miden-core-lib 0.28.0

Miden VM core library
Documentation
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use miden::core::word

# CONSTANTS
# =================================================================================================
const LOWERBOUND_ARRAY_EVENT = event("miden::core::collections::sorted_array::lowerbound_array")
const LOWERBOUND_KEY_VALUE_EVENT = event("miden::core::collections::sorted_array::lowerbound_key_value")

# ===== ARRAY UTILITIES ============================================================================

#! Finds a value in a sorted array of words.
#!
#! **Proof-side contract:** the input array must already be sorted in non-decreasing
#! lexicographic order before this procedure is called.
#!
#! This procedure does not prove that the full memory range is sorted. It uses host-provided
#! lower-bound advice and verifies only that the returned lower-bound witness is locally consistent
#! with the returned pointer. If malicious advice is used on an unsorted range, the local witness can
#! be consistent while the global lookup result is false.
#!
#! Caller code must prove sortedness before relying on this result, unless the range was already
#! authenticated by another proof-side invariant that implies sortedness. Use `assert_sorted_words`
#! when caller code needs to establish this precondition directly.
#!
#! Input:  [VALUE, start_ptr, end_ptr]
#! Output: [is_value_found, value_ptr, start_ptr, end_ptr]
#!
#! # Panics
#!
#! Panics if:
#! - start_ptr, end_ptr are not word-aligned
#! - `start_ptr > end_ptr`
#!
#! Cycles:
#!   Value exists: 46 cycles
#!   Value doesn't exist and the array is empty: 25 cycles
#!   Value doesn't exist and is smaller than all elements: 151 cycles
#!   Value doesn't exist and is larger than all elements: 149 cycles
#!   Value doesn't exist: 286 cycles
pub proc find_word
    # Call the non-deterministic lowerbound advisor (5 cycles)
    emit.LOWERBOUND_ARRAY_EVENT
    adv_push adv_push
    #=> [was_value_found, maybe_value_ptr, VALUE, start_ptr, end_ptr]

    if.true
        # assert `start_ptr <= maybe_value_ptr < end_ptr` (15 cycles)
        dup dup.6 u32assert2.err="maybe_value_ptr is not u32"
        u32gte assert.err="lowerbound_array invariant: maybe_value_ptr must be >= start_ptr"
        dup dup.7 u32assert2.err="maybe_value_ptr is not u32"
        u32lt assert.err="lowerbound_array invariant: maybe_value_ptr must be < end_ptr"
        #=> [maybe_value_ptr, VALUE, start_ptr, end_ptr]

        # dereference maybe_value_ptr (8 cycles)
        dup movdn.5 padw movup.4 mem_loadw_le
        #=> [MAYBE_VALUE, VALUE, maybe_value_ptr, start_ptr, end_ptr]

        # check if it matches the requested VALUE (15 cycles)
        exec.word::eq
        dup assert.err="lowerbound_array invariant: value_ptr must point to VALUE"
        #=> [is_value_found, maybe_value_ptr, start_ptr, end_ptr]
    else
        # the value was not found

        # pre-compute is_start_ptr, is_end_ptr to reduce the depth of the generated MAST
        # (6 cycles)
        dup.6 dup.1 eq
        #=> [is_end_ptr, maybe_value_ptr, VALUE, start_ptr, end_ptr]

        dup.6 dup.2 eq
        #=> [is_start_ptr, is_end_ptr, maybe_value_ptr, VALUE, start_ptr, end_ptr]

        if.true
            # the value was not found, and `maybe_value_ptr = start_ptr`

            if.true
                # the list is empty and `start_ptr = end_ptr` (both are equal to `maybe_value_ptr`)
                #=> [maybe_value_ptr = start_ptr = end_ptr, VALUE, start_ptr, end_ptr]

