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
  28     def action(self, m):
  29         self.get_op(m, self.in_a, self.a, "get_b")
  30
  31
  32 class FPGetOpB(FPState):
  33
  34     def action(self, m):
  35         self.get_op(m, self.in_b, self.b, "special_cases")
  36
  37
  38 class FPAddSpecialCases(FPState):
  39
  40     def action(self, m):
  41         """ special cases: NaNs, infs, zeros, denormalised
  42             NOTE: some of these are unique to add.  see "Special Operations"
  43             https://steve.hollasch.net/cgindex/coding/ieeefloat.html
  44         """
  45         s_nomatch = Signal()
  46         m.d.comb += s_nomatch.eq(self.a.s != self.b.s)
  47
  48         m_match = Signal()
  49         m.d.comb += m_match.eq(self.a.m == self.b.m)
  50
  51         # if a is NaN or b is NaN return NaN
  52         with m.If(self.a.is_nan | self.b.is_nan):
  53             m.next = "put_z"
  54             m.d.sync += self.z.nan(1)
  55
  56         # XXX WEIRDNESS for FP16 non-canonical NaN handling
  57         # under review
  58
  59         ## if a is zero and b is NaN return -b
  60         #with m.If(a.is_zero & (a.s==0) & b.is_nan):
  61         #    m.next = "put_z"
  62         #    m.d.sync += z.create(b.s, b.e, Cat(b.m[3:-2], ~b.m[0]))
  63
  64         ## if b is zero and a is NaN return -a
  65         #with m.Elif(b.is_zero & (b.s==0) & a.is_nan):
  66         #    m.next = "put_z"
  67         #    m.d.sync += z.create(a.s, a.e, Cat(a.m[3:-2], ~a.m[0]))
  68
  69         ## if a is -zero and b is NaN return -b
  70         #with m.Elif(a.is_zero & (a.s==1) & b.is_nan):
  71         #    m.next = "put_z"
  72         #    m.d.sync += z.create(a.s & b.s, b.e, Cat(b.m[3:-2], 1))
  73
  74         ## if b is -zero and a is NaN return -a
  75         #with m.Elif(b.is_zero & (b.s==1) & a.is_nan):
  76         #    m.next = "put_z"
  77         #    m.d.sync += z.create(a.s & b.s, a.e, Cat(a.m[3:-2], 1))
  78
  79         # if a is inf return inf (or NaN)
  80         with m.Elif(self.a.is_inf):
  81             m.next = "put_z"
  82             m.d.sync += self.z.inf(self.a.s)
  83             # if a is inf and signs don't match return NaN
  84             with m.If(self.b.exp_128 & s_nomatch):
  85                 m.d.sync += self.z.nan(1)
  86
  87         # if b is inf return inf
  88         with m.Elif(self.b.is_inf):
  89             m.next = "put_z"
  90             m.d.sync += self.z.inf(self.b.s)
  91
  92         # if a is zero and b zero return signed-a/b
  93         with m.Elif(self.a.is_zero & self.b.is_zero):
  94             m.next = "put_z"
  95             m.d.sync += self.z.create(self.a.s & self.b.s, self.b.e,
  96                                       self.b.m[3:-1])
  97
  98         # if a is zero return b
  99         with m.Elif(self.a.is_zero):
 100             m.next = "put_z"
 101             m.d.sync += self.z.create(self.b.s, self.b.e, self.b.m[3:-1])
 102
 103         # if b is zero return a
 104         with m.Elif(self.b.is_zero):
 105             m.next = "put_z"
 106             m.d.sync += self.z.create(self.a.s, self.a.e, self.a.m[3:-1])
 107
 108         # if a equal to -b return zero (+ve zero)
 109         with m.Elif(s_nomatch & m_match & (self.a.e == self.b.e)):
 110             m.next = "put_z"
 111             m.d.sync += self.z.zero(0)
 112
 113         # Denormalised Number checks
 114         with m.Else():
 115             m.next = "denormalise"
 116
 117
 118 class FPAddDeNorm(FPState):
 119
 120     def action(self, m):
 121         # Denormalised Number checks
 122         m.next = "align"
 123         self.denormalise(m, self.a)
 124         self.denormalise(m, self.b)
 125
 126
 127 class FPAddAlignMulti(FPState):
 128
 129     def action(self, m):
 130         # NOTE: this does *not* do single-cycle multi-shifting,
 131         #       it *STAYS* in the align state until exponents match
 132
 133         # exponent of a greater than b: shift b down
 134         with m.If(self.a.e > self.b.e):
 135             m.d.sync += self.b.shift_down()
 136         # exponent of b greater than a: shift a down
 137         with m.Elif(self.a.e < self.b.e):
 138             m.d.sync += self.a.shift_down()
 139         # exponents equal: move to next stage.
 140         with m.Else():
 141             m.next = "add_0"
 142
 143
 144 class FPAddAlignSingle(FPState):
 145
 146     def action(self, m):
 147         # This one however (single-cycle) will do the shift
 148         # in one go.
