src/ieee754/part/formal/proof_partition.py

   1 """Formal verification of partitioned operations
   2
   3 The approach is to take an arbitrary partition, by choosing its start point
   4 and size at random. Use ``Assume`` to ensure it is a whole unbroken partition
   5 (start and end points are one, with only zeros in between). Shift inputs and
   6 outputs down to zero. Loop over all possible partition sizes and, if it's the
   7 right size, compute the expected value, compare with the result, and assert.
   8
   9 We are turning the for-loops around (on their head), such that we start from
  10 the *lengths* (and positions) and perform the ``Assume`` on the resultant
  11 partition bits.
  12
  13 In other words, we have patterns as follows (assuming 32-bit words)::
  14
  15   8-bit offsets 0,1,2,3
  16   16-bit offsets 0,1,2
  17   24-bit offsets 0,1
  18   32-bit
  19
  20 * for 8-bit the partition bit is 1 and the previous is also 1
  21
  22 * for 16-bit the partition bit at the offset must be 0 and be surrounded by 1
  23
  24 * for 24-bit the partition bits at the offset and at offset+1 must be 0 and at
  25   offset+2 and offset-1 must be 1
  26
  27 * for 32-bit all 3 bits must be 0 and be surrounded by 1 (guard bits are added
  28   at each end for this purpose)
  29
  30 """
  31
  32 import os
  33 import unittest
  34
  35 from nmigen import Elaboratable, Signal, Module, Const
  36 from nmigen.asserts import Assert, Cover
  37
  38 from nmutil.formaltest import FHDLTestCase
  39 from nmutil.gtkw import write_gtkw
  40
  41 from ieee754.part_mul_add.partpoints import PartitionPoints
  42
  43
  44 class PartitionedPattern(Elaboratable):
  45     """ Generate a unique pattern, depending on partition size.
  46
  47     * 1-byte partitions: 0x11
  48     * 2-byte partitions: 0x21 0x22
  49     * 3-byte partitions: 0x31 0x32 0x33
  50
  51     And so on.
  52
  53     Useful as a test vector for testing the formal prover
  54
  55     """
  56     def __init__(self, width, partition_points):
  57         self.width = width
  58         self.partition_points = PartitionPoints(partition_points)
  59         self.mwidth = len(self.partition_points)+1
  60         self.output = Signal(self.width, reset_less=True)
  61
  62     def elaborate(self, platform):
  63         m = Module()
  64         comb = m.d.comb
  65
  66         # Add a guard bit at each end
  67         positions = [0] + list(self.partition_points.keys()) + [self.width]
  68         gates = [Const(1)] + list(self.partition_points.values()) + [Const(1)]
  69         # Begin counting at one
  70         last_start = positions[0]
  71         last_end = positions[1]
  72         comb += self.output[last_start:last_end].eq(1)
  73         # Build an incrementing cascade
  74         for i in range(1, self.mwidth):
  75             start = positions[i]
  76             end = positions[i+1]
  77             # Propagate from the previous byte, adding one to it
  78             comb += self.output[start:end].eq(
  79                 self.output[last_start:last_end] + 1)
  80             last_start = start
  81             last_end = end
  82         return m
  83
  84
  85 # This defines a module to drive the device under test and assert
  86 # properties about its outputs
  87 class Driver(Elaboratable):
  88     def __init__(self):
  89         # inputs and outputs
  90         pass
  91
  92     @staticmethod
  93     def elaborate(_):
  94         m = Module()
  95         comb = m.d.comb
  96         sync = m.d.sync
  97         width = 64
  98         mwidth = 8
  99         out = Signal(width)
 100         # Setup partition points and gates
 101         points = PartitionPoints()
 102         gates = Signal(mwidth-1)
 103         step = int(width/mwidth)
 104         for i in range(mwidth-1):
 105             points[(i+1)*step] = gates[i]
 106         # Instantiate the partitioned pattern producer
 107         m.submodules.dut = dut = PartitionedPattern(width, points)
 108         # Directly check some cases
 109         comb += Assert(dut.output == 0x0807060504030201)
 110         comb += Cover(1)
 111         return m
 112
 113
 114 class PartitionTestCase(FHDLTestCase):
 115     def test_formal(self):
 116         traces = ['output[63:0]']
 117         write_gtkw(
 118             'test_formal_cover.gtkw',
 119             os.path.dirname(__file__) +
 120             '/proof_partition_formal/engine_0/trace0.vcd',
 121             traces,
 122             module='top.dut',
 123             zoom="formal"
 124         )
 125         write_gtkw(
 126             'test_formal_bmc.gtkw',
 127             os.path.dirname(__file__) +
 128             '/proof_partition_formal/engine_0/trace.vcd',
 129             traces,
 130             module='top.dut',
 131             zoom="formal"
 132         )
 133         module = Driver()
 134         self.assertFormal(module, mode="bmc", depth=1)
 135         self.assertFormal(module, mode="cover", depth=1)
 136
 137
 138 if __name__ == '__main__':
 139     unittest.main()