                # Prepare output (6 cycles)
                movdn.4 dropw push.0
                #=> [is_value_found = 0, value_ptr = start_ptr, start_ptr, end_ptr]
            else
                # the value was not found, `maybe_value_ptr = start_ptr`, and the list is not empty
                # assert `the value at start_ptr > VALUE`
                #=> [maybe_value_ptr = start_ptr, VALUE, start_ptr, end_ptr]

                movdn.4
                #=> [VALUE, maybe_value_ptr, start_ptr, end_ptr]

                # dereference maybe_value_ptr (7 cycles)
                dup.4 padw movup.4 mem_loadw_le
                #=> [FIRST_WORD, VALUE, maybe_value_ptr = start_ptr, start_ptr, end_ptr]

                # there was no match, the first array element must be larger than VALUE
                # (123 cycles)
                exec.word::lt
                assert.err="lowerbound_array invariant: start_ptr must point to a word greater than VALUE"

                # No value was found (1 cycle)
                push.0
                #=> [is_value_found = 0, maybe_value_ptr = start_ptr, start_ptr, end_ptr]
            end
        else
            if.true
                # the value was not found, `maybe_value_ptr = end_ptr`
                # the list is not empty, otherwise `maybe_value_ptr = start_ptr` and handled above
                # assert `the value before end_ptr < VALUE`

                #=> [maybe_value_ptr = end_ptr, VALUE, start_ptr, end_ptr]

                # fetch the last word in the array (10 cycles)
                dup movdn.5 sub.4 padw movup.4 mem_loadw_le
                #=> [LAST_WORD, VALUE, maybe_value_ptr = end_ptr, start_ptr, end_ptr]

                # there was no match, the last array element must be smaller than VALUE
                # (119 cycles)
                exec.word::gt
                assert.err="lowerbound_array invariant: last word must be smaller than VALUE"

                # No value was found (1 cycle)
                push.0
                #=> [is_value_found = 0, maybe_value_ptr = end_ptr, start_ptr, end_ptr]
            else
                # The value was not found, and the maybe_value_ptr is neither the start nor the end
                # of the list. Make sure that:
                # - `start_ptr <= maybe_value_ptr < end_ptr`, and
                # - `the value at maybe_value_ptr-1 < VALUE`, and
                # - `the value at maybe_value_ptr > VALUE`.
                # `maybe_value_ptr` must already be word aligned to allow reading values.
                #=> [maybe_value_ptr, VALUE, start_ptr, end_ptr]

                # `maybe_value_ptr` bounds check
                dup dup.6 u32assert2.err="maybe_value_ptr is not u32"
                u32gte assert.err="lowerbound_array invariant: maybe_value_ptr must be >= start_ptr"

                dup dup.7 u32assert2.err="maybe_value_ptr is not u32"
                u32lt assert.err="lowerbound_array invariant: maybe_value_ptr must be < end_ptr"

                # Duplicate VALUE word (5 cycles)
                movdn.4 dupw
                #=> [VALUE, VALUE, maybe_value_ptr, start_ptr, end_ptr]

                # dereference maybe_value_ptr (8 cycles)
                padw dup.12 mem_loadw_le
                #=> [MAYBE_VALUE, VALUE, VALUE, maybe_value_ptr, start_ptr, end_ptr]

                # there was no match, MAYBE_VALUE must be larger than VALUE (123 cycles)
                exec.word::lt
                assert.err="lowerbound_array invariant: *maybe_value_ptr must be greater than VALUE"

                # dereference `maybe_value_ptr-4` (11 cycles)
                padw dup.8 sub.4 mem_loadw_le
                #=> [MAYBE_VALUE_PREV, VALUE, maybe_value_ptr, start_ptr, end_ptr]

                # there was no match, MAYBE_VALUE_PREV must be smaller than VALUE (119 cycles)
                exec.word::gt
                assert.err="lowerbound_array invariant: *(maybe_value_ptr-4) must be smaller than VALUE"

                # No value was found (1 cycle)
                push.0
                #=> [is_value_found = 0, maybe_value_ptr, start_ptr, end_ptr]
            end
        end
    end
end

