src/add/nmigen_add_experiment.py

   1 # IEEE Floating Point Adder (Single Precision)
   2 # Copyright (C) Jonathan P Dawson 2013
   3 # 2013-12-12
   4
   5 from nmigen import Module, Signal, Cat
   6 from nmigen.cli import main, verilog
   7
   8 from fpbase import FPNumIn, FPNumOut, FPOp, Overflow, FPBase
   9
  10
  11 class FPState(FPBase):
  12     def __init__(self, state_from):
  13         self.state_from = state_from
  14
  15     def set_inputs(self, inputs):
  16         self.inputs = inputs
  17         for k,v in inputs.items():
  18             setattr(self, k, v)
  19
  20     def set_outputs(self, outputs):
  21         self.outputs = outputs
  22         for k,v in outputs.items():
  23             setattr(self, k, v)
  24
  25
  26 class FPGetOpA(FPState):
  27     """ gets operand a
  28     """
  29
  30     def __init__(self, in_a, width):
  31         FPState.__init__(self, "get_a")
  32         self.in_a = in_a
  33         self.a = FPNumIn(in_a, width)
  34
  35     def action(self, m):
  36         self.get_op(m, self.in_a, self.a, "get_b")
  37
  38
  39 class FPGetOpB(FPState):
  40     """ gets operand b
  41     """
  42
  43     def action(self, m):
  44         self.get_op(m, self.in_b, self.b, "special_cases")
  45
  46
  47 class FPAddSpecialCases(FPState):
  48     """ special cases: NaNs, infs, zeros, denormalised
  49         NOTE: some of these are unique to add.  see "Special Operations"
  50         https://steve.hollasch.net/cgindex/coding/ieeefloat.html
  51     """
  52
  53     def action(self, m):
  54         s_nomatch = Signal()
  55         m.d.comb += s_nomatch.eq(self.a.s != self.b.s)
  56
  57         m_match = Signal()
  58         m.d.comb += m_match.eq(self.a.m == self.b.m)
  59
  60         # if a is NaN or b is NaN return NaN
  61         with m.If(self.a.is_nan | self.b.is_nan):
  62             m.next = "put_z"
  63             m.d.sync += self.z.nan(1)
  64
  65         # XXX WEIRDNESS for FP16 non-canonical NaN handling
  66         # under review
  67
  68         ## if a is zero and b is NaN return -b
  69         #with m.If(a.is_zero & (a.s==0) & b.is_nan):
  70         #    m.next = "put_z"
  71         #    m.d.sync += z.create(b.s, b.e, Cat(b.m[3:-2], ~b.m[0]))
  72
  73         ## if b is zero and a is NaN return -a
  74         #with m.Elif(b.is_zero & (b.s==0) & a.is_nan):
  75         #    m.next = "put_z"
  76         #    m.d.sync += z.create(a.s, a.e, Cat(a.m[3:-2], ~a.m[0]))
  77
  78         ## if a is -zero and b is NaN return -b
  79         #with m.Elif(a.is_zero & (a.s==1) & b.is_nan):
  80         #    m.next = "put_z"
  81         #    m.d.sync += z.create(a.s & b.s, b.e, Cat(b.m[3:-2], 1))
  82
  83         ## if b is -zero and a is NaN return -a
  84         #with m.Elif(b.is_zero & (b.s==1) & a.is_nan):
  85         #    m.next = "put_z"
  86         #    m.d.sync += z.create(a.s & b.s, a.e, Cat(a.m[3:-2], 1))
  87
  88         # if a is inf return inf (or NaN)
  89         with m.Elif(self.a.is_inf):
  90             m.next = "put_z"
  91             m.d.sync += self.z.inf(self.a.s)
  92             # if a is inf and signs don't match return NaN
  93             with m.If(self.b.exp_128 & s_nomatch):
  94                 m.d.sync += self.z.nan(1)
  95
  96         # if b is inf return inf
  97         with m.Elif(self.b.is_inf):
  98             m.next = "put_z"
  99             m.d.sync += self.z.inf(self.b.s)
 100
 101         # if a is zero and b zero return signed-a/b
 102         with m.Elif(self.a.is_zero & self.b.is_zero):
 103             m.next = "put_z"
 104             m.d.sync += self.z.create(self.a.s & self.b.s, self.b.e,
 105                                       self.b.m[3:-1])
 106
 107         # if a is zero return b
 108         with m.Elif(self.a.is_zero):
 109             m.next = "put_z"
 110             m.d.sync += self.z.create(self.b.s, self.b.e, self.b.m[3:-1])
 111
 112         # if b is zero return a
 113         with m.Elif(self.b.is_zero):
 114             m.next = "put_z"
 115             m.d.sync += self.z.create(self.a.s, self.a.e, self.a.m[3:-1])
 116
 117         # if a equal to -b return zero (+ve zero)
 118         with m.Elif(s_nomatch & m_match & (self.a.e == self.b.e)):
 119             m.next = "put_z"
 120             m.d.sync += self.z.zero(0)
 121
 122         # Denormalised Number checks
 123         with m.Else():
 124             m.next = "denormalise"
 125
 126
 127 class FPAddDeNorm(FPState):
 128
 129     def action(self, m):
 130         # Denormalised Number checks
 131         m.next = "align"
 132         self.denormalise(m, self.a)
 133         self.denormalise(m, self.b)
 134
 135
 136 class FPAddAlignMulti(FPState):
 137
 138     def action(self, m):
 139         # NOTE: this does *not* do single-cycle multi-shifting,
 140         #       it *STAYS* in the align state until exponents match
 141
 142         # exponent of a greater than b: shift b down
 143         with m.If(self.a.e > self.b.e):
 144             m.d.sync += self.b.shift_down()
 145         # exponent of b greater than a: shift a down
 146         with m.Elif(self.a.e < self.b.e):
 147             m.d.sync += self.a.shift_down()
 148         # exponents equal: move to next stage.
