R8 opp-bank Loc slot tables (INJ/RETS/SRC)
DefinitionIntMul_Kappa_R8_Data_BitOppbankLocSlotsbitnbinteger-multiplicationkappaoppbankr8
Packed local-slot tables for the round-eight / R7-plain bit network at auxiliary width .
The tables record, for Jain's joint-frame-stack witness (jfstack_23):
- : the three points of each lex triple (5-bit fields);
- : the three injection slots of each triple (16-bit fields), equal to the schedule's output slots;
- / : the retained slot and DAG node of each centre ;
- : the source slot of each leaf/triple.
They are stored with the same packL limb encoding as the round-six BitNB GenData modules (65536-bit limbs, least significant first).
These constants are the Loc inputs to injS / retS / srcS used by the stage words and by genF when emitting SG* code states at local width .
Formalization Note. Lean module IntMul.Kappa.R8.Bit.Oppbank.LocSlots; source certificates/round7/jfstack_23.json.gz via jfdata.load(23).
Definition code
import Mathlib.Data.Nat.Basic set_option autoImplicit false set_option relaxedAutoImplicit false /-! # R8 opp-bank Loc slot tables (jfstack_23, `R = 27794`) Packed with the same `packL` (65536-bit limbs, LSB first) as R6 BitNB GenData. Fields: `TPTS` 5-bit @ `3T+k`; `INJ`/`RETS`/`RETN`/`SRC` 16-bit. Source: Jain `certificates/round7/jfstack_23.json.gz` via `jfdata.load(23)`. -/ namespace IntMul.Kappa.R8.Bit.Oppbank.LocSlots def packL (l : List Nat) : Nat := l.foldr (fun p acc => Nat.lor p (Nat.shiftLeft acc 65536)) 0 /-- Triple points: field 3T+k (5 bits), lex order. -/ def TPTS : Nat := packL [ 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] /-- Injection slots: field 3T+k (16 bits) = jfstack out(T,c). -/ def INJ : Nat := packL [ 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] /-- Retained slot of centre c. -/ def RETS : Nat := packL [ 0x2b582b552b522b222b1f2a872a84295429512759275624662463204b20481ad81ad513dd13da0b2a0b27008f008c ] /-- Retained node of centre c. -/ def RETN : Nat := packL [ 0xf40ef40cf40af408f406f404f402f400f3fef3fcf3faf3f8f3f6f3f4f3f2f3f0f3eef3ecf3eaf3e8f3e6f3e4f3e2 ] /-- Source (leaf) slot of triple t. -/ def SRC : Nat := packL [ 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] end IntMul.Kappa.R8.Bit.Oppbank.LocSlots
Source
Swapnil Jain integer-mult-kappa, certificates/round7/jfstack_23.json.gz; R6 BitNB Loc field layout from Prove2me IntMul_Kappa_R6_Data_BitNBLocData (Defs51 injS/retS/srcS).