#! Asserts that an array of words is sorted in non-decreasing lexicographic order.
#!
#! This is a full linear proof-side check over the memory range. It does not use advice. Call this
#! before `find_word` when sortedness is not already implied by another proof-side invariant.
#!
#! Input:  [start_ptr, end_ptr, ...]
#! Output: [start_ptr, end_ptr, ...]
#!
#! Panics if:
#! - start_ptr or end_ptr is not a u32 value.
#! - start_ptr, end_ptr are not word-aligned
#! - `start_ptr > end_ptr`
#! - any adjacent word pair is out of order.
@locals(1)
pub proc assert_sorted_words
    # locals:
    # 0: current_ptr
    dup add.4 loc_store.0
    # => [start_ptr, end_ptr, ...]

    dup.1 dup.1 u32assert2.err="sorted_array invariant: range pointers must be u32"
    u32gte assert.err="sorted_array invariant: start_ptr must be <= end_ptr"
    dup u32mod.4 assertz.err="sorted_array invariant: start_ptr must be word-aligned"
    dup.1 u32mod.4 assertz.err="sorted_array invariant: end_ptr must be word-aligned"
    # => [start_ptr, end_ptr, ...]

    loc_load.0 dup.2 u32lt
    while.true
        loc_load.0 sub.4 padw movup.4 mem_loadw_le
        # => [PREVIOUS_WORD, start_ptr, end_ptr, ...]

        loc_load.0 padw movup.4 mem_loadw_le
        # => [CURRENT_WORD, PREVIOUS_WORD, start_ptr, end_ptr, ...]

        exec.word::gt
        not
        assert.err="sorted_array invariant: words must be sorted"
        # => [start_ptr, end_ptr, ...]

        loc_load.0 add.4 loc_store.0
        # => [start_ptr, end_ptr, ...]

        loc_load.0 dup.2 u32lt
    end
end

# ===== KEY-VALUE UTILITIES ============================================================================

#! Finds a key in a sorted array of (key, value) word tuples.
#!
#! **Proof-side contract:** the keys in the array must already be sorted in non-decreasing
#! lexicographic order before this procedure is called.
#!
#! This procedure does not prove that the full memory range is sorted. It uses host-provided
#! lower-bound advice and verifies only that the returned lower-bound witness is locally consistent
#! with the returned pointer. If malicious advice is used on an unsorted range, the local witness can
#! be consistent while the global lookup result is false.
#!
#! Caller code must prove key sortedness before relying on this result, unless the range was already
#! authenticated by another proof-side invariant that implies sortedness. Use `assert_sorted_keys`
#! when caller code needs to establish this precondition directly.
#!
#! Inputs:  [KEY, start_ptr, end_ptr]
#! Outputs: [is_key_found, key_ptr, start_ptr, end_ptr]
#!
#! # Panics
#!
#! Panics if:
#! - start_ptr is not word-aligned
#! - end_ptr is not double-word-aligned with the start_ptr:
#!     - `(end_ptr - start_ptr)` must be divisible by 8
#! - `start_ptr > end_ptr`
pub proc find_key_value
    push.1
    # => [use_full_key = 1, KEY, start_ptr, end_ptr]

    movdn.6
    # => [KEY, start_ptr, end_ptr, use_full_key]

    exec.find_partial_key_value
    # => [is_key_found, key_ptr, start_ptr, end_ptr]
end

