBLAS makes the same choice.

philox4x32(c0, c1, c2, c3, k0, k1) is Random123's philox4x32 with ten rounds; the known-answer vectors from Random123's kat_vectors are tested below. The words are 32-bit values held in Ints.

randla's convention for the counter: (c0, c1) is a 64-bit block index (low word, high word), c2 is the stream, and c3 picks a sub-sequence when one index needs more than four words. The key is the 64-bit seed, split in two.

Used with from randla.philox import ....

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[1]lines 24–138

TWO32: Int = 4294967296
TWO32F = 4294967296.0
# Weyl increments of the key and the two round multipliers (Random123)
PHILOX_W0: Int = 2654435769
PHILOX_W1: Int = 3144134277
PHILOX_M0: Int = 3528531795
PHILOX_M1: Int = 3449720151
PHILOX_ROUNDS: Int = 10
# 2^52 and 2^26, for 52-bit uniforms from two words (26 bits of each)
TWO52F = 4503599627370496.0
TWO26F = 67108864.0
SHIFT_26: Int = 64
TWO_PI = 6.283185307179586
# a word at or above 2^31 has its top bit set
TOP_BIT: Int = 2147483648

#| Philox4x32-10: the four 32-bit words the counter (c0, c1, c2, c3) maps to
#| under the key (k0, k1), as Random123's philox4x32 computes them.
def philox4x32(c0: Int, c1: Int, c2: Int, c3: Int, k0: Int, k1: Int) {
    x0 = c0
    x1 = c1
    x2 = c2
    x3 = c3
    ka = k0
    kb = k1
    for round to PHILOX_ROUNDS {
        if round > 0 {
            ka += PHILOX_W0
            if ka >= TWO32 {
                ka -= TWO32
            }
            kb += PHILOX_W1
            if kb >= TWO32 {
                kb -= TWO32
            }
        }
        # the two 64-bit products M x, split into high and low words with
        # no division: the high word is umulhi(M, x 2^32) = (M x) / 2^32
        # rounded down, and the low word is what is left
        h0 = umulhi(PHILOX_M0, wrap_mul(x0, TWO32))
        l0 = wrap_sub(wrap_mul(PHILOX_M0, x0), wrap_mul(h0, TWO32))
        h1 = umulhi(PHILOX_M1, wrap_mul(x2, TWO32))
        l1 = wrap_sub(wrap_mul(PHILOX_M1, x2), wrap_mul(h1, TWO32))
        y0 = int(bxor(bxor(float(h1), float(x1)), float(ka)))
        y2 = int(bxor(bxor(float(h0), float(x3)), float(kb)))
        x0 = y0
        x1 = l1
        x2 = y2
        x3 = l0
    }
    return x0, x1, x2, x3
}

#| The four words of block `index` of stream `stream` under `seed`, with
#| sub-sequence `sub`: randla's one entry point into Philox.
def block(seed: Int, stream: Int, index: Int, sub: Int) {
    return philox4x32(index % TWO32, index // TWO32, stream % TWO32, sub, seed % TWO32, seed // TWO32)
}

#| A uniform in (0, 1) from two words: the top 26 bits of each make a 52-bit
#| integer k, and the result is (k + 1/2) / 2^52, which is exact in a double,
#| so neither 0 nor 1 comes out. (With 53 bits, k + 1/2 rounds to 2^53 at
#| the top and 1.0 would come out.)
def unit_open(a: Int, b: Int) -> Num {
    hi = float(a // SHIFT_26)
    lo = float(b // SHIFT_26)
    return (hi * TWO26F + lo + 0.5) / TWO52F
}

#| Two standard normals from one block, by Box-Muller.
def normal_pair(w0: Int, w1: Int, w2: Int, w3: Int) {
    u1 = unit_open(w0, w1)
    u2 = unit_open(w2, w3)
    rad = sqrt(-2.0 * log(u1))
    return rad * cos(TWO_PI * u2), rad * sin(TWO_PI * u2)
}

#| A sign from one word: +1 when the top bit is clear, -1 when it is set.
def sign_of(w: Int) -> Num {
    if w >= TOP_BIT {
        return -1.0
    }
    return 1.0
}

#| An integer drawn uniformly from 0 to n - 1 using two words: floor of a
#| 52-bit uniform times n, whose bias is below n / 2^52.
def below(a: Int, b: Int, n: Int) -> Int {
    j: Int = int(floor(unit_open(a, b) * float(n)))
    if j >= n {
        j = n - 1
    }
    return j
}

test "Philox4x32-10's known-answer vectors (Random123, kat_vectors)" {
    a0, a1, a2, a3 = philox4x32(0, 0, 0, 0, 0, 0)
    assert_true(a0 == 1713891541 and a1 == 3781805453 and a2 == 3159862348 and a3 == 2600524760)
    m: Int = 4294967295
    b0, b1, b2, b3 = philox4x32(m, m, m, m, m, m)
    assert_true(b0 == 1083123565 and b1 == 1103641358 and b2 == 2718681030 and b3 == 1834242557)
    c0, c1, c2, c3 = philox4x32(608135816, 2242054355, 320440878, 57701188, 2752067618, 698298832)
    assert_true(c0 == 3513581065 and c1 == 2499661035 and c2 == 1342301216 and c3 == 605187745)
}

test "a uniform from two words lies strictly inside (0, 1)" {
    m: Int = 4294967295
    z: Int = 0
    assert_true(unit_open(z, z) > 0.0)
    assert_true(unit_open(m, m) < 1.0)
    assert_true(below(m, m, 7) == 6)
}

