src/add/fpbase.py

   1 # IEEE Floating Point Adder (Single Precision)
   2 # Copyright (C) Jonathan P Dawson 2013
   3 # 2013-12-12
   4
   5 from nmigen import Signal, Cat, Const, Mux, Module
   6 from math import log
   7 from operator import or_
   8 from functools import reduce
   9
  10 class MultiShiftR:
  11
  12     def __init__(self, width):
  13         self.width = width
  14         self.smax = int(log(width) / log(2))
  15         self.i = Signal(width, reset_less=True)
  16         self.s = Signal(self.smax, reset_less=True)
  17         self.o = Signal(width, reset_less=True)
  18
  19     def elaborate(self, platform):
  20         m = Module()
  21         m.d.comb += self.o.eq(self.i >> self.s)
  22         return m
  23
  24
  25 class MultiShift:
  26     """ Generates variable-length single-cycle shifter from a series
  27         of conditional tests on each bit of the left/right shift operand.
  28         Each bit tested produces output shifted by that number of bits,
  29         in a binary fashion: bit 1 if set shifts by 1 bit, bit 2 if set
  30         shifts by 2 bits, each partial result cascading to the next Mux.
  31
  32         Could be adapted to do arithmetic shift by taking copies of the
  33         MSB instead of zeros.
  34     """
  35
  36     def __init__(self, width):
  37         self.width = width
  38         self.smax = int(log(width) / log(2))
  39
  40     def lshift(self, op, s):
  41         res = op << s
  42         return res[:len(op)]
  43         res = op
  44         for i in range(self.smax):
  45             zeros = [0] * (1<<i)
  46             res = Mux(s & (1<<i), Cat(zeros, res[0:-(1<<i)]), res)
  47         return res
  48
  49     def rshift(self, op, s):
  50         res = op >> s
  51         return res[:len(op)]
  52         res = op
  53         for i in range(self.smax):
  54             zeros = [0] * (1<<i)
  55             res = Mux(s & (1<<i), Cat(res[(1<<i):], zeros), res)
  56         return res
  57
  58
  59 class FPNumBase:
  60     """ Floating-point Base Number Class
  61     """
  62     def __init__(self, width, m_extra=True):
  63         self.width = width
  64         m_width = {16: 11, 32: 24, 64: 53}[width] # 1 extra bit (overflow)
  65         e_width = {16: 7,  32: 10, 64: 13}[width] # 2 extra bits (overflow)
  66         e_max = 1<<(e_width-3)
  67         self.rmw = m_width # real mantissa width (not including extras)
  68         self.e_max = e_max
  69         if m_extra:
  70             # mantissa extra bits (top,guard,round)
  71             self.m_extra = 3
  72             m_width += self.m_extra
  73         else:
  74             self.m_extra = 0
  75         #print (m_width, e_width, e_max, self.rmw, self.m_extra)
  76         self.m_width = m_width
  77         self.e_width = e_width
  78         self.e_start = self.rmw - 1
  79         self.e_end = self.rmw + self.e_width - 3 # for decoding
  80
  81         self.v = Signal(width, reset_less=True)      # Latched copy of value
  82         self.m = Signal(m_width, reset_less=True)    # Mantissa
  83         self.e = Signal((e_width, True), reset_less=True) # Exponent: IEEE754exp+2 bits, signed
  84         self.s = Signal(reset_less=True)           # Sign bit
  85
  86         self.mzero = Const(0, (m_width, False))
  87         self.m1s = Const(-1, (m_width, False))
  88         self.P128 = Const(e_max, (e_width, True))
  89         self.P127 = Const(e_max-1, (e_width, True))
  90         self.N127 = Const(-(e_max-1), (e_width, True))
  91         self.N126 = Const(-(e_max-2), (e_width, True))
  92
  93         self.is_nan = Signal(reset_less=True)
  94         self.is_zero = Signal(reset_less=True)
  95         self.is_inf = Signal(reset_less=True)
  96         self.is_overflowed = Signal(reset_less=True)
  97         self.is_denormalised = Signal(reset_less=True)
  98         self.exp_128 = Signal(reset_less=True)
  99         self.exp_lt_n126 = Signal(reset_less=True)
 100         self.exp_gt_n126 = Signal(reset_less=True)
 101         self.exp_gt127 = Signal(reset_less=True)
 102         self.exp_n127 = Signal(reset_less=True)
 103         self.exp_n126 = Signal(reset_less=True)
 104         self.m_zero = Signal(reset_less=True)
 105         self.m_msbzero = Signal(reset_less=True)
 106
 107     def elaborate(self, platform):
 108         m = Module()
 109         m.d.comb += self.is_nan.eq(self._is_nan())
