All tutorials · Updated September 21, 2026 · tinygrad 8ad8f73
Upcasting and loop unrolling change how a logical coordinate is represented. They must preserve the mapping from every output/reduction coordinate to its input element.
Suppose r ranges over twelve elements. A split by four represents it as 4*outer + inner, with outer in [0,3) and inner in [0,4).
from tinygrad.uop.ops import UOp
outer = UOp.variable("outer", 0, 2)
inner = UOp.variable("inner", 0, 3)
r = outer * 4 + inner
seen = [r.sym_infer({"outer": a, "inner": b}) for a in range(3) for b in range(4)]
assert seen == list(range(12))
print(seen)
This is the coordinate identity a split must preserve. It is not a request to the kernel optimizer; it isolates the indexing argument so it can be checked independently.
If an input’s address expression contains 3*r + j, substitution produces 12*outer + 3*inner + j. If the inner axis is expanded, the compiler can specialize that expression for inner values 0, 1, 2, and 3.
Current Scheduler.shift_to creates ranges and rewrites indexing according to a requested split. Later expansion turns selected UPCAST/UNROLL ranges into shaped constants. The renderer receives the lowered result, not a ShapeTracker.
When a split/padding strategy introduces coordinates beyond the original extent, the accesses must remain guarded or otherwise made valid. A rewrite that preserves the arithmetic for valid points but loses the bounds condition is incorrect.
See movement and indexing for padding validity and reshape composition. When debugging, trace the coordinate expression and its validity together; a pretty simplified address is only half of the access semantics.
Original chapter by Di Zhu: historical version.