 149         with m.Else():
 150             m.next = "add_0"
 151
 152
 153 class FPAddAlignSingle(FPState):
 154
 155     def action(self, m):
 156         # This one however (single-cycle) will do the shift
 157         # in one go.
 158
 159         # XXX TODO: the shifter used here is quite expensive
 160         # having only one would be better
 161
 162         ediff = Signal((len(self.a.e), True), reset_less=True)
 163         ediffr = Signal((len(self.a.e), True), reset_less=True)
 164         m.d.comb += ediff.eq(self.a.e - self.b.e)
 165         m.d.comb += ediffr.eq(self.b.e - self.a.e)
 166         with m.If(ediff > 0):
 167             m.d.sync += self.b.shift_down_multi(ediff)
 168         # exponent of b greater than a: shift a down
 169         with m.Elif(ediff < 0):
 170             m.d.sync += self.a.shift_down_multi(ediffr)
 171
 172         m.next = "add_0"
 173
 174
 175 class FPAddStage0(FPState):
 176     """ First stage of add.  covers same-sign (add) and subtract
 177         special-casing when mantissas are greater or equal, to
 178         give greatest accuracy.
 179     """
 180
 181     def action(self, m):
 182         m.next = "add_1"
 183         m.d.sync += self.z.e.eq(self.a.e)
 184         # same-sign (both negative or both positive) add mantissas
 185         with m.If(self.a.s == self.b.s):
 186             m.d.sync += [
 187                 self.tot.eq(Cat(self.a.m, 0) + Cat(self.b.m, 0)),
 188                 self.z.s.eq(self.a.s)
 189             ]
 190         # a mantissa greater than b, use a
 191         with m.Elif(self.a.m >= self.b.m):
 192             m.d.sync += [
 193                 self.tot.eq(Cat(self.a.m, 0) - Cat(self.b.m, 0)),
 194                 self.z.s.eq(self.a.s)
 195             ]
 196         # b mantissa greater than a, use b
 197         with m.Else():
 198             m.d.sync += [
 199                 self.tot.eq(Cat(self.b.m, 0) - Cat(self.a.m, 0)),
 200                 self.z.s.eq(self.b.s)
 201         ]
 202
 203
 204 class FPAddStage1(FPState):
 205     """ Second stage of add: preparation for normalisation.
 206         detects when tot sum is too big (tot[27] is kinda a carry bit)
 207     """
 208
 209     def action(self, m):
 210         m.next = "normalise_1"
 211         # tot[27] gets set when the sum overflows. shift result down
 212         with m.If(self.tot[-1]):
 213             m.d.sync += [
 214                 self.z.m.eq(self.tot[4:]),
 215                 self.of.m0.eq(self.tot[4]),
 216                 self.of.guard.eq(self.tot[3]),
 217                 self.of.round_bit.eq(self.tot[2]),
 218                 self.of.sticky.eq(self.tot[1] | self.tot[0]),
 219                 self.z.e.eq(self.z.e + 1)
 220         ]
 221         # tot[27] zero case
 222         with m.Else():
 223             m.d.sync += [
 224                 self.z.m.eq(self.tot[3:]),
 225                 self.of.m0.eq(self.tot[3]),
 226                 self.of.guard.eq(self.tot[2]),
 227                 self.of.round_bit.eq(self.tot[1]),
 228                 self.of.sticky.eq(self.tot[0])
 229         ]
 230
 231
 232 class FPNorm1(FPState):
 233
 234     def action(self, m):
 235         self.normalise_1(m, self.z, self.of, "normalise_2")
 236
 237
 238 class FPNorm2(FPState):
 239
 240     def action(self, m):
 241         self.normalise_2(m, self.z, self.of, "round")
 242
 243
 244 class FPRound(FPState):
 245
 246     def action(self, m):
 247         self.roundz(m, self.z, self.of, "corrections")
 248
 249
 250 class FPCorrections(FPState):
 251
 252     def action(self, m):
 253         self.corrections(m, self.z, "pack")
 254
 255
 256 class FPPack(FPState):
 257
 258     def action(self, m):
 259         self.pack(m, self.z, "put_z")
 260
 261
 262 class FPPutZ(FPState):
 263
 264     def action(self, m):
 265         self.put_z(m, self.z, self.out_z, "get_a")
 266
 267
 268 class FPADD:
 269
 270     def __init__(self, width, single_cycle=False):
 271         self.width = width
 272         self.single_cycle = single_cycle
