# Copyright (C) Jonathan P Dawson 2013
# 2013-12-12
-from nmigen import Module, Signal, Cat, Const
+from nmigen import Module, Signal, Cat
from nmigen.cli import main, verilog
+from fpbase import FPNumIn, FPNumOut, FPOp, Overflow, FPBase, FPNumBase
-class FPNum:
- """ Floating-point Number Class, variable-width TODO (currently 32-bit)
- Contains signals for an incoming copy of the value, decoded into
- sign / exponent / mantissa.
- Also contains encoding functions, creation and recognition of
- zero, NaN and inf (all signed)
+class FPState(FPBase):
+ def __init__(self, state_from):
+ self.state_from = state_from
- Four extra bits are included in the mantissa: the top bit
- (m[-1]) is effectively a carry-overflow. The other three are
- guard (m[2]), round (m[1]), and sticky (m[0])
+ def set_inputs(self, inputs):
+ self.inputs = inputs
+ for k,v in inputs.items():
+ setattr(self, k, v)
+
+ def set_outputs(self, outputs):
+ self.outputs = outputs
+ for k,v in outputs.items():
+ setattr(self, k, v)
+
+
+class FPGetOpMod:
+ def __init__(self, width):
+ self.in_op = FPOp(width)
+ self.out_op = FPNumIn(self.in_op, width)
+ self.out_decode = Signal(reset_less=True)
+
+ def setup(self, m, in_op, out_op, out_decode):
+ """ links module to inputs and outputs
+ """
+ m.d.comb += self.in_op.copy(in_op)
+ m.d.comb += out_op.v.eq(self.out_op.v)
+ m.d.comb += out_decode.eq(self.out_decode)
+
+ def elaborate(self, platform):
+ m = Module()
+ m.d.comb += self.out_decode.eq((self.in_op.ack) & (self.in_op.stb))
+ #m.submodules.get_op_in = self.in_op
+ m.submodules.get_op_out = self.out_op
+ with m.If(self.out_decode):
+ m.d.comb += [
+ self.out_op.decode(self.in_op.v),
+ ]
+ return m
+
+
+class FPGetOp(FPState):
+ """ gets operand
"""
- def __init__(self, width, m_width=None):
- self.width = width
- if m_width is None:
- m_width = width - 5 # mantissa extra bits (top,guard,round)
- self.v = Signal(width) # Latched copy of value
- self.m = Signal(m_width) # Mantissa
- self.e = Signal((10, True)) # Exponent: 10 bits, signed
- self.s = Signal() # Sign bit
-
- self.mzero = Const(0, (m_width, False))
- self.m1s = Const(-1, (m_width, False))
- self.P128 = Const(128, (10, True))
- self.P127 = Const(127, (10, True))
- self.N127 = Const(-127, (10, True))
- self.N126 = Const(-126, (10, True))
-
- def decode(self):
- """ decodes a latched value into sign / exponent / mantissa
-
- bias is subtracted here, from the exponent. exponent
- is extended to 10 bits so that subtract 127 is done on
- a 10-bit number
+
+ def __init__(self, in_state, out_state, in_op, width):
+ FPState.__init__(self, in_state)
+ self.out_state = out_state
+ self.mod = FPGetOpMod(width)
+ self.in_op = in_op
+ self.out_op = FPNumIn(in_op, width)
+ self.out_decode = Signal(reset_less=True)
+
+ def action(self, m):
+ with m.If(self.out_decode):
+ m.next = self.out_state
+ m.d.sync += [
+ self.in_op.ack.eq(0),
+ self.out_op.copy(self.mod.out_op)
+ ]
+ with m.Else():
+ m.d.sync += self.in_op.ack.eq(1)
+
+
+class FPGetOpB(FPState):
+ """ gets operand b
+ """
+
+ def __init__(self, in_b, width):
+ FPState.__init__(self, "get_b")
+ self.in_b = in_b
+ self.b = FPNumIn(self.in_b, width)
+
+ def action(self, m):
+ self.get_op(m, self.in_b, self.b, "special_cases")
+
+
+class FPAddSpecialCasesMod:
+ """ special cases: NaNs, infs, zeros, denormalised
+ NOTE: some of these are unique to add. see "Special Operations"
+ https://steve.hollasch.net/cgindex/coding/ieeefloat.html
+ """
+
+ def __init__(self, width):
+ self.in_a = FPNumBase(width)
+ self.in_b = FPNumBase(width)
+ self.out_z = FPNumOut(width, False)
+ self.out_do_z = Signal(reset_less=True)
+
+ def setup(self, m, in_a, in_b, out_z, out_do_z):
+ """ links module to inputs and outputs
"""
- v = self.v
- return [self.m.eq(Cat(0, 0, 0, v[0:23])), # mantissa
- self.e.eq(v[23:31] - self.P127), # exp (minus bias)
- self.s.eq(v[31]), # sign
- ]
+ m.d.comb += self.in_a.copy(in_a)
+ m.d.comb += self.in_b.copy(in_b)
+ m.d.comb += out_z.v.eq(self.out_z.v)
+ m.d.comb += out_do_z.eq(self.out_do_z)
+
+ def elaborate(self, platform):
+ m = Module()
+
+ m.submodules.sc_in_a = self.in_a
