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Float expression precision map (decompile-derived)

Purpose: fast lookup for Python + Zig parity work. This map classifies common expression families by the precision model they need in deterministic gameplay paths.

Use this with float parity policy.

Precision classes

  • F32_STORE: expression result should be stored/kept as float32 state.
  • X87_INTERMEDIATE_THEN_F32: compute with x87-like widened intermediate, then spill to float32 at the native-equivalent store point.
  • F64_BOUNDARY_ONLY: f64/double is acceptable at formatting/IO boundaries, but should not drive gameplay state evolution.

Runtime assumption for this map: - CRT startup sets x87 precision-control to 53-bit (__controlfp(_PC_53, _MCW_PC) equivalent path), so “x87 intermediate” here means x87-shaped evaluation under PC_53 unless a function locally overrides CW. Evidence: crt_set_default_precision returns the control-word mapping call at 0x004636f8; the helper applies the 0x10000 precision selector around 0x00469f8e–0x00469f9e.

Decompile-wide signal counts (for confidence)

Historical Ghidra whole-view scan:

  • float10 occurrences: 1496
  • (float10)fcos/(float10)fsin/(float10)fpatan: 270
  • explicit (float)(...) casts: 996
  • explicit (double) casts: 31 (mostly CRT/vararg boundaries)

Historical IDA whole-view scan:

  • fcos/fsin/fpatan/fsqrt: 62/60/15/36
  • fld/fstp/fmul/fadd/fsub/fcomp/fnstsw: 1094/897/704/363/259/296/296

Expression lookup table

ID Expression family Class Native pattern (decompile) Required model Example anchor
E01 Heading from delta (atan2 path) X87_INTERMEDIATE_THEN_F32 (float10)fpatan((float10)dy,(float10)dx) then (float) store Widen for atan2, spill to f32 immediately when writing heading player_update @ 0x004136b0
E02 Direction from heading (cos) X87_INTERMEDIATE_THEN_F32 (float10)fcos((float10)heading - (float10)1.5707964) Widen for trig op, then f32 spill into velocity/move components player_update @ 0x004136b0
E03 Direction from heading (sin) X87_INTERMEDIATE_THEN_F32 (float10)fsin((float10)heading - (float10)1.5707964) Same as E02 player_update @ 0x004136b0
E04 Creature steering trig+spill X87_INTERMEDIATE_THEN_F32 fpatan target heading; fcos/fsin heading-to-vel; (float) assignments Keep transcendental intermediates widened; persist heading/vel_* as f32 creature_update_all @ 0x00426220
E05 Projectile angle step trig X87_INTERMEDIATE_THEN_F32 (float10)angle - half_pi; fcos/fsin in per-substep motion Widen trig/intermediate multiply chain; spill to f32 locals/state at native stores projectile_update @ 0x00420b90
E06 Length / distance compare X87_INTERMEDIATE_THEN_F32 (branch-sensitive) SQRT(dx*dx + dy*dy) < threshold Preserve op order and compare boundary behavior; treat as branch-sensitive creature_update_all @ 0x00426220
E07 Vec2 length helper return F32_STORE return SQRT(v[1]*v[1] + *v * *v); API return is f32; avoid carrying widened value past the return boundary vec2_length @ 0x00417660
E08 Normalize via reciprocal sqrt X87_INTERMEDIATE_THEN_F32 (1.0 / SQRT(a)) * ... assigned into vector components Keep rsqrt/sqrt intermediate precision; write normalized components as f32 d3dx_c_vec2_normalize @ 0x00455587
E09 Angle wrapping/approach arithmetic F32_STORE add/sub/abs/clamp around tau; no transcendental Keep exact operation order and f32 store cadence; no need for boundary f64 promotion angle_approach @ 0x0041f430
E10 Timers/cooldowns/speeds state updates F32_STORE state = state +/- frame_dt * k, clamp to bounds Keep state as f32; avoid accidental long-lived f64 accumulators in gameplay paths player_update @ 0x004136b0
E11 Float-int conversion hotspots (__ftol family) X87_INTERMEDIATE_THEN_F32 (int boundary) explicit __ftol() calls in movement/effects code Route through native-compatible helper; treat conversion semantics as parity-sensitive projectile_update @ 0x00420b90
E12 Formatting/vararg conversion F64_BOUNDARY_ONLY crt_sprintf(..., (double)f32_value) double here is boundary formatting ABI, not simulation precision policy mods_menu_update @ 0x0040e9a0

Binary Ninja cross-check pattern

Binary Ninja HLIL repeatedly shows the same model:

  • fconvert.t(...) before transcendental/extended arithmetic
  • fconvert.s(...) at storage boundaries

Example: gameplay_update_and_render at 0x00409e1d widens the projectile heading through fpatan before the float32 call boundary.

Practical implementation guidance

  • Python gameplay domain:
  • Keep long-lived runtime state in np.float32/explicit f32 wrappers.
  • For E01..E06/E08/E11, run native-style helper path then spill to f32 at the native-equivalent assignment point.
  • Do not keep replay-decoded f64 values live in gameplay state.
  • Zig gameplay domain:
  • Keep state fields as f32.
  • Use shared native math helpers for trig/atan/angle routines; call roundF32-style spill helpers at explicit store points.

Fast lookup recipes

  • Resolve the function and current tool snapshots:
  • just analysis-function player_update
  • Search live Binary Ninja HLIL:
  • bn search text 'fconvert\\.(t|s)|fpatan|fcos|fsin' --view hlil --target crimsonland.exe.bndb
  • Save a reusable function artifact:
  • bn bundle function player_update --target crimsonland.exe.bndb --out /tmp/player_update.json