github-actions[bot]
5c97379765
date: 2026-08-01T16:05:18 master commit: 3a05c03079d796f533f342489b3f681cfd21f98d
572 lines
34 KiB
Python
572 lines
34 KiB
Python
from typing import Callable
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import math, functools
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from tinygrad.dtype import dtypes, DType, promo_lattice, truncate
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from tinygrad.device import is_dtype_supported
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from tinygrad.helpers import flatten, polyN, Target, EMULATED_DTYPES
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from tinygrad.uop import GroupOp
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from tinygrad.uop.ops import UOp, UPat, Ops, PatternMatcher, graph_rewrite
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TRANSCENDENTAL_DTYPES = (dtypes.float16, dtypes.float32, dtypes.float64)
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def _lazy_map_numbers(x:UOp, inf:UOp, _inf:UOp, nan:UOp, ratio:UOp):
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"""replace inf -> inf, -inf -> _inf, nan -> nan, otherwise -> ratio"""
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return x.ne(math.inf).where(x.ne(x).where(nan, x.ne(-math.inf).where(ratio, _inf)), inf)
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# *** helper functions for bit manipulation ***
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def mantissa_bits(d:DType) -> int: return dtypes.finfo(d.scalar())[1]
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def exponent_bias(d:DType) -> int: return (1 << (dtypes.finfo(d.scalar())[0] - 1)) - (0 if d.scalar() in dtypes.fp8_fnuz else 1)
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def exponent_mask(d:DType) -> int: return (1 << dtypes.finfo(d.scalar())[0]) - 1
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# **** utils ****
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def shr(x:UOp|int, y:UOp|int) -> UOp: return x // (2**(y.simplify().arg) if isinstance(y, UOp) else 2**y)
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def shl(x:UOp|int, y:UOp|int) -> UOp: return x * (2**(y.simplify().arg) if isinstance(y, UOp) else 2**y)
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def rintk(d:UOp) -> UOp:
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"""round d:float to int away from 0"""
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out_dtype = {dtypes.float64: dtypes.int64, dtypes.float32: dtypes.int32, dtypes.float16: dtypes.int16}[d.dtype.scalar()].vec(d.dtype.vcount)
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return (d + (d<0.0).where(d.const_like(-0.5), d.const_like(0.5))).cast(out_dtype)
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def pow2if(q:UOp, float_dtype:DType):
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"""cast(2^q, float_dtype) where q is any integer in the range of [-126, 127]"""
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out_dtype = {dtypes.int64: dtypes.float64, dtypes.int32: dtypes.float32, dtypes.int16: float_dtype.scalar()}[q.dtype.scalar()].vec(q.dtype.vcount)
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return shl(q + exponent_bias(out_dtype), mantissa_bits(out_dtype)).bitcast(out_dtype)
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def ilogb2k(d:UOp) -> UOp:
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"""calculate the integer part of log2(d), where d is normalized fp value in the range of [0, +inf)."""
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assert d.dtype.scalar() in TRANSCENDENTAL_DTYPES
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dint = d.bitcast({dtypes.float64: dtypes.int64, dtypes.float32: dtypes.int32, dtypes.float16: dtypes.int16}[d.dtype.scalar()].vec(d.dtype.vcount))
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# -1 <= ilog2bk(d) <= 128
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return (shr(dint, mantissa_bits(d.dtype)) & exponent_mask(d.dtype)) - exponent_bias(d.dtype)
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def ldexp3k(d:UOp, e:UOp) -> UOp:
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"""d*2^e. e is a number obtained by casting an integer in the range [-127, 127] to a float. d is any float number."""
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assert d.dtype.scalar() in TRANSCENDENTAL_DTYPES and e.dtype.scalar() in TRANSCENDENTAL_DTYPES
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dtype = {dtypes.float64: dtypes.int64, dtypes.float32: dtypes.int32, dtypes.float16: dtypes.int16}[d.dtype.scalar()].vec(d.dtype.count)
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m1 = d.bitcast(dtype)
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m2 = shl(e.cast(dtype), mantissa_bits(d.dtype))
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return (m1 + m2).bitcast(d.dtype)
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def ldexp2k(d:UOp, e:UOp) -> UOp:
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"""d*2^e. much faster than ldexp3k but risky. d > 0 and d is not denormal."""
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assert d.dtype.scalar() in TRANSCENDENTAL_DTYPES and e.dtype.scalar() in (dtypes.int16, dtypes.int32, dtypes.int64)
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return (d * pow2if(shr(e, 1), d.dtype)) * pow2if(e - shr(e, 1), d.dtype)
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def frexp(v:UOp) -> tuple[UOp, UOp]:
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"""frexp(v) -> (mantissa, exponent) assuming v != 0"""
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assert v.dtype.scalar() in TRANSCENDENTAL_DTYPES
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# m1 = masks for mantissa, m2 = masks to normalize the mantissa.
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m1 = {dtypes.float64: 0x000FFFFFFFFFFFFF, dtypes.float32: 0x807FFFFF, dtypes.float16: 0x83FF}[v.dtype.scalar()]
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m2 = {dtypes.float64: 0x3FE0000000000000, dtypes.float32: 0x3F000000, dtypes.float16: 0x3800}[v.dtype.scalar()]
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bits = v.bitcast({dtypes.float64: dtypes.uint64, dtypes.float32: dtypes.uint32, dtypes.float16: dtypes.uint16}[v.dtype.scalar()].vec(v.dtype.count))
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exponent = shr(bits, mantissa_bits(v.dtype)) & exponent_mask(v.dtype)
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# Set the exponent bits appropriately to normalize the mantissa into the range of [0.5, 1.0).
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mantissa = ((bits & m1) | m2).bitcast(v.dtype)
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exp = exponent - exponent_bias(v.dtype) + 1
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return mantissa, exp
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# *** reduction algorithms for sine ***
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def payne_hanek_reduction(d:UOp) -> tuple[UOp, UOp]:
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"""
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Performs Payne-Hanek Reduction: computes the remainder of `d` modulo pi/2 for the values `d` where
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39800.0 <= d <= +Inf
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Returns a tuple of `(r, q)`:
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- `r`[d.dtype] is the reminder value corresponding to `round_to_nearest(x % pi/2)`.
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- `q`[int32] is an integer, and q % 4 is corresponding to the quadrant of the original angle `d`.
