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mlt_core/codecs/
morton.rs

1use geo_types::Coord;
2use wide::u32x8;
3
4use crate::decoder::Morton;
5use crate::encoder::model::CurveParams;
6use crate::{Decoder, MltError, MltResult};
7
8const LANES: usize = 8;
9
10// ── Bit interleaving ─────────────────────────────────────────────────────────
11
12/// Interleave the lower 16 bits of `x` and `y` into a 32-bit Morton code.
13///
14/// Even bit positions (0, 2, 4, …) encode `x`; odd positions (1, 3, 5, …)
15/// encode `y`. Spatially adjacent `(x, y)` pairs produce numerically
16/// adjacent codes, giving Z-order locality when used as a sort key.
17#[must_use]
18#[inline]
19pub fn interleave_bits(coord: Coord<u32>) -> u32 {
20    // Spread each input's lower 16 bits into every other bit position, then
21    // OR the two together: x occupies even positions (0, 2, 4, …) and y
22    // occupies odd positions (1, 3, 5, …).
23    let mut sx = coord.x & 0xFFFF;
24    sx = (sx | (sx << 8)) & 0x00FF_00FF;
25    sx = (sx | (sx << 4)) & 0x0F0F_0F0F;
26    sx = (sx | (sx << 2)) & 0x3333_3333;
27    sx = (sx | (sx << 1)) & 0x5555_5555;
28
29    let mut sy = coord.y & 0xFFFF;
30    sy = (sy | (sy << 8)) & 0x00FF_00FF;
31    sy = (sy | (sy << 4)) & 0x0F0F_0F0F;
32    sy = (sy | (sy << 2)) & 0x3333_3333;
33    sy = (sy | (sy << 1)) & 0x5555_5555;
34
35    sx | (sy << 1)
36}
37
38/// Interleave two 32-bit values into a 64-bit Morton code, `even` on the even bits and `odd` on the odd bits.
39#[cfg(feature = "unstable-v2")]
40#[must_use]
41#[inline]
42pub fn interleave_u32(even: u32, odd: u32) -> u64 {
43    spread_u32(even) | (spread_u32(odd) << 1)
44}
45
46/// Split a 64-bit Morton code back into its even-bit and odd-bit values.
47#[cfg(feature = "unstable-v2")]
48#[must_use]
49#[inline]
50pub fn deinterleave_u64(code: u64) -> (u32, u32) {
51    (compact_u64(code), compact_u64(code >> 1))
52}
53
54#[cfg(feature = "unstable-v2")]
55fn spread_u32(value: u32) -> u64 {
56    let mut s = u64::from(value);
57    s = (s | (s << 16)) & 0x0000_FFFF_0000_FFFF;
58    s = (s | (s << 8)) & 0x00FF_00FF_00FF_00FF;
59    s = (s | (s << 4)) & 0x0F0F_0F0F_0F0F_0F0F;
60    s = (s | (s << 2)) & 0x3333_3333_3333_3333;
61    s = (s | (s << 1)) & 0x5555_5555_5555_5555;
62    s
63}
64
65#[cfg(feature = "unstable-v2")]
66fn compact_u64(code: u64) -> u32 {
67    let mut c = code & 0x5555_5555_5555_5555;
68    c = (c | (c >> 1)) & 0x3333_3333_3333_3333;
69    c = (c | (c >> 2)) & 0x0F0F_0F0F_0F0F_0F0F;
70    c = (c | (c >> 4)) & 0x00FF_00FF_00FF_00FF;
71    c = (c | (c >> 8)) & 0x0000_FFFF_0000_FFFF;
72    c = (c | (c >> 16)) & 0x0000_0000_FFFF_FFFF;
73    u32::try_from(c).expect("infallible: the last mask keeps only the low 32 bits")
74}
75
76/// Compute a Z-order (Morton) sort key from signed integer coordinates.
77///
78/// `shift` is applied to both axes before bit-interleaving to move the
79/// coordinate origin into the non-negative range. It should be computed
80/// once across the entire feature set (typically `min.unsigned_abs()` when
81/// `min < 0`, else `0`) so that the keys are comparable across features.
82///
83/// Each shifted component is truncated to 16 bits before interleaving, so
84/// the returned key fits in a `u32` (32 interleaved bits). This is
85/// sufficient for any tile coordinate system with extent ≤ 65 535.
