codegen: PS2-accurate divide-by-zero semantics for COP1 and VU0 FP + RSQRT operand fix

[jlsandri]

Problem

Five related floating-point codegen corrections for EE COP1 and VU0. All five are mis-emulations of documented PS2 hardware semantics.

1. COP1_S_RSQRT was using the wrong source operand

The previous emitter produced

ctx->f[fd] = 1.0f / sqrtf(ctx->f[fs]);

which is the formula for reciprocal-sqrt of fs. The actual PS2 rsqrt.s operation is

fd = fs / sqrt(ft)

The emitter ignored ft entirely and used fs as the radicand. Fixed to use ft as the radicand and fs as the numerator. (This operand fix is also a prerequisite for the div-by-zero handling below, which rewrites the same line.)

2. COP1_S_DIV divide-by-zero

The PS2 EE does not produce IEEE infinity on divide-by-zero. It returns 0x7F7FFFFF (the largest finite float) with the sign bit set to sign(fs) XOR sign(ft). Previously the codegen emitted copysignf(INFINITY, fs * 0.0f) which produces IEEE ±∞.

3. COP1_S_RSQRT divide-by-zero

Same 0x7F7FFFFF + sign semantics, with sign taken from fs. Also guards the sqrt input with std::max(0.0f, ft) to match the EE behaviour of ignoring the sign bit on the radicand instead of producing a NaN.

4. VU0 vdiv divide-by-zero

Same 0x7F7FFFFF + sign semantics, writing to vu0_q. Previously returned 0.0f on div-by-zero, which is visibly wrong for game code that relies on the max-float fallback.

5. VU0 vrsqrt divide-by-zero

Same 0x7F7FFFFF semantics (unsigned, per the VU0 ISA). Previously returned 0.0f.

Implementation

All five use std::bit_cast<float>(uint32_t) for the bit-level construction of the max-float sentinel, and each site has an inline comment documenting the 0x7F7FFFFF magic constant so it is self-explanatory.

Scope

• One file: ps2xRecomp/src/lib/code_generator.cpp
• +10 / -5

Rationale

All five changes bring the generated code into line with documented PS2 floating-point semantics. The div-by-zero behaviour in particular is well-known to differ from IEEE and is frequently relied upon by EE code that intentionally divides by zero as a cheap max-float construction.

[jlsandri]

Closing as part of a batch cleanup after #107 landed. The runtime ecosystem refactor in #107 substantially reworked the files this PR touched, and I would like to re-audit the underlying fix against the new code structure before putting it back in front of you. If the fix is still needed after that re-audit, I will re-open as a focused PR rebased onto current main. Thanks for your patience.