--- /dev/null
+# IEEE Floating Point Adder (Single Precision)
+# Copyright (C) Jonathan P Dawson 2013
+# 2013-12-12
+
+from nmigen import Module, Signal, Cat, Mux, Array, Const
+from nmigen.lib.coding import PriorityEncoder
+from nmigen.cli import main, verilog
+from math import log
+
+from fpbase import FPNumIn, FPNumOut, FPOp, Overflow, FPBase, FPNumBase
+from fpbase import MultiShiftRMerge, Trigger
+from singlepipe import (ControlBase, StageChain, UnbufferedPipeline,
+ PassThroughStage)
+from multipipe import CombMuxOutPipe
+from multipipe import PriorityCombMuxInPipe
+
+from fpbase import FPState
+from .postcalc import FPAddStage1Data
+
+
+class FPNorm1Data:
+
+ def __init__(self, width, id_wid):
+ self.roundz = Signal(reset_less=True)
+ self.z = FPNumBase(width, False)
+ self.out_do_z = Signal(reset_less=True)
+ self.oz = Signal(width, reset_less=True)
+ self.mid = Signal(id_wid, reset_less=True)
+
+ def eq(self, i):
+ return [self.z.eq(i.z), self.out_do_z.eq(i.out_do_z), self.oz.eq(i.oz),
+ self.roundz.eq(i.roundz), self.mid.eq(i.mid)]
+
+
+class FPNorm1ModSingle:
+
+ def __init__(self, width, id_wid):
+ self.width = width
+ self.id_wid = id_wid
+ self.i = self.ispec()
+ self.o = self.ospec()
+
+ def ispec(self):
+ return FPAddStage1Data(self.width, self.id_wid)
+
+ def ospec(self):
+ return FPNorm1Data(self.width, self.id_wid)
+
+ def setup(self, m, i):
+ """ links module to inputs and outputs
+ """
+ m.submodules.normalise_1 = self
+ m.d.comb += self.i.eq(i)
+
+ def process(self, i):
+ return self.o
+
+ def elaborate(self, platform):
+ m = Module()
+
+ mwid = self.o.z.m_width+2
+ pe = PriorityEncoder(mwid)
+ m.submodules.norm_pe = pe
+
+ of = Overflow()
+ m.d.comb += self.o.roundz.eq(of.roundz)
+
+ m.submodules.norm1_out_z = self.o.z
+ m.submodules.norm1_out_overflow = of
+ m.submodules.norm1_in_z = self.i.z
+ m.submodules.norm1_in_overflow = self.i.of
+
+ i = self.ispec()
+ m.submodules.norm1_insel_z = i.z
+ m.submodules.norm1_insel_overflow = i.of
+
+ espec = (len(i.z.e), True)
+ ediff_n126 = Signal(espec, reset_less=True)
+ msr = MultiShiftRMerge(mwid, espec)
+ m.submodules.multishift_r = msr
+
+ m.d.comb += i.eq(self.i)
+ # initialise out from in (overridden below)
+ m.d.comb += self.o.z.eq(i.z)
+ m.d.comb += of.eq(i.of)
+ # normalisation increase/decrease conditions
+ decrease = Signal(reset_less=True)
+ increase = Signal(reset_less=True)
+ m.d.comb += decrease.eq(i.z.m_msbzero & i.z.exp_gt_n126)
+ m.d.comb += increase.eq(i.z.exp_lt_n126)
+ # decrease exponent
+ with m.If(~self.i.out_do_z):
+ with m.If(decrease):
+ # *sigh* not entirely obvious: count leading zeros (clz)
+ # with a PriorityEncoder: to find from the MSB
+ # we reverse the order of the bits.