86#[must_use]
87#[inline]
88pub fn morton_sort_key(c: Coord<i32>, params: CurveParams) -> u32 {
89    debug_assert!(params.bits >= 1);
90    #[expect(
91        clippy::cast_possible_truncation,
92        clippy::cast_sign_loss,
93        reason = "shift brings value into [0, extent]; masked to 16 bits immediately after"
94    )]
95    let sx = ((i64::from(c.x) + i64::from(params.shift)) as u32) & 0xFFFF;
96    #[expect(
97        clippy::cast_possible_truncation,
98        clippy::cast_sign_loss,
99        reason = "shift brings value into [0, extent]; masked to 16 bits immediately after"
100    )]
101    let sy = ((i64::from(c.y) + i64::from(params.shift)) as u32) & 0xFFFF;
102    interleave_bits((sx, sy).into())
103}
104
105// ── Encoder ─────────────────────────────────────────────────────────────────
106impl Morton {
107    /// Compute `ZOrderCurve` parameters from the vertex value range.
108    ///
109    /// Returns a [`Morton`] whose `bits` and `shift` match Java's
110    /// `SpaceFillingCurve` implementation.
111    pub fn from_vertices(vertices: &[i32]) -> MltResult<Self> {
112        let min_v = vertices.iter().copied().min().unwrap_or(0);
113        let max_v = vertices.iter().copied().max().unwrap_or(0);
114        let shift: u32 = if min_v < 0 { min_v.unsigned_abs() } else { 0 };
115        let tile_extent = i64::from(max_v) + i64::from(shift);
116        let extent =
117            u32::try_from(tile_extent).expect("infallible: max_v + shift lies in 0..=u32::MAX");
118        // ceil(log2(extent + 1)), matching Java's Math.ceil(Math.log(...) / Math.log(2)).
119        // Computed with integer arithmetic: for te >= 1, this equals `te.bit_width()`.
120        // Capped at 16: Morton codes are u32, so each axis may use at most 16 bits.
121        let required_bits = extent.bit_width();
122        if required_bits > 16 {
123            return Err(MltError::VertexMortonNotCompatibleWithExtent {
124                extent,
125                required_bits,
126            });
127        }
128        Self::new(required_bits, shift)
129    }
130
131    /// Encode a single `(x, y)` coordinate pair to its Z-order (Morton) code.
132    ///
133    /// `bits` (≤ 16) bits are used per axis; `shift` is added to each
134    /// component before interleaving so that negative coordinates map to non-negative values.
135    #[inline]
136    pub fn encode_morton(self, x: i32, y: i32) -> MltResult<u32> {
137        let sx = u32::try_from(i64::from(x) + i64::from(self.shift))?;
138        let sy = u32::try_from(i64::from(y) + i64::from(self.shift))?;
139        let mut code = 0u32;
140        for i in 0..self.bits {
141            // bits are capped at 16, so 2*i+1 ≤ 31 - no shift overflow.
142            code |= ((sx >> i) & 1) << (2 * i);
143            code |= ((sy >> i) & 1) << (2 * i + 1);
144        }
145        Ok(code)
146    }
147}
148
149impl Morton {
150    /// Decode a single Morton code to a `Coord<i32>`, applying `shift`.
151    #[inline]
152    fn decode_one(self, morton_code: u32) -> Coord<i32> {
153        let mut x = 0u32;
154        let mut y = 0u32;
155        for i in 0..self.bits {
156            let bit_mask = 1u32 << (2 * i);
157            x |= (morton_code & bit_mask) >> i;
158            y |= ((morton_code >> 1) & bit_mask) >> i;
159        }
160        Coord::<i32> {
161            x: x.wrapping_sub(self.shift).cast_signed(),
162            y: y.wrapping_sub(self.shift).cast_signed(),
163        }
164    }
165
166    /// Decode delta-encoded Morton codes to flat `[x0, y0, x1, y1, ...]`, charging `dec` for the output.
167    ///
168    /// Each input value is a signed delta (stored as u32 with wrapping arithmetic)
169    /// relative to the previous Morton code. The sequential prefix sum is computed
170    /// in chunks of 8 into a stack-allocated buffer, which is then SIMD-decoded.
171    /// This keeps the working set in registers / L1 cache.
