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             with m.If(~gates[i]):
  79                 comb += self.output[start:end].eq(
  80                     self.output[last_start:last_end] + 1)
  81             with m.Else():
  82                 # ... unless it's a partition boundary. If so, start again.
  83                 comb += self.output[start:end].eq(1)
  84             last_start = start
  85             last_end = end
  86         # Mirror the nibbles on the last byte
  87         last_start = positions[-2]
  88         last_end = positions[-1]
  89         last_middle = (last_start+last_end)//2
  90         comb += self.output[last_middle:last_end].eq(
  91             self.output[last_start:last_middle])
  92         for i in range(self.mwidth, 0, -1):
  93             start = positions[i-1]
  94             end = positions[i]
  95             middle = (start + end) // 2
  96             # Propagate from the previous byte.
  97             with m.If(~gates[i]):
  98                 comb += self.output[middle:end].eq(
  99                     self.output[last_middle:last_end])
 100             with m.Else():
 101                 # ... unless it's a partition boundary.
 102                 # If so, mirror the nibbles again.
 103                 comb += self.output[middle:end].eq(
 104                     self.output[start:middle])
 105             last_start = start
 106             last_middle = middle
 107             last_end = end
 108
 109         return m
 110
 111
 112 # This defines a module to drive the device under test and assert
 113 # properties about its outputs
 114 class Driver(Elaboratable):
 115     def __init__(self):
 116         # inputs and outputs
 117         pass
 118
 119     @staticmethod
 120     def elaborate(_):
 121         m = Module()
 122         comb = m.d.comb
 123         width = 64
 124         mwidth = 8
 125         # Setup partition points and gates
 126         points = PartitionPoints()
 127         gates = Signal(mwidth-1)
 128         step = int(width/mwidth)
 129         for i in range(mwidth-1):
 130             points[(i+1)*step] = gates[i]
 131         # Instantiate the partitioned pattern producer
 132         m.submodules.dut = dut = PartitionedPattern(width, points)
 133         # Directly check some cases
 134         with m.If(gates == 0):
 135             comb += Assert(dut.output == 0x_88_87_86_85_84_83_82_81)
 136         with m.If(gates == 0b1100101):
 137             comb += Assert(dut.output == 0x_11_11_33_32_31_22_21_11)
 138         with m.If(gates == 0b0001000):
 139             comb += Assert(dut.output == 0x_44_43_42_41_44_43_42_41)
 140         with m.If(gates == 0b0100001):
 141             comb += Assert(dut.output == 0x_22_21_55_54_53_52_51_11)
 142         with m.If(gates == 0b1000001):
 143             comb += Assert(dut.output == 0x_11_66_65_64_63_62_61_11)
 144         with m.If(gates == 0b0000001):
 145             comb += Assert(dut.output == 0x_77_76_75_74_73_72_71_11)
 146         # Make it interesting, by having three partitions
 147         comb += Cover(sum(gates) == 3)
 148         return m
 149
 150
 151 class PartitionTestCase(FHDLTestCase):
 152     def test_formal(self):
 153         traces = ['output[63:0]', 'gates[6:0]']
 154         write_gtkw(
 155             'test_formal_cover.gtkw',
 156             os.path.dirname(__file__) +
 157             '/proof_partition_formal/engine_0/trace0.vcd',
 158             traces,
 159             module='top.dut',
 160             zoom="formal"
 161         )
 162         write_gtkw(
 163             'test_formal_bmc.gtkw',
 164             os.path.dirname(__file__) +
 165             '/proof_partition_formal/engine_0/trace.vcd',
 166             traces,
 167             module='top.dut',
 168             zoom="formal"
 169         )
 170         module = Driver()
 171         self.assertFormal(module, mode="bmc", depth=1)
 172         self.assertFormal(module, mode="cover", depth=1)
 173
 174
 175 if __name__ == '__main__':
 176     unittest.main()