#! Finds a half-key in a sorted array of (key, value) word tuples.
#!
#! Half-key means that, out of the keys in the array, only half of the key - the most significant
#! element (prefix) and the second most significant element (suffix) - need to match.
#!
#! **Proof-side contract:** the half-keys in the array must already be sorted in non-decreasing
#! lexicographic order before this procedure is called.
#!
#! This procedure does not prove that the full memory range is sorted. It uses host-provided
#! lower-bound advice and verifies only that the returned lower-bound witness is locally consistent
#! with the returned pointer. If malicious advice is used on an unsorted range, the local witness can
#! be consistent while the global lookup result is false.
#!
#! Caller code must prove half-key sortedness before relying on this result, unless the range was
#! already authenticated by another proof-side invariant that implies sortedness. Use
#! `assert_sorted_half_keys` when caller code needs to establish this precondition directly.
#!
#! Inputs: [key_suffix, key_prefix, start_ptr, end_ptr]
#! Output: [is_key_found, key_ptr, start_ptr, end_ptr]
#!
#! # Panics
#!
#! Panics if:
#! - start_ptr is not word-aligned
#! - end_ptr is not double-word-aligned with the start_ptr:
#!     - `(end_ptr - start_ptr)` must be divisible by 8
#! - `start_ptr > end_ptr`
pub proc find_half_key_value
    # Build KEY with key_prefix at word[3] (most significant in BE) and key_suffix at word[2]
    # word[0] and word[1] are 0 (will be zeroed in half-key comparison anyway)
    push.0 push.0
    # => [0, 0, key_suffix, key_prefix, start_ptr, end_ptr]
    # KEY = [0, 0, key_suffix, key_prefix] with w0=0 on top, w3=key_prefix

    push.0
    # => [use_full_key = 0, KEY, start_ptr, end_ptr]

    movdn.6
    # => [KEY, start_ptr, end_ptr, use_full_key]

    exec.find_partial_key_value
    # => [is_key_found, key_ptr, start_ptr, end_ptr]
end

#! Finds a key in a sorted array of (key, value) word tuples.
#!
#! - If use_full_key = 1, then a match on the entire KEY is required.
#! - If use_full_key = 0, then the KEY's two least significant elements *must* be zeroes and
#!   upon loading the key for comparison, its two least significant elements are zeroized.
#!   This effectively means that only a match on the two most significant elements is required.
#!
#! **Proof-side contract:** the relevant keys in the array must already be sorted in
#! non-decreasing lexicographic order before this procedure is called.
#!
#! This procedure does not prove that the full memory range is sorted. It uses host-provided
#! lower-bound advice and verifies only that the returned lower-bound witness is locally consistent
#! with the returned pointer. If malicious advice is used on an unsorted range, the local witness can
#! be consistent while the global lookup result is false.
#!
#! Input:  [KEY, start_ptr, end_ptr, use_full_key]
#! Output: [is_key_found, key_ptr, start_ptr, end_ptr]
#!
#! # Panics
#!
#! Panics if:
#! - start_ptr is not word-aligned
#! - end_ptr is not double-word-aligned with the start_ptr:
#!     - `(end_ptr - start_ptr)` must be divisible by 8
#! - `start_ptr > end_ptr`
#!
#! Cycles:
#!   Key exists: 70 cycles
#!   Key doesn't exist and the array is empty: 25 cycles
#!   Key doesn't exist and is smaller than all stored keys: 166 cycles
#!   Key doesn't exist and is larger than all stored keys: 162 cycles
#!   Key doesn't exist: 322 cycles
@locals(1)
proc find_partial_key_value
    # Call the non-deterministic lowerbound advisor (5 cycles)
    emit.LOWERBOUND_KEY_VALUE_EVENT
    # => [KEY, start_ptr, end_ptr, use_full_key]

    # store use_full_key for later
    movup.6 loc_store.0
    # => [KEY, start_ptr, end_ptr]

    adv_push adv_push
    #=> [was_key_found, maybe_key_ptr, KEY, start_ptr, end_ptr]

    if.true
        # assert `start_ptr <= maybe_key_ptr < end_ptr` (15 cycles)
        dup dup.6 u32assert2.err="maybe_key_ptr is not u32"
        u32gte assert.err="lowerbound_key_value invariant: maybe_key_ptr must be >= start_ptr"
        dup dup.7 u32assert2.err="maybe_key_ptr is not u32"
        u32lt assert.err="lowerbound_key_value invariant: maybe_key_ptr must be < end_ptr"
        #=> [maybe_key_ptr, KEY, start_ptr, end_ptr]