+ m.submodules.sc_in_b = self.in_b
+ m.submodules.sc_out_z = self.out_z
+
+ s_nomatch = Signal()
+ m.d.comb += s_nomatch.eq(self.in_a.s != self.in_b.s)
+
+ m_match = Signal()
+ m.d.comb += m_match.eq(self.in_a.m == self.in_b.m)
+
+ # if a is NaN or b is NaN return NaN
+ with m.If(self.in_a.is_nan | self.in_b.is_nan):
+ m.d.comb += self.out_do_z.eq(1)
+ m.d.comb += self.out_z.nan(0)
+
+ # XXX WEIRDNESS for FP16 non-canonical NaN handling
+ # under review
+
+ ## if a is zero and b is NaN return -b
+ #with m.If(a.is_zero & (a.s==0) & b.is_nan):
+ # m.d.comb += self.out_do_z.eq(1)
+ # m.d.comb += z.create(b.s, b.e, Cat(b.m[3:-2], ~b.m[0]))
+
+ ## if b is zero and a is NaN return -a
+ #with m.Elif(b.is_zero & (b.s==0) & a.is_nan):
+ # m.d.comb += self.out_do_z.eq(1)
+ # m.d.comb += z.create(a.s, a.e, Cat(a.m[3:-2], ~a.m[0]))
+
+ ## if a is -zero and b is NaN return -b
+ #with m.Elif(a.is_zero & (a.s==1) & b.is_nan):
+ # m.d.comb += self.out_do_z.eq(1)
+ # m.d.comb += z.create(a.s & b.s, b.e, Cat(b.m[3:-2], 1))
+
+ ## if b is -zero and a is NaN return -a
+ #with m.Elif(b.is_zero & (b.s==1) & a.is_nan):
+ # m.d.comb += self.out_do_z.eq(1)
+ # m.d.comb += z.create(a.s & b.s, a.e, Cat(a.m[3:-2], 1))
+
+ # if a is inf return inf (or NaN)
+ with m.Elif(self.in_a.is_inf):
+ m.d.comb += self.out_do_z.eq(1)
+ m.d.comb += self.out_z.inf(self.in_a.s)
+ # if a is inf and signs don't match return NaN
+ with m.If(self.in_b.exp_128 & s_nomatch):
+ m.d.comb += self.out_z.nan(0)
+
+ # if b is inf return inf
+ with m.Elif(self.in_b.is_inf):
+ m.d.comb += self.out_do_z.eq(1)
+ m.d.comb += self.out_z.inf(self.in_b.s)
+
+ # if a is zero and b zero return signed-a/b
+ with m.Elif(self.in_a.is_zero & self.in_b.is_zero):
+ m.d.comb += self.out_do_z.eq(1)
+ m.d.comb += self.out_z.create(self.in_a.s & self.in_b.s,
+ self.in_b.e,
+ self.in_b.m[3:-1])
+
+ # if a is zero return b
+ with m.Elif(self.in_a.is_zero):
+ m.d.comb += self.out_do_z.eq(1)
+ m.d.comb += self.out_z.create(self.in_b.s, self.in_b.e,
+ self.in_b.m[3:-1])
+
+ # if b is zero return a
+ with m.Elif(self.in_b.is_zero):
+ m.d.comb += self.out_do_z.eq(1)
+ m.d.comb += self.out_z.create(self.in_a.s, self.in_a.e,
+ self.in_a.m[3:-1])
+
+ # if a equal to -b return zero (+ve zero)
+ with m.Elif(s_nomatch & m_match & (self.in_a.e == self.in_b.e)):
+ m.d.comb += self.out_do_z.eq(1)
+ m.d.comb += self.out_z.zero(0)
+
+ # Denormalised Number checks
+ with m.Else():
+ m.d.comb += self.out_do_z.eq(0)
+
+ return m
+
+
+class FPAddSpecialCases(FPState):
+ """ special cases: NaNs, infs, zeros, denormalised
+ NOTE: some of these are unique to add. see "Special Operations"
+ https://steve.hollasch.net/cgindex/coding/ieeefloat.html
+ """
- def create(self, s, e, m):
- """ creates a value from sign / exponent / mantissa
+ def __init__(self, width):
+ FPState.__init__(self, "special_cases")
+ self.mod = FPAddSpecialCasesMod(width)
+ self.out_z = FPNumOut(width, False)
+ self.out_do_z = Signal(reset_less=True)
+
+ def action(self, m):
+ with m.If(self.out_do_z):
+ m.d.sync += self.z.v.eq(self.out_z.v) # only take the output
+ m.next = "put_z"
+ with m.Else():
+ m.next = "denormalise"
- bias is added here, to the exponent
+
+class FPAddDeNormMod(FPState):
+
+ def __init__(self, width):
+ self.in_a = FPNumBase(width)
+ self.in_b = FPNumBase(width)
+ self.out_a = FPNumBase(width)
+ self.out_b = FPNumBase(width)
+
+ def setup(self, m, in_a, in_b, out_a, out_b):
+ """ links module to inputs and outputs
"""
- return [
- self.v[31].eq(s), # sign
- self.v[23:31].eq(e + self.P127), # exp (add on bias)
- self.v[0:23].eq(m) # mantissa
- ]
+ m.d.comb += self.in_a.copy(in_a)
+ m.d.comb += self.in_b.copy(in_b)
+ m.d.comb += out_a.copy(self.out_a)
+ m.d.comb += out_b.copy(self.out_b)
- def shift_down(self):
- """ shifts a mantissa down by one. exponent is increased to compensate
+ def elaborate(self, platform):
+ m = Module()
+ m.submodules.denorm_in_a = self.in_a
+ m.submodules.denorm_in_b = self.in_b
+ m.submodules.denorm_out_a = self.out_a
+ m.submodules.denorm_out_b = self.out_b
+ # hmmm, don't like repeating identical code
+ m.d.comb += self.out_a.copy(self.in_a)
