Add float8_e8m0_fnu (E8M0) OCP MX scale format

Adding the OCP MX scale format `E8M0`, which has the following properties:
* Unsigned format;
* 8 exponent bits;
* Exponent range from -127 to 127;
* No zero and infinity;
* Single NaN value (0xFF);

`ml_dtypes` `float8_base` C++ class is extended to support floating point formats
which are unsigned and with no zero (i.e. additional `kIsSigned` and `kHasZero` Traits properties).

Base on these traits, `float8_e8m0_fnu` has been implemented using the existing functionalities (convert, unary/binary ops, ...).
Float8 Python unit tests have been extended to be able to cover unsigned floating point formats.

ml_dtypes/__init__.py

@@ -27,6 +27,7 @@
     "float8_e4m3fnuz",
     "float8_e5m2",
     "float8_e5m2fnuz",
+    "float8_e8m0fnu",
     "iinfo",
     "int2",
     "int4",
@@ -49,6 +50,7 @@
 from ml_dtypes._ml_dtypes_ext import float8_e4m3fnuz
 from ml_dtypes._ml_dtypes_ext import float8_e5m2
 from ml_dtypes._ml_dtypes_ext import float8_e5m2fnuz
+from ml_dtypes._ml_dtypes_ext import float8_e8m0fnu
 from ml_dtypes._ml_dtypes_ext import int2
 from ml_dtypes._ml_dtypes_ext import int4
 from ml_dtypes._ml_dtypes_ext import uint2
@@ -66,6 +68,7 @@
 float8_e4m3fnuz: Type[np.generic]
 float8_e5m2: Type[np.generic]
 float8_e5m2fnuz: Type[np.generic]
+float8_e8m0fnu: Type[np.generic]
 int2: Type[np.generic]
 int4: Type[np.generic]
 uint2: Type[np.generic]

ml_dtypes/_finfo.py

@@ -27,6 +27,7 @@
 from ml_dtypes._ml_dtypes_ext import float8_e4m3fnuz
 from ml_dtypes._ml_dtypes_ext import float8_e5m2
 from ml_dtypes._ml_dtypes_ext import float8_e5m2fnuz
+from ml_dtypes._ml_dtypes_ext import float8_e8m0fnu
 import numpy as np
 
 _bfloat16_dtype = np.dtype(bfloat16)
@@ -40,6 +41,7 @@
 _float8_e4m3fnuz_dtype = np.dtype(float8_e4m3fnuz)
 _float8_e5m2_dtype = np.dtype(float8_e5m2)
 _float8_e5m2fnuz_dtype = np.dtype(float8_e5m2fnuz)
+_float8_e8m0fnu_dtype = np.dtype(float8_e8m0fnu)
 
 
 class _Bfloat16MachArLike:
@@ -141,6 +143,15 @@ def __init__(self):
     self.smallest_subnormal = float8_e5m2fnuz(smallest_subnormal)
 
 
+class _Float8E8m0fnuMachArLike:
+
+  def __init__(self):
+    smallest_normal = float.fromhex("0x1p-127")
+    self.smallest_normal = float8_e8m0fnu(smallest_normal)
+    smallest_subnormal = float.fromhex("0x1p-127")
+    self.smallest_subnormal = float8_e8m0fnu(smallest_subnormal)
+
+
 class finfo(np.finfo):  # pylint: disable=invalid-name,missing-class-docstring
   __doc__ = np.finfo.__doc__
   _finfo_cache: Dict[type, np.finfo] = {}  # pylint: disable=g-bare-generic
@@ -628,6 +639,51 @@ def float_to_str(f):
     # pylint: enable=protected-access
     return obj
 
+  @staticmethod
+  def _float8_e8m0fnu_finfo():
+    def float_to_str(f):
+      return "%6.2e" % float(f)
+
+    tiny = float.fromhex("0x1p-127")
+    resolution = 0.1
+    eps = float.fromhex("0x1p+0")
+    epsneg = float.fromhex("0x1p-1")
+    max_ = float.fromhex("0x1p+127")
+
+    obj = object.__new__(np.finfo)
+    obj.dtype = _float8_e8m0fnu_dtype
+    obj.bits = 8
+    obj.eps = float8_e8m0fnu(eps)
+    obj.epsneg = float8_e8m0fnu(epsneg)
+    obj.machep = 0
+    obj.negep = -1
+    obj.max = float8_e8m0fnu(max_)
+    obj.min = float8_e8m0fnu(tiny)
+    obj.nexp = 8
+    obj.nmant = 0
+    obj.iexp = obj.nexp
+    obj.maxexp = 128
+    obj.minexp = -127
+    obj.precision = 1
+    obj.resolution = float8_e8m0fnu(resolution)
+    # pylint: disable=protected-access
+    obj._machar = _Float8E8m0fnuMachArLike()
+    if not hasattr(obj, "tiny"):
+      obj.tiny = float8_e8m0fnu(tiny)
+    if not hasattr(obj, "smallest_normal"):
+      obj.smallest_normal = obj._machar.smallest_normal
+    obj.smallest_subnormal = obj._machar.smallest_subnormal
+
+    obj._str_tiny = float_to_str(tiny)
+    obj._str_smallest_normal = float_to_str(tiny)
+    obj._str_smallest_subnormal = float_to_str(obj.smallest_subnormal)
+    obj._str_max = float_to_str(max_)
+    obj._str_epsneg = float_to_str(epsneg)
+    obj._str_eps = float_to_str(eps)
+    obj._str_resolution = float_to_str(resolution)
+    # pylint: enable=protected-access
+    return obj
+
   _finfo_type_map = {
       _bfloat16_dtype: _bfloat16_finfo,
       _float4_e2m1fn_dtype: _float4_e2m1fn_finfo,
@@ -640,6 +696,7 @@ def float_to_str(f):
       _float8_e4m3b11fnuz_dtype: _float8_e4m3b11fnuz_finfo,
       _float8_e5m2_dtype: _float8_e5m2_finfo,
       _float8_e5m2fnuz_dtype: _float8_e5m2fnuz_finfo,
+      _float8_e8m0fnu_dtype: _float8_e8m0fnu_finfo,
   }
   _finfo_name_map = {t.name: t for t in _finfo_type_map}
 