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"""
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assert d.dtype.scalar() in TRANSCENDENTAL_DTYPES
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# https://stackoverflow.com/questions/30463616/payne-hanek-algorithm-implementation-in-c/30465751#30465751
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# 190 bits of 2/pi for Payne-Hanek style argument reduction
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two_over_pi_f = [0x00000000, 0x28be60db, 0x9391054a, 0x7f09d5f4, 0x7d4d3770, 0x36d8a566, 0x4f10e410]
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intermediate_dtype = dtypes.float32.vec(d.dtype.count) if d.dtype.base.scalar() == dtypes.float16 else d.dtype
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f, e = frexp(d)
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ia = (f.cast(intermediate_dtype) * 4.294967296e9).cast(dtypes.uint64)
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# extract 96 relevant bits of 2/pi based on magnitude of argument
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i = shr(e.cast(dtypes.uint64), 5)
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e = e.cast(dtypes.int32) & 31
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offset = 32 - e
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def _take(an:UOp, offset:int, count:int=0) -> UOp:
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"""an = two_over_pi_f[i+offset]"""
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if count+offset < len(two_over_pi_f) - 1:
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an = i.ne(count).where(_take(an, offset, count=count+1), an.const_like(two_over_pi_f[count+offset]))
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return an
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def _shl_lazy(x:UOp, y:UOp): return (x.cast(dtypes.uint64) * pow2if(y, d.dtype).cast(dtypes.uint64)).cast(dtypes.uint32)
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def _shr_lazy(x:UOp, y:UOp): return (x.cast(dtypes.uint64) // pow2if(y, d.dtype).cast(dtypes.uint64)).cast(dtypes.uint32)
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a = [_take(UOp.const(dtypes.uint32.vec(d.dtype.count), 0), i) for i in range(4)]
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# (two_over_pi_f[Int(i) + n] << e) | (two_over_pi_f[Int(i) + n+1] >> (nbits - e))
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# Note: e >= 1 for all numbers d >= 1.0. assume e != 0
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hi = _shl_lazy(a[0], e) | _shr_lazy(a[1], offset)
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mi = _shl_lazy(a[1], e) | _shr_lazy(a[2], offset)
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lo = _shl_lazy(a[2], e) | _shr_lazy(a[3], offset)
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def _hp_mul(x:UOp, y:UOp) -> UOp: return x.cast(dtypes.uint64) * y.cast(dtypes.uint64)
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# compute x * 2/pi
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p = shl(_hp_mul(ia, hi), 32) + _hp_mul(ia, mi) + shr(_hp_mul(ia, lo), 32)
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# round quotient to nearest
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q = shr(p, 62).cast(dtypes.int32)
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p = p & 0x3fffffffffffffff
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r = (p.cast(intermediate_dtype) * (3.4061215800865545e-19)).cast(d.dtype)
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# if fraction >= 0.5, r -= pi/2, q += 1
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return (f<0.5).where(r, r - math.pi/2), (f<0.5).where(q, q + 1)
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def cody_waite_reduction(d:UOp) -> tuple[UOp, UOp]:
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"""
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Performs Cody-Waite Reduction: computes the reminder of `d` modulo pi/2 for the values `d` where
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0 <= abs(d) <= 39800.0
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Returns a tuple of `(r, q)`, where the output format is the same as that of `payne_hanek_reduction`.
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"""
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def _reduce_d(x:UOp, q:UOp):
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# https://github.com/shibatch/sleef/blob/4e08851f59fc2b545f9c393c6a23dfd311a26308/src/libm/sleefdp.c#L789-L823
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if x.dtype.scalar() == dtypes.float64:
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# https://github.com/shibatch/sleef/blob/f6d8a841fbfddd26ce712834d4da220cd76048fb/src/common/misc.h#L77
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PI_A, PI_B, PI_C, PI_D = 3.1415926218032836914, 3.1786509424591713469e-08, 1.2246467864107188502e-16, 1.2736634327021899816e-24
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d = qdh * -PI_A + x
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d = q * -PI_A + d
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d = qdh * -PI_B + d
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d = q * -PI_B + d
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d = qdh * -PI_C + d
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d = q * -PI_C + d
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d = (qdh + q) * -PI_D + d
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elif x.dtype.scalar() == dtypes.float16:
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# [FIXME] when reducing `d`, FP16 needs FP32 precision to achieve 1.0 ULP precision.
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d = _reduce_d(x.cast(dtypes.float32), q.cast(dtypes.float32)).cast(dtypes.float16)
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else:
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# https://github.com/shibatch/sleef/blob/4e08851f59fc2b545f9c393c6a23dfd311a26308/src/libm/sleefsp.c#L464-L503
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d = q * -3.1414794921875 + x
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d = q * -0.00011315941810607910156 + d
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d = q * -1.9841872589410058936e-09 + d
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d = q * -1.2154201256553420762e-10 + d
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return d
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m_1_pi = 0.318309886183790671537767526745028724
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qdh = (d * (m_1_pi / 2.0**24)).cast(dtypes.int64).cast(d.dtype) * (2.0**24)
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quadrant = rintk(d * m_1_pi -qdh) if d.dtype.base.scalar() == dtypes.float64 else rintk(d * m_1_pi)
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return _reduce_d(d, quadrant.cast(d.dtype)), quadrant.cast(dtypes.int32)
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# *** approximate sine on small angle. ***
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def trig_poly(d:UOp, coeff32, coeff64): return d * (polyN(d*d, coeff64) if d.dtype.scalar() == dtypes.float64 else polyN(d*d, coeff32))
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# approximate sine on [-pi/2, pi/2]
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def sin_poly(d:UOp) -> UOp:
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return trig_poly(d, [2.6083159809786593541503e-06, -0.0001981069071916863322258, 0.00833307858556509017944336, -0.166666597127914428710938, 1.0],
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[-7.97255955009037868891952e-18, 2.81009972710863200091251e-15, -7.64712219118158833288484e-13, 1.60590430605664501629054e-10,
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-2.50521083763502045810755e-08, 2.75573192239198747630416e-06, -0.000198412698412696162806809, 0.00833333333333332974823815,
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-0.166666666666666657414808, 1.0])
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def _ifand(q:UOp, n:int): return (q & n).ne(0)
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def sin_poly_small(d:UOp, q:UOp) -> UOp:
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r = sin_poly(d)
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return r * _ifand(q, 1).where(r.const_like(-1), r.const_like(1))
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def sin_poly_large(d:UOp, q:UOp) -> UOp:
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r = sin_poly(d + _ifand(q, 1).where(d.const_like(math.pi / 2), d.const_like(0)))
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return r * _ifand(q, 2).where(r.const_like(-1), r.const_like(1))
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# *** toplevel functions for xsin/xlog2/xexp2 ***
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def xsin(d:UOp, fast:bool=False, switch_over:float=30.0) -> UOp:
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"""
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Implements a 1.0 ULP approximation for Ops.SIN.
