Native preparation and encoding of shared matrix bands

The input is L :: m :: N :: X ++ Y, with both matrices in row-major order and their signed entries encoded by Signed.encode. The native length header occupies address zero. The program snapshots the complete initialized input before using the encoder's low workspace, computes its subset tables, prepares and encodes each band once, and restores the input.

The dense inverse table uses zero for an unselected mask and rank plus one for a selected mask. The forward table lists the first K0² masks of cardinality m in increasing numeric order. The shared output catalogue consists of all left bands followed by all right bands, with 10^L consecutive cells per band. A tile refers to its two band entries in this catalogue.

LeftVar.equiv and RightVar.equiv identify the mathematical alphabets with Fin 3 ⊕ (Fin 2 × Fin 2), and Term.equiv identifies terms with Option (Fin 3 × Fin 3). The existing native Encoding.leftDigits, Encoding.rightDigits and Encoding.termDigits also fix the executable flat Fin 7/Fin 10 order: the nine product terms are row-major, with digit 3*i+j, and P0 has digit 9. This preparation retains that numbering unchanged.

Main definitions

• BandPreparation.program: fixed native code, including the actual shared encoders.
• BandPreparation.input: flat header and matrix input for State.init.
• BandPreparation.catalogueAddress: the location of a band's encoding leaf.

References

Selective adaptation of the band preparation in [AlmanWilliams2026, Section 2.4.1] and Anthropic's formal-math revision 16a5ce41304fcdaea4e0be7c132e1c361dc26da5, band-array preparation and all-band encoding. The mask scans, dense inverse table, native control and memory layout here are new; the source's Light machine and execution semantics are not used.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.inputEnd (m N : ℕ) : ℕ

Original initialized input prefix, including the native length header and three parameters.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.snapshotBase (L m N : ℕ) : ℕ

The encoder's low workspace and the original input are both below the snapshot.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.inverseBase (L m N : ℕ) : ℕ

Dense mask-to-rank inverse table.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.tableBase (L m N : ℕ) : ℕ

Forward selected-mask table; 2^L cells are reserved.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.catalogueBase (L m N : ℕ) : ℕ

Shared encoding catalogue, after the snapshot and both tables.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.catalogueAddress (L m N : ℕ) (rightSide : Bool) (β leaf : ℕ) : ℕ

Every left band, then every right band, occupies one block of 10^L words.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.memoryEnd (L m N : ℕ) : ℕ

One past all allocated memory.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.wordBudget (L m N : ℕ) : ℕ

Explicit input-parameter bound used to derive every unsigned arithmetic/address fit. The signed magnitude condition is separate. This is an ordinary numerical inequality, without quantification over executions or intermediate states.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.input (L m N : ℕ) (X : Matrix (Fin N) (Fin (MatrixMultiplication.Schonhage.D m)) ℤ) (Y : Matrix (Fin (MatrixMultiplication.Schonhage.D m)) (Fin N) ℤ) : List ℕ

Row-major signed matrix input; no table, power or encoded band is supplied by the caller.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.levels : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.copySrc : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.copyDst : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.copyLen : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.inner : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.rows : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.columns : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.outerSize : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.masks : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.cells : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.leaves : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.prefixSize : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.snapshot : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.inverse : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.table : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.catalogue : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.bands : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.count : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.root : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.square : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.temporary : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.one : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.two : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.three : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.four : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.seven : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.ten : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.counter : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.mask : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.population : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.residue : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.digit : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.limit : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.rank : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.address : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.band : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.index : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.maskAcc : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.outerAcc : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.innerAcc : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.maskPower : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.outerPower : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.innerPower : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.level : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.block : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.row : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.source : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.value : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

@[reducible, inline]

abbrev Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.zero : Fin 96

Low registers are reserved for the existing encoder and copy routines. Persistent parameters and preparation counters occupy registers 32 through 84 of a fixed bank of 96.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.encoderRegisters (i : Fin 32) : Fin 96

Register embedding for the unchanged shared encoders.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.copyRegisters (i : Fin 7) : Fin 96

Register embedding for the unchanged seven-register copy program.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.powerRegisters (v b n : Fin 96) : Fin 5 → Fin 96

