# Copyright (C) Jonathan P Dawson 2013
# 2013-12-12
-from nmigen import Module, Signal, Cat
-from nmigen.cli import main
+from nmigen import Module, Signal, Cat, Const
+from nmigen.cli import main, verilog
+
+
+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)
+
+ 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 __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
+ """
+ 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
+ ]
+
+ def create(self, s, e, m):
+ """ creates a value from sign / exponent / mantissa
+
+ bias is added here, to the exponent
+ """
+ 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
+ ]
+
+ def shift_down(self):
+ """ shifts a mantissa down by one. exponent is increased to compensate
+
+ accuracy is lost as a result in the mantissa however there are 3
+ guard bits (the latter of which is the "sticky" bit)
+ """
+ return [self.e.eq(self.e + 1),
+ self.m.eq(Cat(self.m[0] | self.m[1], self.m[2:], 0))
+ ]
+
+ def nan(self, s):
+ return self.create(s, self.P128, 1<<22)
+
+ def inf(self, s):
+ return self.create(s, self.P128, 0)
+
+ def zero(self, s):
+ return self.create(s, self.N127, 0)
+
+ def is_nan(self):
+ return (self.e == self.P128) & (self.m != 0)
+
+ def is_inf(self):
+ return (self.e == self.P128) & (self.m == 0)
+
+ def is_zero(self):
+ return (self.e == self.N127) & (self.m == self.mzero)
+
+ def is_overflowed(self):
+ return (self.e > self.P127)
+
+ def is_denormalised(self):
+ return (self.e == self.N126) & (self.m[23] == 0)
class FPADD:
self.out_z_stb = Signal()
self.out_z_ack = Signal()
- s_out_z_stb = Signal()
- s_out_z = Signal(width)
- s_in_a_ack = Signal()
- s_in_b_ack = Signal()
-
- def get_fragment(self, platform):
+ def get_fragment(self, platform=None):
m = Module()
# Latches
- a = Signal(self.width)
- b = Signal(self.width)
- z = Signal(self.width)
-
- # Mantissa
- a_m = Signal(27)
- b_m = Signal(27)
- z_m = Signal(23)
+ a = FPNum(self.width)
+ b = FPNum(self.width)
+ z = FPNum(self.width, 24)
- # Exponent
- a_e = Signal(10)
- b_e = Signal(10)
- z_e = Signal(10)
+ tot = Signal(28) # sticky/round/guard bits, 23 result, 1 overflow
- # Sign
- a_s = Signal()
- b_s = Signal()
- z_s = Signal()
-
- guard = Signal()
- round_bit = Signal()
- sticky = Signal()
-
- tot = Signal(28)
+ guard = Signal() # tot[2]
+ round_bit = Signal() # tot[1]
+ sticky = Signal() # tot[0]
with m.FSM() as fsm:
with m.If((self.in_a_ack) & (self.in_a_stb)):
m.next = "get_b"
m.d.sync += [
- a.eq(self.in_a),
+ a.v.eq(self.in_a),
self.in_a_ack.eq(0)
]
with m.Else():
with m.State("get_b"):
with m.If((self.in_b_ack) & (self.in_b_stb)):
- m.next = "get_a"
+ m.next = "unpack"
m.d.sync += [
- b.eq(self.in_b),
+ b.v.eq(self.in_b),
self.in_b_ack.eq(0)
]
with m.Else():
with m.State("unpack"):
m.next = "special_cases"
- m.d.sync += [
- # mantissa
- a_m.eq(Cat(0, 0, 0, a[0:23])),
- b_m.eq(Cat(0, 0, 0, b[0:23])),
- # exponent (take off exponent bias, here)
- a_e.eq(Cat(a[23:31]) - 127),
- b_e.eq(Cat(b[23:31]) - 127),
- # sign
- a_s.eq(Cat(a[31])),
- b_s.eq(Cat(b[31]))
- ]
+ 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_e == 128) & (a_m != 0)) | \
- ((b_e == 128) & (b_m != 0))):
+ with m.If(a.is_nan() | b.is_nan()):
m.next = "put_z"
- m.d.sync += [
- z[31].eq(1), # sign: 1
- z[23:31].eq(255), # exp: 0b11111...
- z[22].eq(1), # mantissa top bit: 1
- z[0:22].eq(0) # mantissa rest: 0b0000...