+ temp_m = Signal(mwid, reset_less=True)
+ temp_s = Signal(mwid+1, reset_less=True)
+ clz = Signal((len(i.z.e), True), reset_less=True)
+ # make sure that the amount to decrease by does NOT
+ # go below the minimum non-INF/NaN exponent
+ limclz = Mux(i.z.exp_sub_n126 > pe.o, pe.o,
+ i.z.exp_sub_n126)
+ m.d.comb += [
+ # cat round and guard bits back into the mantissa
+ temp_m.eq(Cat(i.of.round_bit, i.of.guard, i.z.m)),
+ pe.i.eq(temp_m[::-1]), # inverted
+ clz.eq(limclz), # count zeros from MSB down
+ temp_s.eq(temp_m << clz), # shift mantissa UP
+ self.o.z.e.eq(i.z.e - clz), # DECREASE exponent
+ self.o.z.m.eq(temp_s[2:]), # exclude bits 0&1
+ of.m0.eq(temp_s[2]), # copy of mantissa[0]
+ # overflow in bits 0..1: got shifted too (leave sticky)
+ of.guard.eq(temp_s[1]), # guard
+ of.round_bit.eq(temp_s[0]), # round
+ ]
+ # increase exponent
+ with m.Elif(increase):
+ temp_m = Signal(mwid+1, reset_less=True)
+ m.d.comb += [
+ temp_m.eq(Cat(i.of.sticky, i.of.round_bit, i.of.guard,
+ i.z.m)),
+ ediff_n126.eq(i.z.N126 - i.z.e),
+ # connect multi-shifter to inp/out mantissa (and ediff)
+ msr.inp.eq(temp_m),
+ msr.diff.eq(ediff_n126),
+ self.o.z.m.eq(msr.m[3:]),
+ of.m0.eq(temp_s[3]), # copy of mantissa[0]
+ # overflow in bits 0..1: got shifted too (leave sticky)
+ of.guard.eq(temp_s[2]), # guard
+ of.round_bit.eq(temp_s[1]), # round
+ of.sticky.eq(temp_s[0]), # sticky
+ self.o.z.e.eq(i.z.e + ediff_n126),
+ ]
+
+ m.d.comb += self.o.mid.eq(self.i.mid)
+ m.d.comb += self.o.out_do_z.eq(self.i.out_do_z)
+ m.d.comb += self.o.oz.eq(self.i.oz)
+
+ return m
+
+
+class FPNorm1ModMulti:
+
+ def __init__(self, width, single_cycle=True):
+ self.width = width
+ self.in_select = Signal(reset_less=True)
+ self.in_z = FPNumBase(width, False)
+ self.in_of = Overflow()
+ self.temp_z = FPNumBase(width, False)
+ self.temp_of = Overflow()
+ self.out_z = FPNumBase(width, False)
+ self.out_of = Overflow()
+
+ def elaborate(self, platform):
+ m = Module()
+
+ m.submodules.norm1_out_z = self.out_z
+ m.submodules.norm1_out_overflow = self.out_of
+ m.submodules.norm1_temp_z = self.temp_z
+ m.submodules.norm1_temp_of = self.temp_of
+ m.submodules.norm1_in_z = self.in_z
+ m.submodules.norm1_in_overflow = self.in_of
+
+ in_z = FPNumBase(self.width, False)
+ in_of = Overflow()
+ m.submodules.norm1_insel_z = in_z
+ m.submodules.norm1_insel_overflow = in_of
+
+ # select which of temp or in z/of to use
+ with m.If(self.in_select):
+ m.d.comb += in_z.eq(self.in_z)
+ m.d.comb += in_of.eq(self.in_of)
+ with m.Else():
+ m.d.comb += in_z.eq(self.temp_z)
+ m.d.comb += in_of.eq(self.temp_of)
+ # initialise out from in (overridden below)
+ m.d.comb += self.out_z.eq(in_z)
+ m.d.comb += self.out_of.eq(in_of)
+ # normalisation increase/decrease conditions
+ decrease = Signal(reset_less=True)
+ increase = Signal(reset_less=True)
+ m.d.comb += decrease.eq(in_z.m_msbzero & in_z.exp_gt_n126)
+ m.d.comb += increase.eq(in_z.exp_lt_n126)
+ m.d.comb += self.out_norm.eq(decrease | increase) # loop-end
+ # decrease exponent
+ with m.If(decrease):
+ m.d.comb += [
+ self.out_z.e.eq(in_z.e - 1), # DECREASE exponent
+ self.out_z.m.eq(in_z.m << 1), # shift mantissa UP
