Applicability of this chapter to configurations:
| Configuration | Implementation |
|---|---|
| CV32A60AX | Implemented extension |
| CV32A60X | Implemented extension |
Carry-less multiplication is the multiplication in the polynomial ring over GF(2).
clmul produces the lower half of the carry-less product and clmulh produces the upper half of the 2✕XLEN carry-less product.
clmulr produces bits 2✕XLEN−2:XLEN-1 of the 2✕XLEN carry-less product.
The following instructions (and pseudoinstructions) comprise the Zbc extension:
| RV32 | RV64 | Mnemonic |
|---|---|---|
| ✔ | ✔ | clmul rd, rs1, rs2 |
| ✔ | ✔ | clmulh rd, rs1, rs2 |
| ✔ | ✔ | clmulr rd, rs1, rs2 |
CLMUL: Carry-less multiply (low-part)
Format: clmul rd, rs1, rs2
Description: clmul produces the lower half of the 2.XLEN carry-less product.
Pseudocode: foreach (i from 1 to xlen by 1) { output = if ((rs2 >> i) & 1) then output ^ (rs1 << i); else output; }
Invalid values: NONE
Exception raised: NONE
CLMULH: Carry-less multiply (high-part)
Format: clmulh rd, rs1, rs2
Description: clmulh produces the upper half of the 2.XLEN carry-less product.
Pseudocode: foreach (i from 1 to xlen by 1) { output = if ((rs2_val >> i) & 1) then output ^ (rs1_val >> (xlen - i)) else output }
Invalid values: NONE
Exception raised: NONE
CLMULR: Carry-less multiply (reversed)
Format: clmulr rd, rs1, rs2
Description: clmulr produces bits 2.XLEN-2:XLEN-1 of the 2.XLEN carry-less product.
Pseudocode: foreach (i from 0 to (xlen - 1) by 1) { output = if ((rs2_val >> i) & 1) then output ^ (rs1_val >> (xlen - i - 1)) else output}
Invalid values: NONE
Exception raised: NONE