Notebooks · lib/nprandom/seedseq

NumPy's SeedSequence, the hash behind default_rng(seed)

np.random.default_rng(seed) does not use the seed as the state. It hands the seed to SeedSequence, which hashes its 32-bit words into a pool of four words and draws the generator's initial state from the pool. This is that code from NumPy 1.24.4 (numpy/random/bit_generator.pyx: hashmix, mix, mix_entropy, generate_state; tag v1.24.4, commit 9315a9072b2636f75c831b4eca9f42a5f67ca2fb), with its constants' names. Every product is a 32-bit product that wraps (npr_mul32).

npr_ss_words(n): the words of a non-negative int below 2^53, lowest first, as _int_to_uint32_array splits it ([0] for 0).
npr_ss_pool(entropy): mix_entropy of an array of words into the pool.
npr_ss_generate(pool, n_words): generate_state(n_words) as 32-bit words (for np.uint64 words, pair them up: word 2k is the low half of the k-th).

Used with import nprandom.seedseq.

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[1]lines 22–99

from nprandom.bits import npr_mul32, npr_sub32, NPR_TWO32

NPR_SS_POOL_SIZE = 4
NPR_SS_XSHIFT = 16
# 0x43b0d7e5, 0x931e8875, 0x8b51f9dd, 0x58f38ded, 0xca01f9dd, 0x4973f715
NPR_SS_INIT_A = 1135663077
NPR_SS_MULT_A = 2468251765
NPR_SS_INIT_B = 2337405405
NPR_SS_MULT_B = 1492356589
NPR_SS_MIX_MULT_L = 3389127133
NPR_SS_MIX_MULT_R = 1232336661

#| The 32-bit words of n (0 <= n < 2^53), lowest first.
def npr_ss_words(n) {
    if n < NPR_TWO32 {
        return [n]
    }
    return [mod(n, NPR_TWO32), floor(n / NPR_TWO32)]
}

#| hashmix: value ^ hash_const, times the next hash_const, xor-shifted. The hash
#| constant lives in hc[0] and moves on with each call.
def npr_ss_hashmix(value, hc: Arr) {
    v = bxor(value, hc[0])
    hc[0] = npr_mul32(hc[0], NPR_SS_MULT_A)
    v = npr_mul32(v, hc[0])
    return bxor(v, shr(v, NPR_SS_XSHIFT))
}

#| mix: MIX_MULT_L * x - MIX_MULT_R * y, xor-shifted.
def npr_ss_mix(x, y) {
    r = npr_sub32(npr_mul32(NPR_SS_MIX_MULT_L, x), npr_mul32(NPR_SS_MIX_MULT_R, y))
    return bxor(r, shr(r, NPR_SS_XSHIFT))
}

#| mix_entropy: the pool of four words from the entropy words.
def npr_ss_pool(entropy: Arr) {
    pool = zeros(NPR_SS_POOL_SIZE)
    hc = [NPR_SS_INIT_A]
    n = len(entropy)
    for i to NPR_SS_POOL_SIZE {
        if i < n {
            pool[i] = npr_ss_hashmix(entropy[i], hc)
        }
        else {
            pool[i] = npr_ss_hashmix(0, hc)
        }
    }
    for i_src to NPR_SS_POOL_SIZE {
        for i_dst to NPR_SS_POOL_SIZE {
            if i_src != i_dst {
                pool[i_dst] = npr_ss_mix(pool[i_dst], npr_ss_hashmix(pool[i_src], hc))
            }
        }
    }
    for i_src from NPR_SS_POOL_SIZE to max(n, NPR_SS_POOL_SIZE) {
        for i_dst to NPR_SS_POOL_SIZE {
            pool[i_dst] = npr_ss_mix(pool[i_dst], npr_ss_hashmix(entropy[i_src], hc))
        }
    }
    return pool
}

#| generate_state: n_words 32-bit words from the pool, cycling through it.
def npr_ss_generate(pool: Arr, n_words) {
    out = zeros(n_words)
    hc = NPR_SS_INIT_B
    for i to n_words {
        v = bxor(pool[mod(i, NPR_SS_POOL_SIZE)], hc)
        hc = npr_mul32(hc, NPR_SS_MULT_B)
        v = npr_mul32(v, hc)
        out[i] = bxor(v, shr(v, NPR_SS_XSHIFT))
    }
    return out
}

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

from nprandom.bits import npr_mul32, npr_sub32, NPR_TWO32

NPR_SS_POOL_SIZE = 4
NPR_SS_XSHIFT = 16
# 0x43b0d7e5, 0x931e8875, 0x8b51f9dd, 0x58f38ded, 0xca01f9dd, 0x4973f715
NPR_SS_INIT_A = 1135663077
NPR_SS_MULT_A = 2468251765
NPR_SS_INIT_B = 2337405405
NPR_SS_MULT_B = 1492356589
NPR_SS_MIX_MULT_L = 3389127133
NPR_SS_MIX_MULT_R = 1232336661

#| The 32-bit words of n (0 <= n < 2^53), lowest first.
def npr_ss_words(n) {
    if n < NPR_TWO32 {
        return [n]
    }
    return [mod(n, NPR_TWO32), floor(n / NPR_TWO32)]
}

#| hashmix: value ^ hash_const, times the next hash_const, xor-shifted. The hash
#| constant lives in hc[0] and moves on with each call.
def npr_ss_hashmix(value, hc: Arr) {
    v = bxor(value, hc[0])
    hc[0] = npr_mul32(hc[0], NPR_SS_MULT_A)
    v = npr_mul32(v, hc[0])
    return bxor(v, shr(v, NPR_SS_XSHIFT))
}

#| mix: MIX_MULT_L * x - MIX_MULT_R * y, xor-shifted.
def npr_ss_mix(x, y) {
    r = npr_sub32(npr_mul32(NPR_SS_MIX_MULT_L, x), npr_mul32(NPR_SS_MIX_MULT_R, y))
    return bxor(r, shr(r, NPR_SS_XSHIFT))
}

#| mix_entropy: the pool of four words from the entropy words.
def npr_ss_pool(entropy: Arr) {
    pool = zeros(NPR_SS_POOL_SIZE)
    hc = [NPR_SS_INIT_A]
    n = len(entropy)
    for i to NPR_SS_POOL_SIZE {
        if i < n {
            pool[i] = npr_ss_hashmix(entropy[i], hc)
        }
        else {
            pool[i] = npr_ss_hashmix(0, hc)
        }
    }
    for i_src to NPR_SS_POOL_SIZE {
        for i_dst to NPR_SS_POOL_SIZE {
            if i_src != i_dst {
                pool[i_dst] = npr_ss_mix(pool[i_dst], npr_ss_hashmix(pool[i_src], hc))
            }
        }
    }
    for i_src from NPR_SS_POOL_SIZE to max(n, NPR_SS_POOL_SIZE) {
        for i_dst to NPR_SS_POOL_SIZE {
            pool[i_dst] = npr_ss_mix(pool[i_dst], npr_ss_hashmix(entropy[i_src], hc))
        }
    }
    return pool
}

#| generate_state: n_words 32-bit words from the pool, cycling through it.
def npr_ss_generate(pool: Arr, n_words) {
    out = zeros(n_words)
    hc = NPR_SS_INIT_B
    for i to n_words {
        v = bxor(pool[mod(i, NPR_SS_POOL_SIZE)], hc)
        hc = npr_mul32(hc, NPR_SS_MULT_B)
        v = npr_mul32(v, hc)
        out[i] = bxor(v, shr(v, NPR_SS_XSHIFT))
    }
    return out
}

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