arith.lisp

开源跨平台Lisp编译器

  (:translate shift-towards-start)
  (:note "SHIFT-TOWARDS-START")
  (:generator 1
    (ecase *backend-byte-order*
      (:big-endian
       (inst sll r num amount))
      (:little-endian
       (inst srl r num amount)))))

(define-vop (shift-towards-end shift-towards-someplace)
  (:translate shift-towards-end)
  (:note "SHIFT-TOWARDS-END")
  (:generator 1
    (ecase *backend-byte-order*
      (:big-endian
       (inst srl r num amount))
      (:little-endian
       (inst sll r num amount)))))

;;;; Modular arithmetic
(define-modular-fun +-mod32 (x y) + :untagged nil 32)
(define-vop (fast-+-mod32/unsigned=>unsigned fast-+/unsigned=>unsigned)
  (:translate +-mod32))
(define-vop (fast-+-mod32-c/unsigned=>unsigned fast-+-c/unsigned=>unsigned)
  (:translate +-mod32))
(define-modular-fun --mod32 (x y) - :untagged nil 32)
(define-vop (fast---mod32/unsigned=>unsigned fast--/unsigned=>unsigned)
  (:translate --mod32))
(define-vop (fast---mod32-c/unsigned=>unsigned fast---c/unsigned=>unsigned)
  (:translate --mod32))

(define-vop (fast-ash-left-mod32-c/unsigned=>unsigned
             fast-ash-c/unsigned=>unsigned)
  (:translate ash-left-mod32))

(define-vop (fast-ash-left-mod32/unsigned=>unsigned
             fast-ash-left/unsigned=>unsigned))
(deftransform ash-left-mod32 ((integer count)
                              ((unsigned-byte 32) (unsigned-byte 5)))
  (when (sb!c::constant-lvar-p count)
    (sb!c::give-up-ir1-transform))
  '(%primitive fast-ash-left-mod32/unsigned=>unsigned integer count))

;;; logical operations
(define-modular-fun lognot-mod32 (x) lognot :untagged nil 32)
(define-vop (lognot-mod32/unsigned=>unsigned)
  (:translate lognot-mod32)
  (:args (x :scs (unsigned-reg)))
  (:arg-types unsigned-num)
  (:results (r :scs (unsigned-reg)))
  (:result-types unsigned-num)
  (:policy :fast-safe)
  (:generator 1
    (inst nor r x zero-tn)))

(define-modular-fun lognor-mod32 (x y) lognor :untagged nil 32)
(define-vop (fast-lognor-mod32/unsigned=>unsigned
             fast-lognor/unsigned=>unsigned)
  (:translate lognor-mod32))

(define-source-transform logeqv (&rest args)
  (if (oddp (length args))
      `(logxor ,@args)
      `(lognot (logxor ,@args))))
(define-source-transform logandc1 (x y)
  `(logand (lognot ,x) ,y))
(define-source-transform logandc2 (x y)
  `(logand ,x (lognot ,y)))
(define-source-transform logorc1 (x y)
  `(logior (lognot ,x) ,y))
(define-source-transform logorc2 (x y)
  `(logior ,x (lognot ,y)))
(define-source-transform lognand (x y)
  `(lognot (logand ,x ,y)))
;;;; Bignum stuff.

(define-vop (bignum-length get-header-data)
  (:translate sb!bignum:%bignum-length)
  (:policy :fast-safe))

(define-vop (bignum-set-length set-header-data)
  (:translate sb!bignum:%bignum-set-length)
  (:policy :fast-safe))

(define-full-reffer bignum-ref * bignum-digits-offset other-pointer-lowtag
  (unsigned-reg) unsigned-num sb!bignum:%bignum-ref)

(define-full-setter bignum-set * bignum-digits-offset other-pointer-lowtag
  (unsigned-reg) unsigned-num sb!bignum:%bignum-set)

(define-vop (digit-0-or-plus)
  (:translate sb!bignum:%digit-0-or-plusp)
  (:policy :fast-safe)
  (:args (digit :scs (unsigned-reg)))
  (:arg-types unsigned-num)
  (:conditional)
  (:info target not-p)
  (:generator 2
    (if not-p
        (inst bltz digit target)
        (inst bgez digit target))
    (inst nop)))