+ with m.If(self.in_a.exp_n127):
+ m.d.comb += self.out_a.e.eq(self.in_a.N126) # limit a exponent
+ with m.Else():
+ m.d.comb += self.out_a.m[-1].eq(1) # set top mantissa bit
+
+ m.d.comb += self.out_b.copy(self.in_b)
+ with m.If(self.in_b.exp_n127):
+ m.d.comb += self.out_b.e.eq(self.in_b.N126) # limit a exponent
+ with m.Else():
+ m.d.comb += self.out_b.m[-1].eq(1) # set top mantissa bit
+
+ return m
+
+
+class FPAddDeNorm(FPState):
+
+ def __init__(self, width):
+ FPState.__init__(self, "denormalise")
+ self.mod = FPAddDeNormMod(width)
+ self.out_a = FPNumBase(width)
+ self.out_b = FPNumBase(width)
+
+ def action(self, m):
+ # Denormalised Number checks
+ m.next = "align"
+ m.d.sync += self.a.copy(self.out_a)
+ m.d.sync += self.b.copy(self.out_b)
- accuracy is lost as a result in the mantissa however there are 3
- guard bits (the latter of which is the "sticky" bit)
+
+class FPAddAlignMultiMod(FPState):
+
+ def __init__(self, width):
+ self.in_a = FPNumBase(width)
+ self.in_b = FPNumBase(width)
+ self.out_a = FPNumIn(None, width)
+ self.out_b = FPNumIn(None, width)
+ self.exp_eq = Signal(reset_less=True)
+
+ def setup(self, m, in_a, in_b, out_a, out_b, exp_eq):
+ """ links module to inputs and outputs
"""
- return [self.e.eq(self.e + 1),
- self.m.eq(Cat(self.m[0] | self.m[1], self.m[2:], 0))
- ]
+ m.d.comb += self.in_a.copy(in_a)
+ m.d.comb += self.in_b.copy(in_b)
+ m.d.comb += out_a.copy(self.out_a)
+ m.d.comb += out_b.copy(self.out_b)
+ m.d.comb += exp_eq.eq(self.exp_eq)
- def nan(self, s):
- return self.create(s, self.P128, 1<<22)
+ def elaborate(self, platform):
+ # This one however (single-cycle) will do the shift
+ # in one go.
- def inf(self, s):
- return self.create(s, self.P128, 0)
+ m = Module()
- def zero(self, s):
- return self.create(s, self.N127, 0)
+ #m.submodules.align_in_a = self.in_a
+ #m.submodules.align_in_b = self.in_b
+ m.submodules.align_out_a = self.out_a
+ m.submodules.align_out_b = self.out_b
+
+ # NOTE: this does *not* do single-cycle multi-shifting,
+ # it *STAYS* in the align state until exponents match
+
+ # exponent of a greater than b: shift b down
+ m.d.comb += self.exp_eq.eq(0)
+ m.d.comb += self.out_a.copy(self.in_a)
+ m.d.comb += self.out_b.copy(self.in_b)
+ agtb = Signal(reset_less=True)
+ altb = Signal(reset_less=True)
+ m.d.comb += agtb.eq(self.in_a.e > self.in_b.e)
+ m.d.comb += altb.eq(self.in_a.e < self.in_b.e)
+ with m.If(agtb):
+ m.d.comb += self.out_b.shift_down(self.in_b)
+ # exponent of b greater than a: shift a down
+ with m.Elif(altb):
+ m.d.comb += self.out_a.shift_down(self.in_a)
+ # exponents equal: move to next stage.
+ with m.Else():
+ m.d.comb += self.exp_eq.eq(1)
+ return m
- def is_nan(self):
- return (self.e == self.P128) & (self.m != 0)
- def is_inf(self):
- return (self.e == self.P128) & (self.m == 0)
+class FPAddAlignMulti(FPState):
- def is_zero(self):
- return (self.e == self.N127) & (self.m == self.mzero)
+ def __init__(self, width):
+ FPState.__init__(self, "align")
+ self.mod = FPAddAlignMultiMod(width)
+ self.out_a = FPNumIn(None, width)
+ self.out_b = FPNumIn(None, width)
+ self.exp_eq = Signal(reset_less=True)
+
+ def action(self, m):
+ m.d.sync += self.a.copy(self.out_a)
+ m.d.sync += self.b.copy(self.out_b)
+ with m.If(self.exp_eq):
+ m.next = "add_0"
- def is_overflowed(self):
- return (self.e > self.P127)
- def is_denormalised(self):
- return (self.e == self.N126) & (self.m[23] == 0)
+class FPAddAlignSingleMod:
-class FPOp:
def __init__(self, width):
- self.width = width
+ self.in_a = FPNumBase(width)
+ self.in_b = FPNumBase(width)
+ self.out_a = FPNumIn(None, width)
+ self.out_b = FPNumIn(None, width)
+ #self.out_a = FPNumBase(width)
+ #self.out_b = FPNumBase(width)
+
+ def setup(self, m, in_a, in_b, out_a, out_b):
+ """ links module to inputs and outputs
+ """
+ m.d.comb += self.in_a.copy(in_a)
+ m.d.comb += self.in_b.copy(in_b)
+ m.d.comb += out_a.copy(self.out_a)
+ m.d.comb += out_b.copy(self.out_b)
- self.v = Signal(width)
- self.stb = Signal()
- self.ack = Signal()
+ def elaborate(self, platform):
+ # This one however (single-cycle) will do the shift
+ # in one go.