172    pub fn decode_delta(self, data: &[u32], dec: &mut Decoder) -> MltResult<Vec<i32>> {
173        let alloc_size = data.len() * 2;
174        let mut out = dec.alloc(alloc_size)?;
175        let shift_vec = u32x8::splat(self.shift);
176
177        let mut prev = 0i32;
178        let (chunks, remainder) = data.as_chunks::<LANES>();
179
180        for chunk in chunks {
181            // Sequential prefix sum into a stack buffer - no heap allocation.
182            let mut buf = [0u32; LANES];
183            for (b, &d) in buf.iter_mut().zip(chunk.iter()) {
184                prev = prev.wrapping_add(d.cast_signed());
185                *b = prev.cast_unsigned();
186            }
187            self.decode_chunk(buf, shift_vec, &mut out);
188        }
189
190        // Scalar tail for any codes that didn't fill a full SIMD chunk.
191        for &d in remainder {
192            prev = prev.wrapping_add(d.cast_signed());
193            let coord = self.decode_one(prev.cast_unsigned());
194            out.push(coord.x);
195            out.push(coord.y);
196        }
197
198        dec.adjust_alloc(&out, alloc_size)
199            .expect("infallible: two coordinates pushed per code fill alloc_size exactly");
200        Ok(out)
201    }
202
203    /// SIMD-decode a chunk of exactly 8 resolved Morton codes into the output buffer.
204    ///
205    /// Each code has already been resolved to its absolute value (no delta pending).
206    /// Even-indexed bits encode x, odd-indexed bits encode y.
207    #[inline]
208    fn decode_chunk(self, buf: [u32; LANES], shift_vec: u32x8, out: &mut Vec<i32>) {
209        let codes = u32x8::from(buf);
210        // Odd bits become even after shifting right by 1, giving the y component.
211        let codes_y = codes >> 1;
212
213        let mut x_vec = u32x8::ZERO;
214        let mut y_vec = u32x8::ZERO;
215
216        for i in 0..self.bits {
217            // Mask for the bit position 2*i in the original Morton code.
218            let bit_mask = u32x8::splat(1u32 << (2 * i));
219            // Extract bit 2*i from each code and shift it down to position i.
220            x_vec |= (codes & bit_mask) >> i;
221            y_vec |= (codes_y & bit_mask) >> i;
222        }
223
224        let xs: [u32; LANES] = (x_vec - shift_vec).into();
225        let ys: [u32; LANES] = (y_vec - shift_vec).into();
226
227        for lane in 0..LANES {
228            out.push(xs[lane].cast_signed());
229            out.push(ys[lane].cast_signed());
230        }
231    }
232}
233
234#[cfg(test)]
235mod tests {
236
237    use rstest::rstest;
238
239    use super::*;
240    use crate::test_helpers::{dec, starved_dec};
241
242    const fn c(x: i32, y: i32) -> Coord<i32> {
243        Coord::<i32> { x, y }
244    }
245
246    const fn p(shift: u32, bits: u32) -> CurveParams {
247        CurveParams { shift, bits }
248    }
249
250    // ── interleave_bits / morton_sort_key ─────────────────────────────────────
251
252    fn spread_bits(mut tx: u32) -> u32 {
253        tx = (tx | (tx << 8)) & 0x00FF_00FF;
254        tx = (tx | (tx << 4)) & 0x0F0F_0F0F;
255        tx = (tx | (tx << 2)) & 0x3333_3333;
256        tx = (tx | (tx << 1)) & 0x5555_5555;
257        tx
258    }
259
260    fn compact_bits(mut tx: u32) -> u32 {
261        tx &= 0x5555_5555;
262        tx = (tx | (tx >> 1)) & 0x3333_3333;
263        tx = (tx | (tx >> 2)) & 0x0F0F_0F0F;
264        tx = (tx | (tx >> 4)) & 0x00FF_00FF;
265        tx = (tx | (tx >> 8)) & 0x0000_FFFF;
266        tx
267    }
268
269    #[test]
270    fn spread_then_compact_is_identity() {
271        for x in 0u32..=0xFFFF {
272            assert_eq!(compact_bits(spread_bits(x)), x, "round-trip failed for {x}");
273        }
274    }
275
276    #[test]
277    fn spread_bits_places_bit0_at_position0() {
278        assert_eq!(spread_bits(1), 1);
279    }
280
281    #[test]