(define-vop (add-w/carry)
  (:translate sb!bignum:%add-with-carry)
  (:policy :fast-safe)
  (:args (a :scs (unsigned-reg))
         (b :scs (unsigned-reg))
         (c :scs (any-reg)))
  (:arg-types unsigned-num unsigned-num positive-fixnum)
  (:temporary (:scs (unsigned-reg) :to (:result 0) :target result) res)
  (:results (result :scs (unsigned-reg))
            (carry :scs (unsigned-reg) :from :eval))
  (:result-types unsigned-num positive-fixnum)
  (:temporary (:scs (non-descriptor-reg)) temp)
  (:generator 5
    (let ((carry-in (gen-label))
          (done (gen-label)))
      (inst bne c carry-in)
      (inst addu res a b)

      (inst b done)
      (inst sltu carry res b)

      (emit-label carry-in)
      (inst addu res 1)
      (inst nor temp a zero-tn)
      (inst sltu carry b temp)
      (inst xor carry 1)

      (emit-label done)
      (move result res))))

(define-vop (sub-w/borrow)
  (:translate sb!bignum:%subtract-with-borrow)
  (:policy :fast-safe)
  (:args (a :scs (unsigned-reg))
         (b :scs (unsigned-reg))
         (c :scs (any-reg)))
  (:arg-types unsigned-num unsigned-num positive-fixnum)
  (:temporary (:scs (unsigned-reg) :to (:result 0) :target result) res)
  (:results (result :scs (unsigned-reg))
            (borrow :scs (unsigned-reg) :from :eval))
  (:result-types unsigned-num positive-fixnum)
  (:generator 4
    (let ((no-borrow-in (gen-label))
          (done (gen-label)))

      (inst bne c no-borrow-in)
      (inst subu res a b)

      (inst subu res 1)
      (inst b done)
      (inst sltu borrow b a)

      (emit-label no-borrow-in)
      (inst sltu borrow a b)
      (inst xor borrow 1)

      (emit-label done)
      (move result res))))

(define-vop (bignum-mult-and-add-3-arg)
  (:translate sb!bignum:%multiply-and-add)
  (:policy :fast-safe)
  (:args (x :scs (unsigned-reg))
         (y :scs (unsigned-reg))
         (carry-in :scs (unsigned-reg) :to :save))
  (:arg-types unsigned-num unsigned-num unsigned-num)
  (:temporary (:scs (unsigned-reg) :from (:argument 1)) temp)
  (:results (hi :scs (unsigned-reg))
            (lo :scs (unsigned-reg)))
  (:result-types unsigned-num unsigned-num)
  (:generator 6
    (inst multu x y)
    (inst mflo temp)
    (inst addu lo temp carry-in)
    (inst sltu temp lo carry-in)
    (inst mfhi hi)
    (inst addu hi temp)))

(define-vop (bignum-mult-and-add-4-arg)
  (:translate sb!bignum:%multiply-and-add)
  (:policy :fast-safe)
  (:args (x :scs (unsigned-reg))
         (y :scs (unsigned-reg))
         (prev :scs (unsigned-reg))
         (carry-in :scs (unsigned-reg) :to :save))
  (:arg-types unsigned-num unsigned-num unsigned-num unsigned-num)
  (:temporary (:scs (unsigned-reg) :from (:argument 2)) temp)
  (:results (hi :scs (unsigned-reg))
            (lo :scs (unsigned-reg)))
  (:result-types unsigned-num unsigned-num)
  (:generator 9
    (inst multu x y)
    (inst addu lo prev carry-in)
    (inst sltu temp lo carry-in)
    (inst mfhi hi)
    (inst addu hi temp)
    (inst mflo temp)
    (inst addu lo temp)
    (inst sltu temp lo temp)
    (inst addu hi temp)))

(define-vop (bignum-mult)
  (:translate sb!bignum:%multiply)
  (:policy :fast-safe)
  (:args (x :scs (unsigned-reg))
         (y :scs (unsigned-reg)))
  (:arg-types unsigned-num unsigned-num)
  (:results (hi :scs (unsigned-reg))
            (lo :scs (unsigned-reg)))
  (:result-types unsigned-num unsigned-num)
  (:generator 3
    (inst multu x y)
    (inst mflo lo)
    (inst mfhi hi)))