- def ports(self):
- return [self.v, self.stb, self.ack]
+ m = Module()
+ #m.submodules.align_in_a = self.in_a
+ #m.submodules.align_in_b = self.in_b
+ m.submodules.align_out_a = self.out_a
+ m.submodules.align_out_b = self.out_b
+
+ # XXX TODO: the shifter used here is quite expensive
+ # having only one would be better
+
+ ediff = Signal((len(self.in_a.e), True), reset_less=True)
+ ediffr = Signal((len(self.in_a.e), True), reset_less=True)
+ m.d.comb += ediff.eq(self.in_a.e - self.in_b.e)
+ m.d.comb += ediffr.eq(self.in_b.e - self.in_a.e)
+ m.d.comb += self.out_a.copy(self.in_a)
+ m.d.comb += self.out_b.copy(self.in_b)
+ with m.If(ediff > 0):
+ m.d.comb += self.out_b.shift_down_multi(ediff)
+ # exponent of b greater than a: shift a down
+ with m.Elif(ediff < 0):
+ m.d.comb += self.out_a.shift_down_multi(ediffr)
+ return m
-class Overflow:
- def __init__(self):
- self.guard = Signal() # tot[2]
- self.round_bit = Signal() # tot[1]
- self.sticky = Signal() # tot[0]
+class FPAddAlignSingle(FPState):
-class FPADD:
def __init__(self, width):
- self.width = width
+ FPState.__init__(self, "align")
+ self.mod = FPAddAlignSingleMod(width)
+ self.out_a = FPNumIn(None, width)
+ self.out_b = FPNumIn(None, width)
- self.in_a = FPOp(width)
- self.in_b = FPOp(width)
- self.out_z = FPOp(width)
+ def action(self, m):
+ m.d.sync += self.a.copy(self.out_a)
+ m.d.sync += self.b.copy(self.out_b)
+ m.next = "add_0"
- def get_op(self, m, op, v, next_state):
- with m.If((op.ack) & (op.stb)):
- m.next = next_state
- m.d.sync += [
- v.eq(op.v),
- op.ack.eq(0)
+
+class FPAddStage0Mod:
+
+ def __init__(self, width):
+ self.in_a = FPNumBase(width)
+ self.in_b = FPNumBase(width)
+ self.in_z = FPNumBase(width, False)
+ self.out_z = FPNumBase(width, False)
+ self.out_tot = Signal(self.out_z.m_width + 4, reset_less=True)
+
+ def setup(self, m, in_a, in_b, in_z, out_z, out_tot):
+ """ links module to inputs and outputs
+ """
+ m.d.comb += self.in_a.copy(in_a)
+ m.d.comb += self.in_b.copy(in_b)
+ m.d.comb += self.in_z.copy(in_z)
+ m.d.comb += out_z.copy(self.out_z)
+ m.d.comb += out_tot.eq(self.out_tot)
+
+ def elaborate(self, platform):
+ m = Module()
+ m.submodules.add0_in_a = self.in_a
+ m.submodules.add0_in_b = self.in_b
+ #m.submodules.add0_in_z = self.in_z
+ #m.submodules.add0_out_z = self.out_z
+
+ m.d.comb += self.out_z.e.eq(self.in_a.e)
+
+ # store intermediate tests (and zero-extended mantissas)
+ seq = Signal(reset_less=True)
+ mge = Signal(reset_less=True)
+ am0 = Signal(len(self.in_a.m)+1, reset_less=True)
+ bm0 = Signal(len(self.in_b.m)+1, reset_less=True)
+ m.d.comb += [seq.eq(self.in_a.s == self.in_b.s),
+ mge.eq(self.in_a.m >= self.in_b.m),
+ am0.eq(Cat(self.in_a.m, 0)),
+ bm0.eq(Cat(self.in_b.m, 0))
+ ]
+ # same-sign (both negative or both positive) add mantissas
+ with m.If(seq):
+ m.d.comb += [
+ self.out_tot.eq(am0 + bm0),
+ self.out_z.s.eq(self.in_a.s)
]
- with m.Else():
- m.d.sync += op.ack.eq(1)
-
- def normalise_1(self, m, z, of, next_state):
- with m.If((z.m[-1] == 0) & (z.e > z.N126)):
- m.d.sync +=[
- z.e.eq(z.e - 1), # DECREASE exponent
- z.m.eq(z.m << 1), # shift mantissa UP
- z.m[0].eq(of.guard), # steal guard bit (was tot[2])
- of.guard.eq(of.round_bit), # steal round_bit (was tot[1])
- of.round_bit.eq(0), # reset round bit
+ # a mantissa greater than b, use a
+ with m.Elif(mge):
+ m.d.comb += [
+ self.out_tot.eq(am0 - bm0),
+ self.out_z.s.eq(self.in_a.s)
]
+ # b mantissa greater than a, use b
+ with m.Else():
+ m.d.comb += [
+ self.out_tot.eq(bm0 - am0),
+ self.out_z.s.eq(self.in_b.s)
+ ]
+ return m
+
+
+class FPAddStage0(FPState):
+ """ First stage of add. covers same-sign (add) and subtract
+ special-casing when mantissas are greater or equal, to
+ give greatest accuracy.
+ """
+
+ def __init__(self, width):
+ FPState.__init__(self, "add_0")
+ self.mod = FPAddStage0Mod(width)
+ self.out_z = FPNumBase(width, False)
+ self.out_tot = Signal(self.out_z.m_width + 4, reset_less=True)
+
+ def action(self, m):
+ m.next = "add_1"
+ m.d.sync += self.z.copy(self.out_z)
+
+
+class FPAddStage1Mod(FPState):
+ """ Second stage of add: preparation for normalisation.
