apacheGH-36036: [C++][Python][Parquet] Implement Float16 logical type (…

…apache#36073)

### Rationale for this change

There is currently an active proposal to support half-float types in Parquet. For more details/discussion, see the links in this PR's accompanying issue.

### What changes are included in this PR?

This PR implements basic support for a `Float16LogicalType` in accordance with the proposed spec. More specifically, this includes:

- Changes to `parquet.thrift` and regenerated `parqet_types` files
- Basic `LogicalType` class definition, method impls, and enums
- Support for specialized comparisons and column statistics

In the interest of scope, this PR does not currently deal with arrow integration and byte split encoding - although we will want both of these features resolved before the proposal is approved.

### Are these changes tested?

Yes (tests are included)

### Are there any user-facing changes?

Yes

* Closes: apache#36036

Lead-authored-by: benibus <bpharks@gmx.com>
Co-authored-by: Ben Harkins <60872452+benibus@users.noreply.github.com>
Co-authored-by: Antoine Pitrou <pitrou@free.fr>
Signed-off-by: Antoine Pitrou <antoine@python.org>

cpp/src/arrow/CMakeLists.txt

@@ -223,6 +223,7 @@ set(ARROW_SRCS
     util/debug.cc
     util/decimal.cc
     util/delimiting.cc
+    util/float16.cc
     util/formatting.cc
     util/future.cc
     util/hashing.cc

cpp/src/arrow/util/CMakeLists.txt

@@ -48,6 +48,7 @@ add_arrow_test(utility-test
                checked_cast_test.cc
                compression_test.cc
                decimal_test.cc
+               float16_test.cc
                formatting_util_test.cc
                key_value_metadata_test.cc
                hashing_test.cc

