forked from tinygrad/tinygrad
316 lines
15 KiB
Python
316 lines
15 KiB
Python
from __future__ import annotations
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from typing import Final, ClassVar, Callable, Literal
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import math, struct, ctypes, functools
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from dataclasses import dataclass, fields
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from tinygrad.helpers import getenv, prod
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from enum import Enum, auto
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ConstType = float|int|bool
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FmtStr = Literal['?', 'b', 'B', 'h', 'H', 'i', 'I', 'q', 'Q', 'e', 'f', 'd']
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# all DTypes should only be created once
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class DTypeMetaClass(type):
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dcache: dict[tuple, DType] = {}
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def __call__(cls, *args, **kwargs):
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if (ret:=DTypeMetaClass.dcache.get(args, None)) is not None: return ret
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DTypeMetaClass.dcache[args] = ret = super().__call__(*args)
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return ret
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class AddrSpace(Enum): GLOBAL = auto(); LOCAL = auto(); REG = auto() # noqa: E702
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@dataclass(frozen=True, eq=False)
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class DType(metaclass=DTypeMetaClass):
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priority: int # this determines when things get upcasted
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itemsize: int
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name: str
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fmt: FmtStr|None
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count: int
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_scalar: DType|None
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@staticmethod
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def new(priority:int, itemsize:int, name:str, fmt:FmtStr|None): return DType(priority, itemsize, name, fmt, 1, None)
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def __reduce__(self): return type(self), tuple(getattr(self, f.name) for f in fields(self))
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def __repr__(self): return f"dtypes.{INVERSE_DTYPES_DICT[self.scalar().name]}"+(f".vec({self.count})" if self.count > 1 else "")
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def __lt__(self, o:DType): return (self.priority, self.itemsize, self.name, self.fmt, self.count) < (o.priority, o.itemsize, o.name, o.fmt, o.count)
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@property
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def base(self): return self
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@property
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def vcount(self): return self.count
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@functools.cache # pylint: disable=method-cache-max-size-none
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def vec(self, sz:int) -> DType:
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assert self.count == 1, f"can't vectorize {self} with size {sz}"
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if sz == 1 or self == dtypes.void: return self # void doesn't vectorize, and sz=1 is scalar
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return DType(self.priority, self.itemsize*sz, f"{INVERSE_DTYPES_DICT[self.name]}{sz}", None, sz, self)
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def ptr(self, size=-1, addrspace=AddrSpace.GLOBAL) -> PtrDType:
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return PtrDType(self.priority, self.itemsize, self.name, self.fmt, self.count, None, self, addrspace, 1, size)
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def scalar(self) -> DType: return self._scalar if self._scalar is not None else self
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def nbytes(self): raise RuntimeError("only ptr types have nbytes")
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@property
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def min(self): return dtypes.min(self)
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@property
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def max(self): return dtypes.max(self)
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@dataclass(frozen=True, eq=False)
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class PtrDType(DType):
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_base: DType
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addrspace: AddrSpace
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v: int
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size: int = -1 # -1 is unlimited size
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@property
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def base(self): return self._base
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@functools.cache # pylint: disable=method-cache-max-size-none
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def vec(self, sz:int) -> DType:
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assert self.v == 1, f"can't vectorize ptr {self} with size {sz}"
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if sz == 1: return self # sz=1 is a scalar
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if isinstance(self, ImageDType):
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return ImageDType(self.priority, self.itemsize, self.name, self.fmt, self.count, self, self._base, self.addrspace, sz, self.size, self.shape)
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return type(self)(self.priority, self.itemsize, self.name, self.fmt, self.count, self, self._base, self.addrspace, sz, self.size)