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- fast=True assumes x <= switch_over.
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- switch_over is the threshold for switching to payne_hanek_reduction.
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"""
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assert d.dtype.scalar() in TRANSCENDENTAL_DTYPES
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# mask +-inf/nan as zero
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x = _lazy_map_numbers(d, d.const_like(0.0), d.const_like(0.0), d.const_like(0.0), d)
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# x_sign = sign(x)
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x_sign = x.ne(0).where((x<0).where(x.const_like(-1), x.const_like(1)), x.const_like(0))
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x_abs = x * x_sign
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r, q = (cody_waite_reduction if fast else payne_hanek_reduction)(x_abs)
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if fast: result = sin_poly_small(r, q)
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else:
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# Payne Hanek Reduction assumes abs(x) >= pi/4, so for smaller values, use cody_waite_reduction.
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r_small, q_small = cody_waite_reduction(x_abs)
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result = (x_abs<switch_over).where(sin_poly_small(r_small, q_small), sin_poly_large(r, q))
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# adjusts the sign for abs(x)
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result = result * x_sign
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# sin(Inf) = NaN, sin(-Inf) = NaN, sin(NaN) = NaN
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return _lazy_map_numbers(d, d.const_like(math.nan), d.const_like(math.nan), d.const_like(math.nan), result)
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def xexp2(d:UOp) -> UOp:
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"""
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Implements a 1.0 ULP approximation for Ops.EXP2
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- Paper: https://arxiv.org/pdf/2001.09258
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"""
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assert d.dtype.scalar() in TRANSCENDENTAL_DTYPES
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# mask +=inf/nan as zero.
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x = _lazy_map_numbers(d, d.const_like(0.0), d.const_like(0.0), d.const_like(0.0), d)
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q = rintk(x)
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# s = d - round(d)
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s = x - q.cast(x.dtype)
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# a polynomial approximation with 13 non-zero terms in the range of [−(log 2)/2,(log 2)/2].
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if d.dtype.scalar() == dtypes.float64:
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u = polyN(s, [0.4434359082926529454e-9, 0.7073164598085707425e-8, 0.1017819260921760451e-6, 0.1321543872511327615e-5, 0.1525273353517584730e-4,
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0.1540353045101147808e-3, 0.1333355814670499073e-2, 0.9618129107597600536e-2, 0.5550410866482046596e-1, 0.2402265069591012214e+0,
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0.6931471805599452862e+0, 0.1000000000000000000e+1])
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else: u = polyN(s, [0.1535920892e-3, 0.1339262701e-2, 0.9618384764e-2, 0.5550347269e-1, 0.2402264476e+0, 0.6931471825e+0, 1.0])
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u = ldexp2k(u, q) # u*2^q
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upper, lower = {dtypes.float64: (1024, -2000), dtypes.float32: (128, -150), dtypes.float16: (23, -22)}[d.dtype.scalar()]
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# Replace x >= upper with +inf
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u = (d >= upper).where(d.const_like(math.inf), u)
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# Replace x < lower with zero.
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u = (d<lower).where(d.const_like(0.0), u)
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# exp2(NaN) = NaN
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return d.ne(d).where(d.const_like(math.nan), u)
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def xlog2(d:UOp) -> UOp:
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"""
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Implements a 1.0 ULP approximation for Ops.LOG2
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Paper: https://arxiv.org/pdf/2001.09258 5.5
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"""
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assert d.dtype.scalar() in TRANSCENDENTAL_DTYPES
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# float16 uses 2^10 for denormal scaling (2^64 overflows), float32/64 use 2^64
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denormal_exp = 10 if d.dtype.scalar() == dtypes.float16 else 64
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FLT_MIN = d.const_like({dtypes.float16: 6.1e-5, dtypes.float32: 1e-4, dtypes.float64: 1e-4}[d.dtype.scalar()])
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is_denormal = d<FLT_MIN
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a = is_denormal.where(d * (2 ** denormal_exp), d)
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e = ilogb2k(a * (1.0 / 0.75)).cast(a.dtype)
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m = ldexp3k(a, -e)
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e = is_denormal.where(e - denormal_exp, e)
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x = (m - 1.0) / (m + 1.0)
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x2 = x * x
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if d.dtype.scalar() == dtypes.float64:
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t = polyN(x2, [0.2211941750456081490e+0, 0.2200768693152277689e+0, 0.2623708057488514656e+0, 0.3205977477944495502e+0,
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0.4121985945485324709e+0, 0.5770780162997058982e+0, 0.96179669392608091449])
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r = t * (x * x2) + e + x * 2.885390081777926774
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else:
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t = polyN(x2, [0.4374550283e+0, 0.5764790177e+0, 0.9618012905120])
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# s_lo term (x*3.27e-08) only for float32 - underflows in float16
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r = t * (x * x2) + e + x * 2.8853900432586669922 + (x * 3.2734474483568488616e-08 if d.dtype.scalar() == dtypes.float32 else 0)
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# log2(Inf) = Inf
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r = d.ne(math.inf).where(r, r.const_like(math.inf))
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# log2(0) = -Inf (handle both +0.0 and -0.0)
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r = d.ne(0.0).where(r, r.const_like(-math.inf))
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# log2(x) = NaN for x < 0
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r = (d<-0.0).where(r.const_like(math.nan), r)
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# log2(NaN) = NaN
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r = d.ne(d).where(r.const_like(math.nan), r)
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# log2(-0.0) = -Inf. In certain devices like PTX, x == -0.0 won't be true. so making reciprocal.
