src/add/nmigen_div_experiment.py

   1 # IEEE Floating Point Divider (Single Precision)
   2 # Copyright (C) Jonathan P Dawson 2013
   3 # 2013-12-12
   4
   5 from nmigen import Module, Signal, Const, Cat
   6 from nmigen.cli import main, verilog
   7
   8 from fpbase import FPNumIn, FPNumOut, FPOp, Overflow, FPBase
   9 from nmigen_add_experiment import FPState
  10
  11 class Div:
  12     def __init__(self, width):
  13         self.width = width
  14         self.quot = Signal(width)  # quotient
  15         self.dor = Signal(width)   # divisor
  16         self.dend = Signal(width)  # dividend
  17         self.rem = Signal(width)   # remainder
  18         self.count = Signal(7)     # loop count
  19
  20         self.czero = Const(0, width)
  21
  22     def reset(self, m):
  23         m.d.sync += [
  24             self.quot.eq(self.czero),
  25             self.rem.eq(self.czero),
  26             self.count.eq(Const(0, 7))
  27         ]
  28
  29
  30 class FPDIV(FPBase):
  31
  32     def __init__(self, width):
  33         FPBase.__init__(self)
  34         self.width = width
  35
  36         self.in_a  = FPOp(width)
  37         self.in_b  = FPOp(width)
  38         self.out_z = FPOp(width)
  39
  40         self.states = []
  41
  42     def add_state(self, state):
  43         self.states.append(state)
  44         return state
  45
  46     def get_fragment(self, platform=None):
  47         """ creates the HDL code-fragment for FPDiv
  48         """
  49         m = Module()
  50
  51         # Latches
  52         a = FPNumIn(None, self.width, False)
  53         b = FPNumIn(None, self.width, False)
  54         z = FPNumOut(self.width, False)
  55
  56         div = Div(a.m_width*2 + 3) # double the mantissa width plus g/r/sticky
  57
  58         of = Overflow()
  59         m.submodules.in_a = a
  60         m.submodules.in_b = b
  61         m.submodules.z = z
  62         m.submodules.of = of
  63
  64         with m.FSM() as fsm:
  65
  66             # ******
  67             # gets operand a
  68
  69             with m.State("get_a"):
  70                 self.get_op(m, self.in_a, a, "get_b")
  71
  72             # ******
  73             # gets operand b
  74
  75             with m.State("get_b"):
  76                 self.get_op(m, self.in_b, b, "special_cases")
  77
  78             # ******
  79             # special cases: NaNs, infs, zeros, denormalised
  80             # NOTE: some of these are unique to div.  see "Special Operations"
  81             # https://steve.hollasch.net/cgindex/coding/ieeefloat.html
  82
  83             with m.State("special_cases"):
  84
  85                 # if a is NaN or b is NaN return NaN
  86                 with m.If(a.is_nan | b.is_nan):
  87                     m.next = "put_z"
  88                     m.d.sync += z.nan(1)
  89
  90                 # if a is Inf and b is Inf return NaN
  91                 with m.Elif(a.is_inf & b.is_inf):
  92                     m.next = "put_z"
  93                     m.d.sync += z.nan(1)
  94
  95                 # if a is inf return inf (or NaN if b is zero)
  96                 with m.Elif(a.is_inf):
  97                     m.next = "put_z"
  98                     m.d.sync += z.inf(a.s ^ b.s)
  99
 100                 # if b is inf return zero
 101                 with m.Elif(b.is_inf):
 102                     m.next = "put_z"
 103                     m.d.sync += z.zero(a.s ^ b.s)
 104
 105                 # if a is zero return zero (or NaN if b is zero)
 106                 with m.Elif(a.is_zero):
 107                     m.next = "put_z"
 108                     # if b is zero return NaN
 109                     with m.If(b.is_zero):
 110                         m.d.sync += z.nan(1)
 111                     with m.Else():
 112                         m.d.sync += z.zero(a.s ^ b.s)
 113
 114                 # if b is zero return Inf
 115                 with m.Elif(b.is_zero):
 116                     m.next = "put_z"
 117                     m.d.sync += z.inf(a.s ^ b.s)
 118
 119                 # Denormalised Number checks
 120                 with m.Else():
 121                     m.next = "normalise_a"
 122                     self.denormalise(m, a)
 123                     self.denormalise(m, b)
 124
 125             # ******
 126             # normalise_a
 127
 128             with m.State("normalise_a"):
 129                 self.op_normalise(m, a, "normalise_b")
 130
 131             # ******
 132             # normalise_b
 133
 134             with m.State("normalise_b"):
 135                 self.op_normalise(m, b, "divide_0")
 136
 137             # ******
 138             # First stage of divide.  initialise state
 139
 140             with m.State("divide_0"):
 141                 m.next = "divide_1"
 142                 m.d.sync += [
 143                     z.s.eq(a.s ^ b.s), # sign
 144                     z.e.eq(a.e - b.e), # exponent
 145                     div.dend.eq(a.m<<(a.m_width+3)), # 3 bits for g/r/sticky
 146                     div.dor.eq(b.m),
 147                 ]
 148                 div.reset(m)
 149
 150             # ******
 151             # Second stage of divide.