- ]
+ m.d.sync += z.nan(1)
# if a is inf return inf (or NaN)
- with m.Elif(a_e == 128):
+ 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 += [
- z[31].eq(a_s), # sign: a_s
- z[23:31].eq(255), # exp: 0b11111...
- z[0:23].eq(0) # mantissa rest: 0b0000...
+ tot.eq(a.m + b.m),
+ z.s.eq(a.s)
]
- # if a is inf and signs don't match return NaN
- with m.If((b_e == 128) & (a_s != b_s)):
- m.d.sync += [
- z[31].eq(b_s), # sign: b_s
- z[23:31].eq(255), # exp: 0b11111...
- z[22].eq(1), # mantissa top bit: 1
- z[0:22].eq(0) # mantissa rest: 0b0000...
- ]
+ # 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]),
+ guard.eq(tot[3]),
+ round_bit.eq(tot[2]),
+ 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]),
+ guard.eq(tot[2]),
+ round_bit.eq(tot[1]),
+ 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"):
+ 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(guard), # steal guard bit (was tot[2])
+ guard.eq(round_bit), # steal round_bit (was tot[1])
+ ]
+ with m.Else():
+ m.next = "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"):
+ 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
+ guard.eq(z.m[0]),
+ round_bit.eq(guard),
+ sticky.eq(sticky | round_bit)
+ ]
+ with m.Else():
+ m.next = "round"
+
+ # ******
+ # rounding stage
+
+ with m.State("round"):
+ m.next = "corrections"
+ with m.If(guard & (round_bit | 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
+
+ # ******
+ # correction stage
+
+ with m.State("corrections"):
+ m.next = "pack"
+ # 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)
+
+ # ******
+ # 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.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"
+
return m
-"""
- always @(posedge clk)
- begin
-
- case(state)
-
- get_a:
- begin
- s_in_a_ack <= 1;
- if (s_in_a_ack && in_a_stb) begin
- a <= in_a;
- s_in_a_ack <= 0;
- state <= get_b;
- end
- end
-
- get_b:
- begin
- s_in_b_ack <= 1;
- if (s_in_b_ack && in_b_stb) begin
- b <= in_b;
- s_in_b_ack <= 0;
- state <= unpack;
- end
- end
-
- unpack:
- begin
- a_m <= {a[22 : 0], 3'd0};
- b_m <= {b[22 : 0], 3'd0};
- a_e <= a[30 : 23] - 127;
- b_e <= b[30 : 23] - 127;
- a_s <= a[31];
- b_s <= b[31];
- state <= special_cases;
- end
-
- special_cases:
- begin
- //if a is NaN or b is NaN return NaN
- if ((a_e == 128 && a_m != 0) || (b_e == 128 && b_m != 0)) begin
- z[31] <= 1;
- z[30:23] <= 255;
- z[22] <= 1;
- z[21:0] <= 0;
- state <= put_z;
- //if a is inf return inf
- end else if (a_e == 128) begin
- z[31] <= a_s;
- z[30:23] <= 255;
- z[22:0] <= 0;
- //if a is inf and signs don't match return nan
- if ((b_e == 128) && (a_s != b_s)) begin
- z[31] <= b_s;
- z[30:23] <= 255;
- z[22] <= 1;
- z[21:0] <= 0;
- end
- state <= put_z;
- //if b is inf return inf
- end else if (b_e == 128) begin
- z[31] <= b_s;
- z[30:23] <= 255;
- z[22:0] <= 0;
- state <= put_z;
- //if a is zero return b
- end else if ((($signed(a_e) == -127) && (a_m == 0)) && (($signed(b_e) == -127) && (b_m == 0))) begin
- z[31] <= a_s & b_s;
- z[30:23] <= b_e[7:0] + 127;
- z[22:0] <= b_m[26:3];
- state <= put_z;
- //if a is zero return b
- end else if (($signed(a_e) == -127) && (a_m == 0)) begin
- z[31] <= b_s;
- z[30:23] <= b_e[7:0] + 127;
