• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
    • X86isa
      • Program-execution
      • Sdm-instruction-set-summary
      • Tlb
      • Booting-linux
      • Introduction
      • Asmtest
      • X86isa-build-instructions
      • Publications
      • Contributors
      • Machine
        • X86isa-state
        • Syscalls
        • Cpuid
        • Linear-memory
        • Rflag-specifications
        • Characterizing-undefined-behavior
        • Top-level-memory
        • App-view
        • X86-decoder
        • Physical-memory
        • Decoding-and-spec-utils
        • Instructions
          • Two-byte-opcodes
          • One-byte-opcodes
          • Fp-opcodes
          • Instruction-semantic-functions
            • Sar-spec
            • Shr-spec
            • Sal/shl-spec
            • Rol-spec
            • Ror-spec
            • Rcl-spec
            • Rcr-spec
            • Simd-sub-spec
            • Simd-add-spec
            • Imul-spec
            • Mul-spec
              • Mul-spec-64
              • Mul-spec-8
              • Mul-spec-32
              • Mul-spec-16
            • Idiv-spec
            • Div-spec
            • Shrd-spec
            • Shld-spec
            • Gpr-arith/logic-spec
            • Shrx-spec
            • Shlx-spec
            • Sarx-spec
            • Floating-point-specifications
          • X86-illegal-instruction
          • Implemented-opcodes
          • Opcode-maps
          • X86-general-protection
          • X86-device-not-available
          • X86-step-unimplemented
          • Privileged-opcodes
          • Three-byte-opcodes
        • Register-readers-and-writers
        • X86-modes
        • Segmentation
        • Other-non-deterministic-computations
        • Environment
        • Paging
      • Implemented-opcodes
      • To-do
      • Proof-utilities
      • Peripherals
      • Model-validation
      • Modelcalls
      • Concrete-simulation-examples
      • Utils
      • Debugging-code-proofs
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Mul-spec

Mul-spec-64

Signature

(mul-spec-64 dst src) → (mv * * *)

Definitions and Theorems

Function: mul-spec-64

(defun mul-spec-64 (dst src)
 (declare (type (unsigned-byte 64) dst)
          (type (unsigned-byte 64) src))
 (let ((__function__ 'mul-spec-64))
   (declare (ignorable __function__))
   (b*
     ((dst (mbe :logic (n-size 64 dst) :exec dst))
      (src (mbe :logic (n-size 64 src) :exec src))
      (product (the (unsigned-byte 128) (* dst src)))
      (product-high
           (mbe :logic (part-select product :low 64 :width 64)
                :exec (the (unsigned-byte 64)
                           (ash (the (unsigned-byte 128) product)
                                -64))))
      (product-low
           (mbe :logic (part-select product :low 0 :width 64)
                :exec (the (unsigned-byte 64)
                           (logand 18446744073709551615 product)))))
     (mv product-high product-low product))))

Theorem: n64-mv-nth-0-mul-spec-64

(defthm n64-mv-nth-0-mul-spec-64
 (unsigned-byte-p 64 (mv-nth 0 (mul-spec-64 dst src)))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (mv-nth 0 (mul-spec-64 dst src)))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0 (mv-nth 0 (mul-spec-64 dst src)))
                   (< (mv-nth 0 (mul-spec-64 dst src))
                      18446744073709551616))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: mv-nth-1-mul-spec-64

(defthm mv-nth-1-mul-spec-64
 (unsigned-byte-p 64 (mv-nth 1 (mul-spec-64 dst src)))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (mv-nth 1 (mul-spec-64 dst src)))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0 (mv-nth 1 (mul-spec-64 dst src)))
                   (< (mv-nth 1 (mul-spec-64 dst src))
                      18446744073709551616))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))

Theorem: mv-nth-2-mul-spec-64

(defthm mv-nth-2-mul-spec-64
 (unsigned-byte-p 128 (mv-nth 2 (mul-spec-64 dst src)))
 :rule-classes
 (:rewrite
  (:type-prescription
      :corollary (natp (mv-nth 2 (mul-spec-64 dst src)))
      :hints
      (("Goal" :in-theory '(unsigned-byte-p integer-range-p natp))))
  (:linear
   :corollary (and (<= 0 (mv-nth 2 (mul-spec-64 dst src)))
                   (< (mv-nth 2 (mul-spec-64 dst src))
                      340282366920938463463374607431768211456))
   :hints
   (("Goal"
        :in-theory '(unsigned-byte-p integer-range-p (:e expt)))))))