 110         m.d.comb += self.is_zero.eq(self._is_zero())
 111         m.d.comb += self.is_inf.eq(self._is_inf())
 112         m.d.comb += self.is_overflowed.eq(self._is_overflowed())
 113         m.d.comb += self.is_denormalised.eq(self._is_denormalised())
 114         m.d.comb += self.exp_128.eq(self.e == self.P128)
 115         m.d.comb += self.exp_gt_n126.eq(self.e > self.N126)
 116         m.d.comb += self.exp_lt_n126.eq(self.e < self.N126)
 117         m.d.comb += self.exp_gt127.eq(self.e > self.P127)
 118         m.d.comb += self.exp_n127.eq(self.e == self.N127)
 119         m.d.comb += self.exp_n126.eq(self.e == self.N126)
 120         m.d.comb += self.m_zero.eq(self.m == self.mzero)
 121         m.d.comb += self.m_msbzero.eq(self.m[self.e_start] == 0)
 122
 123         return m
 124
 125     def _is_nan(self):
 126         return (self.exp_128) & (~self.m_zero)
 127
 128     def _is_inf(self):
 129         return (self.exp_128) & (self.m_zero)
 130
 131     def _is_zero(self):
 132         return (self.exp_n127) & (self.m_zero)
 133
 134     def _is_overflowed(self):
 135         return self.exp_gt127
 136
 137     def _is_denormalised(self):
 138         return (self.exp_n126) & (self.m_msbzero)
 139
 140     def copy(self, inp):
 141         return [self.s.eq(inp.s), self.e.eq(inp.e), self.m.eq(inp.m)]
 142
 143
 144 class FPNumOut(FPNumBase):
 145     """ Floating-point Number Class
 146
 147         Contains signals for an incoming copy of the value, decoded into
 148         sign / exponent / mantissa.
 149         Also contains encoding functions, creation and recognition of
 150         zero, NaN and inf (all signed)
 151
 152         Four extra bits are included in the mantissa: the top bit
 153         (m[-1]) is effectively a carry-overflow.  The other three are
 154         guard (m[2]), round (m[1]), and sticky (m[0])
 155     """
 156     def __init__(self, width, m_extra=True):
 157         FPNumBase.__init__(self, width, m_extra)
 158
 159     def elaborate(self, platform):
 160         m = FPNumBase.elaborate(self, platform)
 161
 162         return m
 163
 164     def create(self, s, e, m):
 165         """ creates a value from sign / exponent / mantissa
 166
 167             bias is added here, to the exponent
 168         """
 169         return [
 170           self.v[-1].eq(s),          # sign
 171           self.v[self.e_start:self.e_end].eq(e + self.P127), # exp (add on bias)
 172           self.v[0:self.e_start].eq(m)         # mantissa
 173         ]
 174
 175     def nan(self, s):
 176         return self.create(s, self.P128, 1<<(self.e_start-1))
 177
 178     def inf(self, s):
 179         return self.create(s, self.P128, 0)
 180
 181     def zero(self, s):
 182         return self.create(s, self.N127, 0)
 183
 184
 185 class FPNumShift(FPNumBase):
 186     """ Floating-point Number Class for shifting
 187     """
 188     def __init__(self, mainm, op, inv, width, m_extra=True):
 189         FPNumBase.__init__(self, width, m_extra)
 190         self.latch_in = Signal()
 191         self.mainm = mainm
 192         self.inv = inv
 193         self.op = op
 194
 195     def elaborate(self, platform):
 196         m = FPNumBase.elaborate(self, platform)
 197
 198         m.d.comb += self.s.eq(op.s)
 199         m.d.comb += self.e.eq(op.e)
 200         m.d.comb += self.m.eq(op.m)
 201
 202         with self.mainm.State("align"):
 203             with m.If(self.e < self.inv.e):
 204                 m.d.sync += self.shift_down()
 205
 206         return m
 207
 208     def shift_down(self, inp):
 209         """ shifts a mantissa down by one. exponent is increased to compensate
 210
 211             accuracy is lost as a result in the mantissa however there are 3
 212             guard bits (the latter of which is the "sticky" bit)
 213         """
 214         return [self.e.eq(inp.e + 1),
 215                 self.m.eq(Cat(inp.m[0] | inp.m[1], inp.m[2:], 0))
 216                ]
 217
 218     def shift_down_multi(self, diff):
 219         """ shifts a mantissa down. exponent is increased to compensate
 220
 221             accuracy is lost as a result in the mantissa however there are 3
 222             guard bits (the latter of which is the "sticky" bit)
 223
 224             this code works by variable-shifting the mantissa by up to
 225             its maximum bit-length: no point doing more (it'll still be
 226             zero).
