From e13b049cbef724d4513a9dd30270af91d9292889 Mon Sep 17 00:00:00 2001
From: Michael Nolan <mtnolan2640@gmail.com>
Date: Mon, 27 Jan 2020 19:01:41 -0500
Subject: [PATCH] Add formal proof for FSGNJPipeMod module

---
 src/ieee754/fsgnj/formal/proof.sby          | 13 +++
 src/ieee754/fsgnj/formal/proof_fsgnj_mod.py | 94 +++++++++++++++++++++
 2 files changed, 107 insertions(+)
 create mode 100644 src/ieee754/fsgnj/formal/proof.sby
 create mode 100644 src/ieee754/fsgnj/formal/proof_fsgnj_mod.py

diff --git a/src/ieee754/fsgnj/formal/proof.sby b/src/ieee754/fsgnj/formal/proof.sby
new file mode 100644
index 00000000..6c26b0f6
--- /dev/null
+++ b/src/ieee754/fsgnj/formal/proof.sby
@@ -0,0 +1,13 @@
+[options]
+mode bmc
+depth 5
+
+[engines]
+smtbmc yices
+
+[script]
+read_ilang proof.il
+prep -top top
+
+[files]
+proof.il
diff --git a/src/ieee754/fsgnj/formal/proof_fsgnj_mod.py b/src/ieee754/fsgnj/formal/proof_fsgnj_mod.py
new file mode 100644
index 00000000..9c9610fc
--- /dev/null
+++ b/src/ieee754/fsgnj/formal/proof_fsgnj_mod.py
@@ -0,0 +1,94 @@
+# Proof of correctness for FSGNJ module
+# Copyright (C) 2020 Michael Nolan <mtnolan2640@gmail.com>
+
+from nmigen import Module, Signal, Elaboratable
+from nmigen.asserts import Assert, Assume
+from nmigen.cli import rtlil
+
+from ieee754.fsgnj.fsgnj import FSGNJPipeMod
+from ieee754.pipeline import PipelineSpec
+import subprocess
+
+
+# This defines a module to drive the device under test and assert
+# properties about its outputs
+class FSGNJDriver(Elaboratable):
+    def __init__(self, pspec):
+        # inputs and outputs
+        self.pspec = pspec
+        self.a = Signal(pspec.width)
+        self.b = Signal(pspec.width)
+        self.z = Signal(pspec.width)
+        self.opc = Signal(pspec.op_wid)
+        self.muxid = Signal(pspec.id_wid)
+
+    def elaborate(self, platform):
+        m = Module()
+
+        m.submodules.dut = dut = FSGNJPipeMod(self.pspec)
+
+        # connect up the inputs and outputs. I think these could
+        # theoretically be $anyconst/$anysync but I'm not sure nmigen
+        # has support for that
+        m.d.comb += dut.i.a.eq(self.a)
+        m.d.comb += dut.i.b.eq(self.b)
+        m.d.comb += dut.i.ctx.op.eq(self.opc)
+        m.d.comb += dut.i.muxid.eq(self.muxid)
+        m.d.comb += self.z.eq(dut.o.z)
+
+        # Since the RISCV spec doesn't define what FSGNJ with a funct3
+        # field of 0b011 throug 0b111 does, they should be ignored.
+        m.d.comb += Assume(self.opc != 0b11)
+
+        # The RISCV spec (page 70) says FSGNJ "produces a result that
+        # takes all buts except the sign bit from [operand 1]". This
+        # asserts that that holds true
+        m.d.comb += Assert(self.z[0:31] == self.a[0:31])
+
+        with m.Switch(self.opc):
+
+            # The RISCV Spec (page 70) states that for FSGNJ (opcode
+            # 0b00 in this case) "the result's sign bit is [operand
+            # 2's] sign bit"
+            with m.Case(0b00):
+                m.d.comb += Assert(self.z[-1] == self.b[-1])
+
+            # The RISCV Spec (page 70) states that for FSGNJN (opcode
+            # 0b01 in this case) "the result's sign bit is the opposite
+            # of [operand 2's] sign bit"
+            with m.Case(0b01):
+                m.d.comb += Assert(self.z[-1] == ~self.b[-1])
+            # The RISCV Spec (page 70) states that for FSGNJX (opcode
+            # 0b10 in this case) "the result's sign bit is the XOR of
+            # the sign bits of [operand 1] and [operand 2]"
+            with m.Case(0b10):
+                m.d.comb += Assert(self.z[-1] == (self.a[-1] ^ self.b[-1]))
+
+        return m
+
+    def ports(self):
+        return [self.a, self.b, self.z, self.opc, self.muxid]
+
+
+def run_test():
+    m = FSGNJDriver(PipelineSpec(32, 2, 2))
+
+    il = rtlil.convert(m, ports=m.ports())
+    with open("proof.il", "w") as f:
+        f.write(il)
+    p = subprocess.Popen(['sby', '-f', 'proof.sby'],
+                         stdout=subprocess.PIPE,
+                         stderr=subprocess.PIPE)
+    if p.wait() == 0:
+        out, err = p.communicate()
+        print("Proof successful!")
+        print(out.decode('utf-8'))
+    else:
+        print("Proof failed")
+        out, err = p.communicate()
+        print(out.decode('utf-8'))
+        print(err.decode('utf-8'))
+
+
+if __name__ == "__main__":
+    run_test()
-- 
2.30.2