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return d.reciprocal().ne(-math.inf).where(r, r.const_like(-math.inf))
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def xpow(base:UOp, exponent:UOp) -> UOp:
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# start with b ** e = exp2(e * log2(b))
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ret = (base < 0).where(-base, base).log2().mul(exponent).exp2()
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# negative base: nan for non-integer exponent, negate for odd integer exponent
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non_int = exponent != exponent.cast(dtypes.int32).cast(exponent.dtype)
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is_odd = (exponent < 0).where(-exponent, exponent).cast(dtypes.int32).mod(2).cast(dtypes.bool)
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neg_base = non_int.where(ret.const_like(math.nan), is_odd.where(-ret, ret))
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# fix 0 ** 0 = 1
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return (base.eq(0) & exponent.eq(0)).where(ret.const_like(1), (base < 0).where(neg_base, ret))
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# *** integer division ***
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@functools.lru_cache(None)
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def magicgu(vmax:int, d:int) -> tuple[int,int]:
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# calculate m,s such that x//d == (x*m) >> s for all 0 <= x <= vmax, d>0; adapted from Hacker's Delight, Chapter 10
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nc = (vmax+1)//(d) * d - 1
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nbits = vmax.bit_length()
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for s in range(0, 2*nbits + 1):
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if 2**s > nc*(d - 1 - (2**s - 1) % d):
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m = (2**s + d - 1 - (2**s - 1) % d)//d
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return m, s
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assert False
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def fast_idiv(target: Target, x: UOp, d: int, dont_cast=False) -> UOp|None:
|
||
# NOTE: disable for METAL due to compiler bug. keccak with -O0 works but not with optimization
|
||
if target.device.startswith("METAL"): return None
|
||
# If d is a power of two this is not valid for signed ints!
|
||
is_unsigned = x.vmin>=0 or x.dtype in dtypes.uints
|
||
assert d>0, "Sign should have been taken out of divisor"
|
||
vmin,vmax = max(x.vmin, x.dtype.min), min(x.vmax, x.dtype.max)
|
||
if vmin > -d and vmax < d: return x.const_like(0)
|
||
m,s = magicgu(max(vmax, abs(vmin)), d)
|
||
if m*vmin >= x.dtype.min and m*vmax <= x.dtype.max:
|
||
return ((x*m) >> s) if is_unsigned else ((x*m) >> s) + (x<0).where(x.ufix(1), 0)
|
||
# before we try casting to a larger dtype (slow), we see if there are powers of two in d we can shift to make x smaller
|
||
# use explicit Ops.CDIV (trunc) since the recursion assumes trunc semantics throughout
|
||
if (largest_factor_of_two_in_d := (d & -d)) > 1:
|
||
if (ret:=fast_idiv(target, x.alu(Ops.CDIV, x.const_like(largest_factor_of_two_in_d)),
|
||
d//largest_factor_of_two_in_d, dont_cast=True)) is not None: return ret
|
||
if dont_cast: return None
|
||
# promo_lattice needs to return an unsigned type if the type is unsigned
|
||
if dtypes.is_int(next_dtype := promo_lattice[x.dtype.scalar()][-1]) and is_dtype_supported(next_dtype, target):
|
||
if m*vmin >= next_dtype.min and m*vmax <= next_dtype.max:
|
||
return ((x.cast(next_dtype)*m) >> s).cast(x.dtype) if is_unsigned else ((x.cast(next_dtype)*m) >> s).cast(x.dtype) + (x<0).where(x.ufix(1), 0)
|
||
return None
|
||
|
||
# ***** threefry *****
|
||
|
||
def threefry2x32(x: UOp, key: UOp):
|
||
# split x and key from uint64 to two uint32
|
||
x0, x1 = (x & 0xffffffff).cast(dtypes.uint32), ((x // 2**32) & 0xffffffff).cast(dtypes.uint32)
|
||
key0, key1 = (key & 0xffffffff).cast(dtypes.uint32), ((key // 2**32) & 0xffffffff).cast(dtypes.uint32)
|
||
|
||
rotations = [[13, 15, 26, 6], [17, 29, 16, 24]]
|
||
ks = [key1, key0 ^ key1 ^ 0x1BD11BDA, key0]
|
||
xr:list[UOp] = [x0 + ks[-1], x1 + ks[0]]
|
||
for i in range(5):
|
||
for r in rotations[i % 2]: xr[0], xr[1] = (x0 := xr[0] + xr[1]), x0 ^ ((xr[1] * 2**r) + (xr[1] // 2**(32 - r)))
|
||
xr = [(xr[0] + ks[i % 3]), (xr[1] + ks[(i + 1) % 3] + i + 1)]
|
||
|
||
return xr[1].cast(dtypes.uint64) * 2**32 | xr[0].cast(dtypes.uint64)
|
||
|
||
# ***** long as 2 ints *****
|
||
|
||
l2i_dt = {dtypes.long: dtypes.int, dtypes.ulong: dtypes.uint}
