Initial commit

src/embedded_flash/store/bitfield.rs

@@ -0,0 +1,172 @@
+// Copyright 2019 Google LLC
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//      http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+/// Defines a consecutive sequence of bits.
+#[derive(Copy, Clone)]
+pub struct BitRange {
+    /// The first bit of the sequence.
+    pub start: usize,
+
+    /// The length in bits of the sequence.
+    pub length: usize,
+}
+
+impl BitRange {
+    /// Returns the first bit following a bit range.
+    pub fn end(self) -> usize {
+        self.start + self.length
+    }
+}
+
+/// Defines a consecutive sequence of bytes.
+///
+/// The bits in those bytes are ignored which essentially creates a gap in a sequence of bits. The
+/// gap is necessarily at byte boundaries. This is used to ignore the user data in an entry
+/// essentially providing a view of the entry information (header and footer).
+#[derive(Copy, Clone)]
+pub struct ByteGap {
+    pub start: usize,
+    pub length: usize,
+}
+
+/// Empty gap. All bits count.
+pub const NO_GAP: ByteGap = ByteGap {
+    start: 0,
+    length: 0,
+};
+
+impl ByteGap {
+    /// Translates a bit to skip the gap.
+    fn shift(self, bit: usize) -> usize {
+        if bit < 8 * self.start {
+            bit
+        } else {
+            bit + 8 * self.length
+        }
+    }
+}
+
+/// Returns whether a bit is set in a sequence of bits.
+///
+/// The sequence of bits is little-endian (both for bytes and bits) and defined by the bits that
+/// are in `data` but not in `gap`.
+pub fn is_zero(bit: usize, data: &[u8], gap: ByteGap) -> bool {
+    let bit = gap.shift(bit);
+    debug_assert!(bit < 8 * data.len());
+    data[bit / 8] & (1 << (bit % 8)) == 0
+}
+
+/// Sets a bit to zero in a sequence of bits.
+///
+/// The sequence of bits is little-endian (both for bytes and bits) and defined by the bits that
+/// are in `data` but not in `gap`.
+pub fn set_zero(bit: usize, data: &mut [u8], gap: ByteGap) {
+    let bit = gap.shift(bit);
+    debug_assert!(bit < 8 * data.len());
+    data[bit / 8] &= !(1 << (bit % 8));
+}
+
+/// Returns a little-endian value in a sequence of bits.
+///
+/// The sequence of bits is little-endian (both for bytes and bits) and defined by the bits that
+/// are in `data` but not in `gap`. The range of bits where the value is stored in defined by
+/// `range`. The value must fit in a `usize`.
+pub fn get_range(range: BitRange, data: &[u8], gap: ByteGap) -> usize {
+    debug_assert!(range.length <= 8 * core::mem::size_of::<usize>());
+    let mut result = 0;
+    for i in 0..range.length {
+        if !is_zero(range.start + i, data, gap) {
+            result |= 1 << i;
+        }
+    }
+    result
+}
+
+/// Sets a little-endian value in a sequence of bits.
+///
+/// The sequence of bits is little-endian (both for bytes and bits) and defined by the bits that
+/// are in `data` but not in `gap`. The range of bits where the value is stored in defined by
+/// `range`. The bits set to 1 in `value` must also be set to `1` in the sequence of bits.
+pub fn set_range(range: BitRange, data: &mut [u8], gap: ByteGap, value: usize) {
+    debug_assert!(range.length == 8 * core::mem::size_of::<usize>() || value < 1 << range.length);
+    for i in 0..range.length {
+        if value & 1 << i == 0 {
+            set_zero(range.start + i, data, gap);
+        }
+    }
+}
+
+/// Tests the `is_zero` and `set_zero` pair of functions.
+#[test]
+fn zero_ok() {
+    const GAP: ByteGap = ByteGap {
+        start: 2,
+        length: 1,
+    };
+    for i in 0..24 {
+        assert!(!is_zero(i, &[0xffu8, 0xff, 0x00, 0xff] as &[u8], GAP));
+    }
+    // Tests reading and setting a bit. The result should have all bits set to 1 except for the bit
+    // to test and the gap.