 227
 228             the sticky bit is computed by shifting a batch of 1s by
 229             the same amount, which will introduce zeros.  it's then
 230             inverted and used as a mask to get the LSBs of the mantissa.
 231             those are then |'d into the sticky bit.
 232         """
 233         sm = MultiShift(self.width)
 234         mw = Const(self.m_width-1, len(diff))
 235         maxslen = Mux(diff > mw, mw, diff)
 236         rs = sm.rshift(self.m[1:], maxslen)
 237         maxsleni = mw - maxslen
 238         m_mask = sm.rshift(self.m1s[1:], maxsleni) # shift and invert
 239
 240         stickybits = reduce(or_, self.m[1:] & m_mask) | self.m[0]
 241         return [self.e.eq(self.e + diff),
 242                 self.m.eq(Cat(stickybits, rs))
 243                ]
 244
 245     def shift_up_multi(self, diff):
 246         """ shifts a mantissa up. exponent is decreased to compensate
 247         """
 248         sm = MultiShift(self.width)
 249         mw = Const(self.m_width, len(diff))
 250         maxslen = Mux(diff > mw, mw, diff)
 251
 252         return [self.e.eq(self.e - diff),
 253                 self.m.eq(sm.lshift(self.m, maxslen))
 254                ]
 255
 256 class FPNumIn(FPNumBase):
 257     """ Floating-point Number Class
 258
 259         Contains signals for an incoming copy of the value, decoded into
 260         sign / exponent / mantissa.
 261         Also contains encoding functions, creation and recognition of
 262         zero, NaN and inf (all signed)
 263
 264         Four extra bits are included in the mantissa: the top bit
 265         (m[-1]) is effectively a carry-overflow.  The other three are
 266         guard (m[2]), round (m[1]), and sticky (m[0])
 267     """
 268     def __init__(self, op, width, m_extra=True):
 269         FPNumBase.__init__(self, width, m_extra)
 270         self.latch_in = Signal()
 271         self.op = op
 272
 273     def elaborate(self, platform):
 274         m = FPNumBase.elaborate(self, platform)
 275
 276         #m.d.comb += self.latch_in.eq(self.op.ack & self.op.stb)
 277         #with m.If(self.latch_in):
 278         #    m.d.sync += self.decode(self.v)
 279
 280         return m
 281
 282     def decode(self, v):
 283         """ decodes a latched value into sign / exponent / mantissa
 284
 285             bias is subtracted here, from the exponent.  exponent
 286             is extended to 10 bits so that subtract 127 is done on
 287             a 10-bit number
 288         """
 289         args = [0] * self.m_extra + [v[0:self.e_start]] # pad with extra zeros
 290         #print ("decode", self.e_end)
 291         return [self.m.eq(Cat(*args)), # mantissa
 292                 self.e.eq(v[self.e_start:self.e_end] - self.P127), # exp
 293                 self.s.eq(v[-1]),                 # sign
 294                 ]
 295
 296     def shift_down(self, inp):
 297         """ shifts a mantissa down by one. exponent is increased to compensate
 298
 299             accuracy is lost as a result in the mantissa however there are 3
 300             guard bits (the latter of which is the "sticky" bit)
 301         """
 302         return [self.e.eq(inp.e + 1),
 303                 self.m.eq(Cat(inp.m[0] | inp.m[1], inp.m[2:], 0))
 304                ]
 305
 306     def shift_down_multi(self, diff):
 307         """ shifts a mantissa down. exponent is increased to compensate
 308
 309             accuracy is lost as a result in the mantissa however there are 3
 310             guard bits (the latter of which is the "sticky" bit)
 311
 312             this code works by variable-shifting the mantissa by up to
 313             its maximum bit-length: no point doing more (it'll still be
 314             zero).