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def ptr(self, size=-1, addrspace=AddrSpace.GLOBAL): raise RuntimeError("can't make a pointer from a pointer")
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def nbytes(self) -> int:
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if self.size == -1: return 0 # TODO: this should be an exception
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return self.size*self.itemsize
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@property
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def vcount(self): return self.v
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def __repr__(self):
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return f"{self.base.__repr__()}.ptr({self.size}{', '+str(self.addrspace) if self.addrspace != AddrSpace.GLOBAL else ''})" + \
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(f'.vec({self.v})' if self.v != 1 else '')
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@dataclass(frozen=True, eq=False)
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class ImageDType(PtrDType):
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shape: tuple[int, ...] = () # shape of the Image
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def ptr(self, size=-1, addrspace=AddrSpace.GLOBAL) -> PtrDType:
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assert addrspace == AddrSpace.GLOBAL, "images can't be local"
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return self
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def __repr__(self): return f"dtypes.{self.name}({self.shape})" + (f'.vec({self.v})' if self.v != 1 else '')
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class dtypes:
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@staticmethod
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@functools.cache
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def is_float(x: DType) -> bool: return x.scalar() in dtypes.floats or isinstance(x, ImageDType)
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@staticmethod # static methods on top, or bool in the type info will refer to dtypes.bool
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@functools.cache
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def is_int(x: DType) -> bool: return x.scalar() in dtypes.ints
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@staticmethod
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@functools.cache
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def is_unsigned(x: DType) -> bool: return x.scalar() in dtypes.uints
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@staticmethod
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def is_bool(x: DType) -> bool: return x.scalar() == dtypes.bool
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@staticmethod
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def from_py(x) -> DType:
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if x.__class__ is float: return dtypes.default_float
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if x.__class__ is int: return dtypes.default_int
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if x.__class__ is bool: return dtypes.bool
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# put this in the last is faster because there are more items than lists/tuples to check
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if x.__class__ is list or x.__class__ is tuple: return max(dtypes.from_py(xi) for xi in x) if x else dtypes.default_float
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raise RuntimeError(f"Could not infer dtype of {x} with type {type(x)}")
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@staticmethod
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def as_const(val: tuple[ConstType, ...]|ConstType, dtype:DType):
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if isinstance(val, tuple):
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assert len(val) == dtype.count, f"mismatch {val} {dtype}"
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return tuple(dtypes.as_const(x, dtype) for x in val)
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# TODO: should truncate here
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return int(val) if dtypes.is_int(dtype) else float(val) if dtypes.is_float(dtype) else bool(val)
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@staticmethod
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@functools.cache
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def min(dtype:DType):
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if dtypes.is_int(dtype): return 0 if dtypes.is_unsigned(dtype) else -2**(dtype.itemsize*8-1)
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return -float("inf") if dtypes.is_float(dtype) else False
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@staticmethod
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@functools.cache
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def max(dtype:DType):
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if dtypes.is_int(dtype): return 2**(dtype.itemsize*8)-1+dtypes.min(dtype)
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return float("inf") if dtypes.is_float(dtype) else True
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@staticmethod
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def finfo(dtype:DType) -> tuple[int, int]:
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"""(exponent, mantissa)"""
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if not dtypes.is_float(dtype): raise ValueError(f"{dtype} is not a floating point type")
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return {dtypes.float16: (5, 10), dtypes.bfloat16: (8, 7), dtypes.float32: (8, 23), dtypes.float64: (11, 52),
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dtypes.fp8e5m2: (5, 2), dtypes.fp8e4m3: (4, 3)}[dtype]
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@staticmethod
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def fields() -> dict[str, DType]: return DTYPES_DICT
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void: Final[DType] = DType.new(-1, 0, "void", None)
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bool: Final[DType] = DType.new(0, 1, "bool", '?')
