pitrou commented on code in PR #47896:
URL: https://github.com/apache/arrow/pull/47896#discussion_r2452356455


##########
cpp/src/arrow/util/bit_util.h:
##########
@@ -118,6 +118,16 @@ constexpr uint64_t LeastSignificantBitMask(int64_t 
bit_index) {
   return (static_cast<uint64_t>(1) << bit_index) - 1;
 }
 
+// Returns a mask for the bit_index lower order bits.
+// Only valid for bit_index in the range [0, sizeof(Uint)].
+template <typename Uint>
+constexpr auto LeastSignificantBitMaskInc(Uint bit_index) {

Review Comment:
   What does `Inc` mean here?
   
   And I wonder if we cannot just reconcile the two functions, for example:
   ```c++
   template <typename Uint, bool kAllowUpperBound = false>
   constexpr auto LeastSignificantBitMask(Uint bit_index) {
     if constexpr (kAllowUpperBound) {
       if (bit_index == 8 * sizeof(Uint)) {
         return ~Uint{0};
       }
     }
     return (Uint{1} << bit_index) - Uint{1};
   }
   ```
   



##########
cpp/src/arrow/util/bpacking_dispatch_internal.h:
##########
@@ -47,7 +49,113 @@ int unpack_full(const uint8_t* in, Uint* out, int 
batch_size) {
       out[k] = FromLittleEndian(SafeLoadAs<Uint>(in + (k * sizeof(Uint))));
     }
   }
-  return batch_size;
+}
+
+/// Compute the maximum spread in bytes that a packed integer can cover.
+///
+/// This is assuming contiguous packed integer starting with the given bit 
offset away
+/// from a byte boundary.
+/// This function is non-monotonic, for instance with zero offset, three bit 
integers
+/// will be split on the first byte boundary (hence having a spread of two 
bytes) while
+/// four bit integer will be well behaved and never spread over byte boundary 
(hence
+/// having a spread of one).
+constexpr int PackedMaxSpreadBytes(int width, int bit_offset) {

Review Comment:
   This function looks complicated, but if I recode it in Python it looks like 
it can be reduced to a much simpler form that's more amenable to compile-time 
execution:
   ```python
   >>> def spread(width, bit_offset):
   ...:     max_spread = (width >> 3) + ((width & 7) != 0);
   ...:     start = bit_offset
   ...:     while True:
   ...:         byte_start = start // 8
   ...:         byte_end = (start + width - 1) // 8
   ...:         spread = byte_end - byte_start + 1
   ...:         max_spread = max(spread, max_spread)
   ...:         start += width
   ...:         if start % 8 == bit_offset:
   ...:             return max_spread
   ...: 
   >>> [spread(8, b) for b in range(8)]
   [1, 2, 2, 2, 2, 2, 2, 2]
   >>> [spread(16, b) for b in range(8)]
   [2, 3, 3, 3, 3, 3, 3, 3]
   >>> [spread(32, b) for b in range(8)]
   [4, 5, 5, 5, 5, 5, 5, 5]
   ```
   



##########
cpp/src/arrow/util/bpacking_dispatch_internal.h:
##########
@@ -47,7 +49,113 @@ int unpack_full(const uint8_t* in, Uint* out, int 
batch_size) {
       out[k] = FromLittleEndian(SafeLoadAs<Uint>(in + (k * sizeof(Uint))));
     }
   }
-  return batch_size;
+}
+
+/// Compute the maximum spread in bytes that a packed integer can cover.
+///
+/// This is assuming contiguous packed integer starting with the given bit 
offset away
+/// from a byte boundary.
+/// This function is non-monotonic, for instance with zero offset, three bit 
integers
+/// will be split on the first byte boundary (hence having a spread of two 
bytes) while
+/// four bit integer will be well behaved and never spread over byte boundary 
(hence
+/// having a spread of one).
+constexpr int PackedMaxSpreadBytes(int width, int bit_offset) {
+  int max = static_cast<int>(bit_util::BytesForBits(width));
+  int start = bit_offset;
+  do {
+    const int byte_start = start / 8;
+    const int byte_end = (start + width - 1) / 8;  // inclusive end bit
+    const int spread = byte_end - byte_start + 1;
+    max = spread > max ? spread : max;
+    start += width;
+  } while (start % 8 != bit_offset);
+  return max;
+}
+
+/// Compute the maximum spread in bytes that a packed integer can cover across 
all bit
+/// offsets.
+constexpr int PackedMaxSpreadBytes(int width) {

Review Comment:
   This is constexpr, but will the compiler actually reduce it to a 
compile-time constant? It does not seem obvious to me.
   