+ detects when tot sum is too big (tot[27] is kinda a carry bit)
+ """
+
+ def __init__(self, width):
+ self.out_norm = Signal(reset_less=True)
+ self.in_z = FPNumBase(width, False)
+ self.in_tot = Signal(self.in_z.m_width + 4, reset_less=True)
+ self.out_z = FPNumBase(width, False)
+ self.out_of = Overflow()
+
+ def setup(self, m, in_tot, in_z, out_z, out_of):
+ """ links module to inputs and outputs
+ """
+ m.d.comb += self.in_z.copy(in_z)
+ m.d.comb += self.in_tot.eq(in_tot)
+ m.d.comb += out_z.copy(self.out_z)
+ #m.d.comb += out_of.copy(self.out_of)
+
+ def elaborate(self, platform):
+ m = Module()
+ #m.submodules.norm1_in_overflow = self.in_of
+ #m.submodules.norm1_out_overflow = self.out_of
+ #m.submodules.norm1_in_z = self.in_z
+ #m.submodules.norm1_out_z = self.out_z
+ m.d.comb += self.out_z.copy(self.in_z)
+ # tot[27] gets set when the sum overflows. shift result down
+ with m.If(self.in_tot[-1]):
+ m.d.comb += [
+ self.out_z.m.eq(self.in_tot[4:]),
+ self.out_of.m0.eq(self.in_tot[4]),
+ self.out_of.guard.eq(self.in_tot[3]),
+ self.out_of.round_bit.eq(self.in_tot[2]),
+ self.out_of.sticky.eq(self.in_tot[1] | self.in_tot[0]),
+ self.out_z.e.eq(self.in_z.e + 1)
+ ]
+ # tot[27] zero case
with m.Else():
- m.next = next_state
-
- def normalise_2(self, m, z, of, next_state):
- with m.If(z.e < z.N126):
- m.d.sync +=[
- z.e.eq(z.e + 1), # INCREASE exponent
- z.m.eq(z.m >> 1), # shift mantissa DOWN
- of.guard.eq(z.m[0]),
- of.round_bit.eq(of.guard),
- of.sticky.eq(of.sticky | of.round_bit)
+ m.d.comb += [
+ self.out_z.m.eq(self.in_tot[3:]),
+ self.out_of.m0.eq(self.in_tot[3]),
+ self.out_of.guard.eq(self.in_tot[2]),
+ self.out_of.round_bit.eq(self.in_tot[1]),
+ self.out_of.sticky.eq(self.in_tot[0])
+ ]
+ return m
+
+
+class FPAddStage1(FPState):
+
+ def __init__(self, width):
+ FPState.__init__(self, "add_1")
+ self.mod = FPAddStage1Mod(width)
+ self.out_z = FPNumBase(width, False)
+ self.out_of = Overflow()
+
+ def action(self, m):
+ m.submodules.add1_out_overflow = self.out_of
+ m.d.sync += self.out_of.copy(self.mod.out_of)
+ m.d.sync += self.z.copy(self.out_z)
+ m.next = "normalise_1"
+
+
+class FPNorm1Mod:
+
+ def __init__(self, width):
+ self.out_norm = Signal(reset_less=True)
+ self.in_z = FPNumBase(width, False)
+ self.out_z = FPNumBase(width, False)
+ self.in_of = Overflow()
+ self.out_of = Overflow()
+
+ def setup(self, m, in_z, out_z, in_of, out_of, out_norm):
+ """ links module to inputs and outputs
+ """
+ m.d.comb += self.in_z.copy(in_z)
+ m.d.comb += out_z.copy(self.out_z)
+ m.d.comb += self.in_of.copy(in_of)
+ m.d.comb += out_of.copy(self.out_of)
+ m.d.comb += out_norm.eq(self.out_norm)
+
+ def elaborate(self, platform):
+ m = Module()
+ m.submodules.norm1_in_overflow = self.in_of
+ m.submodules.norm1_out_overflow = self.out_of
+ m.submodules.norm1_in_z = self.in_z
+ m.submodules.norm1_out_z = self.out_z
+ m.d.comb += self.out_z.copy(self.in_z)
+ m.d.comb += self.out_of.copy(self.in_of)
+ decrease = Signal(reset_less=True)
+ increase = Signal(reset_less=True)
+ m.d.comb += decrease.eq(self.in_z.m_msbzero & self.in_z.exp_gt_n126)
+ m.d.comb += increase.eq(self.in_z.exp_lt_n126)
+ m.d.comb += self.out_norm.eq(decrease | increase)
+ with m.If(decrease):
+ m.d.comb += [
+ self.out_z.e.eq(self.in_z.e - 1), # DECREASE exponent
+ self.out_z.m.eq(self.in_z.m << 1), # shift mantissa UP
+ self.out_z.m[0].eq(self.in_of.guard), # steal guard (was tot[2])
+ self.out_of.guard.eq(self.in_of.round_bit), # round (was tot[1])
+ self.out_of.round_bit.eq(0), # reset round bit
+ self.out_of.m0.eq(self.in_of.guard),
]
+ with m.If(increase):