+    fn test(bit: usize, result: &[u8]) {
+        assert!(is_zero(bit, result, GAP));
+        let mut data = vec![0xff; result.len()];
+        // Set the gap bits to 0.
+        for i in 0..GAP.length {
+            data[GAP.start + i] = 0x00;
+        }
+        set_zero(bit, &mut data, GAP);
+        assert_eq!(data, result);
+    }
+    test(0, &[0xfe, 0xff, 0x00, 0xff]);
+    test(1, &[0xfd, 0xff, 0x00, 0xff]);
+    test(2, &[0xfb, 0xff, 0x00, 0xff]);
+    test(7, &[0x7f, 0xff, 0x00, 0xff]);
+    test(8, &[0xff, 0xfe, 0x00, 0xff]);
+    test(15, &[0xff, 0x7f, 0x00, 0xff]);
+    test(16, &[0xff, 0xff, 0x00, 0xfe]);
+    test(17, &[0xff, 0xff, 0x00, 0xfd]);
+    test(23, &[0xff, 0xff, 0x00, 0x7f]);
+}
+
+/// Tests the `get_range` and `set_range` pair of functions.
+#[test]
+fn range_ok() {
+    // Tests reading and setting a range. The result should have all bits set to 1 except for the
+    // range to test and the gap.
+    fn test(start: usize, length: usize, value: usize, result: &[u8], gap: ByteGap) {
+        let range = BitRange { start, length };
+        assert_eq!(get_range(range, result, gap), value);
+        let mut data = vec![0xff; result.len()];
+        for i in 0..gap.length {
+            data[gap.start + i] = 0x00;
+        }
+        set_range(range, &mut data, gap, value);
+        assert_eq!(data, result);
+    }
+    test(0, 8, 42, &[42], NO_GAP);
+    test(3, 12, 0b11_0101, &[0b1010_1111, 0b1000_0001], NO_GAP);
+    test(0, 16, 0x1234, &[0x34, 0x12], NO_GAP);
+    test(4, 16, 0x1234, &[0x4f, 0x23, 0xf1], NO_GAP);
+    let mut gap = ByteGap {
+        start: 1,
+        length: 1,
+    };
+    test(3, 12, 0b11_0101, &[0b1010_1111, 0x00, 0b1000_0001], gap);
+    gap.length = 2;
+    test(0, 16, 0x1234, &[0x34, 0x00, 0x00, 0x12], gap);
+    gap.start = 2;
+    gap.length = 1;
+    test(4, 16, 0x1234, &[0x4f, 0x23, 0x00, 0xf1], gap);
+}

src/embedded_flash/store/format.rs

@@ -0,0 +1,514 @@
+// Copyright 2019 Google LLC
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//      http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+use super::super::{Index, Storage};
+use super::{bitfield, StoreConfig, StoreEntry, StoreError};
+use alloc::vec::Vec;
+
+/// Whether a user entry is a replace entry.
+pub enum IsReplace {
+    /// This is a replace entry.
+    Replace,
+
+    /// This is an insert entry.
+    Insert,
+}
+
+/// Helpers to parse the store format.
+///
+/// See the store module-level documentation for information about the format.
+pub struct Format {
+    pub word_size: usize,
+    pub page_size: usize,
+    pub num_pages: usize,
+    pub max_page_erases: usize,
+    pub num_tags: usize,
+
+    /// Whether an entry is present.
+    ///
+    /// - 0 for entries (user entries or internal entries).
+    /// - 1 for free space until the end of the page.
+    present_bit: usize,
+
+    /// Whether an entry is deleted.
+    ///
+    /// - 0 for deleted entries.
+    /// - 1 for alive entries.
+    deleted_bit: usize,
+
+    /// Whether an entry is internal.
+    ///
+    /// - 0 for internal entries.
+    /// - 1 for user entries.
+    internal_bit: usize,
+
+    /// Whether a user entry is a replace entry.
+    ///
+    /// - 0 for replace entries.
+    /// - 1 for insert entries.
+    replace_bit: usize,
+
+    /// The data length of a user entry.
+    length_range: bitfield::BitRange,
+
+    /// The tag of a user entry.
+    tag_range: bitfield::BitRange,
+
+    /// The page index of a replace entry.
+    replace_page_range: bitfield::BitRange,
+
+    /// The byte index of a replace entry.