##########
cpp/src/arrow/util/bpacking_dispatch_internal.h:
##########
@@ -47,7 +49,113 @@ int unpack_full(const uint8_t* in, Uint* out, int 
batch_size) {
       out[k] = FromLittleEndian(SafeLoadAs<Uint>(in + (k * sizeof(Uint))));
     }
   }
-  return batch_size;
+}
+
+/// Compute the maximum spread in bytes that a packed integer can cover.
+///
+/// This is assuming contiguous packed integer starting with the given bit 
offset away
+/// from a byte boundary.
+/// This function is non-monotonic, for instance with zero offset, three bit 
integers
+/// will be split on the first byte boundary (hence having a spread of two 
bytes) while
+/// four bit integer will be well behaved and never spread over byte boundary 
(hence
+/// having a spread of one).
+constexpr int PackedMaxSpreadBytes(int width, int bit_offset) {
+  int max = static_cast<int>(bit_util::BytesForBits(width));
+  int start = bit_offset;
+  do {
+    const int byte_start = start / 8;
+    const int byte_end = (start + width - 1) / 8;  // inclusive end bit
+    const int spread = byte_end - byte_start + 1;
+    max = spread > max ? spread : max;
+    start += width;
+  } while (start % 8 != bit_offset);
+  return max;
+}
+
+/// Compute the maximum spread in bytes that a packed integer can cover across 
all bit
+/// offsets.
+constexpr int PackedMaxSpreadBytes(int width) {
+  int max = 0;
+  for (int offset = 0; offset < 8; ++offset) {
+    const int spread = PackedMaxSpreadBytes(width, offset);
+    max = spread > max ? spread : max;
+  }
+  return max;
+}
+
+// Integer type that tries to contain as much as the spread as possible.
+template <int kSpreadBytes>
+using SpreadBufferUint = std::conditional_t<
+    (kSpreadBytes <= sizeof(uint8_t)), uint_fast8_t,
+    std::conditional_t<(kSpreadBytes <= sizeof(uint16_t)), uint_fast16_t,
+                       std::conditional_t<(kSpreadBytes <= sizeof(uint32_t)),
+                                          uint_fast32_t, uint_fast64_t>>>;
+
+/// Unpack integers.
+/// This function works for all input batch sizes but is not the fastest.
+/// In prolog mode, instead of unpacking all required element, the function 
will
+/// stop if it finds a byte aligned value start.
+template <int kPackedBitWidth, bool kIsProlog, typename Uint>
+int unpack_exact(const uint8_t* in, Uint* out, int batch_size, int bit_offset) 
{
+  // For the epilog we adapt the max spread since better alignment give 
shorter spreads
+  ARROW_DCHECK(kIsProlog || bit_offset == 0);

Review Comment:
   Also, IIUC:
   ```suggestion
     ARROW_DCHECK(kIsProlog || bit_offset == 0);
     ARROW_DCHECK(bit_offset >= 0 && bit_offset < 8);
   ```



##########
cpp/src/arrow/util/bpacking_dispatch_internal.h:
##########
@@ -47,7 +49,113 @@ int unpack_full(const uint8_t* in, Uint* out, int 
batch_size) {
       out[k] = FromLittleEndian(SafeLoadAs<Uint>(in + (k * sizeof(Uint))));
     }
   }
-  return batch_size;
+}
+
+/// Compute the maximum spread in bytes that a packed integer can cover.
+///
+/// This is assuming contiguous packed integer starting with the given bit 
offset away
+/// from a byte boundary.
+/// This function is non-monotonic, for instance with zero offset, three bit 
integers
+/// will be split on the first byte boundary (hence having a spread of two 
bytes) while
+/// four bit integer will be well behaved and never spread over byte boundary 
(hence
+/// having a spread of one).
+constexpr int PackedMaxSpreadBytes(int width, int bit_offset) {
+  int max = static_cast<int>(bit_util::BytesForBits(width));
+  int start = bit_offset;
+  do {
+    const int byte_start = start / 8;
+    const int byte_end = (start + width - 1) / 8;  // inclusive end bit
+    const int spread = byte_end - byte_start + 1;
+    max = spread > max ? spread : max;
+    start += width;
+  } while (start % 8 != bit_offset);

Review Comment:
   Note that this will be an infinite loop if `bit_offset >= 8` (hence the 
DCHECK suggestion below)



##########
cpp/src/arrow/util/bpacking_dispatch_internal.h:
##########
@@ -47,7 +49,113 @@ int unpack_full(const uint8_t* in, Uint* out, int 
batch_size) {
       out[k] = FromLittleEndian(SafeLoadAs<Uint>(in + (k * sizeof(Uint))));
     }
   }
-  return batch_size;
+}
+
+/// Compute the maximum spread in bytes that a packed integer can cover.
+///
+/// This is assuming contiguous packed integer starting with the given bit 
offset away
+/// from a byte boundary.
+/// This function is non-monotonic, for instance with zero offset, three bit 
integers
+/// will be split on the first byte boundary (hence having a spread of two 
bytes) while
+/// four bit integer will be well behaved and never spread over byte boundary 
(hence
+/// having a spread of one).
+constexpr int PackedMaxSpreadBytes(int width, int bit_offset) {

Review Comment:
   And, as noted below, calling with `bit_offset` equal to 8 or larger results 
in an infinite loop...



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