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int8: Final[DType] = DType.new(1, 1, "signed char", 'b')
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uint8: Final[DType] = DType.new(2, 1, "unsigned char", 'B')
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int16: Final[DType] = DType.new(3, 2, "short", 'h')
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uint16: Final[DType] = DType.new(4, 2, "unsigned short", 'H')
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int32: Final[DType] = DType.new(5, 4, "int", 'i')
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uint32: Final[DType] = DType.new(6, 4, "unsigned int", 'I')
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int64: Final[DType] = DType.new(7, 8, "long", 'q')
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uint64: Final[DType] = DType.new(8, 8, "unsigned long", 'Q')
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fp8e4m3: Final[DType] = DType.new(9, 1, "float8_e4m3", None)
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fp8e5m2: Final[DType] = DType.new(10, 1, "float8_e5m2", None)
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float16: Final[DType] = DType.new(11, 2, "half", 'e')
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# bfloat16 has higher priority than float16, so least_upper_dtype(dtypes.int64, dtypes.uint64) = dtypes.float16
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bfloat16: Final[DType] = DType.new(12, 2, "__bf16", None)
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float32: Final[DType] = DType.new(13, 4, "float", 'f')
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float64: Final[DType] = DType.new(14, 8, "double", 'd')
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# dtype aliases
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half = float16; float = float32; double = float64 # noqa: E702
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uchar = uint8; ushort = uint16; uint = uint32; ulong = uint64 # noqa: E702
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char = int8; short = int16; int = int32; long = int64 # noqa: E702
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# NOTE: these are image dtypes
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@staticmethod
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def imageh(shp): return ImageDType(100, 2, "imageh", 'e', 1, None, dtypes.float32, AddrSpace.GLOBAL, 1, prod(shp), shp)
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@staticmethod
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def imagef(shp): return ImageDType(100, 4, "imagef", 'f', 1, None, dtypes.float32, AddrSpace.GLOBAL, 1, prod(shp), shp)
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default_float: ClassVar[DType] = float32
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default_int: ClassVar[DType] = int32
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fp8s = (fp8e4m3, fp8e5m2)
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floats = fp8s + (float16, bfloat16, float32, float64)
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uints = (uint8, uint16, uint32, uint64)
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sints = (int8, int16, int32, int64)
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ints = uints + sints
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all = floats + ints + (bool,)
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if (env_default_float := getenv("DEFAULT_FLOAT", "")):
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dtypes.default_float = getattr(dtypes, env_default_float.lower())
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assert dtypes.is_float(dtypes.default_float), f"{env_default_float} is not a float dtype"
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DTypeLike = str|DType
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def to_dtype(dtype:DTypeLike) -> DType: return dtype if isinstance(dtype, DType) else getattr(dtypes, dtype.lower())
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# https://jax.readthedocs.io/en/latest/jep/9407-type-promotion.html
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# we don't support weak type and complex type
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promo_lattice = { dtypes.bool: [dtypes.int8, dtypes.uint8], dtypes.int8: [dtypes.int16], dtypes.int16: [dtypes.int32], dtypes.int32: [dtypes.int64],
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dtypes.int64: [dtypes.float16, dtypes.bfloat16], dtypes.uint8: [dtypes.int16, dtypes.uint16], dtypes.uint16: [dtypes.int32, dtypes.uint32],
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dtypes.uint32: [dtypes.int64, dtypes.uint64], dtypes.uint64: [dtypes.float16, dtypes.bfloat16],
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dtypes.fp8e5m2: [dtypes.float16, dtypes.bfloat16], dtypes.fp8e4m3: [dtypes.float16, dtypes.bfloat16],
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dtypes.float16: [dtypes.float32], dtypes.bfloat16: [dtypes.float32], dtypes.float32: [dtypes.float64], }
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@functools.cache
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def _get_recursive_parents(dtype:DType) -> set[DType]:
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return set.union(*[_get_recursive_parents(d) for d in promo_lattice[dtype]], {dtype}) if dtype != dtypes.float64 else {dtypes.float64}
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@functools.cache
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def least_upper_dtype(*ds:DType) -> DType:
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return min(set.intersection(*[_get_recursive_parents(d) for d in ds])) if not (images:=[d for d in ds if isinstance(d, ImageDType)]) else images[0]
