1 # IEEE Floating Point Adder (Single Precision)
2 # Copyright (C) Jonathan P Dawson 2013
5 from nmigen
import Module
, Signal
, Cat
6 from nmigen
.cli
import main
, verilog
8 from fpbase
import FPNum
, FPOp
, Overflow
, FPBase
13 def __init__(self
, width
, single_cycle
=False):
16 self
.single_cycle
= single_cycle
18 self
.in_a
= FPOp(width
)
19 self
.in_b
= FPOp(width
)
20 self
.out_z
= FPOp(width
)
22 def get_fragment(self
, platform
=None):
23 """ creates the HDL code-fragment for FPAdd
30 z
= FPNum(self
.width
, False)
32 w
= {32: 28, 64:57}[self
.width
]
33 tot
= Signal(w
) # sticky/round/guard, {mantissa} result, 1 overflow
42 with m
.State("get_a"):
43 self
.get_op(m
, self
.in_a
, a
, "get_b")
48 with m
.State("get_b"):
49 self
.get_op(m
, self
.in_b
, b
, "special_cases")
52 # special cases: NaNs, infs, zeros, denormalised
53 # NOTE: some of these are unique to add. see "Special Operations"
54 # https://steve.hollasch.net/cgindex/coding/ieeefloat.html
56 with m
.State("special_cases"):
58 # if a is NaN or b is NaN return NaN
59 with m
.If(a
.is_nan() | b
.is_nan()):
63 # if a is inf return inf (or NaN)
64 with m
.Elif(a
.is_inf()):
66 m
.d
.sync
+= z
.inf(a
.s
)
67 # if a is inf and signs don't match return NaN
68 with m
.If((b
.e
== b
.P128
) & (a
.s
!= b
.s
)):
69 m
.d
.sync
+= z
.nan(b
.s
)
71 # if b is inf return inf
72 with m
.Elif(b
.is_inf()):
74 m
.d
.sync
+= z
.inf(b
.s
)
76 # if a is zero and b zero return signed-a/b
77 with m
.Elif(a
.is_zero() & b
.is_zero()):
79 m
.d
.sync
+= z
.create(a
.s
& b
.s
, b
.e
, b
.m
[3:-1])
81 # if a is zero return b
82 with m
.Elif(a
.is_zero()):
84 m
.d
.sync
+= z
.create(b
.s
, b
.e
, b
.m
[3:-1])
86 # if b is zero return a
87 with m
.Elif(b
.is_zero()):
89 m
.d
.sync
+= z
.create(a
.s
, a
.e
, a
.m
[3:-1])
91 # Denormalised Number checks
94 self
.denormalise(m
, a
)
95 self
.denormalise(m
, b
)
100 with m
.State("align"):
101 if not self
.single_cycle
:
102 # NOTE: this does *not* do single-cycle multi-shifting,
103 # it *STAYS* in the align state until exponents match
105 # exponent of a greater than b: shift b down
106 with m
.If(a
.e
> b
.e
):
107 m
.d
.sync
+= b
.shift_down()
108 # exponent of b greater than a: shift a down
109 with m
.Elif(a
.e
< b
.e
):
110 m
.d
.sync
+= a
.shift_down()
111 # exponents equal: move to next stage.
115 # This one however (single-cycle) will do the shift
118 # XXX TODO: the shifter used here is quite expensive
119 # having only one would be better
121 ediff
= Signal((len(a
.e
), True))
122 ediffr
= Signal((len(a
.e
), True))
123 m
.d
.comb
+= ediff
.eq(a
.e
- b
.e
)
124 m
.d
.comb
+= ediffr
.eq(b
.e
- a
.e
)
125 with m
.If(ediff
> 0):
126 m
.d
.sync
+= b
.shift_down_multi(ediff
)
127 # exponent of b greater than a: shift a down
128 with m
.Elif(ediff
< 0):
129 m
.d
.sync
+= a
.shift_down_multi(ediffr
)
134 # First stage of add. covers same-sign (add) and subtract
135 # special-casing when mantissas are greater or equal, to
136 # give greatest accuracy.
138 with m
.State("add_0"):
140 m
.d
.sync
+= z
.e
.eq(a
.e
)
141 # same-sign (both negative or both positive) add mantissas
142 with m
.If(a
.s
== b
.s
):
144 tot
.eq(Cat(a
.m
, 0) + Cat(b
.m
, 0)),
147 # a mantissa greater than b, use a
148 with m
.Elif(a
.m
>= b
.m
):
150 tot
.eq(Cat(a
.m
, 0) - Cat(b
.m
, 0)),
153 # b mantissa greater than a, use b
156 tot
.eq(Cat(b
.m
, 0) - Cat(a
.m
, 0)),
161 # Second stage of add: preparation for normalisation.
162 # detects when tot sum is too big (tot[27] is kinda a carry bit)
164 with m
.State("add_1"):
165 m
.next
= "normalise_1"
166 # tot[27] gets set when the sum overflows. shift result down
171 of
.round_bit
.eq(tot
[2]),
172 of
.sticky
.eq(tot
[1] | tot
[0]),
180 of
.round_bit
.eq(tot
[1]),
185 # First stage of normalisation.
187 with m
.State("normalise_1"):
188 self
.normalise_1(m
, z
, of
, "normalise_2")
191 # Second stage of normalisation.
193 with m
.State("normalise_2"):
194 self
.normalise_2(m
, z
, of
, "round")
199 with m
.State("round"):
200 self
.roundz(m
, z
, of
, "corrections")
205 with m
.State("corrections"):
206 self
.corrections(m
, z
, "pack")
211 with m
.State("pack"):
212 self
.pack(m
, z
, "put_z")
217 with m
.State("put_z"):
218 self
.put_z(m
, z
, self
.out_z
, "get_a")
223 if __name__
== "__main__":
224 alu
= FPADD(width
=32)
225 main(alu
, ports
=alu
.in_a
.ports() + alu
.in_b
.ports() + alu
.out_z
.ports())
228 # works... but don't use, just do "python fname.py convert -t v"
229 #print (verilog.convert(alu, ports=[
230 # ports=alu.in_a.ports() + \
231 # alu.in_b.ports() + \