+    replace_byte_range: bitfield::BitRange,
+
+    /// The index of the page to erase.
+    ///
+    /// This is only present for internal entries.
+    old_page_range: bitfield::BitRange,
+
+    /// The current erase count of the page to erase.
+    ///
+    /// This is only present for internal entries.
+    saved_erase_count_range: bitfield::BitRange,
+
+    /// Whether a page is initialized.
+    ///
+    /// - 0 for initialized pages.
+    /// - 1 for uninitialized pages.
+    initialized_bit: usize,
+
+    /// The erase count of a page.
+    erase_count_range: bitfield::BitRange,
+
+    /// Whether a page is being compacted.
+    ///
+    /// - 0 for pages being compacted.
+    /// - 1 otherwise.
+    compacting_bit: usize,
+
+    /// The page index to which a page is being compacted.
+    new_page_range: bitfield::BitRange,
+}
+
+impl Format {
+    /// Returns a helper to parse the store format for a given storage and config.
+    ///
+    /// # Errors
+    ///
+    /// Returns `None` if any of the following conditions does not hold:
+    /// - The word size must be a power of two.
+    /// - The page size must be a power of two.
+    /// - There should be at least 2 pages in the storage.
+    /// - It should be possible to write a word at least twice.
+    /// - It should be possible to erase a page at least once.
+    /// - There should be at least 1 tag.
+    pub fn new<S: Storage, C: StoreConfig>(storage: &S, config: &C) -> Option<Format> {
+        let word_size = storage.word_size();
+        let page_size = storage.page_size();
+        let num_pages = storage.num_pages();
+        let max_word_writes = storage.max_word_writes();
+        let max_page_erases = storage.max_page_erases();
+        let num_tags = config.num_tags();
+        if !(word_size.is_power_of_two()
+            && page_size.is_power_of_two()
+            && num_pages > 1
+            && max_word_writes >= 2
+            && max_page_erases > 0
+            && num_tags > 0)
+        {
+            return None;
+        }
+        // Compute how many bits we need to store the fields.
+        let page_bits = num_bits(num_pages);
+        let byte_bits = num_bits(page_size);
+        let tag_bits = num_bits(num_tags);
+        let erase_bits = num_bits(max_page_erases + 1);
+        // Compute the bit position of the fields.
+        let present_bit = 0;
+        let deleted_bit = present_bit + 1;
+        let internal_bit = deleted_bit + 1;
+        let replace_bit = internal_bit + 1;
+        let length_range = bitfield::BitRange {
+            start: replace_bit + 1,
+            length: byte_bits,
+        };
+        let tag_range = bitfield::BitRange {
+            start: length_range.end(),
+            length: tag_bits,
+        };
+        let replace_page_range = bitfield::BitRange {
+            start: tag_range.end(),
+            length: page_bits,
+        };
+        let replace_byte_range = bitfield::BitRange {
+            start: replace_page_range.end(),
+            length: byte_bits,
+        };
+        let old_page_range = bitfield::BitRange {
+            start: internal_bit + 1,
+            length: page_bits,
+        };
+        let saved_erase_count_range = bitfield::BitRange {
+            start: old_page_range.end(),
+            length: erase_bits,
+        };
+        let initialized_bit = 0;
+        let erase_count_range = bitfield::BitRange {
+            start: initialized_bit + 1,
+            length: erase_bits,
+        };
+        let compacting_bit = erase_count_range.end();
+        let new_page_range = bitfield::BitRange {
+            start: compacting_bit + 1,
+            length: page_bits,
+        };
+        let format = Format {
+            word_size,
+            page_size,
+            num_pages,
+            max_page_erases,
+            num_tags,
+            present_bit,
+            deleted_bit,
+            internal_bit,
+            replace_bit,
+            length_range,
+            tag_range,
+            replace_page_range,
+            replace_byte_range,
+            old_page_range,
+            saved_erase_count_range,
+            initialized_bit,
+            erase_count_range,
+            compacting_bit,
+            new_page_range,
+        };
+        // Make sure all the following conditions hold:
+        // - The page header is one word.
+        // - The internal entry is one word.
+        // - The entry header fits in one word.
