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, FPNumBase
   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 FPRoundMod:
 245
 246     def __init__(self, width):
 247         self.in_roundz = Signal(reset_less=True)
 248         self.in_z = FPNumBase(width, False)
 249         self.out_z = FPNumBase(width, False)
 250
 251     def setup(self, m, in_z, out_z, in_of):
 252         """ links module to inputs and outputs
 253         """
 254         m.d.comb += self.in_z.copy(in_z)
 255         m.d.comb += out_z.copy(self.out_z)
 256         m.d.comb += self.in_roundz.eq(in_of.roundz)
 257
 258     def elaborate(self, platform):
 259         m = Module()
 260         m.d.comb += self.out_z.copy(self.in_z)
 261         with m.If(self.in_roundz):
 262             m.d.comb += self.out_z.m.eq(self.in_z.m + 1) # mantissa rounds up
 263             with m.If(self.in_z.m == self.in_z.m1s): # all 1s
 264                 m.d.comb += self.out_z.e.eq(self.in_z.e + 1) # exponent up
 265         return m
 266
 267
 268 class FPRound(FPState):
 269
 270     def __init__(self, width):
 271         FPState.__init__(self, "round")
 272         self.mod = FPRoundMod(width)
 273         self.out_z = FPNumBase(width)
 274
 275     def action(self, m):
 276         m.d.sync += self.z.copy(self.out_z)
 277         m.next = "corrections"
 278
 279
 280 class FPCorrectionsMod:
 281
 282     def __init__(self, width):
 283         self.in_z = FPNumOut(width, False)
 284         self.out_z = FPNumOut(width, False)
 285
 286     def setup(self, m, in_z, out_z):
 287         """ links module to inputs and outputs
 288         """
 289         m.d.comb += self.in_z.copy(in_z)
 290         m.d.comb += out_z.copy(self.out_z)
 291
 292     def elaborate(self, platform):
 293         m = Module()
 294         m.submodules.corr_in_z = self.in_z
 295         m.submodules.corr_out_z = self.out_z
 296         m.d.comb += self.out_z.copy(self.in_z)
 297         with m.If(self.in_z.is_denormalised):
 298             m.d.comb += self.out_z.e.eq(self.in_z.N127)
 299
 300         #        with m.If(self.in_z.is_overflowed):
 301         #            m.d.comb += self.out_z.inf(self.in_z.s)
 302         #        with m.Else():
 303         #            m.d.comb += self.out_z.create(self.in_z.s, self.in_z.e, self.in_z.m)
 304         return m
 305
 306
 307 class FPCorrections(FPState):
 308
 309     def __init__(self, width):
 310         FPState.__init__(self, "corrections")
 311         self.mod = FPCorrectionsMod(width)
 312         self.out_z = FPNumBase(width)
 313
 314     def action(self, m):
 315         m.d.sync += self.z.copy(self.out_z)
 316         m.next = "pack"
 317
 318
 319 class FPPackMod:
 320
 321     def __init__(self, width):
 322         self.in_z = FPNumOut(width, False)
 323         self.out_z = FPNumOut(width, False)
 324
 325     def setup(self, m, in_z, out_z):
 326         """ links module to inputs and outputs
 327         """
 328         m.d.comb += self.in_z.copy(in_z)
 329         #m.d.comb += out_z.copy(self.out_z)
 330         m.d.comb += out_z.v.eq(self.out_z.v)
 331
 332     def elaborate(self, platform):
 333         m = Module()
 334         m.submodules.pack_in_z = self.in_z
 335         with m.If(self.in_z.is_overflowed):
 336             m.d.comb += self.out_z.inf(self.in_z.s)
 337         with m.Else():
 338             m.d.comb += self.out_z.create(self.in_z.s, self.in_z.e, self.in_z.m)
 339         return m
 340
 341
 342 class FPPack(FPState):
 343
 344     def __init__(self, width):
 345         FPState.__init__(self, "pack")
 346         self.mod = FPPackMod(width)
 347         self.out_z = FPNumOut(width, False)
 348
 349     def action(self, m):
 350         m.d.sync += self.z.v.eq(self.out_z.v)
 351         m.next = "put_z"
 352
 353
 354 class FPPutZ(FPState):
 355
 356     def action(self, m):
 357         self.put_z(m, self.z, self.out_z, "get_a")
 358
 359
 360 class FPADD:
 361
 362     def __init__(self, width, single_cycle=False):
 363         self.width = width
 364         self.single_cycle = single_cycle
 365
 366         self.in_a  = FPOp(width)
 367         self.in_b  = FPOp(width)
 368         self.out_z = FPOp(width)
 369
 370         self.states = []