        # make sure maybe_key_ptr is pointing to a key, not value (10 cycles)
        dup dup.6 sub u32mod.8 assertz.err="lowerbound_key_value invariant: key_ptr must be double-word aligned with start_ptr"
        #=> [maybe_key_ptr, KEY, start_ptr, end_ptr]

        # dereference maybe_key_ptr (22 cycles)
        dup movdn.5
        #=> [maybe_key_ptr, KEY, maybe_key_ptr, start_ptr, end_ptr]

        loc_load.0 exec.load_key
        #=> [MAYBE_KEY, KEY, maybe_key_ptr, start_ptr, end_ptr]

        # check if it matches the requested KEY (15 cycles)
        exec.word::eq
        dup assert.err="lowerbound_key_value invariant: key_ptr must point to KEY"
        #=> [is_key_found, maybe_key_ptr, start_ptr, end_ptr]
    else
        # pre-compute is_start_ptr, is_end_ptr to reduce the depth of the
        # generated MAST (6 cycles)
        dup.6 dup.1 eq
        #=> [is_end_ptr, maybe_key_ptr, KEY, start_ptr, end_ptr]

        dup.6 dup.2 eq
        #=> [is_start_ptr, is_end_ptr, maybe_key_ptr, KEY, start_ptr, end_ptr]

        if.true
            # the key was not found, `maybe_key_ptr = start_ptr`

            if.true
                # the list is empty and `start_ptr = end_ptr` (both are equal to `maybe_key_ptr`)
                #=> [maybe_key_ptr = start_ptr = end_ptr, KEY, start_ptr, end_ptr]

                # Prepare output (6 cycles)
                movdn.4 dropw push.0
                #=> [is_key_found = 0, key_ptr = start_ptr, start_ptr, end_ptr]
            else
                # the key was not found, `maybe_key_ptr = start_ptr` and the list is not empty
                # assert `the key at start_ptr > KEY`
                #=> [maybe_key_ptr = start_ptr, KEY, start_ptr, end_ptr]

                # load key (22 cycles)
                dup movdn.5
                #=> [maybe_key_ptr, KEY, maybe_key_ptr, start_ptr, end_ptr]

                loc_load.0 exec.load_key
                #=> [FIRST_KEY, KEY, maybe_key_ptr = start_ptr, start_ptr, end_ptr]

                # there was no match, the first map element must be larger than KEY
                # (123 cycles)
                exec.word::lt
                assert.err="lowerbound_key_value invariant: start_ptr must point to a key greater than KEY"

                # No value was found (1 cycle)
                push.0
                #=> [is_key_found = 0, maybe_key_ptr = start_ptr, start_ptr, end_ptr]
            end
        else
            if.true
                # the key was not found, `maybe_key_ptr = end_ptr`
                # the list is not empty, otherwise `maybe_key_ptr = start_ptr` and handled above
                # assert `the key before end_ptr < KEY`

                #=> [maybe_key_ptr = end_ptr, KEY, start_ptr, end_ptr]

                # fetch the last key in the array (23 cycles)
                dup movdn.5 sub.8
                #=> [maybe_key_ptr-8, KEY, maybe_key_ptr, start_ptr, end_ptr]

                loc_load.0 exec.load_key
                #=> [LAST_KEY, KEY, maybe_key_ptr = end_ptr, start_ptr, end_ptr]

                # there was no match, the last map element must be smaller than KEY
                # (119 cycles)
                exec.word::gt
                assert.err="lowerbound_key_value invariant: last key-value pair must be smaller than KEY"

