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Exec-srai32

Semantics of the SRAI instruction [ISA:2.4.1] in 32-bit mode.

Signature
(exec-srai32 rd rs1 imm stat feat) → new-stat
Arguments: rd — Guard (ubyte5p rd).; rs1 — Guard (ubyte5p rs1).; imm — Guard (ubyte5p imm).; stat — Guard (statp stat).; feat — Guard (featp feat).
Returns: new-stat — Type (statp new-stat).

We read a signed 32-bit integer from rs1. The immediate is the shift amount, from 0 to 31. We shift the integer right by the shift amount; this is an arithmetic shift, since the integer is signed. We write the result to rd. We increment the program counter.

Definitions and Theorems

Function: exec-srai32

(defun exec-srai32 (rd rs1 imm stat feat)
  (declare (xargs :guard (and (ubyte5p rd)
                              (ubyte5p rs1)
                              (ubyte5p imm)
                              (statp stat)
                              (featp feat))))
  (declare (xargs :guard (and (feat-32p feat)
                              (stat-validp stat feat))))
  (let ((__function__ 'exec-srai32))
    (declare (ignorable __function__))
    (b* ((rs1-operand (read-xreg-signed (ubyte5-fix rs1)
                                        stat feat))
         (shift-amount (ubyte5-fix imm))
         (result (ash rs1-operand (- shift-amount)))
         (stat (write-xreg (ubyte5-fix rd)
                           result stat feat))
         (stat (inc4-pc stat feat)))
      stat)))

Theorem: statp-of-exec-srai32

(defthm statp-of-exec-srai32
  (b* ((new-stat (exec-srai32 rd rs1 imm stat feat)))
    (statp new-stat))
  :rule-classes :rewrite)

Theorem: exec-srai32-of-ubyte5-fix-rd

(defthm exec-srai32-of-ubyte5-fix-rd
  (equal (exec-srai32 (ubyte5-fix rd)
                      rs1 imm stat feat)
         (exec-srai32 rd rs1 imm stat feat)))

Theorem: exec-srai32-ubyte5-equiv-congruence-on-rd

(defthm exec-srai32-ubyte5-equiv-congruence-on-rd
  (implies (ubyte5-equiv rd rd-equiv)
           (equal (exec-srai32 rd rs1 imm stat feat)
                  (exec-srai32 rd-equiv rs1 imm stat feat)))
  :rule-classes :congruence)

Theorem: exec-srai32-of-ubyte5-fix-rs1

(defthm exec-srai32-of-ubyte5-fix-rs1
  (equal (exec-srai32 rd (ubyte5-fix rs1)
                      imm stat feat)
         (exec-srai32 rd rs1 imm stat feat)))

Theorem: exec-srai32-ubyte5-equiv-congruence-on-rs1

(defthm exec-srai32-ubyte5-equiv-congruence-on-rs1
  (implies (ubyte5-equiv rs1 rs1-equiv)
           (equal (exec-srai32 rd rs1 imm stat feat)
                  (exec-srai32 rd rs1-equiv imm stat feat)))
  :rule-classes :congruence)

Theorem: exec-srai32-of-ubyte5-fix-imm

(defthm exec-srai32-of-ubyte5-fix-imm
  (equal (exec-srai32 rd rs1 (ubyte5-fix imm)
                      stat feat)
         (exec-srai32 rd rs1 imm stat feat)))

Theorem: exec-srai32-ubyte5-equiv-congruence-on-imm

(defthm exec-srai32-ubyte5-equiv-congruence-on-imm
  (implies (ubyte5-equiv imm imm-equiv)
           (equal (exec-srai32 rd rs1 imm stat feat)
                  (exec-srai32 rd rs1 imm-equiv stat feat)))
  :rule-classes :congruence)

Theorem: exec-srai32-of-stat-fix-stat

(defthm exec-srai32-of-stat-fix-stat
  (equal (exec-srai32 rd rs1 imm (stat-fix stat)
                      feat)
         (exec-srai32 rd rs1 imm stat feat)))

Theorem: exec-srai32-stat-equiv-congruence-on-stat

(defthm exec-srai32-stat-equiv-congruence-on-stat
  (implies (stat-equiv stat stat-equiv)
           (equal (exec-srai32 rd rs1 imm stat feat)
                  (exec-srai32 rd rs1 imm stat-equiv feat)))
  :rule-classes :congruence)

Theorem: exec-srai32-of-feat-fix-feat

(defthm exec-srai32-of-feat-fix-feat
  (equal (exec-srai32 rd rs1 imm stat (feat-fix feat))
         (exec-srai32 rd rs1 imm stat feat)))

Theorem: exec-srai32-feat-equiv-congruence-on-feat

(defthm exec-srai32-feat-equiv-congruence-on-feat
  (implies (feat-equiv feat feat-equiv)
           (equal (exec-srai32 rd rs1 imm stat feat)
                  (exec-srai32 rd rs1 imm stat feat-equiv)))
  :rule-classes :congruence)