#2839 decides f32 product tininess after rounding, in all four f32
round modes, from the exponents and a UMulHi and IMul of the
significands, and builds the flushed value from them. To nearest even,
the mode of shaders without a known float mode and of the 0xc0 most
titles use, one multiply decides it: one factor times 2^64, which is
exact below 2^64, times the other factor rounds the exact product once
to 24 bits in the normal range, and 0 < |that| < 2^-62 is tininess
after rounding. A product that rounds up to 2^-126 is then not tiny and
keeps the emitted product, which is 2^-126 there, so nothing has to be
built from the significands.
The flush of v_mul_f32 v5, v6, v7 takes 12 IR instructions instead of
34, counted as the instructions the flush select needs beyond the
product. vector_constant_factor_tininess pins 12 to nearest and 36 for
the directed path of the same instruction, and checks that the
directed modes and v_mad_legacy_f32 (before rounding) keep #2839's
check. Its round-to-nearest branches are removed as unreachable.
The f32 denormals entry says which rounding the check inherits: the
multiply is a plain OpFMul like the product, with no f32 rounding mode
requested, so it relies on the driver rounding f32 to nearest even, as
the products do. F32ConstantFactorTininess names the row a check before
rounding flushes, 0x3f7ffffe * 0x00800001, which keeps the emitted
0x00800000.
Against #2839 to nearest even, a model of both checks agrees on
1,074,977,546 operand pairs (every 24-bit significand at both rounding
thresholds, random pairs, specials) with each other and with an exact
reference. On an RTX 5070 the outputs of #2839's own tininess and
mixed-source shaders are bit-identical with either lowering over
165,298 and 164,008 generated rows in all six float modes tested.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
With f32 denormals flushed, every f32 multiply and fma checks whether the
exact product is below 2^-126 (#1850): two exponent extracts, a 32-bit
significand multiply-high and a chain of compares and selects. When a
factor is a literal or inline constant, its exponent settles the check
during translation:
- a factor that is zero (after the input flush), infinite, NaN or at least
1 in magnitude never gives a tiny product, so the check is not emitted;
- a power-of-two factor never carries out of the significand product, so
the multiply-high is not emitted.
Constant sources are folded with their abs, neg and denormal flush, so the
factor reaches the check as a constant.
AlxcBTW
Karan Vora