- z[22:0] <= b_m[26:3];
- state <= put_z;
- //if b is zero return a
- end else if (($signed(b_e) == -127) && (b_m == 0)) begin
- z[31] <= a_s;
- z[30:23] <= a_e[7:0] + 127;
- z[22:0] <= a_m[26:3];
- state <= put_z;
- end else begin
- //Denormalised Number
- if ($signed(a_e) == -127) begin
- a_e <= -126;
- end else begin
- a_m[26] <= 1;
- end
- //Denormalised Number
- if ($signed(b_e) == -127) begin
- b_e <= -126;
- end else begin
- b_m[26] <= 1;
- end
- state <= align;
- end
- end
-
- align:
- begin
- if ($signed(a_e) > $signed(b_e)) begin
- b_e <= b_e + 1;
- b_m <= b_m >> 1;
- b_m[0] <= b_m[0] | b_m[1];
- end else if ($signed(a_e) < $signed(b_e)) begin
- a_e <= a_e + 1;
- a_m <= a_m >> 1;
- a_m[0] <= a_m[0] | a_m[1];
- end else begin
- state <= add_0;
- end
- end
-
- add_0:
- begin
- z_e <= a_e;
- if (a_s == b_s) begin
- tot <= a_m + b_m;
- z_s <= a_s;
- end else begin
- if (a_m >= b_m) begin
- tot <= a_m - b_m;
- z_s <= a_s;
- end else begin
- tot <= b_m - a_m;
- z_s <= b_s;
- end
- end
- state <= add_1;
- end
-
- add_1:
- begin
- if (tot[27]) begin
- z_m <= tot[27:4];
- guard <= tot[3];
- round_bit <= tot[2];
- sticky <= tot[1] | tot[0];
- z_e <= z_e + 1;
- end else begin
- z_m <= tot[26:3];
- guard <= tot[2];
- round_bit <= tot[1];
- sticky <= tot[0];
- end
- state <= normalise_1;
- end
-
- normalise_1:
- begin
- if (z_m[23] == 0 && $signed(z_e) > -126) begin
- z_e <= z_e - 1;
- z_m <= z_m << 1;
- z_m[0] <= guard;
- guard <= round_bit;
- round_bit <= 0;
- end else begin
- state <= normalise_2;
- end
- end
-
- normalise_2:
- begin
- if ($signed(z_e) < -126) begin
- z_e <= z_e + 1;
- z_m <= z_m >> 1;
- guard <= z_m[0];
- round_bit <= guard;
- sticky <= sticky | round_bit;
- end else begin
- state <= round;
- end
- end
-
- round:
- begin
- if (guard && (round_bit | sticky | z_m[0])) begin
- z_m <= z_m + 1;
- if (z_m == 24'hffffff) begin
- z_e <=z_e + 1;
- end
- end
- state <= pack;
- end
-
- pack:
- begin
- z[22 : 0] <= z_m[22:0];
- z[30 : 23] <= z_e[7:0] + 127;
- z[31] <= z_s;
- if ($signed(z_e) == -126 && z_m[23] == 0) begin
- z[30 : 23] <= 0;
- end
- if ($signed(z_e) == -126 && z_m[23:0] == 24'h0) begin
- z[31] <= 1'b0; // FIX SIGN BUG: -a + a = +0.
- end
- //if overflow occurs, return inf
- if ($signed(z_e) > 127) begin
- z[22 : 0] <= 0;
- z[30 : 23] <= 255;
- z[31] <= z_s;
- end
- state <= put_z;
- end
-
- put_z:
- begin
- s_out_z_stb <= 1;
- s_out_z <= z;
- if (s_out_z_stb && out_z_ack) begin
- s_out_z_stb <= 0;
- state <= get_a;
- end
- end
-
- endcase
-
- if (rst == 1) begin
- state <= get_a;
- s_in_a_ack <= 0;
- s_in_b_ack <= 0;
- s_out_z_stb <= 0;
- end
-
- end
- assign in_a_ack = s_in_a_ack;
- assign in_b_ack = s_in_b_ack;
- assign out_z_stb = s_out_z_stb;
- assign out_z = s_out_z;
-
-endmodule
-"""
if __name__ == "__main__":
alu = FPADD(width=32)
alu.in_b, alu.in_b_stb, alu.in_b_ack,
alu.out_z, alu.out_z_stb, alu.out_z_ack,
])
+
+
+ # works... but don't use, just do "python fname.py convert -t v"
+ #print (verilog.convert(alu, ports=[
+ # alu.in_a, alu.in_a_stb, alu.in_a_ack,
+ # alu.in_b, alu.in_b_stb, alu.in_b_ack,
+ # alu.out_z, alu.out_z_stb, alu.out_z_ack,
+ # ]))
projects / ieee754fpu.git / blobdiff