+ self.out_z.m[0].eq(in_of.guard), # steal guard (was tot[2])
+ self.out_of.guard.eq(in_of.round_bit), # round (was tot[1])
+ self.out_of.round_bit.eq(0), # reset round bit
+ self.out_of.m0.eq(in_of.guard),
+ ]
+ # increase exponent
+ with m.Elif(increase):
+ m.d.comb += [
+ self.out_z.e.eq(in_z.e + 1), # INCREASE exponent
+ self.out_z.m.eq(in_z.m >> 1), # shift mantissa DOWN
+ self.out_of.guard.eq(in_z.m[0]),
+ self.out_of.m0.eq(in_z.m[1]),
+ self.out_of.round_bit.eq(in_of.guard),
+ self.out_of.sticky.eq(in_of.sticky | in_of.round_bit)
+ ]
+
+ return m
+
+
+class FPNorm1Single(FPState):
+
+ def __init__(self, width, id_wid, single_cycle=True):
+ FPState.__init__(self, "normalise_1")
+ self.mod = FPNorm1ModSingle(width)
+ self.o = self.ospec()
+ self.out_z = FPNumBase(width, False)
+ self.out_roundz = Signal(reset_less=True)
+
+ def ispec(self):
+ return self.mod.ispec()
+
+ def ospec(self):
+ return self.mod.ospec()
+
+ def setup(self, m, i):
+ """ links module to inputs and outputs
+ """
+ self.mod.setup(m, i)
+
+ def action(self, m):
+ m.next = "round"
+
+
+class FPNorm1Multi(FPState):
+
+ def __init__(self, width, id_wid):
+ FPState.__init__(self, "normalise_1")
+ self.mod = FPNorm1ModMulti(width)
+ self.stb = Signal(reset_less=True)
+ self.ack = Signal(reset=0, reset_less=True)
+ self.out_norm = Signal(reset_less=True)
+ self.in_accept = Signal(reset_less=True)
+ self.temp_z = FPNumBase(width)
+ self.temp_of = Overflow()
+ self.out_z = FPNumBase(width)
+ self.out_roundz = Signal(reset_less=True)
+
+ def setup(self, m, in_z, in_of, norm_stb):
+ """ links module to inputs and outputs
+ """
+ self.mod.setup(m, in_z, in_of, norm_stb,
+ self.in_accept, self.temp_z, self.temp_of,
+ self.out_z, self.out_norm)
+
+ m.d.comb += self.stb.eq(norm_stb)
+ m.d.sync += self.ack.eq(0) # sets to zero when not in normalise_1 state
+
+ def action(self, m):
+ m.d.comb += self.in_accept.eq((~self.ack) & (self.stb))
+ m.d.sync += self.temp_of.eq(self.mod.out_of)
+ m.d.sync += self.temp_z.eq(self.out_z)
+ with m.If(self.out_norm):
+ with m.If(self.in_accept):
+ m.d.sync += [
+ self.ack.eq(1),
+ ]
+ with m.Else():
+ m.d.sync += self.ack.eq(0)
+ with m.Else():
+ # normalisation not required (or done).
+ m.next = "round"
+ m.d.sync += self.ack.eq(1)
+ m.d.sync += self.out_roundz.eq(self.mod.out_of.roundz)
+
+
from fpbase import FPState
from fpcommon.getop import (FPGetOpMod, FPGetOp, FPNumBase2Ops, FPADDBaseData, FPGet2OpMod, FPGet2Op)
from fpcommon.denorm import (FPSCData, FPAddDeNormMod, FPAddDeNorm)
+from fpcommon.postcalc import FPAddStage1Data
+from fpcommon.postnormalise import (FPNorm1Data, FPNorm1ModSingle,
+ FPNorm1ModMulti, FPNorm1Single, FPNorm1Multi)
class FPAddSpecialCasesMod:
m.next = "add_1"
-class FPAddStage1Data:
-
- def __init__(self, width, id_wid):
- self.z = FPNumBase(width, False)
- self.out_do_z = Signal(reset_less=True)
- self.oz = Signal(width, reset_less=True)
- self.of = Overflow()
- self.mid = Signal(id_wid, reset_less=True)
-
- def eq(self, i):
- return [self.z.eq(i.z), self.out_do_z.eq(i.out_do_z), self.oz.eq(i.oz),
- self.of.eq(i.of), self.mid.eq(i.mid)]
-
-
-
class FPAddStage1Mod(FPState):
""" Second stage of add: preparation for normalisation.