 149
 150         # XXX TODO: the shifter used here is quite expensive
 151         # having only one would be better
 152
 153         ediff = Signal((len(self.a.e), True), reset_less=True)
 154         ediffr = Signal((len(self.a.e), True), reset_less=True)
 155         m.d.comb += ediff.eq(self.a.e - self.b.e)
 156         m.d.comb += ediffr.eq(self.b.e - self.a.e)
 157         with m.If(ediff > 0):
 158             m.d.sync += self.b.shift_down_multi(ediff)
 159         # exponent of b greater than a: shift a down
 160         with m.Elif(ediff < 0):
 161             m.d.sync += self.a.shift_down_multi(ediffr)
 162
 163         m.next = "add_0"
 164
 165
 166 class FPAddStage0(FPState):
 167
 168     def action(self, m):
 169         """ First stage of add.  covers same-sign (add) and subtract
 170             special-casing when mantissas are greater or equal, to
 171             give greatest accuracy.
 172         """
 173         m.next = "add_1"
 174         m.d.sync += self.z.e.eq(self.a.e)
 175         # same-sign (both negative or both positive) add mantissas
 176         with m.If(self.a.s == self.b.s):
 177             m.d.sync += [
 178                 self.tot.eq(Cat(self.a.m, 0) + Cat(self.b.m, 0)),
 179                 self.z.s.eq(self.a.s)
 180             ]
 181         # a mantissa greater than b, use a
 182         with m.Elif(self.a.m >= self.b.m):
 183             m.d.sync += [
 184                 self.tot.eq(Cat(self.a.m, 0) - Cat(self.b.m, 0)),
 185                 self.z.s.eq(self.a.s)
 186             ]
 187         # b mantissa greater than a, use b
 188         with m.Else():
 189             m.d.sync += [
 190                 self.tot.eq(Cat(self.b.m, 0) - Cat(self.a.m, 0)),
 191                 self.z.s.eq(self.b.s)
 192         ]
 193
 194
 195         """ Second stage of add: preparation for normalisation.
 196             detects when tot sum is too big (tot[27] is kinda a carry bit)
 197         """
 198
 199 class FPAddStage1(FPState):
 200
 201     def action(self, m):
 202         m.next = "normalise_1"
 203         # tot[27] gets set when the sum overflows. shift result down
 204         with m.If(self.tot[-1]):
 205             m.d.sync += [
 206                 self.z.m.eq(self.tot[4:]),
 207                 self.of.m0.eq(self.tot[4]),
 208                 self.of.guard.eq(self.tot[3]),
 209                 self.of.round_bit.eq(self.tot[2]),
 210                 self.of.sticky.eq(self.tot[1] | self.tot[0]),
 211                 self.z.e.eq(self.z.e + 1)
 212         ]
 213         # tot[27] zero case
 214         with m.Else():
 215             m.d.sync += [
 216                 self.z.m.eq(self.tot[3:]),
 217                 self.of.m0.eq(self.tot[3]),
 218                 self.of.guard.eq(self.tot[2]),
 219                 self.of.round_bit.eq(self.tot[1]),
 220                 self.of.sticky.eq(self.tot[0])
 221         ]
 222
 223
 224 class FPNorm1(FPState):
 225
 226     def action(self, m):
 227         self.normalise_1(m, self.z, self.of, "normalise_2")
 228
 229
 230 class FPNorm2(FPState):
 231
 232     def action(self, m):
 233         self.normalise_2(m, self.z, self.of, "round")
 234
 235
 236 class FPRound(FPState):
 237
 238     def action(self, m):
 239         self.roundz(m, self.z, self.of, "corrections")
 240
 241 class FPCorrections(FPState):
 242
 243     def action(self, m):
 244         self.corrections(m, self.z, "pack")
 245
 246
 247 class FPADD(FPBase):
 248
 249     def __init__(self, width, single_cycle=False):
 250         FPBase.__init__(self)
 251         self.width = width
 252         self.single_cycle = single_cycle
 253
 254         self.in_a  = FPOp(width)
 255         self.in_b  = FPOp(width)
 256         self.out_z = FPOp(width)
 257
 258     def get_fragment(self, platform=None):
 259         """ creates the HDL code-fragment for FPAdd
 260         """
 261         m = Module()
 262
 263         # Latches
 264         a = FPNumIn(self.in_a, self.width)
 265         b = FPNumIn(self.in_b, self.width)
 266         z = FPNumOut(self.width, False)
 267
 268         m.submodules.fpnum_a = a
 269         m.submodules.fpnum_b = b
 270         m.submodules.fpnum_z = z
 271
 272         w = z.m_width + 4
 273         tot = Signal(w, reset_less=True) # sticky/round/guard, {mantissa} result, 1 overflow
 274
 275         of = Overflow()
 276         m.submodules.overflow = of
 277
 278         geta = FPGetOpA("get_a")
 279         geta.set_inputs({"in_a": self.in_a})
 280         geta.set_outputs({"a": a})
 281         m.d.comb += a.v.eq(self.in_a.v) # links in_a to a
 282
 283         getb = FPGetOpB("get_b")
 284         getb.set_inputs({"in_b": self.in_b})