+        if format.page_header_size() != word_size
+            || format.internal_entry_size() != word_size
+            || format.header_size() > word_size
+        {
+            return None;
+        }
+        Some(format)
+    }
+
+    /// Ensures a user entry is valid.
+    pub fn validate_entry(&self, entry: StoreEntry) -> Result<(), StoreError> {
+        if entry.tag >= self.num_tags {
+            return Err(StoreError::InvalidTag);
+        }
+        if entry.data.len() >= self.page_size {
+            return Err(StoreError::StoreFull);
+        }
+        Ok(())
+    }
+
+    /// Returns the entry header length in bytes.
+    ///
+    /// This is the smallest number of bytes necessary to store all fields of the entry info up to
+    /// and including `length`.
+    pub fn header_size(&self) -> usize {
+        self.bits_to_bytes(self.length_range.end())
+    }
+
+    /// Returns the entry info length in bytes.
+    ///
+    /// This is the number of bytes necessary to store all fields of the entry info. This also
+    /// includes the internal padding to protect the `committed` bit from the `deleted` bit.
+    fn info_size(&self, is_replace: IsReplace) -> usize {
+        let suffix_bits = 2; // committed + complete
+        let info_bits = match is_replace {
+            IsReplace::Replace => self.replace_byte_range.end() + suffix_bits,
+            IsReplace::Insert => self.tag_range.end() + suffix_bits,
+        };
+        let info_size = self.bits_to_bytes(info_bits);
+        // If the suffix bits would end up in the header, we need to add one byte for them.
+        if info_size == self.header_size() {
+            info_size + 1
+        } else {
+            info_size
+        }
+    }
+
+    /// Returns the length in bytes of an entry.
+    ///
+    /// This depends on the length of the user data and whether the entry replaces an old entry or
+    /// is an insertion. This also includes the internal padding to protect the `committed` bit from
+    /// the `deleted` bit.
+    pub fn entry_size(&self, is_replace: IsReplace, length: usize) -> usize {
+        let mut entry_size = length + self.info_size(is_replace);
+        let word_size = self.word_size;
+        entry_size = self.align_word(entry_size);
+        // The entry must be at least 2 words such that the `committed` and `deleted` bits are on
+        // different words.
+        if entry_size == word_size {
+            entry_size += word_size;
+        }
+        entry_size
+    }
+
+    /// Returns the length in bytes of an internal entry.
+    pub fn internal_entry_size(&self) -> usize {
+        let length = self.bits_to_bytes(self.saved_erase_count_range.end());
+        self.align_word(length)
+    }
+
+    pub fn is_present(&self, header: &[u8]) -> bool {
+        bitfield::is_zero(self.present_bit, header, bitfield::NO_GAP)
+    }
+
+    pub fn set_present(&self, header: &mut [u8]) {
+        bitfield::set_zero(self.present_bit, header, bitfield::NO_GAP)
+    }
+
+    pub fn is_deleted(&self, header: &[u8]) -> bool {
+        bitfield::is_zero(self.deleted_bit, header, bitfield::NO_GAP)
+    }
+
+    /// Returns whether an entry is present and not deleted.
+    pub fn is_alive(&self, header: &[u8]) -> bool {
+        self.is_present(header) && !self.is_deleted(header)
+    }
+
+    pub fn set_deleted(&self, header: &mut [u8]) {
+        bitfield::set_zero(self.deleted_bit, header, bitfield::NO_GAP)
+    }
+
+    pub fn is_internal(&self, header: &[u8]) -> bool {
+        bitfield::is_zero(self.internal_bit, header, bitfield::NO_GAP)
+    }
+
+    pub fn set_internal(&self, header: &mut [u8]) {
+        bitfield::set_zero(self.internal_bit, header, bitfield::NO_GAP)
+    }
+
+    pub fn is_replace(&self, header: &[u8]) -> IsReplace {
+        if bitfield::is_zero(self.replace_bit, header, bitfield::NO_GAP) {
+            IsReplace::Replace
+        } else {
+            IsReplace::Insert
+        }
+    }
+
+    fn set_replace(&self, header: &mut [u8]) {
+        bitfield::set_zero(self.replace_bit, header, bitfield::NO_GAP)
+    }
+
+    pub fn get_length(&self, header: &[u8]) -> usize {
+        bitfield::get_range(self.length_range, header, bitfield::NO_GAP)
+    }
+
+    fn set_length(&self, header: &mut [u8], length: usize) {
+        bitfield::set_range(self.length_range, header, bitfield::NO_GAP, length)
+    }
+
+    pub fn get_data<'a>(&self, entry: &'a [u8]) -> &'a [u8] {
+        &entry[self.header_size()..][..self.get_length(entry)]
+    }
+
+    /// Returns the span of user data in an entry.