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def least_upper_float(dt:DType) -> DType: return dt if dtypes.is_float(dt) else least_upper_dtype(dt, dtypes.default_float)
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DTYPES_DICT = {k: v for k, v in dtypes.__dict__.items() if isinstance(v, DType) and not k.startswith(("default", "void"))}
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INVERSE_DTYPES_DICT = {**{v.name:k for k,v in DTYPES_DICT.items()}, "void": "void"}
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@functools.cache
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def can_safe_cast(dt0:DType, dt1:DType) -> bool:
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# return if dt1 preserves value of dt0
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# https://numpy.org/doc/stable/reference/generated/numpy.can_cast.html
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if dt0 == dt1 or dt0 == dtypes.bool: return True
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match dt1:
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case dtypes.double: return dt0 in (dtypes.float, dtypes.half, dtypes.bfloat16)
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case dtypes.float: return dt0 in (dtypes.half, dtypes.bfloat16)
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case dtypes.uint64: return dt0 in (dtypes.uint32, dtypes.uint16, dtypes.uint8)
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case dtypes.uint32: return dt0 in (dtypes.uint16, dtypes.uint8)
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case dtypes.int64: return dt0 in (dtypes.uint32, dtypes.uint16, dtypes.uint8, dtypes.int32, dtypes.int16, dtypes.int8)
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case dtypes.int32: return dt0 in (dtypes.uint16, dtypes.uint8, dtypes.int16, dtypes.int8)
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case dtypes.int16: return dt0 in (dtypes.uint8, dtypes.int8)
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case _: return False
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def sum_acc_dtype(dt:DType):
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# default acc dtype for sum
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if dtypes.is_unsigned(dt): return least_upper_dtype(dt, dtypes.uint)
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if dtypes.is_int(dt) or dt == dtypes.bool: return least_upper_dtype(dt, dtypes.int)
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return least_upper_dtype(dt, to_dtype(getenv("SUM_DTYPE", "float32")))
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def truncate_fp16(x):
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try: return struct.unpack("@e", struct.pack("@e", float(x)))[0]
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except OverflowError: return math.copysign(math.inf, x)
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def truncate_bf16(x):
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max_bf16 = struct.unpack('f', struct.pack('I', 0x7f7f0000))[0]
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if abs(x) > max_bf16: return math.copysign(math.inf, x)
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f32_int = struct.unpack('I', struct.pack('f', x))[0]
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bf = struct.unpack('f', struct.pack('I', f32_int & 0xFFFF0000))[0]
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return bf
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# fp8-float conversions based on https://gitlab.com/nvidia/headers/cuda-individual/cudart/-/blob/main/cuda_fp8.hpp
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def float_to_fp8(x: float, dtype: DType) -> int:
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assert dtype in dtypes.fp8s, "Only for fp8s"
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config = {
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dtypes.fp8e4m3: {"EXP_BIAS": 7, "SIGNIFICAND_BITS": 4, "MANTISSA_MASK": 0x7, "MINDENORM_O2": 0x3F50000000000000,
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"OVERFLOW_THRESHOLD": 0x407D000000000000, "MAXNORM": 0x7E, "MINNORM": 0x3F90000000000000, "INF_VALUE": 0x7F},
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dtypes.fp8e5m2: {"EXP_BIAS": 15, "SIGNIFICAND_BITS": 3, "MANTISSA_MASK": 0x3, "MINDENORM_O2": 0x3EE0000000000000,
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"OVERFLOW_THRESHOLD": 0x40EE000000000000 - 1, "MAXNORM": 0x7B, "MINNORM": 0x3F10000000000000, "INF_VALUE": 0x7E}
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}[dtype]
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xbits, = struct.unpack('Q', struct.pack('d', x))
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FP8_DP_HALF_ULP = 1 << (53 - config["SIGNIFICAND_BITS"] - 1)
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sign = ((xbits >> 63) & 1) << 7
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exp = (((xbits >> 52) & 0x7FF) - 1023 + config["EXP_BIAS"])
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mantissa = (xbits >> (53 - config["SIGNIFICAND_BITS"])) & config["MANTISSA_MASK"]
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absx = xbits & 0x7FFFFFFFFFFFFFFF
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if absx <= config["MINDENORM_O2"]: res = 0
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elif absx > 0x7FF0000000000000: res = 0x7F if dtype == dtypes.fp8e4m3 else 0x7E | mantissa
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elif absx > config["OVERFLOW_THRESHOLD"]: res = config["MAXNORM"]
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elif absx >= config["MINNORM"]:
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res = ((exp << (config["SIGNIFICAND_BITS"] - 1)) | mantissa)