|
||
def unpack32(v:UOp) -> tuple[UOp, UOp]: return v.bitcast(dtypes.uint) & 0xFFFF, shr(v.bitcast(dtypes.uint), 16)
|
||
def reindex(idx:UOp, off:int, mul=2) -> UOp: return idx.replace(src=(idx.src[0], idx.src[1]*mul+off, *idx.src[2:]))
|
||
|
||
# 4.3.1 is the relevant section in TAOCP
|
||
def l2i(op: Ops, dt: DType, *uops:UOp):
|
||
zero = UOp.const(dt, 0)
|
||
if len(uops) == 2: a0, a1 = uops
|
||
elif len(uops) == 4: a0, a1, b0, b1 = uops
|
||
match op:
|
||
case Ops.NEG: return l2i(Ops.SUB, dt, zero, zero, *uops)
|
||
case Ops.CAST if dt in (dtypes.long, dtypes.ulong) and uops[0].dtype not in dtypes.floats:
|
||
return uops[0].cast(l2i_dt[dt]), (uops[0] < 0).where(UOp.const(l2i_dt[dt], -1), UOp.const(l2i_dt[dt], 0))
|
||
case Ops.CAST if dt in (dtypes.long, dtypes.ulong):
|
||
return (lo:=uops[0].cast(l2i_dt[dt])), (uops[0] / 2**32).cast(l2i_dt[dt]) - ((uops[0] < 0) & lo.ne(0)).cast(l2i_dt[dt])
|
||
case Ops.CAST if dt in dtypes.floats:
|
||
small = (a1.eq(0) & (a0 >= 0)) | (a1.eq(-1) & (a0 < 0))
|
||
return small.where(a0.cast(dt), ((a1.cast(dtypes.float32) * (2**32)) + a0.bitcast(dtypes.uint).cast(dtypes.float32)).cast(dt))
|
||
case Ops.CAST: return a0.bitcast(dtypes.uint).cast(dt)
|
||
case Ops.BITCAST: return a0.bitcast(dt), a1.bitcast(dt)
|
||
case Ops.SHL:
|
||
lo, hi = shl(a0, b0_mod:=b0 & 31), shl(a1, b0_mod) | shr(shr(a0, 1), 31 - b0_mod)
|
||
return (b0 >= 32).where(zero, lo), (b0 >= 32).where(lo, hi)
|
||
case Ops.SHR:
|
||
lo, hi = shr(a0, b0_mod:=b0 & 31) | shl(shl(a1, 1), 31 - b0_mod), shr(a1, b0_mod)
|
||
return (b0 >= 32).where(hi, lo), (b0 >= 32).where(zero, hi)
|
||
case Ops.ADD: return (low:=a0+b0), (a1 + b1).replace(dtype=dt) + (low.bitcast(dtypes.uint) < a0.bitcast(dtypes.uint)).cast(dt)
|
||
case Ops.SUB: return a0 - b0, a1 - b1 - (a0.bitcast(dtypes.uint) < b0.bitcast(dtypes.uint)).cast(dt)
|
||
case Ops.MUL:
|
||
(a00, a01), (b00, b01) = unpack32(a0), unpack32(b0)
|
||
mid = l2i(Ops.ADD, dt, shl(a00*b01, 16).bitcast(dt), shr(a00*b01, 16).bitcast(dt), shl(a01*b00, 16).bitcast(dt), shr(a01*b00, 16).bitcast(dt))
|
||
return l2i(Ops.ADD, dt, *mid, (a00*b00).bitcast(dt), (a01*b01).bitcast(dt) + a0*b1 + a1*b0)
|
||
case Ops.CDIV | Ops.CMOD:
|
||
# TAOCP Algorithm 4.3.1D could be faster here, but must be parameterized over the width of b
|
||
if dt == dtypes.int:
|
||
ua0, ua1, ub0, ub1 = a0.bitcast(dtypes.uint), a1.bitcast(dtypes.uint), b0.bitcast(dtypes.uint), b1.bitcast(dtypes.uint)
|
||
a0, a1 = (a_neg:=a1 < zero).where((n:=l2i(Ops.NEG, dtypes.uint, ua0, ua1))[0], ua0), a_neg.where(n[1], ua1)
|
||
b0, b1 = (b_neg:=b1 < zero).where((n:=l2i(Ops.NEG, dtypes.uint, ub0, ub1))[0], ub0), b_neg.where(n[1], ub1)
|
||
q, r = (z:=UOp.const(dtypes.uint, 0), z), (z, z)
|
||
for i in range(63, -1, -1):
|
||
r = l2i(Ops.SHL, dtypes.uint, *r, UOp.const(dtypes.uint, 1), z)
|
||
r = (r[0] | l2i(Ops.SHR, dtypes.uint, a0, a1, UOp.const(dtypes.uint, i), z)[0] & 1), r[1]
|
||
cond = l2i(Ops.CMPLT, dtypes.uint, *r, b0, b1).logical_not()
|
||
diff = l2i(Ops.SUB, dtypes.uint, *r, b0, b1)
|
||
q = ((q[0] | shl(cond.cast(dtypes.uint), i % 32), q[1]) if i < 32 else (q[0], q[1] | shl(cond.cast(dtypes.uint), i % 32)))
|
||
r = l2i(Ops.WHERE, dtypes.uint, cond, *diff, *r)
|
||
if dt == dtypes.int:
|
||
(nq0, nq1), (nr0, nr1) = l2i(Ops.BITCAST, dt, *l2i(Ops.NEG, dtypes.uint, *q)), l2i(Ops.BITCAST, dt, *l2i(Ops.NEG, dtypes.uint, *r))
|
||
(q0, q1), (r0, r1) = l2i(Ops.BITCAST, dt, *q), l2i(Ops.BITCAST, dt, *r)
|
||
return (a_neg.where(nr0, r0), a_neg.where(nr1, r1)) if op == Ops.CMOD else ((a_neg^b_neg).where(nq0, q0), (a_neg^b_neg).where(nq1, q1))
|
||
return (r[0].bitcast(dt), r[1].bitcast(dt)) if op == Ops.CMOD else (q[0].bitcast(dt), q[1].bitcast(dt))
|
||
case Ops.CMPLT: return (a1 < b1) | ((a1.eq(b1)) & (a0.bitcast(dtypes.uint) < b0.bitcast(dtypes.uint)))
|
||
case Ops.CMPEQ: return a0.eq(b0) & a1.eq(b1)
|
||
case Ops.CMPNE: return a0.ne(b0) | a1.ne(b1)
|
||
case Ops.XOR | Ops.OR | Ops.AND: return UOp(op, dt, src=(a0, b0)), UOp(op, dt, src=(a1, b1))
|
||
case Ops.WHERE: return uops[0].where(uops[1], uops[3]), uops[0].where(uops[2], uops[4])
|
||
case Ops.MAX: return l2i(Ops.WHERE, dt, l2i(Ops.CMPLT, dt, *uops), b0, b1, a0, a1)
|
||
case _: raise NotImplementedError(f"long decomposition of {op} unsupported")
|
||
|
||
# ***** floats *****
|
||
f2f_dt = { f:getattr(dtypes, f"uint{f.bitsize}") for f in dtypes.floats }
|
||
|
||
def rne(v: UOp, s) -> UOp: return shr(v, s) + ((shr(v, s - 1) & 1) & ((v & ((1 << (s - 1)) - 1)).ne(0).cast(v.dtype) | (shr(v, s) & 1)))
|
||
|
||
def f2f(v, fr:DType, to:DType):
|
||
fs, fb, (fe, fm), ts, tb, (te, tm) = fr.bitsize, exponent_bias(fr), dtypes.finfo(fr), to.bitsize, exponent_bias(to), dtypes.finfo(to)