+    ///
+    /// The complement of this gap in the entry is exactly the entry info. The header is before the
+    /// gap and the footer is after the gap.
+    fn entry_gap(&self, entry: &[u8]) -> bitfield::ByteGap {
+        let start = self.header_size();
+        let length = self.get_length(entry);
+        bitfield::ByteGap { start, length }
+    }
+
+    pub fn get_tag(&self, entry: &[u8]) -> usize {
+        bitfield::get_range(self.tag_range, entry, self.entry_gap(entry))
+    }
+
+    fn set_tag(&self, entry: &mut [u8], tag: usize) {
+        bitfield::set_range(self.tag_range, entry, self.entry_gap(entry), tag)
+    }
+
+    pub fn get_replace_index(&self, entry: &[u8]) -> Index {
+        let gap = self.entry_gap(entry);
+        let page = bitfield::get_range(self.replace_page_range, entry, gap);
+        let byte = bitfield::get_range(self.replace_byte_range, entry, gap);
+        Index { page, byte }
+    }
+
+    fn set_replace_page(&self, entry: &mut [u8], page: usize) {
+        bitfield::set_range(self.replace_page_range, entry, self.entry_gap(entry), page)
+    }
+
+    fn set_replace_byte(&self, entry: &mut [u8], byte: usize) {
+        bitfield::set_range(self.replace_byte_range, entry, self.entry_gap(entry), byte)
+    }
+
+    /// Returns the bit position of the `committed` bit.
+    ///
+    /// This cannot be precomputed like other fields since it depends on the length of the entry.
+    fn committed_bit(&self, entry: &[u8]) -> usize {
+        8 * entry.len() - 2
+    }
+
+    /// Returns the bit position of the `complete` bit.
+    ///
+    /// This cannot be precomputed like other fields since it depends on the length of the entry.
+    fn complete_bit(&self, entry: &[u8]) -> usize {
+        8 * entry.len() - 1
+    }
+
+    pub fn is_committed(&self, entry: &[u8]) -> bool {
+        bitfield::is_zero(self.committed_bit(entry), entry, bitfield::NO_GAP)
+    }
+
+    pub fn set_committed(&self, entry: &mut [u8]) {
+        bitfield::set_zero(self.committed_bit(entry), entry, bitfield::NO_GAP)
+    }
+
+    pub fn is_complete(&self, entry: &[u8]) -> bool {
+        bitfield::is_zero(self.complete_bit(entry), entry, bitfield::NO_GAP)
+    }
+
+    fn set_complete(&self, entry: &mut [u8]) {
+        bitfield::set_zero(self.complete_bit(entry), entry, bitfield::NO_GAP)
+    }
+
+    pub fn get_old_page(&self, header: &[u8]) -> usize {
+        bitfield::get_range(self.old_page_range, header, bitfield::NO_GAP)
+    }
+
+    pub fn set_old_page(&self, header: &mut [u8], old_page: usize) {
+        bitfield::set_range(self.old_page_range, header, bitfield::NO_GAP, old_page)
+    }
+
+    pub fn get_saved_erase_count(&self, header: &[u8]) -> usize {
+        bitfield::get_range(self.saved_erase_count_range, header, bitfield::NO_GAP)
+    }
+
+    pub fn set_saved_erase_count(&self, header: &mut [u8], erase_count: usize) {
+        bitfield::set_range(
+            self.saved_erase_count_range,
+            header,
+            bitfield::NO_GAP,
+            erase_count,
+        )
+    }
+
+    /// Builds an entry for replace or insert operations.