                # No value was found (1 cycle)
                push.0
                #=> [is_key_found = 0, maybe_key_ptr = end_ptr, start_ptr, end_ptr]
            else
                # The key was not found, and the maybe_key_ptr is neither the start nor the end
                # of the list. Make sure that:
                # - `start_ptr <= maybe_key_ptr < end_ptr`, and
                # - `maybe_key_ptr` is word aligned with `start_ptr`, and
                # - `the key at maybe_key_ptr-1 < KEY`, and
                # - `the key at maybe_key_ptr > KEY`
                #=> [maybe_key_ptr, KEY, start_ptr, end_ptr]

                # `maybe_key_ptr` bounds check
                dup dup.6 u32assert2.err="maybe_key_ptr is not u32"
                u32gte assert.err="lowerbound_key_value invariant: maybe_key_ptr must be >= start_ptr"

                dup dup.7 u32assert2.err="maybe_key_ptr is not u32"
                u32lt assert.err="lowerbound_key_value invariant: maybe_key_ptr must be < end_ptr"

                # make sure maybe_key_ptr is pointing to a key, not value (10 cycles)
                dup dup.6 sub u32assert2.err="maybe_key_ptr is not u32"
                u32mod.8 assertz.err="lowerbound_key_value invariant: key_ptr must be double-word aligned with start_ptr"

                # Duplicate KEY word (5 cycles)
                movdn.4 dupw
                #=> [KEY, KEY, maybe_key_ptr, start_ptr, end_ptr]

                # load key (21 cycles)
                dup.8 loc_load.0 exec.load_key
                #=> [MAYBE_KEY, KEY, KEY, maybe_key_ptr, start_ptr, end_ptr]

                # there was no match, `*maybe_key_ptr` must be larger than KEY (123 cycles)
                exec.word::lt
                assert.err="lowerbound_key_value invariant: MAYBE_KEY must be greater than KEY"
                #=> [KEY, maybe_key_ptr, start_ptr, end_ptr]

                # dereference `maybe_key_ptr-8` (previous key) (22 cycles)
                dup.4 sub.8
                #=> [maybe_key_ptr-8, KEY, maybe_key_ptr, start_ptr, end_ptr]

                loc_load.0 exec.load_key
                #=> [MAYBE_KEY_PREV, KEY, maybe_key_ptr, start_ptr, end_ptr]

                # there was no match, `*(maybe_key_ptr-8)` must be smaller than KEY (119 cycles)
                exec.word::gt
                assert.err="lowerbound_key_value invariant: MAYBE_KEY_PREV must be smaller than KEY"

                # No value was found (1 cycle)
                push.0
                #=> [is_key_found = 0, maybe_key_ptr, start_ptr, end_ptr]
            end
        end
    end
end

#! Asserts that keys in an array of (key, value) word tuples are sorted in non-decreasing
#! lexicographic order.
#!
#! This is a full linear proof-side check over the memory range. It does not use advice. Call this
#! before `find_key_value` when key sortedness is not already implied by another proof-side invariant.
#!
#! Input:  [start_ptr, end_ptr, ...]
#! Output: [start_ptr, end_ptr, ...]
#!
#! Panics if:
#! - start_ptr or end_ptr is not a u32 value.
#! - start_ptr is not word-aligned
#! - end_ptr is not double-word-aligned with start_ptr
#! - `start_ptr > end_ptr`
#! - any adjacent key pair is out of order.
@locals(2)
pub proc assert_sorted_keys
    # locals:
    # 0: current_ptr
    # 1: use_full_key
    dup add.8 loc_store.0
    push.1 loc_store.1
    # => [start_ptr, end_ptr, ...]

    dup.1 dup.1 u32assert2.err="sorted_array invariant: range pointers must be u32"
    u32gte assert.err="sorted_array invariant: start_ptr must be <= end_ptr"
    dup u32mod.4 assertz.err="sorted_array invariant: start_ptr must be word-aligned"
    dup.1 dup.1 sub u32mod.8 assertz.err="sorted_array invariant: key-value range must be double-word aligned"
    # => [start_ptr, end_ptr, ...]