|
||
# NB: denormals are zero!
|
||
if fe <= te and fm < tm:
|
||
sign, nosign = shl((v & shl(1, fs-1)).cast(f2f_dt[to]), ts - fs), (v & (shl(1, fs-1) - 1)).cast(f2f_dt[to])
|
||
exp, norm = shr(nosign, fm), shl(nosign, tm - fm) + shl(tb - fb, tm)
|
||
nan = shl(nosign, tm - fm) | shl((shl(1, te) - 1), tm)
|
||
if fr in dtypes.fp8_fnuz:
|
||
fnuz_nan = sign.ne(0) & nosign.eq(0)
|
||
qnan = shl(shl(1, te) - 1, tm) | shl(1, tm - 1)
|
||
return fnuz_nan.where(qnan, sign | exp.eq(0).where(0, norm)).bitcast(to)
|
||
# fp8e4m3 has only one nan
|
||
is_nan = (nosign.eq(shl(1, fm + fe) - 1) if fr == dtypes.fp8e4m3 else exp.eq(shl(1, fe) - 1))
|
||
return (sign | exp.eq(0).where(0, is_nan.where(nan, norm))).bitcast(to)
|
||
elif fe >= te and fm > tm:
|
||
v = f2f_clamp(v.bitcast(fr), to).bitcast(f2f_dt[fr])
|
||
sign, nosign = shr(v, fs - ts) & shl(1, ts - 1), v & (shl(1, fs - 1) - 1)
|
||
norm = (rne(nosign, fm - tm) - shl(fb - tb, tm)).cast(f2f_dt[to])
|
||
underflow = (shr(v, fm) & (shl(1, fe) - 1)) < (1 + fb - tb)
|
||
nan_mantissa = (shl(1, tm) - 1) if to == dtypes.fp8e4m3 else (shr(nosign, fm - tm) & (shl(1, tm) - 1))
|
||
nan = (sign | nan_mantissa | shl(shl(1, te) - 1, tm)).cast(f2f_dt[to])
|
||
is_nan = (shr(v, fm) & (shl(1, fe) - 1)).eq(shl(1, fe) - 1)
|
||
if to in dtypes.fp8_fnuz: return is_nan.where(shl(1, ts - 1), underflow.where(0, sign.cast(f2f_dt[to]) | norm))
|
||
return is_nan.where(nan, sign.cast(f2f_dt[to]) | underflow.where(0, norm))
|
||
else: raise NotImplementedError(f"unsupported decomp {fr} -> {to}")
|
||
|
||
def f2f_clamp(val:UOp, dt:DType) -> UOp:
|
||
e, m = dtypes.finfo(dt)
|
||
if dt in dtypes.fp8_fnuz: max_exp, max_man = (1 << e) - 1, (1 << m) - 1
|
||
else: max_exp, max_man = ((1 << e) - 1, (1 << m) - 2) if dt == dtypes.fp8e4m3 else ((1 << e) - 2, (1 << m) - 1)
|
||
mx = val.const_like(2.0**(max_exp - exponent_bias(dt)) * (1.0 + max_man / (1 << m)))
|
||
sat = mx if dt in dtypes.fp8s else val.const_like(float('inf'))
|
||
# FIXME: CMPLT of nan is undefined
|
||
return val.ne(val).where(val, (val < -mx).where(-sat, (mx < val).where(sat, val)))
|
||
|
||
def f2f_load(x: UOp, fr:DType, to:DType) -> UOp:
|
||
if (n:=x.dtype.count) == 1: return f2f(x.replace(dtype=f2f_dt[fr]), fr, to)
|
||
return UOp.vectorize(*(f2f(x.replace(dtype=f2f_dt[fr], src=(reindex(x.src[0].src[0], i, 1),)), fr, to) for i in range(n)))
|
||
|
||
def f2f_store(st, idx, val, fr:DType, to:DType):
|
||
if (n:=val.dtype.count) == 1: return st.replace(src=(idx, f2f(val.bitcast(f2f_dt[to]), to, fr)))
|
||
return UOp.group(*(st.replace(src=(reindex(idx, i, 1), f2f(val.gep(i).bitcast(f2f_dt[to]), to, fr))) for i in range(n)))
|
||
|
||
# ***** decomposition patterns *****
|
||
|
||
@functools.cache
|
||
def get_transcendental_patterns(ops:tuple[Ops, ...], force_transcendental:bool) -> PatternMatcher:
|
||
pat: list[tuple[UPat, Callable]] = []
|
||
for op,f in ((Ops.EXP2, xexp2), (Ops.LOG2, xlog2), (Ops.SIN, xsin)):
|
||
if op not in ops or force_transcendental:
|
||
pat += [(UPat(op, dtype=TRANSCENDENTAL_DTYPES, src=(UPat.var("d"),)), f),
|
||
(UPat(op, dtype=tuple(dt for dt in dtypes.floats if dt not in TRANSCENDENTAL_DTYPES), src=(UPat.var("d"),), name="x"),
|
||
lambda x,d: d.cast(dtypes.float32).alu(x.op).cast(x.dtype))]
|
||
# rewrite SQRT to xpow 0.5
|
||
if Ops.SQRT not in ops or force_transcendental: pat.append((UPat(Ops.SQRT, src=UPat.var("d")), lambda d: xpow(d, d.const_like(0.5))))
|
||
return PatternMatcher(pat)
|
||
|
||
def floordiv_to_idiv(a:UOp, b:UOp) -> UOp:
|
||
if (a.vmin >= 0 and b.vmin > 0) or (a.vmax <= 0 and b.vmax < 0): return a.alu(Ops.CDIV, b)
|
||
return a.alu(Ops.CDIV, b) - (a.alu(Ops.CMOD, b).ne(0) & (a<0).ne(b<0)).cast(a.dtype)
|
||
|
||
def floormod_to_mod(a:UOp, b:UOp) -> UOp:
|
||
if (a.vmin >= 0 and b.vmin > 0) or (a.vmax <= 0 and b.vmax < 0): return a.alu(Ops.CMOD, b)
|
||
r = a.alu(Ops.CMOD, b)
|
||
# use where instead of mul to avoid being fused into MULACC (which int64 long-decomp doesn't handle)
|
||
return r + (r.ne(0) & (a<0).ne(b<0)).where(b, b.const_like(0))
|
||
|
||
powers_of_two: dict[int, int] = {2**i:i for i in range(64)}
|
||
@functools.cache
|
||
def get_late_rewrite_patterns(ops:tuple[Ops, ...], disable_fast_idiv:bool) -> PatternMatcher:
|
||
pat: list[tuple[UPat, Callable]] = [(UPat.var("a")//UPat.var("b"), floordiv_to_idiv)]
|
||
# FLOORMOD by 2**y -> x & (2**y-1) (correct floor mod for any sign in two's complement); fires before floormod_to_mod
|
||
if Ops.AND in ops: pat.append((UPat.var("x", dtypes.ints)%UPat.cvar("c"), lambda x,c: x & (c.arg-1) if c.arg in powers_of_two else None))
