add initial f16 fadd formal proof

diff --git a/src/ieee754/fpadd/test/test_add_formal.py b/src/ieee754/fpadd/test/test_add_formal.py
new file mode 100644 (file)
index 0000000..9540de9
--- /dev/null
+++ b/src/ieee754/fpadd/test/test_add_formal.py
@@ -0,0 +1,45 @@
+import unittest
+from nmutil.formaltest import FHDLTestCase
+from ieee754.fpadd.pipeline import FPADDBasePipe
+from nmigen.hdl.dsl import Module
+from nmigen.hdl.ast import AnySeq, Assert, AnyConst, Signal, Assume
+from nmigen.hdl.smtlib2 import (SmtFloatingPoint, SmtSortFloat16,
+                                ROUND_NEAREST_TIES_TO_EVEN)
+from ieee754.pipeline import PipelineSpec
+
+
+class TestFAdd16Formal(FHDLTestCase):
+    def test_fadd16_rne_formal(self):
+        dut = FPADDBasePipe(PipelineSpec(width=16, id_width=4))
+        m = Module()
+        m.submodules.dut = dut
+        m.d.comb += dut.n.i_ready.eq(AnySeq(1))
+        m.d.comb += dut.p.i_valid.eq(AnySeq(1))
+        a = dut.p.i_data.a
+        b = dut.p.i_data.b
+        z = dut.n.o_data.z
+        f16 = SmtSortFloat16()
+        rm = ROUND_NEAREST_TIES_TO_EVEN
+        a_fp = SmtFloatingPoint.from_bits(a, sort=f16)
+        b_fp = SmtFloatingPoint.from_bits(b, sort=f16)
+        z_fp = SmtFloatingPoint.from_bits(z, sort=f16)
+        expected_fp = a_fp.add(b_fp, rm=rm)
+        expected = Signal(16)
+        m.d.comb += expected.eq(AnySeq(16))
+        # Important Note: expected and z won't necessarily match bit-exactly
+        # if it's a NaN, all this checks for is z is also any NaN
+        m.d.comb += Assume((SmtFloatingPoint.from_bits(expected, sort=f16)
+                            == expected_fp).as_value())
+        # FIXME: check that it produces the correct NaNs
+        m.d.comb += a.eq(AnyConst(16))
+        m.d.comb += b.eq(AnyConst(16))
+        with m.If(dut.n.trigger):
+            m.d.sync += Assert((z_fp == expected_fp).as_value())
+        self.assertFormal(m, depth=5, solver="z3")
+
+    # FIXME: check other rounding modes
+    # FIXME: check exception flags
+
+
+if __name__ == '__main__':
+    unittest.main()