282    fn spread_bits_places_bit1_at_position2() {
283        assert_eq!(spread_bits(2), 4);
284    }
285
286    #[test]
287    fn spread_bits_places_bit2_at_position4() {
288        assert_eq!(spread_bits(4), 16);
289    }
290
291    #[cfg(feature = "unstable-v2")]
292    #[rstest]
293    #[case::zero(0, 0, 0)]
294    #[case::even_only(1, 0, 1)]
295    #[case::odd_only(0, 1, 2)]
296    #[case::one_byte_varint(15, 7, 0x7F)]
297    #[case::u32_max_both(u32::MAX, u32::MAX, u64::MAX)]
298    #[case::u32_max_even(u32::MAX, 0, 0x5555_5555_5555_5555)]
299    fn interleave_u32_places_even_and_odd_bits(
300        #[case] even: u32,
301        #[case] odd: u32,
302        #[case] code: u64,
303    ) {
304        assert_eq!(interleave_u32(even, odd), code);
305        assert_eq!(deinterleave_u64(code), (even, odd));
306    }
307
308    #[test]
309    fn origin_maps_to_zero() {
310        assert_eq!(morton_sort_key(c(0, 0), p(0, 16)), 0);
311    }
312
313    #[test]
314    fn x_axis_produces_even_bits() {
315        assert_eq!(
316            morton_sort_key(c(1, 0), p(0, 16)),
317            1,
318            "x bit 0 lands at Morton bit 0"
319        );
320        assert_eq!(
321            morton_sort_key(c(2, 0), p(0, 16)),
322            4,
323            "x bit 1 lands at Morton bit 2"
324        );
325    }
326
327    #[test]
328    fn y_axis_produces_odd_bits() {
329        assert_eq!(
330            morton_sort_key(c(0, 1), p(0, 16)),
331            2,
332            "y bit 0 lands at Morton bit 1"
333        );
334        assert_eq!(
335            morton_sort_key(c(0, 2), p(0, 16)),
336            8,
337            "y bit 1 lands at Morton bit 3"
338        );
339    }
340
341    #[test]
342    fn negative_coords_shift_correctly() {
343        assert_eq!(
344            morton_sort_key(c(-1, -1), p(1, 16)),
345            0,
346            "a shift of 1 maps (-1, -1) onto (0, 0)"
347        );
348        assert_eq!(
349            morton_sort_key(c(-1, 0), p(1, 16)),
350            2,
351            "a shift of 1 maps (-1, 0) onto (0, 1)"
352        );
353    }
354
355    #[test]
356    fn spatial_locality_z_order() {
357        let k00 = morton_sort_key(c(0, 0), p(0, 16));
358        let k10 = morton_sort_key(c(1, 0), p(0, 16));
359        let k01 = morton_sort_key(c(0, 1), p(0, 16));
360        let k11 = morton_sort_key(c(1, 1), p(0, 16));
361        assert!(k00 < k10, "(0,0) precedes (1,0) in Z-order");
362        assert!(k10 < k01, "(1,0) precedes (0,1) in Z-order");
363        assert!(k01 < k11, "(0,1) precedes (1,1) in Z-order");
364    }
365
366    #[test]
367    fn interleave_round_trips_via_deinterleave() {
368        for x in 0u32..16 {
369            for y in 0u32..16 {
370                let code = interleave_bits((x, y).into());
371                let mut rx = 0u32;
372                let mut ry = 0u32;
373                for bit in 0..16 {
374                    rx |= ((code >> (2 * bit)) & 1) << bit;
375                    ry |= ((code >> (2 * bit + 1)) & 1) << bit;
376                }
377                assert_eq!(rx, x, "x mismatch for ({x}, {y})");
378                assert_eq!(ry, y, "y mismatch for ({x}, {y})");
379            }
380        }
381    }
382
383    // ── Morton encode/decode tests ────────────────────────────────────────────
384
385    const NUM_BITS: u32 = 15;
386    const COORD_SHIFT: u32 = 1 << (NUM_BITS - 1);
387    const MORTON: Morton = Morton {
388        bits: NUM_BITS,
389        shift: COORD_SHIFT,
390    };
391
392    #[must_use]
393    #[inline]
394    pub fn encode_morton_15(coord: Coord<u32>) -> u32 {
395        let mut code = 0u32;
396        for bit in 0..15 {
397            code |= ((coord.x >> bit) & 1) << (2 * bit);
398            code |= ((coord.y >> bit) & 1) << (2 * bit + 1);
399        }
400        code
401    }
402
403    #[test]
404    fn test_decode_morton_delta_origin() {