+ m.d.comb += [
+ self.out_z.e.eq(self.in_z.e + 1), # INCREASE exponent
+ self.out_z.m.eq(self.in_z.m >> 1), # shift mantissa DOWN
+ self.out_of.guard.eq(self.in_z.m[0]),
+ self.out_of.m0.eq(self.in_z.m[1]),
+ self.out_of.round_bit.eq(self.in_of.guard),
+ self.out_of.sticky.eq(self.in_of.sticky | self.in_of.round_bit)
+ ]
+
+ return m
+
+
+class FPNorm1(FPState):
+
+ def __init__(self, width):
+ FPState.__init__(self, "normalise_1")
+ self.mod = FPNorm1Mod(width)
+ self.out_norm = Signal(reset_less=True)
+ self.out_z = FPNumBase(width)
+ self.out_of = Overflow()
+
+ def action(self, m):
+ m.d.sync += self.of.copy(self.out_of)
+ m.d.sync += self.z.copy(self.out_z)
+ with m.If(~self.out_norm):
+ m.next = "round"
+
+
+class FPRoundMod:
+
+ def __init__(self, width):
+ self.in_roundz = Signal(reset_less=True)
+ self.in_z = FPNumBase(width, False)
+ self.out_z = FPNumBase(width, False)
+
+ def setup(self, m, in_z, out_z, in_of):
+ """ links module to inputs and outputs
+ """
+ m.d.comb += self.in_z.copy(in_z)
+ m.d.comb += out_z.copy(self.out_z)
+ m.d.comb += self.in_roundz.eq(in_of.roundz)
+
+ def elaborate(self, platform):
+ m = Module()
+ m.d.comb += self.out_z.copy(self.in_z)
+ with m.If(self.in_roundz):
+ m.d.comb += self.out_z.m.eq(self.in_z.m + 1) # mantissa rounds up
+ with m.If(self.in_z.m == self.in_z.m1s): # all 1s
+ m.d.comb += self.out_z.e.eq(self.in_z.e + 1) # exponent up
+ return m
+
+
+class FPRound(FPState):
+
+ def __init__(self, width):
+ FPState.__init__(self, "round")
+ self.mod = FPRoundMod(width)
+ self.out_z = FPNumBase(width)
+
+ def action(self, m):
+ m.d.sync += self.z.copy(self.out_z)
+ m.next = "corrections"
+
+
+class FPCorrectionsMod:
+
+ def __init__(self, width):
+ self.in_z = FPNumOut(width, False)
+ self.out_z = FPNumOut(width, False)
+
+ def setup(self, m, in_z, out_z):
+ """ links module to inputs and outputs
+ """
+ m.d.comb += self.in_z.copy(in_z)
+ m.d.comb += out_z.copy(self.out_z)
+
+ def elaborate(self, platform):
+ m = Module()
+ m.submodules.corr_in_z = self.in_z
+ m.submodules.corr_out_z = self.out_z
+ m.d.comb += self.out_z.copy(self.in_z)
+ with m.If(self.in_z.is_denormalised):
+ m.d.comb += self.out_z.e.eq(self.in_z.N127)
+
+ # with m.If(self.in_z.is_overflowed):
+ # m.d.comb += self.out_z.inf(self.in_z.s)
+ # with m.Else():
+ # m.d.comb += self.out_z.create(self.in_z.s, self.in_z.e, self.in_z.m)
+ return m
+
+
+class FPCorrections(FPState):
+
+ def __init__(self, width):
+ FPState.__init__(self, "corrections")
+ self.mod = FPCorrectionsMod(width)
+ self.out_z = FPNumBase(width)
+
+ def action(self, m):
+ m.d.sync += self.z.copy(self.out_z)
+ m.next = "pack"
+
+
+class FPPackMod:
+
+ def __init__(self, width):
+ self.in_z = FPNumOut(width, False)
+ self.out_z = FPNumOut(width, False)
+
+ def setup(self, m, in_z, out_z):
+ """ links module to inputs and outputs
+ """
+ m.d.comb += self.in_z.copy(in_z)
+ m.d.comb += out_z.v.eq(self.out_z.v)
+
+ def elaborate(self, platform):
+ m = Module()
+ m.submodules.pack_in_z = self.in_z
+ with m.If(self.in_z.is_overflowed):
+ m.d.comb += self.out_z.inf(self.in_z.s)
with m.Else():
- m.next = next_state
-
- def round(self, m, z, of, next_state):
- m.next = next_state
- with m.If(of.guard & (of.round_bit | of.sticky | z.m[0])):
- m.d.sync += z.m.eq(z.m + 1) # mantissa rounds up
- with m.If(z.m == z.m1s): # all 1s
- m.d.sync += z.e.eq(z.e + 1) # exponent rounds up
-
- def corrections(self, m, z, next_state):
- m.next = next_state
- # denormalised, correct exponent to zero
- with m.If(z.is_denormalised()):
- m.d.sync += z.m.eq(-127)
- # FIX SIGN BUG: -a + a = +0.