@@ -656,6 +713,6 @@ def __new__(cls, dtype):
 
     init = cls._finfo_type_map.get(key)
     if init is not None:
-      cls._finfo_cache[dtype] = init()
+      cls._finfo_cache[dtype] = init.__func__()
       return cls._finfo_cache[dtype]
     return super().__new__(cls, dtype)

ml_dtypes/_src/dtypes.cc

@@ -216,6 +216,21 @@ struct TypeDescriptor<float4_e2m1fn> : CustomFloatType<float4_e2m1fn> {
   static constexpr char kNpyDescrByteorder = '=';
 };
 
+template <>
+struct TypeDescriptor<float8_e8m0fnu> : CustomFloatType<float8_e8m0fnu> {
+  typedef float8_e8m0fnu T;
+  static constexpr bool is_floating = true;
+  static constexpr bool is_integral = false;
+  static constexpr const char* kTypeName = "float8_e8m0fnu";
+  static constexpr const char* kQualifiedTypeName = "ml_dtypes.float8_e8m0fnu";
+  static constexpr const char* kTpDoc = "float8_e8m0fnu floating-point values";
+  static constexpr char kNpyDescrKind = 'V';
+  // TODO(phawkins): there doesn't seem to be a way of guaranteeing a type
+  // character is unique.
+  static constexpr char kNpyDescrType = 'W';
+  static constexpr char kNpyDescrByteorder = '=';
+};
+
 template <>
 struct TypeDescriptor<int2> : IntNTypeDescriptor<int2> {
   typedef int2 T;
@@ -379,6 +394,9 @@ bool Initialize() {
       !RegisterFloatDtype<float4_e2m1fn>(numpy.get())) {
     return false;
   }
+  if (!RegisterFloatDtype<float8_e8m0fnu>(numpy.get())) {
+    return false;
+  }
 
   if (!RegisterIntNDtype<int2>(numpy.get()) ||
       !RegisterIntNDtype<uint2>(numpy.get()) ||
@@ -393,6 +411,9 @@ bool Initialize() {
                             float8_e4m3b11fnuz, float8_e4m3fn, float8_e4m3fnuz,
                             float8_e5m2, float8_e5m2fnuz, float6_e2m3fn,
                             float6_e3m2fn, float4_e2m1fn>();
+  // Only registering to/from BF16 and FP32 for float8_e8m0fnu.
+  success &= RegisterTwoWayCustomCast<float8_e8m0fnu, bfloat16, float>();
+  success &= RegisterTwoWayCustomCast<bfloat16, float8_e8m0fnu, float>();
   success &= RegisterOneWayCustomCast<int2, int4, int8_t>();
   success &= RegisterOneWayCustomCast<uint2, uint4, uint8_t>();
   return success;
@@ -433,6 +454,7 @@ extern "C" EXPORT_SYMBOL PyObject* PyInit__ml_dtypes_ext() {
       !InitModuleType<float8_e4m3fnuz>(m.get(), "float8_e4m3fnuz") ||
       !InitModuleType<float8_e5m2>(m.get(), "float8_e5m2") ||
       !InitModuleType<float8_e5m2fnuz>(m.get(), "float8_e5m2fnuz") ||
+      !InitModuleType<float8_e8m0fnu>(m.get(), "float8_e8m0fnu") ||
       !InitModuleType<bfloat16>(m.get(), "bfloat16") ||
       !InitModuleType<int2>(m.get(), "int2") ||
       !InitModuleType<int4>(m.get(), "int4") ||

ml_dtypes/_src/ufuncs.h

@@ -322,6 +322,12 @@ using BitsType = typename GetUnsignedInteger<sizeof(T)>::type;
 
 template <typename T>
 std::pair<BitsType<T>, BitsType<T>> SignAndMagnitude(T x) {
+  const BitsType<T> x_bits = Eigen::numext::bit_cast<BitsType<T>>(x);
+  // Unsigned floating point format (e.g. E8M0) => no sign bit (zero by
+  // default).
+  if constexpr (!std::numeric_limits<T>::is_signed) {
+    return {BitsType<T>(0), x_bits};
+  }
   // For types that represent NaN by -0, (i.e. *fnuz), abs(x) remains -0 without
   // flipping the sign. Therefore, we need to explicitly check the
   // most-significant bit.
@@ -332,13 +338,16 @@ std::pair<BitsType<T>, BitsType<T>> SignAndMagnitude(T x) {
   constexpr bool has_nan = std::numeric_limits<T>::has_quiet_NaN;
   const BitsType<T> x_abs_bits =
       Eigen::numext::bit_cast<BitsType<T>>(Eigen::numext::abs(x));
-  const BitsType<T> x_bits = Eigen::numext::bit_cast<BitsType<T>>(x);
   return {has_nan ? x_bits & kSignMask : x_bits ^ x_abs_bits, x_abs_bits};
 }
 
 template <typename T>
 struct CopySign {
   T operator()(T a, T b) {
+    // Unsigned floating point format => no change.
+    if constexpr (!std::numeric_limits<T>::is_signed) {
+      return a;
+    }
     auto [a_sign, a_abs_bits] = SignAndMagnitude(a);
     auto [b_sign, b_abs_bits] = SignAndMagnitude(b);
     BitsType<T> rep = a_abs_bits | b_sign;