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Add HOL Light rej_uniform_eta4 proof for AArch64
Add formal correctness proof for the AArch64 mld_rej_uniform_eta4_asm function, which performs rejection sampling with eta=4 for ML-DSA. The proof verifies that the assembly implementation correctly: - Extracts 4-bit nibbles from input bytes - Filters nibbles < 9 using SIMD comparison + TBL permutation - Maps accepted values n to (4 - n) as signed 32-bit integers - Returns at most 256 coefficients with the correct count Verified against the compiled object code (post-hoc, not trusting the assembler) using the s2n-bignum ARM verification framework in HOL Light. All 86 AArch64 instructions are mechanically verified across every execution path (360+ ARM simulation steps). No CHEAT_TAC remains. New files: - mldsa_rej_uniform_eta4.S: standalone assembly for proof bytecodes - mldsa_rej_uniform_eta4.ml: 547-line HOL Light correctness proof - mldsa_rej_uniform_eta_table.ml: 256-entry lookup table constants Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com> Signed-off-by: Jake Massimo <jakemas@amazon.com>
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‎.github/workflows/hol_light.yml‎

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@@ -95,6 +95,8 @@ jobs:
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needs: ["aarch64_utils.ml"]
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- name: mldsa_poly_chknorm
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needs: ["aarch64_utils.ml"]
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- name: mldsa_rej_uniform_eta4
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needs: ["mldsa_specs.ml", "aarch64_utils.ml", "mldsa_rej_uniform_eta_table.ml", "subroutine_signatures.ml"]
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- name: keccak_f1600_x1_scalar
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needs: ["keccak_spec.ml"]
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- name: keccak_f1600_x1_v84a

‎dev/aarch64_opt/src/arith_native_aarch64.h‎

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@@ -86,7 +86,19 @@ uint64_t mld_rej_uniform_eta2_asm(int32_t *r, const uint8_t *buf,
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#define mld_rej_uniform_eta4_asm MLD_NAMESPACE(rej_uniform_eta4_asm)
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MLD_MUST_CHECK_RETURN_VALUE
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uint64_t mld_rej_uniform_eta4_asm(int32_t *r, const uint8_t *buf,
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unsigned buflen, const uint8_t *table);
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unsigned buflen, const uint8_t *table)
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/* This must be kept in sync with the HOL-Light specification
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* in proofs/hol_light/aarch64/proofs/mldsa_rej_uniform_eta4.ml */
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__contract__(
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requires(buflen % 8 == 0)
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requires(buflen >= 8)
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requires(memory_no_alias(r, sizeof(int32_t) * MLDSA_N))
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requires(memory_no_alias(buf, buflen))
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requires(memory_no_alias(table, 4096)) /* check-magic: 4096 == 256 * 16 */
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assigns(memory_slice(r, sizeof(int32_t) * MLDSA_N))
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ensures(return_value <= MLDSA_N)
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ensures(array_abs_bound(r, 0, return_value, MLDSA_ETA + 1))
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);
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#define mld_poly_decompose_32_asm MLD_NAMESPACE(poly_decompose_32_asm)
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void mld_poly_decompose_32_asm(int32_t *a1, int32_t *a0);

‎mldsa/src/native/aarch64/src/arith_native_aarch64.h‎

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@@ -86,7 +86,19 @@ uint64_t mld_rej_uniform_eta2_asm(int32_t *r, const uint8_t *buf,
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#define mld_rej_uniform_eta4_asm MLD_NAMESPACE(rej_uniform_eta4_asm)
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MLD_MUST_CHECK_RETURN_VALUE
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uint64_t mld_rej_uniform_eta4_asm(int32_t *r, const uint8_t *buf,
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unsigned buflen, const uint8_t *table);
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unsigned buflen, const uint8_t *table)
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/* This must be kept in sync with the HOL-Light specification
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* in proofs/hol_light/aarch64/proofs/mldsa_rej_uniform_eta4.ml */
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__contract__(
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requires(buflen % 8 == 0)
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requires(buflen >= 8)
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requires(memory_no_alias(r, sizeof(int32_t) * MLDSA_N))
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requires(memory_no_alias(buf, buflen))
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requires(memory_no_alias(table, 4096)) /* check-magic: 4096 == 256 * 16 */
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assigns(memory_slice(r, sizeof(int32_t) * MLDSA_N))
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ensures(return_value <= MLDSA_N)
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ensures(array_abs_bound(r, 0, return_value, MLDSA_ETA + 1))
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);
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#define mld_poly_decompose_32_asm MLD_NAMESPACE(poly_decompose_32_asm)
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void mld_poly_decompose_32_asm(int32_t *a1, int32_t *a0);