(define-vop (bignum-lognot lognot-mod32/unsigned=>unsigned)
  (:translate sb!bignum:%lognot))

(define-vop (fixnum-to-digit)
  (:translate sb!bignum:%fixnum-to-digit)
  (:policy :fast-safe)
  (:args (fixnum :scs (any-reg)))
  (:arg-types tagged-num)
  (:results (digit :scs (unsigned-reg)))
  (:result-types unsigned-num)
  (:generator 1
    (inst sra digit fixnum n-fixnum-tag-bits)))

(define-vop (bignum-floor)
  (:translate sb!bignum:%floor)
  (:policy :fast-safe)
  (:args (num-high :scs (unsigned-reg) :target rem)
         (num-low :scs (unsigned-reg) :target rem-low)
         (denom :scs (unsigned-reg) :to (:eval 1)))
  (:arg-types unsigned-num unsigned-num unsigned-num)
  (:temporary (:scs (unsigned-reg) :from (:argument 1)) rem-low)
  (:temporary (:scs (unsigned-reg) :from (:eval 0)) temp)
  (:results (quo :scs (unsigned-reg) :from (:eval 0))
            (rem :scs (unsigned-reg) :from (:argument 0)))
  (:result-types unsigned-num unsigned-num)
  (:generator 325 ; number of inst assuming targeting works.
    (move rem num-high)
    (move rem-low num-low)
    (flet ((maybe-subtract (&optional (guess temp))
             (inst subu temp guess 1)
             (inst and temp denom)
             (inst subu rem temp)))
      (inst sltu quo rem denom)
      (maybe-subtract quo)
      (dotimes (i 32)
        (inst sll rem 1)
        (inst srl temp rem-low 31)
        (inst or rem temp)
        (inst sll rem-low 1)
        (inst sltu temp rem denom)
        (inst sll quo 1)
        (inst or quo temp)
        (maybe-subtract)))
    (inst nor quo zero-tn)))

(define-vop (signify-digit)
  (:translate sb!bignum:%fixnum-digit-with-correct-sign)
  (:policy :fast-safe)
  (:args (digit :scs (unsigned-reg) :target res))
  (:arg-types unsigned-num)
  (:results (res :scs (any-reg signed-reg)))
  (:result-types signed-num)
  (:generator 1
    (sc-case res
      (any-reg
       (inst sll res digit n-fixnum-tag-bits))
      (signed-reg
       (move res digit)))))


(define-vop (digit-ashr)
  (:translate sb!bignum:%ashr)
  (:policy :fast-safe)
  (:args (digit :scs (unsigned-reg))
         (count :scs (unsigned-reg)))
  (:arg-types unsigned-num positive-fixnum)
  (:results (result :scs (unsigned-reg)))
  (:result-types unsigned-num)
  (:generator 1
    (inst sra result digit count)))

(define-vop (digit-lshr digit-ashr)
  (:translate sb!bignum:%digit-logical-shift-right)
  (:generator 1
    (inst srl result digit count)))

(define-vop (digit-ashl digit-ashr)
  (:translate sb!bignum:%ashl)
  (:generator 1
    (inst sll result digit count)))


;;;; Static functions.

(define-static-fun two-arg-gcd (x y) :translate gcd)
(define-static-fun two-arg-lcm (x y) :translate lcm)

(define-static-fun two-arg-+ (x y) :translate +)
(define-static-fun two-arg-- (x y) :translate -)
(define-static-fun two-arg-* (x y) :translate *)
(define-static-fun two-arg-/ (x y) :translate /)

(define-static-fun two-arg-< (x y) :translate <)
(define-static-fun two-arg-<= (x y) :translate <=)
(define-static-fun two-arg-> (x y) :translate >)
(define-static-fun two-arg->= (x y) :translate >=)
(define-static-fun two-arg-= (x y) :translate =)
(define-static-fun two-arg-/= (x y) :translate /=)

(define-static-fun %negate (x) :translate %negate)

(define-static-fun two-arg-and (x y) :translate logand)
(define-static-fun two-arg-ior (x y) :translate logior)
(define-static-fun two-arg-xor (x y) :translate logxor)