detects when tot sum is too big (tot[27] is kinda a carry bit)
m.next = "normalise_1"
-class FPNorm1Data:
-
- def __init__(self, width, id_wid):
- self.roundz = Signal(reset_less=True)
- self.z = FPNumBase(width, False)
- self.out_do_z = Signal(reset_less=True)
- self.oz = Signal(width, reset_less=True)
- self.mid = Signal(id_wid, reset_less=True)
-
- def eq(self, i):
- return [self.z.eq(i.z), self.out_do_z.eq(i.out_do_z), self.oz.eq(i.oz),
- self.roundz.eq(i.roundz), self.mid.eq(i.mid)]
-
-
-class FPNorm1ModSingle:
-
- def __init__(self, width, id_wid):
- self.width = width
- self.id_wid = id_wid
- self.i = self.ispec()
- self.o = self.ospec()
-
- def ispec(self):
- return FPAddStage1Data(self.width, self.id_wid)
-
- def ospec(self):
- return FPNorm1Data(self.width, self.id_wid)
- def setup(self, m, i):
- """ links module to inputs and outputs
- """
- m.submodules.normalise_1 = self
- m.d.comb += self.i.eq(i)
-
- def process(self, i):
- return self.o
-
- def elaborate(self, platform):
- m = Module()
-
- mwid = self.o.z.m_width+2
- pe = PriorityEncoder(mwid)
- m.submodules.norm_pe = pe
-
- of = Overflow()
- m.d.comb += self.o.roundz.eq(of.roundz)
-
- m.submodules.norm1_out_z = self.o.z
- m.submodules.norm1_out_overflow = of
- m.submodules.norm1_in_z = self.i.z
- m.submodules.norm1_in_overflow = self.i.of
-
- i = self.ispec()
- m.submodules.norm1_insel_z = i.z
- m.submodules.norm1_insel_overflow = i.of
-
- espec = (len(i.z.e), True)
- ediff_n126 = Signal(espec, reset_less=True)
- msr = MultiShiftRMerge(mwid, espec)
- m.submodules.multishift_r = msr
-
- m.d.comb += i.eq(self.i)
- # initialise out from in (overridden below)
- m.d.comb += self.o.z.eq(i.z)
- m.d.comb += of.eq(i.of)
- # normalisation increase/decrease conditions
- decrease = Signal(reset_less=True)
- increase = Signal(reset_less=True)
- m.d.comb += decrease.eq(i.z.m_msbzero & i.z.exp_gt_n126)
- m.d.comb += increase.eq(i.z.exp_lt_n126)
- # decrease exponent
- with m.If(~self.i.out_do_z):
- with m.If(decrease):
- # *sigh* not entirely obvious: count leading zeros (clz)
- # with a PriorityEncoder: to find from the MSB
- # we reverse the order of the bits.