cpp/src/arrow/util/float16.cc

@@ -0,0 +1,226 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you 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.
+
+#include <ostream>
+#include <type_traits>
+
+#include "arrow/util/float16.h"
+#include "arrow/util/ubsan.h"
+
+namespace arrow {
+namespace util {
+
+namespace {
+
+// --------------------------------------------------------
+// Binary conversions
+// --------------------------------------------------------
+// These routines are partially adapted from Numpy's C implementation
+//
+// Some useful metrics for conversions between different precisions:
+// |-----------------------------------------|
+// | precision | half    | single  | double  |
+// |-----------------------------------------|
+// | mantissa  | 10 bits | 23 bits | 52 bits |
+// | exponent  | 5 bits  | 8 bits  | 11 bits |
+// | sign      | 1 bit   | 1 bit   | 1 bit   |
+// | exp bias  | 15      | 127     | 1023    |
+// |-----------------------------------------|
+
+template <typename T>
+struct BinaryConverter {
+  static_assert(std::is_same_v<T, uint32_t> || std::is_same_v<T, uint64_t>);
+
+  static constexpr int kNumBits = sizeof(T) * 8;
+  static constexpr int kMantNumBits = (kNumBits == 32) ? 23 : 52;
+  static constexpr int kExpNumBits = kNumBits - kMantNumBits - 1;
+
+  static constexpr int kExpBias = (1 << (kExpNumBits - 1)) - 1;
+
+  static constexpr T kMantMask = (T(1) << kMantNumBits) - 1;
+  static constexpr T kExpMask = ((T(1) << kExpNumBits) - 1) << kMantNumBits;
+  static constexpr T kSignMask = T(1) << (kNumBits - 1);
+
+  static_assert(kMantNumBits + kExpNumBits + 1 == kNumBits);
+  static_assert(kSignMask + kExpMask + kMantMask == ~T(0));
+
+  static uint16_t ToBinary16(T);
+  static T FromBinary16(uint16_t);
+};
+
+// Converts a IEEE binary32/64 into a binary16. Rounds to nearest with ties to zero
+template <typename T>
+uint16_t BinaryConverter<T>::ToBinary16(T f_bits) {
+  // Sign mask for output binary16
+  const uint16_t h_sign = uint16_t((f_bits >> (kNumBits - 16)) & 0x8000);
+
+  // Exponent mask for input binary
+  const T f_exp = f_bits & kExpMask;
+  // Exponents as signed pre-shifted values for convenience. Here, we need to re-bias the
+  // exponent for a binary16. If, after re-biasing, the binary16 exponent falls outside of
+  // the range [1,30] then we need to handle the under/overflow case specially.
+  const int16_t f_biased_exp = int16_t(f_exp >> kMantNumBits);
+  const int16_t unbiased_exp = f_biased_exp - kExpBias;
+  const int16_t h_biased_exp = unbiased_exp + 15;
+
+  // Mantissa mask for input
+  const T f_mant = f_bits & kMantMask;
+
+  // We define a "rounding bit", which is the most significant bit to be dropped
+  // (e.g. for a binary32, 0x1000).
+  constexpr T rounding_bit = T(1) << (kMantNumBits - (10 + 1));
+
+  // Handle exponent overflow, NaN, and +/-Inf
+  if (h_biased_exp >= 0x1f) {
+    // The input is a NaN representation
+    if (f_exp == kExpMask && f_mant != 0) {
+      uint16_t h_mant = uint16_t(f_mant >> (kMantNumBits - 10));
+      // If the mantissa bit(s) indicating NaN were shifted out, add one back. Otherwise,
+      // the result would be infinity.
+      if (h_mant == 0) {
+        h_mant = 0x1;
+      }
+      return uint16_t(h_sign | 0x7c00u | h_mant);
+    }
+
+    // Clamp to +/-infinity
+    return uint16_t(h_sign | 0x7c00u);
+  }
+
+  // Handle exponent underflow, subnormals, and +/-0
+  if (h_biased_exp <= 0) {
+    // If the underflow exceeds the number of bits in a binary16 mantissa (10) then we
+    // can't round, so just clamp to 0. Note that this also weeds out any input values
+    // that are subnormal - including +/-0;
+    if (h_biased_exp < -10) {
+      return h_sign;
+    }
+
+    // Convert to a rounded subnormal value starting with the mantissa. Since the input
+    // input is known to be normal at this point, we need to prepend its implicit leading
+    // bit - which also necessitates an additional right-shift.
+    T rounded_mant = (T(1) << kMantNumBits) | f_mant;
+    rounded_mant >>= (1 - h_biased_exp);
+
+    // Here, we implement rounding to nearest (with ties to even)
+    //
+    // By now, our new mantissa has two conceptual ranges:
+    //  - The lower 13 bits, which will be shifted out
+    //  - The upper 10 bits, which will become the binary16's mantissa
+    //
+    // "Rounding to nearest" basically just means that we add 1 to the rounding bit. If
+    // it's set, then the bit will cascade upwards into the 10-bit mantissa (and
+    // potentially the exponent). The only time where we may NOT do this is when a "tie"
+    // occurs - i.e. when the rounding bit is set but all of the lower bits are 0. In that
+    // case, we don't add 1 if the retained mantissa is "even" (its least significant bit
+    // is 0).
+    if ((rounded_mant & ((rounding_bit << 2) - 1)) != rounding_bit ||
+        (f_mant & 0x7ffu) != 0) {
+      rounded_mant += rounding_bit;
+    }
+
+    const uint16_t h_mant = uint16_t(rounded_mant >> (kMantNumBits - 10));
+    return h_sign + h_mant;
+  }
+
+  const uint16_t h_exp = uint16_t(h_biased_exp) << 10;
+
+  // See comment on rounding behavior above
+  T rounded_mant = f_mant;
+  if ((rounded_mant & ((rounding_bit << 2) - 1)) != rounding_bit) {
+    rounded_mant += rounding_bit;
+  }
+
+  const uint16_t h_mant = uint16_t(rounded_mant >> (kMantNumBits - 10));
+  // Note that we ADD (rather than OR) the components because we want the carryover bit
+  // from rounding the mantissa to cascade through the exponent (it shouldn't affect the
+  // sign bit though).
+  return h_sign + h_exp + h_mant;
+}
+
+// Converts a IEEE binary16 into a binary32/64
+template <typename T>
+T BinaryConverter<T>::FromBinary16(uint16_t h_bits) {
+  // Sign mask for output
+  const T f_sign = T(h_bits & 0x8000u) << (kNumBits - 16);
+
+  // Exponent mask for input binary16
+  const uint16_t h_exp = h_bits & 0x7c00;
+  // Mantissa mask for input binary16
+  const uint16_t h_mant = h_bits & 0x3ffu;
+
+  switch (h_exp) {
+    // Handle Inf and NaN
+    case 0x7c00u:
+      return f_sign | kExpMask | (T(h_mant) << (kMantNumBits - 10));
+    // Handle zeros and subnormals
+    case 0x0000u: {
+      // Input is +/-0
+      if (h_mant == 0) {
+        return f_sign;
+      }
+      // Subnormal binary16 to normal binary32/64
+      //
+      // Start with an f32/64-biased exponent of 2^-15. We then decrement it until the
+      // most significant set bit is left-shifted out - as it doesn't get explicitly
+      // stored in normalized floating point values. Instead, its existence is implied by
+      // the new exponent.
+      T f_exp = kExpBias - 15;
+      T f_mant = T(h_mant) << 1;
+      while ((f_mant & 0x0400u) == 0) {
+        --f_exp;
+        f_mant <<= 1;
+      }
+      f_exp <<= kMantNumBits;
+      f_mant = (f_mant & 0x03ffu) << (kMantNumBits - 10);
+      return f_sign | f_exp | f_mant;
+    } break;
+    // Handle normals
+    default:
+      // Equivalent to rebiasing the exponent and shifting everything by the remaining
+      // mantissa bits.
+      return f_sign |
+             ((T(h_bits & 0x7fffu) + (T(kExpBias - 15) << 10)) << (kMantNumBits - 10));
+  }
+}
+
+}  // namespace
+
+float Float16::ToFloat() const {
+  const uint32_t f_bits = BinaryConverter<uint32_t>::FromBinary16(bits_);
+  return SafeCopy<float>(f_bits);
+}
+
+Float16 Float16::FromFloat(float f) {
+  const uint32_t f_bits = SafeCopy<uint32_t>(f);
+  return FromBits(BinaryConverter<uint32_t>::ToBinary16(f_bits));
+}
+
+double Float16::ToDouble() const {
+  const uint64_t d_bits = BinaryConverter<uint64_t>::FromBinary16(bits_);
+  return SafeCopy<double>(d_bits);
+}
+
+Float16 Float16::FromDouble(double d) {
+  const uint64_t d_bits = SafeCopy<uint64_t>(d);
+  return FromBits(BinaryConverter<uint64_t>::ToBinary16(d_bits));
+}
+
+std::ostream& operator<<(std::ostream& os, Float16 arg) { return (os << arg.ToFloat()); }
+
+}  // namespace util
+}  // namespace arrow