 152
 153             with m.State("divide_1"):
 154                 m.next = "divide_2"
 155                 m.d.sync += [
 156                     div.quot.eq(div.quot << 1),
 157                     div.rem.eq(Cat(div.dend[-1], div.rem[0:])),
 158                     div.dend.eq(div.dend << 1),
 159                 ]
 160
 161             # ******
 162             # Third stage of divide.
 163             # This stage ends by jumping out to divide_3
 164             # However it defaults to jumping to divide_1 (which comes back here)
 165
 166             with m.State("divide_2"):
 167                 with m.If(div.rem >= div.dor):
 168                     m.d.sync += [
 169                         div.quot[0].eq(1),
 170                         div.rem.eq(div.rem - div.dor),
 171                     ]
 172                 with m.If(div.count == div.width-2):
 173                     m.next = "divide_3"
 174                 with m.Else():
 175                     m.next = "divide_1"
 176                     m.d.sync += [
 177                         div.count.eq(div.count + 1),
 178                     ]
 179
 180             # ******
 181             # Fourth stage of divide.
 182
 183             with m.State("divide_3"):
 184                 m.next = "normalise_1"
 185                 m.d.sync += [
 186                     z.m.eq(div.quot[3:]),
 187                     of.guard.eq(div.quot[2]),
 188                     of.round_bit.eq(div.quot[1]),
 189                     of.sticky.eq(div.quot[0] | (div.rem != 0))
 190                 ]
 191
 192             # ******
 193             # First stage of normalisation.
 194
 195             with m.State("normalise_1"):
 196                 self.normalise_1(m, z, of, "normalise_2")
 197
 198             # ******
 199             # Second stage of normalisation.
 200
 201             with m.State("normalise_2"):
 202                 self.normalise_2(m, z, of, "round")
 203
 204             # ******
 205             # rounding stage
 206
 207             with m.State("round"):
 208                 self.roundz(m, z, of.roundz)
 209                 m.next = "corrections"
 210
 211             # ******
 212             # correction stage
 213
 214             with m.State("corrections"):
 215                 self.corrections(m, z, "pack")
 216
 217             # ******
 218             # pack stage
 219
 220             with m.State("pack"):
 221                 self.pack(m, z, "put_z")
 222
 223             # ******
 224             # put_z stage
 225
 226             with m.State("put_z"):
 227                 self.put_z(m, z, self.out_z, "get_a")
 228
 229         return m
 230
 231
 232 if __name__ == "__main__":
 233     alu = FPDIV(width=32)
 234     main(alu, ports=alu.in_a.ports() + alu.in_b.ports() + alu.out_z.ports())
 235
 236
 237     # works... but don't use, just do "python fname.py convert -t v"
 238     #print (verilog.convert(alu, ports=[
 239     #                        ports=alu.in_a.ports() + \
 240     #                              alu.in_b.ports() + \
 241     #                              alu.out_z.ports())