implement f16

[AJ0070]

Stacked on #8. I cannot set a fork branch as the base, so the diff also shows #8's two commits; the change here is the last one, implement f16. Without #8 .target sm_53 does not parse, so none of this is reachable.

cvt to and from f16 threw conversion not implemented, and add, sub, mul, abs, neg, min, max, fma, set, setp, mov and ex2 rejected f16 as an instruction type. So nothing targeting sm_53 or newer could use half, and for a CUDA 12 toolchain that is every target, since sm_35 is gone.

f32 represents every f16 exactly, so operandAsHalf widens an operand and the existing f32 paths are reused: cvt takes f16 as a source by falling through to the f32 case, set and setp likewise, and destinations narrow with floatToHalf. The reuse is exact rather than merely convenient: half significands are 11 bits, so the exact product of two halves needs 22 of f32's 24 and the exact sum fits too, which makes computing in f32 and rounding once correctly rounded rather than double rounded. ex2 is .approx in PTX, so the f32 approximation is in spec.

Reading an operand cannot key off the declared type. tinygrad's PTX renderer declares halves .f16; nvrtc declares them .b16 and puts the op in inline asm:

.reg .b16 %rs<5>;
{mul.f16 %rs2,%rs3,%rs1;}

The half is in the low 16 bits either way. Immediates keep the f32 handling, because the parser types an immediate from the instruction and the lexer has no 0H half literal, so a constant reaching an .f16 instruction was written as a float and lives in imm_single; reading it as bits picks up the wrong member of the union.

cvt needed one more thing. relaxedConvert stores the mnemonic's type in a.relaxedType and leaves a.type as the register declaration, so operandAsF32 has to honour either. Without that, half loads on the nvrtc path came back as denormals like 2.15e-41, which is 0x3C00 sitting in a float. set also accepts a .b16 destination, since that is the register nvrtc writes the 1.0h/0.0h into.

halfToFloat and floatToHalf were checked against numpy before being wired in: all 65536 half bit patterns widen to the exact f32 bit pattern, and 531082 narrowing cases including every exact tie midpoint round identically, ties to even.

mad still rejects f16, since it is not implemented for it. Opening a gate without an implementation turns a clean abort into a wrong answer.

Measured on tinygrad's emulated CI, test/backend, on both emulator consumers, DEV=MOCK+CUDA:PTX and DEV=MOCK+NV:

ocelot	target	ptx cell	nv cell
master	sm_35	1738 pass, 0 fail, 453 skip	1669 pass, 0 fail, 458 skip
this	sm_35	1738 pass, 0 fail, 453 skip	1669 pass, 0 fail, 458 skip
this	sm_53	1738 pass, 0 fail, 443 skip	1669 pass, 0 fail, 449 skip

Zero failures everywhere, and sm_35 is unchanged on both cells, so this is a no-op at the current target. The freed skips at sm_53 are the fp16 tests, which have never been able to run: tinygrad disables half below sm_53, so a Kepler-reporting mock meant the NV emulator never tested fp16 at all. The nv cell at sm_53 runs on nvrtc 12.9 with matching cudart headers.

I closed the earlier version of this PR because it only handled tinygrad's PTX and silently returned wrong values on the nvrtc path. That is fixed and both paths are now verified.

[AJ0070]

Closing: this is incomplete and I found it after opening, so it does not meet the bar.

nvrtc declares half registers .b16 rather than .f16 and emits the ops inside inline asm:

.reg .b16 %rs<5>;
{mul.f16 %rs2,%rs3,%rs1;}

The widening here keys off the operand type, so those reads are wrong. Worse, before this change the validator cleanly rejected mul.f16 on .b16 registers; after it, they are accepted and return garbage. That is the exact abort-turned-into-wrong-answer failure I cited in the description as the reason for leaving mad and min closed, so it should not ship.

It is unreachable at sm_35, since half is disabled below sm_53, and I verified no change there. But unreachable is not correct.

Reopening once an operandAsHalf helper handles both register declarations and immediates, and both emulator consumers verify: tinygrad's own PTX renderer and nvrtc-generated PTX.

#8 is independent of this and unaffected.