    loc_load.0 dup.2 u32lt
    while.true
        loc_load.0 sub.8 loc_load.1 exec.load_key
        # => [PREVIOUS_KEY, start_ptr, end_ptr, ...]

        loc_load.0 loc_load.1 exec.load_key
        # => [CURRENT_KEY, PREVIOUS_KEY, start_ptr, end_ptr, ...]

        exec.word::gt
        not
        assert.err="sorted_array invariant: keys must be sorted"
        # => [start_ptr, end_ptr, ...]

        loc_load.0 add.8 loc_store.0
        # => [start_ptr, end_ptr, ...]

        loc_load.0 dup.2 u32lt
    end
end

#! Asserts that half-keys in an array of (key, value) word tuples are sorted in non-decreasing
#! lexicographic order.
#!
#! A half-key comparison ignores the two least significant key elements, matching
#! `find_half_key_value`.
#!
#! This is a full linear proof-side check over the memory range. It does not use advice. Call this
#! before `find_half_key_value` when half-key sortedness is not already implied by another proof-side
#! invariant.
#!
#! Input:  [start_ptr, end_ptr, ...]
#! Output: [start_ptr, end_ptr, ...]
#!
#! Panics if:
#! - start_ptr or end_ptr is not a u32 value.
#! - start_ptr is not word-aligned
#! - end_ptr is not double-word-aligned with start_ptr
#! - `start_ptr > end_ptr`
#! - any adjacent half-key pair is out of order.
@locals(2)
pub proc assert_sorted_half_keys
    # locals:
    # 0: current_ptr
    # 1: use_full_key
    dup add.8 loc_store.0
    push.0 loc_store.1
    # => [start_ptr, end_ptr, ...]

    dup.1 dup.1 u32assert2.err="sorted_array invariant: range pointers must be u32"
    u32gte assert.err="sorted_array invariant: start_ptr must be <= end_ptr"
    dup u32mod.4 assertz.err="sorted_array invariant: start_ptr must be word-aligned"
    dup.1 dup.1 sub u32mod.8 assertz.err="sorted_array invariant: key-value range must be double-word aligned"
    # => [start_ptr, end_ptr, ...]

    loc_load.0 dup.2 u32lt
    while.true
        loc_load.0 sub.8 loc_load.1 exec.load_key
        # => [PREVIOUS_HALF_KEY, start_ptr, end_ptr, ...]

        loc_load.0 loc_load.1 exec.load_key
        # => [CURRENT_HALF_KEY, PREVIOUS_HALF_KEY, start_ptr, end_ptr, ...]

        exec.word::gt
        not
        assert.err="sorted_array invariant: half-keys must be sorted"
        # => [start_ptr, end_ptr, ...]

        loc_load.0 add.8 loc_store.0
        # => [start_ptr, end_ptr, ...]

        loc_load.0 dup.2 u32lt
    end
end

#! Loads a key from the pointer.
#!
#! If use_full_key is 0, the key is loaded with the two least significant elements (word[0] and
#! word[1]) set to zero, keeping only word[2] and word[3] for half-key comparison.
#! If use_full_key is 1, the full key is loaded unchanged.
#!
#! This procedure avoids branches as an optimization.
#!
#! Inputs:  [use_full_key, key_ptr]
#! Outputs: [KEY]
#!
#! Cycles: 16
proc load_key
    padw movup.5 mem_loadw_le
    # => [w0, w1, w2, w3, use_full_key]

    # For half-key comparison (use_full_key=0), zero w0 and w1 (the BE least significant elements)
    # keeping w2 and w3 for comparison
    dup.4 mul
    # => [w0', w1, w2, w3, use_full_key] where w0' = w0 * use_full_key

    swap dup.4 mul swap
    # => [w0', w1', w2, w3, use_full_key] where w1' = w1 * use_full_key

    movup.4 drop
    # => [w0', w1', w2, w3]
end