They're truncated to float24 with one AND, and their exponents, fractions
and signs worked out for all terms at once, each term then broadcasting its
lane (new CrossSIMD Vec4S32::SplatLane). The term count becomes a template
parameter so the lanes are constants. About 75-83 M transforms/s on an M1,
from 68; results unchanged.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Four rows sharing their left operands, like a vertex transform's: with
float24 operands each exact product is a 32-bit integer, (1.a' * 1.b') >> 15
= 32768 + a' + b' + (a' b' >> 15), and the terms are aligned by scaling with
a power of two and truncating. Lanes whose result exponent is out of a
single float scale's reach take the scalar GERowSum. Tested bit for bit
against GERowSum on random operands (arm64 and x86-64). Not used yet.
Also adds an arithmetic Vec4S32::Shr and the float/int bit casts to
CrossSIMD.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
The minor offset walks from v0 with a slope quantized like a triangle
plane's gradient (setup reciprocal, 14 fraction bits per subpixel,
floored), rather than one product per pixel. Makes gpu/probe exp112
exact, and Virtua Tennis and echochrome lose their AA line misses.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Both were fit as exceptions with a K off the formula, but the probes that
pinned them are as happy with the formula's K and a slope of -128, which
the large-w UV planes need (gpu/probe exp136, exp138 now exact).
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
The minor-axis offset an antialiased line's alpha comes from is computed
with the triangle setup's reciprocal of the line's major length, walking
from v0, and floored; diagonal lines are y-major. exp112 went from 101
differing pixels to 23; the misses left sit at reciprocal segment starts.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Nearly every segment's K is floor(2^39 / (65536 + 256 i) / 16) * 16. The
fit to probe data left a few segments loose and slightly low; segment 39
made Blade Dancer's large triangle one depth unit high where the PSP's
depth test rejects it (frame dump now exact). Segments 39, 162, 253 and 255
now use the formula, which every probe accepts.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Segment 161's K was 16 low: exp54's one inexact Gouraud triangle needs
q >= 40211 at index 41275 (its y gradient -1366), and exp39/exp41 bound K
from above, leaving a window of 16 that the depth-only fit had missed. Every
color and depth probe is now exact.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
The exponent times the log (the float's bits) keeps units of 16 in the bits,
truncated toward zero, not floored at 1. Fixes the last specular pixels at
small exponents (gpu/probe exp102 e = 0.3, exp3, exp4 e = 0.05); all lighting
probes are now bit exact.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
GEProduct multiplies the significands as integers instead of going through
frexpf/ldexp/trunc in doubles, and GERowSum aligns and adds them as integers.
About 4.5x faster per matrix row on arm64, same results.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
The float24 truncations, reciprocal and rsqrt tables, GE adder and row sums,
the setup reciprocal for planes, the mip log2, texture coordinate precision,
the lighting pow and color scaling, and the antialiased line alpha, from
TransformUnit, Rasterizer and Lighting, so they can be unit tested. No
behavior change.
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