 371
 372     def add_state(self, state):
 373         self.states.append(state)
 374         return state
 375
 376     def get_fragment(self, platform=None):
 377         """ creates the HDL code-fragment for FPAdd
 378         """
 379         m = Module()
 380
 381         # Latches
 382         #a = FPNumIn(self.in_a, self.width)
 383         b = FPNumIn(self.in_b, self.width)
 384         z = FPNumOut(self.width, False)
 385
 386         m.submodules.fpnum_b = b
 387         m.submodules.fpnum_z = z
 388
 389         w = z.m_width + 4
 390         tot = Signal(w, reset_less=True) # sticky/round/guard, {mantissa} result, 1 overflow
 391
 392         of = Overflow()
 393         m.submodules.overflow = of
 394
 395         geta = self.add_state(FPGetOpA(self.in_a, self.width))
 396         #geta.set_inputs({"in_a": self.in_a})
 397         #geta.set_outputs({"a": a})
 398         a = geta.a
 399         # XXX m.d.comb += a.v.eq(self.in_a.v) # links in_a to a
 400         m.submodules.fpnum_a = a
 401
 402         getb = self.add_state(FPGetOpB("get_b"))
 403         getb.set_inputs({"in_b": self.in_b})
 404         getb.set_outputs({"b": b})
 405         # XXX m.d.comb += b.v.eq(self.in_b.v) # links in_b to b
 406
 407         sc = self.add_state(FPAddSpecialCases("special_cases"))
 408         sc.set_inputs({"a": a, "b": b})
 409         sc.set_outputs({"z": z})
 410
 411         dn = self.add_state(FPAddDeNorm("denormalise"))
 412         dn.set_inputs({"a": a, "b": b})
 413         dn.set_outputs({"a": a, "b": b}) # XXX outputs same as inputs
 414
 415         if self.single_cycle:
 416             alm = self.add_state(FPAddAlignSingle("align"))
 417         else:
 418             alm = self.add_state(FPAddAlignMulti("align"))
 419         alm.set_inputs({"a": a, "b": b})
 420         alm.set_outputs({"a": a, "b": b}) # XXX outputs same as inputs
 421
 422         add0 = self.add_state(FPAddStage0("add_0"))
 423         add0.set_inputs({"a": a, "b": b})
 424         add0.set_outputs({"z": z, "tot": tot})
 425
 426         add1 = self.add_state(FPAddStage1("add_1"))
 427         add1.set_inputs({"tot": tot, "z": z}) # Z input passes through
 428         add1.set_outputs({"z": z, "of": of})  # XXX Z as output
 429
 430         n1 = self.add_state(FPNorm1("normalise_1"))
 431         n1.set_inputs({"z": z, "of": of})  # XXX Z as output
 432         n1.set_outputs({"z": z})  # XXX Z as output
 433
 434         n2 = self.add_state(FPNorm2("normalise_2"))
 435         n2.set_inputs({"z": z, "of": of})  # XXX Z as output
 436         n2.set_outputs({"z": z})  # XXX Z as output
 437
 438         rn = self.add_state(FPRound(self.width))
 439         rn.set_inputs({"z": z, "of": of})  # XXX Z as output
 440         rn.set_outputs({"z": z})  # XXX Z as output
 441         rn.mod.setup(m, z, rn.out_z, of)
 442         m.submodules.roundz = rn.mod
 443
 444         cor = self.add_state(FPCorrections(self.width))
 445         cor.set_inputs({"z": z})  # XXX Z as output
 446         cor.set_outputs({"z": z})  # XXX Z as output
 447         cor.mod.setup(m, z, cor.out_z)
 448         m.submodules.corrections = cor.mod
 449
 450         pa = self.add_state(FPPack(self.width))
 451         pa.set_inputs({"z": z})  # XXX Z as output
 452         pa.set_outputs({"z": z})  # XXX Z as output
 453         pa.mod.setup(m, z, pa.out_z)
 454         m.submodules.pack = pa.mod
 455
 456         pz = self.add_state(FPPutZ("put_z"))
 457         pz.set_inputs({"z": z})
 458         pz.set_outputs({"out_z": self.out_z})
 459
 460         with m.FSM() as fsm:
 461
 462             for state in self.states:
 463                 with m.State(state.state_from):
 464                     state.action(m)
 465
 466         return m
 467
 468
 469 if __name__ == "__main__":
 470     alu = FPADD(width=32)
 471     main(alu, ports=alu.in_a.ports() + alu.in_b.ports() + alu.out_z.ports())
 472
 473
 474     # works... but don't use, just do "python fname.py convert -t v"
 475     #print (verilog.convert(alu, ports=[
 476     #                        ports=alu.in_a.ports() + \
 477     #                              alu.in_b.ports() + \
 478     #                              alu.out_z.ports())