# Copyright (c) 2025, Tri Dao. from typing import Tuple import cutlass import cutlass.cute as cute from cutlass import Int32, Uint32 from cutlass.cutlass_dsl import T, dsl_user_op from cutlass._mlir.dialects import llvm @cute.jit def clz(x: Int32) -> Int32: # for i in cutlass.range_constexpr(32): # if (1 << (31 - i)) & x: # return Int32(i) # return Int32(32) # Early exit is not supported yet res = Int32(32) done = False for i in cutlass.range(32): if ((1 << (31 - i)) & x) and not done: res = Int32(i) done = True return res def find_log2(x: Int32) -> Int32: a: Int32 = Int32(31 - clz(x)) return a + ((x & (x - 1)) != 0) # Round up, add 1 if not a power of 2. @dsl_user_op def umulhi(a: Int32, b: Int32, *, loc=None, ip=None) -> Uint32: return Uint32( llvm.inline_asm( T.i32(), [Int32(a).ir_value(loc=loc, ip=ip), Int32(b).ir_value(loc=loc, ip=ip)], "mul.hi.u32 $0, $1, $2;", "=r,r,r", has_side_effects=False, is_align_stack=False, asm_dialect=llvm.AsmDialect.AD_ATT, ) ) class FastDivmod: def __init__( self, divisor: Int32, multipler: Uint32, shift_right: Uint32, *, loc=None, ip=None ): self.divisor = divisor self.multiplier = multipler self.shift_right = shift_right self._loc = loc # called by host @staticmethod def create(divisor: Int32, *, loc=None, ip=None) -> "FastDivmod": """Construct the FastDivmod object, in host code. This precomputes some values based on the divisor and is computationally expensive. """ p = Uint32(31 + find_log2(divisor)) divisor_u32 = Uint32(divisor) multiplier = Uint32(((cutlass.Uint64(1) << p) + divisor_u32 - 1) // divisor_u32) shift_right = Uint32(p - 32) return FastDivmod(divisor, multiplier, shift_right, loc=loc, ip=ip) @cute.jit def div(self, dividend: Int32) -> Int32: return ( Int32(umulhi(dividend, self.multiplier) >> self.shift_right) if self.divisor != 1 else dividend ) def divmod(self, dividend: Int32) -> Tuple[Int32, Int32]: quotient = self.div(dividend) remainder = dividend - quotient * self.divisor return quotient, remainder def __extract_mlir_values__(self): values, self._values_pos = [], [] for obj in [self.divisor, self.multiplier, self.shift_right]: obj_values = cutlass.extract_mlir_values(obj) values += obj_values self._values_pos.append(len(obj_values)) return values def __new_from_mlir_values__(self, values): obj_list = [] for obj, n_items in zip( [self.divisor, self.multiplier, self.shift_right], self._values_pos ): obj_list.append(cutlass.new_from_mlir_values(obj, values[:n_items])) values = values[n_items:] return FastDivmod(*(tuple(obj_list)), loc=self._loc)