- with m.If((z.e == z.N126) & (z.m[0:] == 0)):
- m.d.sync += z.s.eq(0)
+ m.d.comb += self.out_z.create(self.in_z.s, self.in_z.e, self.in_z.m)
+ return m
+
+
+class FPPack(FPState):
+
+ def __init__(self, width):
+ FPState.__init__(self, "pack")
+ self.mod = FPPackMod(width)
+ self.out_z = FPNumOut(width, False)
+
+ def action(self, m):
+ m.d.sync += self.z.v.eq(self.out_z.v)
+ m.next = "pack_put_z"
+
+
+class FPPutZ(FPState):
+
+ def action(self, m):
+ self.put_z(m, self.z, self.out_z, "get_a")
+
+
+class FPADD:
+
+ def __init__(self, width, single_cycle=False):
+ self.width = width
+ self.single_cycle = single_cycle
+
+ self.in_a = FPOp(width)
+ self.in_b = FPOp(width)
+ self.out_z = FPOp(width)
+
+ self.states = []
+
+ def add_state(self, state):
+ self.states.append(state)
+ return state
def get_fragment(self, platform=None):
+ """ creates the HDL code-fragment for FPAdd
+ """
m = Module()
# Latches
- a = FPNum(self.width)
- b = FPNum(self.width)
- z = FPNum(self.width, 24)
-
- tot = Signal(28) # sticky/round/guard bits, 23 result, 1 overflow
-
- of = Overflow()
+ z = FPNumOut(self.width, False)
+ m.submodules.fpnum_z = z
+
+ w = z.m_width + 4
+
+ #of = Overflow()
+ #m.submodules.overflow = of
+
+ geta = self.add_state(FPGetOp("get_a", "get_b",
+ self.in_a, self.width))
+ a = geta.out_op
+ geta.mod.setup(m, self.in_a, geta.out_op, geta.out_decode)
+ m.submodules.get_a = geta.mod
+
+ getb = self.add_state(FPGetOp("get_b", "special_cases",
+ self.in_b, self.width))
+ b = getb.out_op
+ getb.mod.setup(m, self.in_b, getb.out_op, getb.out_decode)
+ m.submodules.get_b = getb.mod
+
+ sc = self.add_state(FPAddSpecialCases(self.width))
+ sc.set_inputs({"a": a, "b": b})
+ sc.set_outputs({"z": z})
+ sc.mod.setup(m, a, b, sc.out_z, sc.out_do_z)
+ m.submodules.specialcases = sc.mod
+
+ dn = self.add_state(FPAddDeNorm(self.width))
+ dn.set_inputs({"a": a, "b": b})
+ #dn.set_outputs({"a": a, "b": b}) # XXX outputs same as inputs
+ dn.mod.setup(m, a, b, dn.out_a, dn.out_b)
+ m.submodules.denormalise = dn.mod
+
+ if self.single_cycle:
+ alm = self.add_state(FPAddAlignSingle(self.width))
+ alm.set_inputs({"a": a, "b": b})
+ alm.set_outputs({"a": a, "b": b}) # XXX outputs same as inputs
+ alm.mod.setup(m, a, b, alm.out_a, alm.out_b)
+ else:
+ alm = self.add_state(FPAddAlignMulti(self.width))
+ alm.set_inputs({"a": a, "b": b})
+ #alm.set_outputs({"a": a, "b": b}) # XXX outputs same as inputs
+ alm.mod.setup(m, a, b, alm.out_a, alm.out_b, alm.exp_eq)
+ m.submodules.align = alm.mod
+
+ az = FPNumOut(self.width, False)
+ m.submodules.fpnum_az = az
+
+ add0 = self.add_state(FPAddStage0(self.width))
+ add0.set_inputs({"a": alm.out_a, "b": alm.out_b})
+ add0.set_outputs({"z": az})
+ add0.mod.setup(m, alm.out_a, alm.out_b, az, add0.out_z, add0.out_tot)
+ m.submodules.add0 = add0.mod
+
+ add1 = self.add_state(FPAddStage1(self.width))
+ add1.set_outputs({"z": az}) # XXX Z as output
+ add1.mod.setup(m, add0.out_tot, az, add1.out_z, add1.out_of)
+ m.submodules.add1 = add1.mod
+
+ of = add1.out_of
+
+ n1 = self.add_state(FPNorm1(self.width))
+ n1.set_inputs({"z": az, "of": add1.out_of}) # XXX Z as output
+ n1.set_outputs({"z": az}) # XXX Z as output
+ n1.mod.setup(m, az, n1.out_z, add1.out_of, n1.out_of, n1.out_norm)
+ m.submodules.normalise_1 = n1.mod
+
+ rn = self.add_state(FPRound(self.width))
+ rn.set_inputs({"z": n1.out_z, "of": n1.out_of})
+ rn.set_outputs({"z": az})
+ rn.mod.setup(m, n1.out_z, rn.out_z, of)
+ m.submodules.roundz = rn.mod
+
+ cor = self.add_state(FPCorrections(self.width))
+ cor.set_inputs({"z": az}) # XXX Z as output
+ cor.set_outputs({"z": az}) # XXX Z as output
+ cor.mod.setup(m, az, cor.out_z)
+ m.submodules.corrections = cor.mod
+
+ pa = self.add_state(FPPack(self.width))
+ pa.set_inputs({"z": az}) # XXX Z as output
+ pa.set_outputs({"z": az}) # XXX Z as output
+ pa.mod.setup(m, az, pa.out_z)
+ m.submodules.pack = pa.mod
+
+ pz = self.add_state(FPPutZ("pack_put_z"))
+ pz.set_inputs({"z": az})
+ pz.set_outputs({"out_z": self.out_z})
+
+ pz = self.add_state(FPPutZ("put_z"))
+ pz.set_inputs({"z": z})
+ pz.set_outputs({"out_z": self.out_z})
with m.FSM() as fsm:
- # ******
- # gets operand a
-
- with m.State("get_a"):
- self.get_op(m, self.in_a, a.v, "get_b")
-
- # ******
- # gets operand b
-
- with m.State("get_b"):
- self.get_op(m, self.in_b, b.v, "unpack")
-
- # ******
- # unpacks operands into sign, mantissa and exponent
-
- with m.State("unpack"):
- m.next = "special_cases"
- m.d.sync += a.decode()