 285         getb.set_outputs({"b": b})
 286         m.d.comb += b.v.eq(self.in_b.v) # links in_b to b
 287
 288         sc = FPAddSpecialCases("special_cases")
 289         sc.set_inputs({"a": a, "b": b})
 290         sc.set_outputs({"z": z})
 291
 292         dn = FPAddDeNorm("denormalise")
 293         dn.set_inputs({"a": a, "b": b})
 294         dn.set_outputs({"a": a, "b": b}) # XXX outputs same as inputs
 295
 296         if self.single_cycle:
 297             alm = FPAddAlignSingle("align")
 298         else:
 299             alm = FPAddAlignMulti("align")
 300         alm.set_inputs({"a": a, "b": b})
 301         alm.set_outputs({"a": a, "b": b}) # XXX outputs same as inputs
 302
 303         add0 = FPAddStage0("add_0")
 304         add0.set_inputs({"a": a, "b": b})
 305         add0.set_outputs({"z": z, "tot": tot})
 306
 307         add1 = FPAddStage1("add_1")
 308         add1.set_inputs({"tot": tot, "z": z}) # Z input passes through
 309         add1.set_outputs({"z": z, "of": of})  # XXX Z as output
 310
 311         n1 = FPNorm1("normalise_1")
 312         n1.set_inputs({"z": z, "of": of})  # XXX Z as output
 313         n1.set_outputs({"z": z})  # XXX Z as output
 314
 315         n2 = FPNorm2("normalise_2")
 316         n2.set_inputs({"z": z, "of": of})  # XXX Z as output
 317         n2.set_outputs({"z": z})  # XXX Z as output
 318
 319         rn = FPRound("round")
 320         rn.set_inputs({"z": z, "of": of})  # XXX Z as output
 321         rn.set_outputs({"z": z})  # XXX Z as output
 322
 323         cor = FPCorrections("corrections")
 324         cor.set_inputs({"z": z})  # XXX Z as output
 325         cor.set_outputs({"z": z})  # XXX Z as output
 326
 327         with m.FSM() as fsm:
 328
 329             # ******
 330             # gets operand a
 331
 332             with m.State("get_a"):
 333                 geta.action(m)
 334
 335             # ******
 336             # gets operand b
 337
 338             with m.State("get_b"):
 339                 #self.get_op(m, self.in_b, b, "special_cases")
 340                 getb.action(m)
 341
 342             # ******
 343             # special cases: NaNs, infs, zeros, denormalised
 344             # NOTE: some of these are unique to add.  see "Special Operations"
 345             # https://steve.hollasch.net/cgindex/coding/ieeefloat.html
 346
 347             with m.State("special_cases"):
 348                 sc.action(m)
 349
 350             # ******
 351             # denormalise.
 352
 353             with m.State("denormalise"):
 354                 dn.action(m)
 355
 356             # ******
 357             # align.
 358
 359             with m.State("align"):
 360                 alm.action(m)
 361
 362             # ******
 363             # First stage of add.  covers same-sign (add) and subtract
 364             # special-casing when mantissas are greater or equal, to
 365             # give greatest accuracy.
 366
 367             with m.State("add_0"):
 368                 add0.action(m)
 369
 370             # ******
 371             # Second stage of add: preparation for normalisation.
 372             # detects when tot sum is too big (tot[27] is kinda a carry bit)
 373
 374             with m.State("add_1"):
 375                 add1.action(m)
 376
 377             # ******
 378             # First stage of normalisation.
 379
 380             with m.State("normalise_1"):
 381                 n1.action(m)
 382
 383             # ******
 384             # Second stage of normalisation.
 385
 386             with m.State("normalise_2"):
 387                 n2.action(m)
 388
 389             # ******
 390             # rounding stage
 391
 392             with m.State("round"):
 393                 rn.action(m)
 394
 395             # ******
 396             # correction stage
 397
 398             with m.State("corrections"):
 399                 cor.action(m)
 400
 401             # ******
 402             # pack stage
 403
 404             with m.State("pack"):
 405                 self.pack(m, z, "put_z")
 406
 407             # ******
 408             # put_z stage
 409
 410             with m.State("put_z"):
 411                 self.put_z(m, z, self.out_z, "get_a")
 412
 413         return m
 414
 415
 416 if __name__ == "__main__":
 417     alu = FPADD(width=32)
 418     main(alu, ports=alu.in_a.ports() + alu.in_b.ports() + alu.out_z.ports())
 419
 420
 421     # works... but don't use, just do "python fname.py convert -t v"
 422     #print (verilog.convert(alu, ports=[
 423     #                        ports=alu.in_a.ports() + \
 424     #                              alu.in_b.ports() + \
 425     #                              alu.out_z.ports())