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round_bits = xbits & ((FP8_DP_HALF_ULP << 1) - 1)
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if (round_bits > FP8_DP_HALF_ULP) or (round_bits == FP8_DP_HALF_ULP and (mantissa & 1)): res = res + 1
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else:
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shift = 1 - exp
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mantissa |= 1 << (config["SIGNIFICAND_BITS"] - 1)
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res = (mantissa >> shift)
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round_bits = (xbits | (1 << (53 - 1))) & ((FP8_DP_HALF_ULP << (shift + 1)) - 1)
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if (round_bits > (FP8_DP_HALF_ULP << shift)) or (round_bits == (FP8_DP_HALF_ULP << shift) and (res & 1)):
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res = res + 1
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res |= sign
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return int(res)
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def fp8_to_float(x: int, dtype: DType) -> float:
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assert dtype in dtypes.fp8s, "Only for fp8s"
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ur = x << 8
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if dtype == dtypes.fp8e5m2 and (ur & 0x7FFF) > 0x7C00: ur = 0x7FFF
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elif dtype == dtypes.fp8e4m3:
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sign = ur & 0x8000
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exponent = ((ur & 0x7800) >> 1) + 0x2000
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mantissa = (ur & 0x0700) >> 1
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absx = x & 0x7F
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if absx == 0x7F: ur = 0x7FFF
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elif exponent == 0x2000:
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if mantissa != 0:
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mantissa <<= 1
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while (mantissa & 0x0400) == 0:
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mantissa <<= 1
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exponent -= 0x0400
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mantissa &= 0x03FF
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else:
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exponent = 0
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ur = (sign | exponent) | mantissa
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else:
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ur = (sign | exponent) | mantissa
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half_bytes = struct.pack('<H', ur)
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float32_val = struct.unpack('e', half_bytes)[0]
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return float(float32_val)
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truncate: dict[DType, Callable] = {dtypes.bool: bool,
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dtypes.float16: truncate_fp16, dtypes.bfloat16: truncate_bf16,
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**{fp8: (lambda x, dtype=fp8: fp8_to_float(float_to_fp8(x, dtype), dtype)) for fp8 in dtypes.fp8s},
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dtypes.float32: lambda x: ctypes.c_float(x).value, dtypes.float64: lambda x: ctypes.c_double(x).value,
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dtypes.uint8: lambda x: ctypes.c_uint8(x).value, dtypes.uint16: lambda x: ctypes.c_uint16(x).value,
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dtypes.uint32: lambda x: ctypes.c_uint32(x).value, dtypes.uint64: lambda x: ctypes.c_uint64(x).value,
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dtypes.int8: lambda x: ctypes.c_int8(x).value, dtypes.int16: lambda x: ctypes.c_int16(x).value, dtypes.int32: lambda x: ctypes.c_int32(x).value,
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dtypes.int64: lambda x: ctypes.c_int64(x).value}
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# numpy and torch dtype interop
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def _to_np_dtype(dtype:DType) -> type|None:
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import numpy as np
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return np.dtype(dtype.fmt).type if dtype.fmt is not None else None
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def _from_np_dtype(npdtype:'np.dtype') -> DType: # type: ignore [name-defined] # noqa: F821
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import numpy as np
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return dtypes.fields()[np.dtype(npdtype).name]
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@functools.cache
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def _to_torch_dtype(dtype:DType) -> 'torch.dtype'|None: # type: ignore [name-defined] # noqa: F821
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import numpy as np, torch
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# NOTE: torch doesn't expose this mapping with a stable API
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try: return torch.from_numpy(np.array([], dtype=_to_np_dtype(dtype))).dtype
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except TypeError: return None
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@functools.cache
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def _from_torch_dtype(torchdtype:'torch.dtype') -> DType: # type: ignore [name-defined] # noqa: F821
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return {v:k for k in dtypes.all if (v:=_to_torch_dtype(k)) is not None}[torchdtype] |