|
||
pat.append((UPat.var("a")%UPat.var("b"), floormod_to_mod))
|
||
# no real hardware supports THREEFRY, but NullRenderer does
|
||
if Ops.THREEFRY not in ops: pat.append((UPat(Ops.THREEFRY, dtype=dtypes.uint64, src=(UPat.var("x"), UPat.var("key"))), threefry2x32))
|
||
# MAX can be rewritten as CMPLT + WHERE (max function is annoying on many cstyle backends)
|
||
if Ops.MAX not in ops and Ops.CMPLT in ops: pat.append((UPat(Ops.MAX, name="m"), lambda m: (m.src[0] < m.src[1]).where(m.src[1], m.src[0])))
|
||
if Ops.OR in ops: pat += [(UPat.var("x", dtypes.bool).logical_not()&UPat.var("y", dtypes.bool).logical_not(),
|
||
lambda x,y: (x | y).logical_not())]
|
||
# rewrite MUL/CDIV to SHL+SHR: x*(2**y) -> shl(x,y) and x//(2**y) -> shr(x,y)
|
||
if Ops.SHL in ops: pat += [(UPat.var("x", dtypes.ints)*UPat.cvar("c"), lambda c,x: x << v if (v:=powers_of_two.get(c.arg, 0)) else None)]
|
||
if Ops.SHR in ops:
|
||
# uint CDIV by 2**v -> x >> v (FLOORDIV is lowered to CDIV by the rule above before reaching here)
|
||
pat += [(UPat(Ops.CDIV, src=(UPat.var("x", dtypes.uints), UPat.cvar("c"))),
|
||
lambda x,c: x >> v if (v:=powers_of_two.get(c.arg, 0)) else None)]
|
||
# signed CDIV (trunc) by 2**v -> (x + (x<0 ? c-1 : 0)) >> v
|
||
pat += [(UPat(Ops.CDIV, src=(UPat.var("x", dtypes.ints), UPat.cvar("c"))),
|
||
lambda x,c: (x+(l.const_like(l.vmin) if (l:=(x<0)).vmin==l.vmax else l).where(c-1, 0)) >> v
|
||
if (v:=powers_of_two.get(c.arg, 0)) else None)]
|
||
if not disable_fast_idiv:
|
||
# fast_idiv handles non-pow2: only fire on non-negative inputs (signed magic-mul is unreliable for x<0)
|
||
pat += [(UPat(Ops.CDIV, src=(UPat.var("x", dtypes.ints), UPat.cvar("d", vec=False))),
|
||
lambda ctx, x, d: fast_idiv(ctx, x, d.arg) if x.vmin >= 0 or x.dtype in dtypes.uints else None)]
|
||
# rewrite raw CMOD -> x - d*CDIV(x,d) so fast_idiv can pick up the CDIV. only on non-negative inputs;
|
||
# avoids disturbing floormod_to_mod's general-path output (which uses a trunc Ops.CMOD as an implementation detail)
|
||
pat += [(UPat(Ops.CMOD, src=(UPat.var("x", dtypes.ints), UPat.var("d"))),
|
||
lambda x, d: x - d * x.alu(Ops.CDIV, d) if x.vmin >= 0 or x.dtype in dtypes.uints else None)]
|
||
if Ops.NEG in ops:
|
||
pat += [(UPat.var('x')*-1, lambda ctx,x: x.alu(Ops.NEG))]
|
||
if Ops.SUB in ops: pat += [(UPat.var('x')+UPat.var('y').alu(Ops.NEG), lambda ctx,x,y: x.alu(Ops.SUB, y))]
|
||
if Ops.CMPLT in ops:
|
||
# These are late rewrites because simplex expects equalities to be a certain format
|
||
pat += [
|
||
((UPat.var("x", dtypes.sints) < UPat.cvar("c", dtypes.sints)).logical_not(), lambda x,c: c-1<x),
|
||
((UPat.cvar("c", dtypes.sints) < UPat.var("x", dtypes.sints)).logical_not(), lambda x,c: x<c+1),
|
||
(UPat.var("x", dtypes.sints)*-1 < UPat.var("y", dtypes.sints)*UPat.cvar("c"), lambda x,y,c: y*(-c)<x),
|
||
(UPat.var("x", dtypes.sints)*-1 < UPat.cvar("c"), lambda x,c:-c<x),
|
||
((UPat.cvar("c1",vec=False)<UPat.var("x", dtypes.sints)) & (UPat.var("x", dtypes.sints)<UPat.cvar("c2",vec=False)),
|
||
lambda x,c1,c2: x.eq(c1+1) if c1.arg+1==c2.arg-1 else None), # (c-1)<x & x<(c+1) -> x==c
|
||
]
|
||
if Ops.CMPEQ in ops: pat += [(UPat.var('x').ne(UPat.var('y')).logical_not(), lambda x,y: x.alu(Ops.CMPEQ, y))]
|
||
if Ops.MULACC in ops:
|
||
pat += [(UPat.var('a')*UPat.var('b')+UPat.var('c'), lambda a,b,c: a.alu(Ops.MULACC, b, c))]
|
||
# also fuse (x << n) + c → MULACC(x, 2^n, c) since MUL→SHL may run first
|
||
if Ops.SHL in ops: pat += [(UPat.var('x').alu(Ops.SHL, UPat.cvar('n'))+UPat.var('c'), lambda x,n,c: x.alu(Ops.MULACC, x.const_like(1<<n.arg), c))]
|
||
# some backends emit FDIV for RECIP, in that case: a*(1/b) -> a/b
|
||
if Ops.FDIV in ops:
|
||
pat += [(UPat.var("x").reciprocal(), lambda x: x.const_like(1).alu(Ops.FDIV, x))]
|
||
pat += [(UPat.var("a", dtypes.floats) * UPat.const(dtypes.floats, 1).alu(Ops.FDIV, UPat.var("b")), lambda a,b: a.alu(Ops.FDIV, b))]
|
||
return PatternMatcher(pat)
|
||
|
||
pm_long_decomp = PatternMatcher([
|
||
(UPat((*GroupOp.Defines, Ops.INDEX), name="x"), lambda x:
|
||
x.replace(dtype=l2i_dt[x.dtype.base].ptr(x.dtype.size * 2)) if hasattr(x.dtype, 'size') and x.dtype.base in l2i_dt else None),
|
||
(UPat(Ops.INDEX, tuple(l2i_dt.keys()), name='x'), lambda x: reindex(x, x.tag).replace(dtype=l2i_dt[x.dtype])),
|
||
(UPat(Ops.STORE, src=(UPat.var('idx'), UPat.var('val', tuple(l2i_dt.keys()))), name='st'), lambda st,idx,val:
|
||