‎proofs/cbmc/rej_uniform_eta4_native_aarch64/Makefile‎

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# Copyright (c) The mldsa-native project authors
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# SPDX-License-Identifier: Apache-2.0 OR ISC OR MIT
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include ../Makefile_params.common
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HARNESS_ENTRY = harness
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HARNESS_FILE = rej_uniform_eta4_native_aarch64_harness
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# This should be a unique identifier for this proof, and will appear on the
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# Litani dashboard. It can be human-readable and contain spaces if you wish.
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PROOF_UID = rej_uniform_eta4_native_aarch64
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# We need to set MLD_CHECK_APIS as otherwise mldsa/src/native/api.h won't be
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# included, which contains the CBMC specifications.
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DEFINES += -DMLD_CONFIG_USE_NATIVE_BACKEND_ARITH -DMLD_CONFIG_ARITH_BACKEND_FILE="\"$(SRCDIR)/mldsa/src/native/aarch64/meta.h\"" -DMLD_CHECK_APIS
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INCLUDES +=
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REMOVE_FUNCTION_BODY +=
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UNWINDSET +=
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PROOF_SOURCES += $(PROOFDIR)/$(HARNESS_FILE).c
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PROJECT_SOURCES += $(SRCDIR)/mldsa/src/poly_kl.c
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CHECK_FUNCTION_CONTRACTS=mld_rej_uniform_eta4_native
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USE_FUNCTION_CONTRACTS = mld_rej_uniform_eta4_asm
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USE_FUNCTION_CONTRACTS += mld_sys_check_capability
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APPLY_LOOP_CONTRACTS=on
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USE_DYNAMIC_FRAMES=1
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# Disable any setting of EXTERNAL_SAT_SOLVER, and choose SMT backend instead
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EXTERNAL_SAT_SOLVER=
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CBMCFLAGS=--bitwuzla
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FUNCTION_NAME = rej_uniform_eta4_native_aarch64
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# If this proof is found to consume huge amounts of RAM, you can set the
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# EXPENSIVE variable. With new enough versions of the proof tools, this will
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# restrict the number of EXPENSIVE CBMC jobs running at once. See the
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# documentation in Makefile.common under the "Job Pools" heading for details.
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# EXPENSIVE = true
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# This function is large enough to need...
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CBMC_OBJECT_BITS = 8
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include ../Makefile.common

‎proofs/cbmc/rej_uniform_eta4_native_aarch64/rej_uniform_eta4_native_aarch64_harness.c‎

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// Copyright (c) The mldsa-native project authors
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// SPDX-License-Identifier: Apache-2.0 OR ISC OR MIT
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#include <stdint.h>
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#include "cbmc.h"
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#include "params.h"
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int mld_rej_uniform_eta4_native(int32_t *r, unsigned len, const uint8_t *buf,
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unsigned buflen);
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void harness(void)
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{
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int32_t *r;
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unsigned len;
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const uint8_t *buf;
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unsigned buflen;
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int t;
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t = mld_rej_uniform_eta4_native(r, len, buf, buflen);
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}

‎proofs/hol_light/README.md‎

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@@ -58,6 +58,7 @@ echo '1+1;;' | nc -w 5 127.0.0.1 2012
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* AArch64 pointwise multiplication-accumulation (l=4): [mldsa_pointwise_acc_l4.S](aarch64/mldsa/mldsa_pointwise_acc_l4.S)
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* AArch64 pointwise multiplication-accumulation (l=5): [mldsa_pointwise_acc_l5.S](aarch64/mldsa/mldsa_pointwise_acc_l5.S)
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* AArch64 pointwise multiplication-accumulation (l=7): [mldsa_pointwise_acc_l7.S](aarch64/mldsa/mldsa_pointwise_acc_l7.S)
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* AArch64 rejection sampling (eta=4): [mldsa_rej_uniform_eta4.S](aarch64/mldsa/mldsa_rej_uniform_eta4.S)
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* x86_64 forward NTT: [mldsa_ntt.S](x86_64/mldsa/mldsa_ntt.S)
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* x86_64 inverse NTT: [mldsa_intt.S](x86_64/mldsa/mldsa_intt.S)
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* x86_64 pointwise multiplication: [mldsa_pointwise.S](x86_64/mldsa/mldsa_pointwise.S)

‎proofs/hol_light/aarch64/Makefile‎

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@@ -60,6 +60,7 @@ OBJ = mldsa/mldsa_ntt.o \
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mldsa/mldsa_pointwise_acc_l4.o \
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mldsa/mldsa_pointwise_acc_l5.o \
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mldsa/mldsa_pointwise_acc_l7.o \
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mldsa/mldsa_rej_uniform_eta4.o \
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mldsa/keccak_f1600_x1_scalar.o \
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mldsa/keccak_f1600_x1_v84a.o \
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mldsa/keccak_f1600_x2_v84a.o \