- m.d.sync += b.decode()
-
- # ******
- # special cases: NaNs, infs, zeros, denormalised
-
- with m.State("special_cases"):
-
- # if a is NaN or b is NaN return NaN
- with m.If(a.is_nan() | b.is_nan()):
- m.next = "put_z"
- m.d.sync += z.nan(1)
-
- # if a is inf return inf (or NaN)
- with m.Elif(a.is_inf()):
- m.next = "put_z"
- m.d.sync += z.inf(a.s)
- # if a is inf and signs don't match return NaN
- with m.If((b.e == b.P128) & (a.s != b.s)):
- m.d.sync += z.nan(b.s)
-
- # if b is inf return inf
- with m.Elif(b.is_inf()):
- m.next = "put_z"
- m.d.sync += z.inf(b.s)
-
- # if a is zero and b zero return signed-a/b
- with m.Elif(a.is_zero() & b.is_zero()):
- m.next = "put_z"
- m.d.sync += z.create(a.s & b.s, b.e[0:8], b.m[3:-1])
-
- # if a is zero return b
- with m.Elif(a.is_zero()):
- m.next = "put_z"
- m.d.sync += z.create(b.s, b.e[0:8], b.m[3:-1])
-
- # if b is zero return a
- with m.Elif(b.is_zero()):
- m.next = "put_z"
- m.d.sync += z.create(a.s, a.e[0:8], a.m[3:-1])
-
- # Denormalised Number checks
- with m.Else():
- m.next = "align"
- # denormalise a check
- with m.If(a.e == a.N127):
- m.d.sync += a.e.eq(-126) # limit a exponent
- with m.Else():
- m.d.sync += a.m[-1].eq(1) # set top mantissa bit
- # denormalise b check
- with m.If(b.e == a.N127):
- m.d.sync += b.e.eq(-126) # limit b exponent
- with m.Else():
- m.d.sync += b.m[-1].eq(1) # set top mantissa bit
-
- # ******
- # align. NOTE: this does *not* do single-cycle multi-shifting,
- # it *STAYS* in the align state until the exponents match
-
- with m.State("align"):
- # exponent of a greater than b: increment b exp, shift b mant
- with m.If(a.e > b.e):
- m.d.sync += b.shift_down()
- # exponent of b greater than a: increment a exp, shift a mant
- with m.Elif(a.e < b.e):
- m.d.sync += a.shift_down()
- # exponents equal: move to next stage.
- with m.Else():
- m.next = "add_0"
-
- # ******
- # First stage of add. covers same-sign (add) and subtract
- # special-casing when mantissas are greater or equal, to
- # give greatest accuracy.
-
- with m.State("add_0"):
- m.next = "add_1"
- m.d.sync += z.e.eq(a.e)
- # same-sign (both negative or both positive) add mantissas
- with m.If(a.s == b.s):
- m.d.sync += [
- tot.eq(a.m + b.m),
- z.s.eq(a.s)
- ]
- # a mantissa greater than b, use a
- with m.Elif(a.m >= b.m):
- m.d.sync += [
- tot.eq(a.m - b.m),
- z.s.eq(a.s)
- ]
- # b mantissa greater than a, use b
- with m.Else():
- m.d.sync += [
- tot.eq(b.m - a.m),
- z.s.eq(b.s)
- ]
-
- # ******
- # Second stage of add: preparation for normalisation.
- # detects when tot sum is too big (tot[27] is kinda a carry bit)
-
- with m.State("add_1"):
- m.next = "normalise_1"
- # tot[27] gets set when the sum overflows. shift result down
- with m.If(tot[27]):
- m.d.sync += [
- z.m.eq(tot[4:28]),
- of.guard.eq(tot[3]),
- of.round_bit.eq(tot[2]),
- of.sticky.eq(tot[1] | tot[0]),
- z.e.eq(z.e + 1)
- ]
- # tot[27] zero case
- with m.Else():
- m.d.sync += [
- z.m.eq(tot[3:27]),
- of.guard.eq(tot[2]),
- of.round_bit.eq(tot[1]),
- of.sticky.eq(tot[0])
- ]
-
- # ******
- # First stage of normalisation.
- # NOTE: just like "align", this one keeps going round every clock
- # until the result's exponent is within acceptable "range"
- # NOTE: the weirdness of reassigning guard and round is due to
- # the extra mantissa bits coming from tot[0..2]
-
- with m.State("normalise_1"):
- self.normalise_1(m, z, of, "normalise_2")
-
- # ******
- # Second stage of normalisation.
- # NOTE: just like "align", this one keeps going round every clock
- # until the result's exponent is within acceptable "range"
- # NOTE: the weirdness of reassigning guard and round is due to
- # the extra mantissa bits coming from tot[0..2]
-
- with m.State("normalise_2"):
- self.normalise_2(m, z, of, "round")
-
- # ******
- # rounding stage
-
- with m.State("round"):
- self.round(m, z, of, "corrections")
-
- # ******
- # correction stage
-
- with m.State("corrections"):
- self.corrections(m, z, "pack")
-
- # ******
- # pack stage
-
- with m.State("pack"):
- m.next = "put_z"
- # if overflow occurs, return inf
- with m.If(z.is_overflowed()):
- m.d.sync += z.inf(0)
- with m.Else():
- m.d.sync += z.create(z.s, z.e, z.m)
-
- # ******
- # put_z stage
-
- with m.State("put_z"):
- m.d.sync += [
- self.out_z.stb.eq(1),
- self.out_z.v.eq(z.v)
- ]
- with m.If(self.out_z.stb & self.out_z.ack):
- m.d.sync += self.out_z.stb.eq(0)
- m.next = "get_a"
+ for state in self.states:
+ with m.State(state.state_from):
+ state.action(m)
return m