405        let code = encode_morton_15((COORD_SHIFT, COORD_SHIFT).into());
406        let decoded = MORTON.decode_delta(&[code], &mut dec()).unwrap();
407        assert_eq!(
408            decoded,
409            [0, 0],
410            "the code for (COORD_SHIFT, COORD_SHIFT) sits at the origin"
411        );
412    }
413
414    #[test]
415    fn test_decode_morton_delta_known_values() {
416        let x: u32 = 1;
417        let y: u32 = 2;
418        let code = encode_morton_15((x, y).into());
419        let expected_x = x.cast_signed() - COORD_SHIFT.cast_signed();
420        let expected_y = y.cast_signed() - COORD_SHIFT.cast_signed();
421        let decoded = MORTON.decode_delta(&[code], &mut dec()).unwrap();
422        assert_eq!(
423            decoded,
424            [expected_x, expected_y],
425            "decoding subtracts COORD_SHIFT from each axis"
426        );
427    }
428
429    #[test]
430    fn test_decode_morton_delta_scalar_tail() {
431        let pairs: [Coord<u32>; _] = [(0, 1).into(), (2, 3).into(), (4, 5).into()];
432        let codes: Vec<u32> = pairs.iter().map(|&c| encode_morton_15(c)).collect();
433        let result = MORTON
434            .decode_delta(&signed_deltas(&codes), &mut dec())
435            .unwrap();
436        let expected = expected_coords(&pairs);
437        assert_eq!(result, expected, "3 codes take the scalar tail alone");
438    }
439
440    #[test]
441    fn test_decode_morton_delta_full_simd_chunk() {
442        let pairs: [Coord<u32>; _] = [
443            (0, 0).into(),
444            (1, 0).into(),
445            (0, 1).into(),
446            (1, 1).into(),
447            (2, 3).into(),
448            (7, 5).into(),
449            (10, 9).into(),
450            (15, 15).into(),
451        ];
452        let codes: Vec<u32> = pairs.iter().map(|&c| encode_morton_15(c)).collect();
453        let result = MORTON
454            .decode_delta(&signed_deltas(&codes), &mut dec())
455            .unwrap();
456        let expected = expected_coords(&pairs);
457        assert_eq!(result, expected, "8 codes fill one SIMD chunk with no tail");
458    }
459
460    #[test]
461    fn test_decode_morton_delta_simd_plus_tail() {
462        let pairs: Vec<Coord<u32>> = (0..11u32)
463            .map(|i| (i * 3 % 100, i * 7 % 100).into())
464            .collect();
465        let codes: Vec<u32> = pairs.iter().map(|&c| encode_morton_15(c)).collect();
466        let result = MORTON
467            .decode_delta(&signed_deltas(&codes), &mut dec())
468            .unwrap();
469        let expected = expected_coords(&pairs);
470        assert_eq!(
471            result, expected,
472            "11 codes take one SIMD chunk plus a tail of 3"
473        );
474    }
475
476    #[test]
477    fn test_decode_morton_delta_empty() {
478        assert_eq!(
479            MORTON.decode_delta(&[], &mut dec()).unwrap(),
480            [] as [i32; 0]
481        );
482    }
483
484    #[test]
485    fn test_decode_morton_delta_identity_with_zero_deltas() {
486        let deltas = vec![0u32; 3];
487        let result = MORTON.decode_delta(&deltas, &mut dec()).unwrap();
488        let shift = -COORD_SHIFT.cast_signed();
489        assert_eq!(
490            result,
491            vec![shift, shift, shift, shift, shift, shift],
492            "zero deltas resolve every code to 0, which decodes to (-COORD_SHIFT, -COORD_SHIFT)"
493        );
494    }
495
496    #[test]
497    fn test_decode_morton_delta_matches_codes_after_prefix_sum() {
498        let pairs: Vec<Coord<u32>> = (0..11u32)
499            .map(|i| (i * 5 % 200, i * 9 % 200).into())
500            .collect();
501        let codes: Vec<u32> = pairs.iter().map(|&c| encode_morton_15(c)).collect();
502        let result = MORTON
503            .decode_delta(&signed_deltas(&codes), &mut dec())
504            .unwrap();