‎proofs/hol_light/aarch64/mldsa/mldsa_rej_uniform_eta4.S‎

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/*
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* Copyright (c) The mldsa-native project authors
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* Copyright (c) The mlkem-native project authors
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* SPDX-License-Identifier: Apache-2.0 OR ISC OR MIT
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*/
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/*
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* WARNING: This file is auto-derived from the mldsa-native source file
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* mldsa/src/native/aarch64/src/rej_uniform_eta4_asm.S using scripts/simpasm. Do not modify it directly.
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*/
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#if defined(__ELF__)
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.section .note.GNU-stack,"",@progbits
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#endif
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.text
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.balign 4
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#ifdef __APPLE__
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.global _PQCP_MLDSA_NATIVE_MLDSA44_rej_uniform_eta4_asm
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_PQCP_MLDSA_NATIVE_MLDSA44_rej_uniform_eta4_asm:
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#else
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.global PQCP_MLDSA_NATIVE_MLDSA44_rej_uniform_eta4_asm
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PQCP_MLDSA_NATIVE_MLDSA44_rej_uniform_eta4_asm:
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#endif
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.cfi_startproc
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sub sp, sp, #0x240
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.cfi_adjust_cfa_offset 0x240
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mov x7, #0x1 // =1
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movk x7, #0x2, lsl #16
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movk x7, #0x4, lsl #32
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movk x7, #0x8, lsl #48
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mov v31.d[0], x7
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mov x7, #0x10 // =16
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movk x7, #0x20, lsl #16
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movk x7, #0x40, lsl #32
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movk x7, #0x80, lsl #48
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mov v31.d[1], x7
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movi v30.8h, #0x9
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movi v7.8h, #0x4
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mov x8, sp
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mov x7, x8
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mov x11, #0x0 // =0
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eor v16.16b, v16.16b, v16.16b
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Lrej_uniform_eta4_initial_zero:
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str q16, [x7], #0x40
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stur q16, [x7, #-0x30]
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stur q16, [x7, #-0x20]
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stur q16, [x7, #-0x10]
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add x11, x11, #0x20
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cmp x11, #0x100
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b.lt Lrej_uniform_eta4_initial_zero
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mov x7, x8
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mov x9, #0x0 // =0
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mov x4, #0x100 // =256
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Lrej_uniform_eta4_loop8:
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cmp x9, x4
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b.hs Lrej_uniform_eta4_memory_copy
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sub x2, x2, #0x8
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ld1 { v0.8b }, [x1], #8
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movi v26.8b, #0xf
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and v27.8b, v0.8b, v26.8b
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ushr v28.8b, v0.8b, #0x4
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zip1 v26.8b, v27.8b, v28.8b
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zip2 v29.8b, v27.8b, v28.8b
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ushll v16.8h, v26.8b, #0x0
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ushll v17.8h, v29.8b, #0x0
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cmhi v4.8h, v30.8h, v16.8h
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cmhi v5.8h, v30.8h, v17.8h
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and v4.16b, v4.16b, v31.16b
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and v5.16b, v5.16b, v31.16b
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uaddlv s20, v4.8h
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uaddlv s21, v5.8h
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fmov w12, s20
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fmov w13, s21
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ldr q24, [x3, x12, lsl #4]
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ldr q25, [x3, x13, lsl #4]
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cnt v4.16b, v4.16b
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cnt v5.16b, v5.16b
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uaddlv s20, v4.8h
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uaddlv s21, v5.8h
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fmov w12, s20
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fmov w13, s21
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tbl v16.16b, { v16.16b }, v24.16b
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tbl v17.16b, { v17.16b }, v25.16b
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st1 { v16.8h }, [x7]
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add x7, x7, x12, lsl #1
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st1 { v17.8h }, [x7]
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add x7, x7, x13, lsl #1
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add x12, x12, x13
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add x9, x9, x12
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cmp x2, #0x8
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b.hs Lrej_uniform_eta4_loop8
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Lrej_uniform_eta4_memory_copy:
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cmp x9, x4
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csel x9, x9, x4, lo
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mov x11, #0x0 // =0
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mov x7, x8
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Lrej_uniform_eta4_final_copy:
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ldr q16, [x7], #0x20
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ldur q18, [x7, #-0x10]
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sub v16.8h, v7.8h, v16.8h
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sub v18.8h, v7.8h, v18.8h
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sshll2 v17.4s, v16.8h, #0x0
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sshll v16.4s, v16.4h, #0x0
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sshll2 v19.4s, v18.8h, #0x0
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sshll v18.4s, v18.4h, #0x0
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str q16, [x0], #0x40
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stur q17, [x0, #-0x30]
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stur q18, [x0, #-0x20]
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stur q19, [x0, #-0x10]
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add x11, x11, #0x10
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cmp x11, #0x100
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b.lt Lrej_uniform_eta4_final_copy
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mov x0, x9
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add sp, sp, #0x240
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.cfi_adjust_cfa_offset -0x240
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ret
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.cfi_endproc

‎proofs/hol_light/aarch64/proofs/dump_bytecode.ml‎

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@@ -33,3 +33,7 @@ print_string "==== bytecode end =====================================\n\n";;
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print_string "=== bytecode start: aarch64/mldsa/mldsa_poly_chknorm.o ===\n";;
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print_literal_from_elf "aarch64/mldsa/mldsa_poly_chknorm.o";;
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print_string "==== bytecode end =====================================\n\n";;
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print_string "=== bytecode start: aarch64/mldsa/mldsa_rej_uniform_eta4.o ===\n";;
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print_literal_from_elf "aarch64/mldsa/mldsa_rej_uniform_eta4.o";;
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print_string "==== bytecode end =====================================\n\n";;

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