 273
 274         self.in_a  = FPOp(width)
 275         self.in_b  = FPOp(width)
 276         self.out_z = FPOp(width)
 277
 278         self.states = []
 279
 280     def add_state(self, state):
 281         self.states.append(state)
 282         return state
 283
 284     def get_fragment(self, platform=None):
 285         """ creates the HDL code-fragment for FPAdd
 286         """
 287         m = Module()
 288
 289         # Latches
 290         b = FPNumIn(self.in_b, self.width)
 291         z = FPNumOut(self.width, False)
 292
 293         m.submodules.fpnum_b = b
 294         m.submodules.fpnum_z = z
 295
 296         w = z.m_width + 4
 297         tot = Signal(w, reset_less=True) # sticky/round/guard, {mantissa} result, 1 overflow
 298
 299         of = Overflow()
 300         m.submodules.overflow = of
 301
 302         geta = self.add_state(FPGetOpA(self.in_a, self.width))
 303         #geta.set_inputs({"in_a": self.in_a})
 304         #geta.set_outputs({"a": a})
 305         a = geta.a
 306         m.d.comb += a.v.eq(self.in_a.v) # links in_a to a
 307         m.submodules.fpnum_a = a
 308
 309         getb = self.add_state(FPGetOpB("get_b"))
 310         getb.set_inputs({"in_b": self.in_b})
 311         getb.set_outputs({"b": b})
 312         m.d.comb += b.v.eq(self.in_b.v) # links in_b to b
 313
 314         sc = self.add_state(FPAddSpecialCases("special_cases"))
 315         sc.set_inputs({"a": a, "b": b})
 316         sc.set_outputs({"z": z})
 317
 318         dn = self.add_state(FPAddDeNorm("denormalise"))
 319         dn.set_inputs({"a": a, "b": b})
 320         dn.set_outputs({"a": a, "b": b}) # XXX outputs same as inputs
 321
 322         if self.single_cycle:
 323             alm = self.add_state(FPAddAlignSingle("align"))
 324         else:
 325             alm = self.add_state(FPAddAlignMulti("align"))
 326         alm.set_inputs({"a": a, "b": b})
 327         alm.set_outputs({"a": a, "b": b}) # XXX outputs same as inputs
 328
 329         add0 = self.add_state(FPAddStage0("add_0"))
 330         add0.set_inputs({"a": a, "b": b})
 331         add0.set_outputs({"z": z, "tot": tot})
 332
 333         add1 = self.add_state(FPAddStage1("add_1"))
 334         add1.set_inputs({"tot": tot, "z": z}) # Z input passes through
 335         add1.set_outputs({"z": z, "of": of})  # XXX Z as output
 336
 337         n1 = self.add_state(FPNorm1("normalise_1"))
 338         n1.set_inputs({"z": z, "of": of})  # XXX Z as output
 339         n1.set_outputs({"z": z})  # XXX Z as output
 340
 341         n2 = self.add_state(FPNorm2("normalise_2"))
 342         n2.set_inputs({"z": z, "of": of})  # XXX Z as output
 343         n2.set_outputs({"z": z})  # XXX Z as output
 344
 345         rn = self.add_state(FPRound("round"))
 346         rn.set_inputs({"z": z, "of": of})  # XXX Z as output
 347         rn.set_outputs({"z": z})  # XXX Z as output
 348
 349         cor = self.add_state(FPCorrections("corrections"))
 350         cor.set_inputs({"z": z})  # XXX Z as output
 351         cor.set_outputs({"z": z})  # XXX Z as output
 352
 353         pa = self.add_state(FPPack("pack"))
 354         pa.set_inputs({"z": z})  # XXX Z as output
 355         pa.set_outputs({"z": z})  # XXX Z as output
 356
 357         pz = self.add_state(FPPutZ("put_z"))
 358         pz.set_inputs({"z": z})
 359         pz.set_outputs({"out_z": self.out_z})
 360
 361         with m.FSM() as fsm:
 362
 363             for state in self.states:
 364                 with m.State(state.state_from):
 365                     state.action(m)
 366
 367         return m
 368
 369
 370 if __name__ == "__main__":
 371     alu = FPADD(width=32)
 372     main(alu, ports=alu.in_a.ports() + alu.in_b.ports() + alu.out_z.ports())
 373
 374
 375     # works... but don't use, just do "python fname.py convert -t v"
 376     #print (verilog.convert(alu, ports=[
 377     #                        ports=alu.in_a.ports() + \
 378     #                              alu.in_b.ports() + \
 379     #                              alu.out_z.ports())