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 FPNumIn
, FPNumOut
, FPOp
, Overflow
, FPBase
11 class FPState(FPBase
):
12 def __init__(self
, state_from
):
13 self
.state_from
= state_from
15 def set_inputs(self
, inputs
):
17 for k
,v
in inputs
.items():
20 def set_outputs(self
, outputs
):
21 self
.outputs
= outputs
22 for k
,v
in outputs
.items():
26 class FPGetOpA(FPState
):
29 self
.get_op(m
, self
.in_a
, self
.a
, "get_b")
32 class FPGetOpB(FPState
):
35 self
.get_op(m
, self
.in_b
, self
.b
, "special_cases")
38 class FPAddSpecialCases(FPState
):
42 m
.d
.comb
+= s_nomatch
.eq(self
.a
.s
!= self
.b
.s
)
45 m
.d
.comb
+= m_match
.eq(self
.a
.m
== self
.b
.m
)
47 # if a is NaN or b is NaN return NaN
48 with m
.If(self
.a
.is_nan | self
.b
.is_nan
):
50 m
.d
.sync
+= self
.z
.nan(1)
52 # XXX WEIRDNESS for FP16 non-canonical NaN handling
55 ## if a is zero and b is NaN return -b
56 #with m.If(a.is_zero & (a.s==0) & b.is_nan):
58 # m.d.sync += z.create(b.s, b.e, Cat(b.m[3:-2], ~b.m[0]))
60 ## if b is zero and a is NaN return -a
61 #with m.Elif(b.is_zero & (b.s==0) & a.is_nan):
63 # m.d.sync += z.create(a.s, a.e, Cat(a.m[3:-2], ~a.m[0]))
65 ## if a is -zero and b is NaN return -b
66 #with m.Elif(a.is_zero & (a.s==1) & b.is_nan):
68 # m.d.sync += z.create(a.s & b.s, b.e, Cat(b.m[3:-2], 1))
70 ## if b is -zero and a is NaN return -a
71 #with m.Elif(b.is_zero & (b.s==1) & a.is_nan):
73 # m.d.sync += z.create(a.s & b.s, a.e, Cat(a.m[3:-2], 1))
75 # if a is inf return inf (or NaN)
76 with m
.Elif(self
.a
.is_inf
):
78 m
.d
.sync
+= self
.z
.inf(self
.a
.s
)
79 # if a is inf and signs don't match return NaN
80 with m
.If(self
.b
.exp_128
& s_nomatch
):
81 m
.d
.sync
+= self
.z
.nan(1)
83 # if b is inf return inf
84 with m
.Elif(self
.b
.is_inf
):
86 m
.d
.sync
+= self
.z
.inf(self
.b
.s
)
88 # if a is zero and b zero return signed-a/b
89 with m
.Elif(self
.a
.is_zero
& self
.b
.is_zero
):
91 m
.d
.sync
+= self
.z
.create(self
.a
.s
& self
.b
.s
, self
.b
.e
,
94 # if a is zero return b
95 with m
.Elif(self
.a
.is_zero
):
97 m
.d
.sync
+= self
.z
.create(self
.b
.s
, self
.b
.e
, self
.b
.m
[3:-1])
99 # if b is zero return a
100 with m
.Elif(self
.b
.is_zero
):
102 m
.d
.sync
+= self
.z
.create(self
.a
.s
, self
.a
.e
, self
.a
.m
[3:-1])
104 # if a equal to -b return zero (+ve zero)
105 with m
.Elif(s_nomatch
& m_match
& (self
.a
.e
== self
.b
.e
)):
107 m
.d
.sync
+= self
.z
.zero(0)
109 # Denormalised Number checks
111 m
.next
= "denormalise"
116 def __init__(self
, width
, single_cycle
=False):
117 FPBase
.__init
__(self
)
119 self
.single_cycle
= single_cycle
121 self
.in_a
= FPOp(width
)
122 self
.in_b
= FPOp(width
)
123 self
.out_z
= FPOp(width
)
125 def get_fragment(self
, platform
=None):
126 """ creates the HDL code-fragment for FPAdd
131 a
= FPNumIn(self
.in_a
, self
.width
)
132 b
= FPNumIn(self
.in_b
, self
.width
)
133 z
= FPNumOut(self
.width
, False)
135 m
.submodules
.fpnum_a
= a
136 m
.submodules
.fpnum_b
= b
137 m
.submodules
.fpnum_z
= z
140 tot
= Signal(w
, reset_less
=True) # sticky/round/guard, {mantissa} result, 1 overflow
143 m
.submodules
.overflow
= of
145 geta
= FPGetOpA("get_a")
146 geta
.set_inputs({"in_a": self
.in_a
})
147 geta
.set_outputs({"a": a
})
148 m
.d
.comb
+= a
.v
.eq(self
.in_a
.v
) # links in_a to a
150 getb
= FPGetOpB("get_b")
151 getb
.set_inputs({"in_b": self
.in_b
})
152 getb