- temp_m = Signal(mwid, reset_less=True)
- temp_s = Signal(mwid+1, reset_less=True)
- clz = Signal((len(i.z.e), True), reset_less=True)
- # make sure that the amount to decrease by does NOT
- # go below the minimum non-INF/NaN exponent
- limclz = Mux(i.z.exp_sub_n126 > pe.o, pe.o,
- i.z.exp_sub_n126)
- m.d.comb += [
- # cat round and guard bits back into the mantissa
- temp_m.eq(Cat(i.of.round_bit, i.of.guard, i.z.m)),
- pe.i.eq(temp_m[::-1]), # inverted
- clz.eq(limclz), # count zeros from MSB down
- temp_s.eq(temp_m << clz), # shift mantissa UP
- self.o.z.e.eq(i.z.e - clz), # DECREASE exponent
- self.o.z.m.eq(temp_s[2:]), # exclude bits 0&1
- of.m0.eq(temp_s[2]), # copy of mantissa[0]
- # overflow in bits 0..1: got shifted too (leave sticky)
- of.guard.eq(temp_s[1]), # guard
- of.round_bit.eq(temp_s[0]), # round
- ]
- # increase exponent
- with m.Elif(increase):
- temp_m = Signal(mwid+1, reset_less=True)
- m.d.comb += [
- temp_m.eq(Cat(i.of.sticky, i.of.round_bit, i.of.guard,
- i.z.m)),
- ediff_n126.eq(i.z.N126 - i.z.e),
- # connect multi-shifter to inp/out mantissa (and ediff)
- msr.inp.eq(temp_m),
- msr.diff.eq(ediff_n126),
- self.o.z.m.eq(msr.m[3:]),
- of.m0.eq(temp_s[3]), # copy of mantissa[0]
- # overflow in bits 0..1: got shifted too (leave sticky)
- of.guard.eq(temp_s[2]), # guard
- of.round_bit.eq(temp_s[1]), # round
- of.sticky.eq(temp_s[0]), # sticky
- self.o.z.e.eq(i.z.e + ediff_n126),
- ]
-
- m.d.comb += self.o.mid.eq(self.i.mid)
- m.d.comb += self.o.out_do_z.eq(self.i.out_do_z)
- m.d.comb += self.o.oz.eq(self.i.oz)
-
- return m
-
-
-class FPNorm1ModMulti:
def __init__(self, width, single_cycle=True):
self.width = width
return m
-class FPNorm1Single(FPState):
-
- def __init__(self, width, id_wid, single_cycle=True):
- FPState.__init__(self, "normalise_1")
- self.mod = FPNorm1ModSingle(width)
- self.o = self.ospec()
- self.out_z = FPNumBase(width, False)
- self.out_roundz = Signal(reset_less=True)
-
- def ispec(self):
- return self.mod.ispec()
-
- def ospec(self):
- return self.mod.ospec()
-
- def setup(self, m, i):
- """ links module to inputs and outputs
- """
- self.mod.setup(m, i)
-
- def action(self, m):
- m.next = "round"
-
-
-class FPNorm1Multi(FPState):
-
- def __init__(self, width, id_wid):
- FPState.__init__(self, "normalise_1")
- self.mod = FPNorm1ModMulti(width)
- self.stb = Signal(reset_less=True)
- self.ack = Signal(reset=0, reset_less=True)
- self.out_norm = Signal(reset_less=True)
- self.in_accept = Signal(reset_less=True)
- self.temp_z = FPNumBase(width)
- self.temp_of = Overflow()
- self.out_z = FPNumBase(width)
- self.out_roundz = Signal(reset_less=True)
-
- def setup(self, m, in_z, in_of, norm_stb):
- """ links module to inputs and outputs
- """
- self.mod.setup(m, in_z, in_of, norm_stb,
- self.in_accept, self.temp_z, self.temp_of,
- self.out_z, self.out_norm)
-
- m.d.comb += self.stb.eq(norm_stb)
- m.d.sync += self.ack.eq(0) # sets to zero when not in normalise_1 state
-
- def action(self, m):
- m.d.comb += self.in_accept.eq((~self.ack) & (self.stb))
- m.d.sync += self.temp_of.eq(self.mod.out_of)
- m.d.sync += self.temp_z.eq(self.out_z)
- with m.If(self.out_norm):
- with m.If(self.in_accept):
- m.d.sync += [
- self.ack.eq(1),
- ]
- with m.Else():
- m.d.sync += self.ack.eq(0)
- with m.Else():
- # normalisation not required (or done).
- m.next = "round"
- m.d.sync += self.ack.eq(1)
- m.d.sync += self.out_roundz.eq(self.mod.out_of.roundz)
-
-
class FPNormToPack(FPState, UnbufferedPipeline):
def __init__(self, width, id_wid):
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