Embed the five-register native power routine in the caller's chosen scalar registers.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.powerCode (v b n : Fin 96) : WordRAM.Code WordRAM.Basis.standard 96

The actual native power routine, with register renaming only.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.populationCode : WordRAM.Code WordRAM.Basis.standard 96

Popcount is computed by an explicit fixed-depth loop of divisions and remainders.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.headerLoads : WordRAM.Code WordRAM.Basis.standard 96

Load the three actual header parameters and the small constants.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.headerPowers : WordRAM.Code WordRAM.Basis.standard 96

Compute all five powers with actual renamed native routines.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.headerLayout : WordRAM.Code WordRAM.Basis.standard 96

Compute concrete snapshot, table and catalogue addresses.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.header : WordRAM.Code WordRAM.Basis.standard 96

Compute the three header parameters, powers and addresses with charged native code.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.saveInput : WordRAM.Code WordRAM.Basis.standard 96

Save every original input word, including the actual length header.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.countBody : WordRAM.Code WordRAM.Basis.standard 96

Visit one mask and update the number of accepted masks.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.countMasks : WordRAM.Code WordRAM.Basis.standard 96

Count every size-m mask.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.rootBody : WordRAM.Code WordRAM.Basis.standard 96

One explicitly squared trial in the integer square-root search.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.rootCode : WordRAM.Code WordRAM.Basis.standard 96

Compute the integer square root by squared comparisons. No square-root instruction is added to the native basis.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.bandCount : WordRAM.Code WordRAM.Basis.standard 96

Compute the ceiling quotient giving the number of bands.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.countCode : WordRAM.Code WordRAM.Basis.standard 96

Complete scalar band parameters from native mask counting and root computation.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.tableWrite : WordRAM.Code WordRAM.Basis.standard 96

Store the two table entries belonging to the current mask and advance both counters.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.tableBody : WordRAM.Code WordRAM.Basis.standard 96

One complete table iteration, including the actual population scan.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.tablesCode : WordRAM.Code WordRAM.Basis.standard 96

Materialize both tables, explicitly initializing every inverse-table cell.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.splitHead : WordRAM.Code WordRAM.Basis.standard 96

Initialize the three digit accumulators and their positional weights.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.splitBody : WordRAM.Code WordRAM.Basis.standard 96

One base-seven digit, with only ordinary native arithmetic and control.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.splitCode : WordRAM.Code WordRAM.Basis.standard 96

Decode a base-seven string into its inner mask and compressed base-three/base-four offsets, in increasing level order. Every division, remainder, product and increment is native.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.readCell (rightSide : Bool) : WordRAM.Code WordRAM.Basis.standard 96

Read a real matrix cell only after checking the padded row/column against N. In particular, the potentially oversized row-major product is inside the guard.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.prepareHead : WordRAM.Code WordRAM.Basis.standard 96

Actual header and counter initialization for each band.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.prepareBody (rightSide : Bool) : WordRAM.Code WordRAM.Basis.standard 96

Decode, guard, load and store one band-array entry.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.prepareBand (rightSide : Bool) : WordRAM.Code WordRAM.Basis.standard 96

Prepare every entry of one low-workspace band array, including all zero padding.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.collectHead (rightSide : Bool) : WordRAM.Code WordRAM.Basis.standard 96

Set up the actual encoder-output copy, including its catalogue address arithmetic.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.collectBand (rightSide : Bool) : WordRAM.Code WordRAM.Basis.standard 96

Copy the actual encoder output to this band's shared catalogue entry.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.bandBody (rightSide : Bool) : WordRAM.Code WordRAM.Basis.standard 96

Prepare, encode and collect one shared band, then advance its counter.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.encodeBands (rightSide : Bool) : WordRAM.Code WordRAM.Basis.standard 96

Each row/column band calls the actual unchanged finite native encoder exactly once.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.restoreInput : WordRAM.Code WordRAM.Basis.standard 96

Restore the complete original initialized input after all low-workspace calls.

def Cslib.Algorithms.WordRAM.MatrixMultiplication.Schonhage.BandPreparation.program : WordRAM.Code WordRAM.Basis.standard 96

One fixed finite native program for the entire band-preparation component. Halt returns catalogue, the base address of the shared encodings; it is appended by Code.program.