 315
 316             the sticky bit is computed by shifting a batch of 1s by
 317             the same amount, which will introduce zeros.  it's then
 318             inverted and used as a mask to get the LSBs of the mantissa.
 319             those are then |'d into the sticky bit.
 320         """
 321         sm = MultiShift(self.width)
 322         mw = Const(self.m_width-1, len(diff))
 323         maxslen = Mux(diff > mw, mw, diff)
 324         rs = sm.rshift(self.m[1:], maxslen)
 325         maxsleni = mw - maxslen
 326         m_mask = sm.rshift(self.m1s[1:], maxsleni) # shift and invert
 327
 328         stickybits = reduce(or_, self.m[1:] & m_mask) | self.m[0]
 329         return [self.e.eq(self.e + diff),
 330                 self.m.eq(Cat(stickybits, rs))
 331                ]
 332
 333     def shift_up_multi(self, diff):
 334         """ shifts a mantissa up. exponent is decreased to compensate
 335         """
 336         sm = MultiShift(self.width)
 337         mw = Const(self.m_width, len(diff))
 338         maxslen = Mux(diff > mw, mw, diff)
 339
 340         return [self.e.eq(self.e - diff),
 341                 self.m.eq(sm.lshift(self.m, maxslen))
 342                ]
 343
 344 class FPOp:
 345     def __init__(self, width):
 346         self.width = width
 347
 348         self.v   = Signal(width)
 349         self.stb = Signal(reset=0)
 350         self.ack = Signal()
 351
 352     def chain_inv(self, in_op, extra=None):
 353         stb = in_op.stb
 354         if extra is not None:
 355             stb = stb & extra
 356         return [self.v.eq(in_op.v),          # receive value
 357                 self.stb.eq(stb),      # receive STB
 358                 in_op.ack.eq(~self.ack), # send ACK
 359                ]
 360
 361     def chain_from(self, in_op, extra=None):
 362         stb = in_op.stb
 363         if extra is not None:
 364             stb = stb & extra
 365         return [self.v.eq(in_op.v),          # receive value
 366                 self.stb.eq(stb),      # receive STB
 367                 in_op.ack.eq(self.ack), # send ACK
 368                ]
 369
 370     def ports(self):
 371         return [self.v, self.stb, self.ack]
 372
 373
 374 class Overflow:
 375     def __init__(self):
 376         self.guard = Signal(reset_less=True)     # tot[2]
 377         self.round_bit = Signal(reset_less=True) # tot[1]
 378         self.sticky = Signal(reset_less=True)    # tot[0]
 379         self.m0 = Signal(reset_less=True)        # mantissa zero bit
 380
 381         self.roundz = Signal(reset_less=True)
 382
 383     def copy(self, inp):
 384         return [self.guard.eq(inp.guard),
 385                 self.round_bit.eq(inp.round_bit),
 386                 self.sticky.eq(inp.sticky),
 387                 self.m0.eq(inp.m0)]
 388
 389     def elaborate(self, platform):
 390         m = Module()
 391         m.d.comb += self.roundz.eq(self.guard & \
 392                                    (self.round_bit | self.sticky | self.m0))
 393         return m
 394
 395
 396 class FPBase:
 397     """ IEEE754 Floating Point Base Class
 398
 399         contains common functions for FP manipulation, such as
 400         extracting and packing operands, normalisation, denormalisation,
 401         rounding etc.
 402     """
 403
 404     def get_op(self, m, op, v, next_state):
 405         """ this function moves to the next state and copies the operand
 406             when both stb and ack are 1.
 407             acknowledgement is sent by setting ack to ZERO.
 408         """
 409         with m.If((op.ack) & (op.stb)):
 410             m.next = next_state
 411             m.d.sync += [
 412                 # op is latched in from FPNumIn class on same ack/stb
 413                 v.decode(op.v),
 414                 op.ack.eq(0)
 415             ]
 416         with m.Else():
 417             m.d.sync += op.ack.eq(1)
 418
 419     def denormalise(self, m, a):
 420         """ denormalises a number.  this is probably the wrong name for
 421             this function.  for normalised numbers (exponent != minimum)
 422             one *extra* bit (the implicit 1) is added *back in*.
 423             for denormalised numbers, the mantissa is left alone
 424             and the exponent increased by 1.
 425
 426             both cases *effectively multiply the number stored by 2*,
 427             which has to be taken into account when extracting the result.