505        assert_eq!(
506            result,
507            expected_coords(&pairs),
508            "the prefix sum rebuilds the absolute codes"
509        );
510    }
511
512    #[test]
513    fn test_decode_morton_delta_wrapping() {
514        let pairs: [Coord<u32>; _] = [(500, 300).into(), (10, 10).into()];
515        let codes: Vec<u32> = pairs.iter().map(|&c| encode_morton_15(c)).collect();
516        assert_eq!(
517            MORTON
518                .decode_delta(&signed_deltas(&codes), &mut dec())
519                .unwrap(),
520            expected_coords(&pairs),
521            "a delta onto a smaller code wraps and still resolves"
522        );
523    }
524
525    #[test]
526    fn decode_delta_past_the_memory_budget_is_rejected() {
527        let err = MORTON
528            .decode_delta(&[0, 1], &mut starved_dec())
529            .unwrap_err();
530        assert!(
531            matches!(err, MltError::MemoryLimitExceeded { .. }),
532            "{err:?}"
533        );
534    }
535
536    // ── from_vertices / encode_morton ─────────────────────────────────────────
537
538    #[rstest]
539    #[case::empty(&[], 0, 0)]
540    #[case::non_negative_needs_no_shift(&[0, 100], 0, 7)]
541    #[case::negative_min_shifts_onto_zero(&[-5, 10], 5, 4)]
542    #[case::widest_accepted_extent(&[0, 65_535], 0, 16)]
543    fn from_vertices_derives_shift_and_bits(
544        #[case] vertices: &[i32],
545        #[case] shift: u32,
546        #[case] bits: u32,
547    ) {
548        let morton = Morton::from_vertices(vertices).unwrap();
549        assert_eq!(
550            (morton.shift, morton.bits),
551            (shift, bits),
552            "shift cancels a negative min, bits covers max + shift"
553        );
554    }
555
556    #[rstest]
557    #[case::past_the_cap_outright(&[0, 65_536])]
558    #[case::pushed_past_the_cap_by_the_shift(&[-1, 65_535])]
559    fn from_vertices_rejects_an_extent_wider_than_sixteen_bits(#[case] vertices: &[i32]) {
560        let err = Morton::from_vertices(vertices).unwrap_err();
561        assert!(
562            matches!(
563                err,
564                MltError::VertexMortonNotCompatibleWithExtent {
565                    extent: 65_536,
566                    required_bits: 17,
567                }
568            ),
569            "{err:?}"
570        );
571    }
572
573    #[rstest]
574    #[case::origin(0, 0)]
575    #[case::x_only(1, 0)]
576    #[case::y_only(0, 1)]
577    #[case::both_axes(500, 300)]
578    #[case::negative_coords(-4000, -9000)]
579    fn encode_morton_round_trips_through_decode_delta(#[case] x: i32, #[case] y: i32) {
580        let code = MORTON.encode_morton(x, y).unwrap();
581        assert_eq!(MORTON.decode_delta(&[code], &mut dec()).unwrap(), [x, y]);
582    }
583
584    #[rstest]
585    #[case::x_below_the_shift(-20_000, 0)]
586    #[case::y_below_the_shift(0, -20_000)]
587    fn encode_morton_rejects_a_coordinate_the_shift_cannot_lift(#[case] x: i32, #[case] y: i32) {
588        let err = MORTON.encode_morton(x, y).unwrap_err();
589        assert!(matches!(err, MltError::TryFromIntError(_)), "{err:?}");
590    }
591
592    fn expected_coords(pairs: &[Coord<u32>]) -> Vec<i32> {
593        pairs
594            .iter()
595            .flat_map(|&Coord { x, y }| {
596                [
597                    x.cast_signed() - COORD_SHIFT.cast_signed(),
598                    y.cast_signed() - COORD_SHIFT.cast_signed(),
599                ]
600            })
601            .collect()
602    }
603
604    fn signed_deltas(codes: &[u32]) -> Vec<u32> {
605        let mut prev = 0i32;
606        codes
607            .iter()
608            .map(|&c| {
609                let delta = c.cast_signed().wrapping_sub(prev).cast_unsigned();
610                prev = c.cast_signed();
611                delta
612            })
613            .collect()
614    }
615}