+    pub fn build_entry(&self, replace: Option<Index>, user_entry: StoreEntry) -> Vec<u8> {
+        let StoreEntry { tag, data } = user_entry;
+        let is_replace = match replace {
+            None => IsReplace::Insert,
+            Some(_) => IsReplace::Replace,
+        };
+        let entry_len = self.entry_size(is_replace, data.len());
+        let mut entry = Vec::with_capacity(entry_len);
+        // Build the header.
+        entry.resize(self.header_size(), 0xff);
+        self.set_present(&mut entry[..]);
+        self.set_length(&mut entry[..], data.len());
+        // Add the data.
+        entry.extend_from_slice(data);
+        // Build the footer.
+        entry.resize(entry_len, 0xff);
+        self.set_tag(&mut entry[..], tag);
+        self.set_complete(&mut entry[..]);
+        match replace {
+            None => self.set_committed(&mut entry[..]),
+            Some(Index { page, byte }) => {
+                self.set_replace(&mut entry[..]);
+                self.set_replace_page(&mut entry[..], page);
+                self.set_replace_byte(&mut entry[..], byte);
+            }
+        }
+        entry
+    }
+
+    /// Builds an entry for replace or insert operations.
+    pub fn build_erase_entry(&self, old_page: usize, saved_erase_count: usize) -> Vec<u8> {
+        let mut entry = vec![0xff; self.internal_entry_size()];
+        self.set_present(&mut entry[..]);
+        self.set_internal(&mut entry[..]);
+        self.set_old_page(&mut entry[..], old_page);
+        self.set_saved_erase_count(&mut entry[..], saved_erase_count);
+        entry
+    }
+
+    /// Returns the length in bytes of a page header entry.
+    ///
+    /// This includes the word padding.
+    pub fn page_header_size(&self) -> usize {
+        self.align_word(self.bits_to_bytes(self.erase_count_range.end()))
+    }
+
+    pub fn is_initialized(&self, header: &[u8]) -> bool {
+        bitfield::is_zero(self.initialized_bit, header, bitfield::NO_GAP)
+    }
+
+    pub fn set_initialized(&self, header: &mut [u8]) {
+        bitfield::set_zero(self.initialized_bit, header, bitfield::NO_GAP)
+    }
+
+    pub fn get_erase_count(&self, header: &[u8]) -> usize {
+        bitfield::get_range(self.erase_count_range, header, bitfield::NO_GAP)
+    }
+
+    pub fn set_erase_count(&self, header: &mut [u8], count: usize) {
+        bitfield::set_range(self.erase_count_range, header, bitfield::NO_GAP, count)
+    }
+
+    pub fn is_compacting(&self, header: &[u8]) -> bool {
+        bitfield::is_zero(self.compacting_bit, header, bitfield::NO_GAP)
+    }
+
+    pub fn set_compacting(&self, header: &mut [u8]) {
+        bitfield::set_zero(self.compacting_bit, header, bitfield::NO_GAP)
+    }
+
+    pub fn get_new_page(&self, header: &[u8]) -> usize {
+        bitfield::get_range(self.new_page_range, header, bitfield::NO_GAP)
+    }
+
+    pub fn set_new_page(&self, header: &mut [u8], new_page: usize) {
+        bitfield::set_range(self.new_page_range, header, bitfield::NO_GAP, new_page)
+    }
+
+    /// Returns the smallest word boundary greater or equal to a value.
+    fn align_word(&self, value: usize) -> usize {
+        let word_size = self.word_size;
+        (value + word_size - 1) / word_size * word_size
+    }
+
+    /// Returns the minimum number of bytes to represent a given number of bits.
+    fn bits_to_bytes(&self, bits: usize) -> usize {
+        (bits + 7) / 8
+    }
+}
+
+/// Returns the number of bits necessary to write numbers smaller than `x`.
+fn num_bits(x: usize) -> usize {
+    x.next_power_of_two().trailing_zeros() as usize
+}
+
+#[test]
+fn num_bits_ok() {
+    assert_eq!(num_bits(0), 0);
+    assert_eq!(num_bits(1), 0);
+    assert_eq!(num_bits(2), 1);
+    assert_eq!(num_bits(3), 2);
+    assert_eq!(num_bits(4), 2);
+    assert_eq!(num_bits(5), 3);
+    assert_eq!(num_bits(8), 3);
+    assert_eq!(num_bits(9), 4);
+    assert_eq!(num_bits(16), 4);
+}