 428         """
 429         with m.If(a.e == a.N127):
 430             m.d.sync += a.e.eq(a.N126) # limit a exponent
 431         with m.Else():
 432             m.d.sync += a.m[-1].eq(1) # set top mantissa bit
 433
 434     def op_normalise(self, m, op, next_state):
 435         """ operand normalisation
 436             NOTE: just like "align", this one keeps going round every clock
 437                   until the result's exponent is within acceptable "range"
 438         """
 439         with m.If((op.m[-1] == 0)): # check last bit of mantissa
 440             m.d.sync +=[
 441                 op.e.eq(op.e - 1),  # DECREASE exponent
 442                 op.m.eq(op.m << 1), # shift mantissa UP
 443             ]
 444         with m.Else():
 445             m.next = next_state
 446
 447     def normalise_1(self, m, z, of, next_state):
 448         """ first stage normalisation
 449
 450             NOTE: just like "align", this one keeps going round every clock
 451                   until the result's exponent is within acceptable "range"
 452             NOTE: the weirdness of reassigning guard and round is due to
 453                   the extra mantissa bits coming from tot[0..2]
 454         """
 455         with m.If((z.m[-1] == 0) & (z.e > z.N126)):
 456             m.d.sync += [
 457                 z.e.eq(z.e - 1),  # DECREASE exponent
 458                 z.m.eq(z.m << 1), # shift mantissa UP
 459                 z.m[0].eq(of.guard),       # steal guard bit (was tot[2])
 460                 of.guard.eq(of.round_bit), # steal round_bit (was tot[1])
 461                 of.round_bit.eq(0),        # reset round bit
 462                 of.m0.eq(of.guard),
 463             ]
 464         with m.Else():
 465             m.next = next_state
 466
 467     def normalise_2(self, m, z, of, next_state):
 468         """ second stage normalisation
 469
 470             NOTE: just like "align", this one keeps going round every clock
 471                   until the result's exponent is within acceptable "range"
 472             NOTE: the weirdness of reassigning guard and round is due to
 473                   the extra mantissa bits coming from tot[0..2]
 474         """
 475         with m.If(z.e < z.N126):
 476             m.d.sync +=[
 477                 z.e.eq(z.e + 1),  # INCREASE exponent
 478                 z.m.eq(z.m >> 1), # shift mantissa DOWN
 479                 of.guard.eq(z.m[0]),
 480                 of.m0.eq(z.m[1]),
 481                 of.round_bit.eq(of.guard),
 482                 of.sticky.eq(of.sticky | of.round_bit)
 483             ]
 484         with m.Else():
 485             m.next = next_state
 486
 487     def roundz(self, m, z, out_z, roundz):
 488         """ performs rounding on the output.  TODO: different kinds of rounding
 489         """
 490         m.d.comb += out_z.copy(z) # copies input to output first
 491         with m.If(roundz):
 492             m.d.comb += out_z.m.eq(z.m + 1) # mantissa rounds up
 493             with m.If(z.m == z.m1s): # all 1s
 494                 m.d.comb += out_z.e.eq(z.e + 1) # exponent rounds up
 495
 496     def corrections(self, m, z, next_state):
 497         """ denormalisation and sign-bug corrections
 498         """
 499         m.next = next_state
 500         # denormalised, correct exponent to zero
 501         with m.If(z.is_denormalised):
 502             m.d.sync += z.e.eq(z.N127)
 503
 504     def pack(self, m, z, next_state):
 505         """ packs the result into the output (detects overflow->Inf)
 506         """
 507         m.next = next_state
 508         # if overflow occurs, return inf
 509         with m.If(z.is_overflowed):
 510             m.d.sync += z.inf(z.s)
 511         with m.Else():
 512             m.d.sync += z.create(z.s, z.e, z.m)
 513
 514     def put_z(self, m, z, out_z, next_state):
 515         """ put_z: stores the result in the output.  raises stb and waits
 516             for ack to be set to 1 before moving to the next state.
 517             resets stb back to zero when that occurs, as acknowledgement.
 518         """
 519         m.d.sync += [
 520           out_z.v.eq(z.v)
 521         ]
 522         with m.If(out_z.stb & out_z.ack):
 523             m.d.sync += out_z.stb.eq(0)
 524             m.next = next_state
 525         with m.Else():
 526             m.d.sync += out_z.stb.eq(1)
 527
 528