.set_outputs({"b": b
})
153 m
.d
.comb
+= b
.v
.eq(self
.in_b
.v
) # links in_b to b
155 sc
= FPAddSpecialCases("special_cases")
156 sc
.set_inputs({"a": a
, "b": b
})
157 sc
.set_outputs({"z": z
})
164 with m
.State("get_a"):
170 with m
.State("get_b"):
171 #self.get_op(m, self.in_b, b, "special_cases")
175 # special cases: NaNs, infs, zeros, denormalised
176 # NOTE: some of these are unique to add. see "Special Operations"
177 # https://steve.hollasch.net/cgindex/coding/ieeefloat.html
179 with m
.State("special_cases"):
185 with m
.State("denormalise"):
186 # Denormalised Number checks
188 self
.denormalise(m
, a
)
189 self
.denormalise(m
, b
)
194 with m
.State("align"):
195 if not self
.single_cycle
:
196 # NOTE: this does *not* do single-cycle multi-shifting,
197 # it *STAYS* in the align state until exponents match
199 # exponent of a greater than b: shift b down
200 with m
.If(a
.e
> b
.e
):
201 m
.d
.sync
+= b
.shift_down()
202 # exponent of b greater than a: shift a down
203 with m
.Elif(a
.e
< b
.e
):
204 m
.d
.sync
+= a
.shift_down()
205 # exponents equal: move to next stage.
209 # This one however (single-cycle) will do the shift
212 # XXX TODO: the shifter used here is quite expensive
213 # having only one would be better
215 ediff
= Signal((len(a
.e
), True), reset_less
=True)
216 ediffr
= Signal((len(a
.e
), True), reset_less
=True)
217 m
.d
.comb
+= ediff
.eq(a
.e
- b
.e
)
218 m
.d
.comb
+= ediffr
.eq(b
.e
- a
.e
)
219 with m
.If(ediff
> 0):
220 m
.d
.sync
+= b
.shift_down_multi(ediff
)
221 # exponent of b greater than a: shift a down
222 with m
.Elif(ediff
< 0):
223 m
.d
.sync
+= a
.shift_down_multi(ediffr
)
228 # First stage of add. covers same-sign (add) and subtract
229 # special-casing when mantissas are greater or equal, to
230 # give greatest accuracy.
232 with m
.State("add_0"):
234 m
.d
.sync
+= z
.e
.eq(a
.e
)
235 # same-sign (both negative or both positive) add mantissas
236 with m
.If(a
.s
== b
.s
):
238 tot
.eq(Cat(a
.m
, 0) + Cat(b
.m
, 0)),
241 # a mantissa greater than b, use a
242 with m
.Elif(a
.m
>= b
.m
):
244 tot
.eq(Cat(a
.m
, 0) - Cat(b
.m
, 0)),
247 # b mantissa greater than a, use b
250 tot
.eq(Cat(b
.m
, 0) - Cat(a
.m
, 0)),
255 # Second stage of add: preparation for normalisation.
256 # detects when tot sum is too big (tot[27] is kinda a carry bit)
258 with m
.State("add_1"):
259 m
.next
= "normalise_1"
260 # tot[27] gets set when the sum overflows. shift result down
266 of
.round_bit
.eq(tot
[2]),
267 of
.sticky
.eq(tot
[1] | tot
[0]),
276 of
.round_bit
.eq(tot
[1]),
281 # First stage of normalisation.
283 with m
.State("normalise_1"):
284 self
.normalise_1(m
, z
, of
, "normalise_2")
287 # Second stage of normalisation.
289 with m
.State("normalise_2"):
290 self
.normalise_2(m
, z
, of
, "round")
295 with m
.State("round"):
296 self
.roundz(m
, z
, of
, "corrections")
301 with m
.State("corrections"):
302 self
.corrections(m
, z
, "pack")
307 with m
.State("pack"):
308 self
.pack(m
, z
, "put_z")
313 with m
.State("put_z"):
314 self
.put_z(m
, z
, self
.out_z
, "get_a")
319 if __name__
== "__main__":
320 alu
= FPADD(width
=32)
321 main(alu
, ports
=alu
.in_a
.ports() + alu
.in_b
.ports() + alu
.out_z
.ports())
324 # works... but don't use, just do "python fname.py convert -t v"
325 #print (verilog.convert(alu, ports=[
326 # ports=alu.in_a.ports() + \
327 # alu.in_b.ports() + \