st.replace(src=(reindex(idx, 0), val.rtag(0))).group(st.replace(src=(reindex(idx, 1), val.rtag(1)))) if val.tag is None else None),
|
||
(UPat(GroupOp.Comparison, src=(UPat.var('a', tuple(l2i_dt.keys())), UPat.var('b', tuple(l2i_dt.keys()))), name="x"), lambda a,b,x:
|
||
l2i(x.op, dt:=l2i_dt[a.dtype], a.rtag(0).cast(dt), a.rtag(1).cast(dt), b.rtag(0).cast(dt), b.rtag(1).cast(dt))),
|
||
(UPat(Ops.CAST, tuple(l2i_dt.keys()), src=(UPat.var('a'),), name="x"), lambda a,x:
|
||
l2i(x.op, x.dtype, a)[x.tag] if x.tag is not None and a.dtype not in l2i_dt else None),
|
||
(UPat(Ops.CAST, tuple(l2i_dt.keys()), src=(UPat.var('a', tuple(l2i_dt.keys())),), name="x"), lambda a,x:
|
||
(a.rtag(0).cast(dt:=l2i_dt[a.dtype]).bitcast(xdt:=l2i_dt[x.dtype]), a.rtag(1).cast(dt).bitcast(xdt))[x.tag]),
|
||
(UPat(Ops.CAST, src=(UPat.var('a', tuple(l2i_dt.keys())),), name="x"), lambda a,x:
|
||
l2i(x.op, x.dtype, a.rtag(0).cast(dt:=l2i_dt[a.dtype]), a.rtag(1).cast(dt)) if x.dtype not in l2i_dt and a.tag is None else None),
|
||
(UPat((*(GroupOp.ALU - GroupOp.Comparison), Ops.BITCAST), tuple(l2i_dt.keys()), name="x"), lambda x:
|
||
l2i(x.op, l2i_dt[x.dtype], *flatten((a.rtag(0).cast(dt:=l2i_dt[x.src[-1].dtype]), a.rtag(1).cast(dt))
|
||
if a.dtype in l2i_dt else (a,) for a in x.src))[x.tag] if x.tag is not None else None),
|
||
(UPat(Ops.LOAD, tuple(l2i_dt.keys()), src=(UPat.var('idx'),), name='x'), lambda x,idx: x.replace(dtype=l2i_dt[x.dtype],src=(reindex(idx, x.tag),))),
|
||
(UPat(Ops.CONST, tuple(l2i_dt.keys()), name='x'), lambda x:
|
||
UOp.const(dt:=l2i_dt[x.dtype], truncate[dt]((x.arg >> 32) if x.tag == 1 else (x.arg & 0xFFFFFFFF))))
|
||
])
|
||
|
||
# float decomposition patterns - ctx is (fr, to) tuple
|
||
pm_float_decomp = PatternMatcher([
|
||
(UPat((*GroupOp.Defines, Ops.INDEX), name="x"), lambda ctx,x:
|
||
x.replace(dtype=f2f_dt[ctx[0]].ptr(x.dtype.size), tag=ctx[0]) if x.dtype.base == ctx[0] else None),
|
||
(UPat(Ops.LOAD, dtypes.floats, name="x"), lambda ctx,x: f2f_load(x, *ctx) if x.dtype.scalar() == ctx[0] else None),
|
||
# bitcasted load should just replace load
|
||
(UPat(Ops.BITCAST, src=(UPat(Ops.LOAD, name="ld"),), name="bc"), lambda ctx,bc,ld:
|
||
ld.replace(dtype=f2f_dt[ctx[0]]).bitcast(bc.dtype) if ld.dtype == ctx[0] else None),
|
||
# bitcast from
|
||
(UPat(Ops.BITCAST, src=(UPat.var("x", dtypes.floats),), name="bc"), lambda ctx,bc,x:
|
||
bc.replace(src=(f2f(x.bitcast(f2f_dt[ctx[1]]), ctx[1], ctx[0]),)) if x.dtype == ctx[1] and bc.dtype.bitsize == ctx[0].bitsize else None),
|
||
# bitcast to
|
||
(UPat(Ops.BITCAST, src=(UPat.var("x"),), name="bc"), lambda ctx,bc,x:
|
||
f2f(x.bitcast(f2f_dt[ctx[0]]), ctx[0], ctx[1]) if bc.dtype == ctx[0] else None),
|
||
(UPat(Ops.CAST, dtypes.floats, src=(UPat.var("val"),), name="x"), lambda ctx,x,val:
|
||
f2f_clamp(val.cast(ctx[1]), ctx[0]) if x.dtype.scalar() == ctx[0] else None),
|
||
(UPat(GroupOp.All-{Ops.BITCAST}, dtypes.floats, name="x"), lambda ctx,x:
|
||
x.replace(dtype=ctx[1].vec(x.dtype.count), src=tuple(s.cast(ctx[1]) if s.dtype == ctx[0] else s for s in x.src))
|
||
if x.dtype.scalar() == ctx[0] else None),
|
||
(UPat(Ops.STORE, src=(UPat.var("idx"), UPat(Ops.BITCAST, dtypes.floats, name="val")), name='st'), lambda ctx,st,idx,val:
|
||
st.replace(src=(idx, val.replace(dtype=f2f_dt[ctx[0]]))) if val.dtype == ctx[0] and idx.tag == ctx[0] else None),
|
||
(UPat(Ops.STORE, src=(UPat.var("idx"), UPat.var("val", dtypes.floats)), name='st'), lambda ctx,st,idx,val:
|
||
f2f_store(st, idx, val, *ctx) if val.dtype.scalar() == ctx[1] and (idx:=idx.src[0] if idx.op == Ops.CAST else idx).tag == ctx[0] else None),
|
||
])
|
||
|
||
def do_dtype_decomps(sink:UOp, ctx:tuple[set[DType], Target]) -> UOp:
|
||
def _should_emulate(dt): return dt in EMULATED_DTYPES.tolist(dtypes) or not is_dtype_supported(dt, ctx[1])
|
||
for fr in sorted(filter(_should_emulate, ctx[0])):
|
||
if fr in dtypes.floats:
|
||
to = dtypes.half if not _should_emulate(dtypes.half) and fr in dtypes.fp8s else dtypes.float
|
||
sink = graph_rewrite(sink, pm_float_decomp, name=f"decomp {fr} -> {to}", ctx=(fr, to), bottom_up=True)
|
||
else: sink = graph_rewrite(sink, pm_long_decomp, name="decomp long -> int", bottom_up=True)
|
||
return sink
|
||
|
||
pm_dtype_decomps = PatternMatcher([
|
||
# detect dtypes to decompose
|
||
(UPat(GroupOp.All, (*dtypes.fp8s, dtypes.bfloat16, dtypes.half, dtypes.long, dtypes.ulong), name="x"), lambda x,ctx:
|
||
ctx[0].add({dtypes.ulong:dtypes.long}.get(dt:=x.dtype.base.scalar(), dt))),
|
||
# do the rewrites
|
||
(UPat(Ops.SINK, name="sink"), do_dtype_decomps),
|
||
])
|