# SPDX-License-Identifier: MIT OR Apache-2.0
# SPDX-FileCopyrightText: 2026 The Viv authors

TWO32: Int = 4294967296
TWO32F = 4294967296.0
# Weyl increments of the key and the two round multipliers (Random123)
PHILOX_W0: Int = 2654435769
PHILOX_W1: Int = 3144134277
PHILOX_M0: Int = 3528531795
PHILOX_M1: Int = 3449720151
PHILOX_ROUNDS: Int = 10
# 2^52 and 2^26, for 52-bit uniforms from two words (26 bits of each)
TWO52F = 4503599627370496.0
TWO26F = 67108864.0
SHIFT_26: Int = 64
TWO_PI = 6.283185307179586
# a word at or above 2^31 has its top bit set
TOP_BIT: Int = 2147483648

#| Philox4x32-10: the four 32-bit words the counter (c0, c1, c2, c3) maps to
#| under the key (k0, k1), as Random123's philox4x32 computes them.
def philox4x32(c0: Int, c1: Int, c2: Int, c3: Int, k0: Int, k1: Int) {
    x0 = c0
    x1 = c1
    x2 = c2
    x3 = c3
    ka = k0
    kb = k1
    for round to PHILOX_ROUNDS {
        if round > 0 {
            ka += PHILOX_W0
            if ka >= TWO32 {
                ka -= TWO32
            }
            kb += PHILOX_W1
            if kb >= TWO32 {
                kb -= TWO32
            }
        }
        # the two 64-bit products M x, split into high and low words with
        # no division: the high word is umulhi(M, x 2^32) = (M x) / 2^32
        # rounded down, and the low word is what is left
        h0 = umulhi(PHILOX_M0, wrap_mul(x0, TWO32))
        l0 = wrap_sub(wrap_mul(PHILOX_M0, x0), wrap_mul(h0, TWO32))
        h1 = umulhi(PHILOX_M1, wrap_mul(x2, TWO32))
        l1 = wrap_sub(wrap_mul(PHILOX_M1, x2), wrap_mul(h1, TWO32))
        y0 = int(bxor(bxor(float(h1), float(x1)), float(ka)))
        y2 = int(bxor(bxor(float(h0), float(x3)), float(kb)))
        x0 = y0
        x1 = l1
        x2 = y2
        x3 = l0
    }
    return x0, x1, x2, x3
}

#| The four words of block `index` of stream `stream` under `seed`, with
#| sub-sequence `sub`: randla's one entry point into Philox.
def block(seed: Int, stream: Int, index: Int, sub: Int) {
    return philox4x32(index % TWO32, index // TWO32, stream % TWO32, sub, seed % TWO32, seed // TWO32)
}

#| A uniform in (0, 1) from two words: the top 26 bits of each make a 52-bit
#| integer k, and the result is (k + 1/2) / 2^52, which is exact in a double,
#| so neither 0 nor 1 comes out. (With 53 bits, k + 1/2 rounds to 2^53 at
#| the top and 1.0 would come out.)
def unit_open(a: Int, b: Int) -> Num {
    hi = float(a // SHIFT_26)
    lo = float(b // SHIFT_26)
    return (hi * TWO26F + lo + 0.5) / TWO52F
}

#| Two standard normals from one block, by Box-Muller.
def normal_pair(w0: Int, w1: Int, w2: Int, w3: Int) {
    u1 = unit_open(w0, w1)
    u2 = unit_open(w2, w3)
    rad = sqrt(-2.0 * log(u1))
    return rad * cos(TWO_PI * u2), rad * sin(TWO_PI * u2)
}

#| A sign from one word: +1 when the top bit is clear, -1 when it is set.
def sign_of(w: Int) -> Num {
    if w >= TOP_BIT {
        return -1.0
    }
    return 1.0
}

#| An integer drawn uniformly from 0 to n - 1 using two words: floor of a
#| 52-bit uniform times n, whose bias is below n / 2^52.
def below(a: Int, b: Int, n: Int) -> Int {
    j: Int = int(floor(unit_open(a, b) * float(n)))
    if j >= n {
        j = n - 1
    }
    return j
}

test "Philox4x32-10's known-answer vectors (Random123, kat_vectors)" {
    a0, a1, a2, a3 = philox4x32(0, 0, 0, 0, 0, 0)
    assert_true(a0 == 1713891541 and a1 == 3781805453 and a2 == 3159862348 and a3 == 2600524760)
    m: Int = 4294967295
    b0, b1, b2, b3 = philox4x32(m, m, m, m, m, m)
    assert_true(b0 == 1083123565 and b1 == 1103641358 and b2 == 2718681030 and b3 == 1834242557)
    c0, c1, c2, c3 = philox4x32(608135816, 2242054355, 320440878, 57701188, 2752067618, 698298832)
    assert_true(c0 == 3513581065 and c1 == 2499661035 and c2 == 1342301216 and c3 == 605187745)
}

test "a uniform from two words lies strictly inside (0, 1)" {
    m: Int = 4294967295
    z: Int = 0
    assert_true(unit_open(z, z) > 0.0)
    assert_true(unit_open(m, m) < 1.0)
    assert_true(below(m, m, 7) == 6)
}

# SPDX-License-Identifier: MIT OR Apache-2.0
# SPDX-FileCopyrightText: 2026 The Viv authors