LZA (Leading zeros anticipation)

coreblocks/func_blocks/fu/fpu/lza.py

@@ -0,0 +1,111 @@
+from amaranth import *
+from amaranth.utils import ceil_log2
+from transactron import TModule, Method, def_method
+from coreblocks.func_blocks.fu.fpu.fpu_common import FPUParams
+from transactron.utils.amaranth_ext import count_leading_zeros
+
+
+class LZAMethodLayout:
+    """LZA module layouts for methods
+
+    Parameters
+    ----------
+    fpu_params: FPUParams
+        FPU parameters
+    """
+
+    def __init__(self, *, fpu_params: FPUParams):
+        """
+        sig_a - significand of a
+        sig_b - significand of b
+        carry - indicates if we want to predict result of a+b or a+b+1
+        shift_amount - position to shift needed to normalize number
+        is_zero - indicates if result is zero
+        """
+        self.predict_in_layout = [
+            ("sig_a", fpu_params.sig_width),
+            ("sig_b", fpu_params.sig_width),
+            ("carry", 1),
+        ]
+        self.predict_out_layout = [
+            ("shift_amount", range(fpu_params.sig_width)),
+            ("is_zero", 1),
+        ]
+
+
+class LZAModule(Elaboratable):
+    """LZA module
+    Based on: https://userpages.cs.umbc.edu/phatak/645/supl/lza/lza-survey-arith01.pdf
+    After performing subtracion, we may have to normalize floating point numbers and
+    For that, we have to know the number of leading zeros.
+    The most basic approach includes using LZC (leading zero counter) after subtracion,
+    a more advanced approach includes using LZA (Leading Zero Anticipator) to predict the number of
+    leading zeroes. It is worth noting that this LZA module works under assumptions that
+    significands are in two's complement and that before complementation sig_a was greater
+    or equal to sig_b. Another thing worth noting is that LZA works with error = 1.
+    That means that if 'n' is the result of the LZA module, in reality, to normalize
+    number we may have to shift left by 'n' or 'n+1'. There are few techniques of
+    dealing with that error like specially designed shifters or predicting the error
+    but the most basic approach is to just use multiplexer after shifter to perform
+    one more shift left if necessary.
+
+    Parameters
+    ----------
+    fpu_params: FPUParams
+        FPU rounding module parameters
+
+    Attributes
+    ----------
+    predict_request: Method
+        Transactional method for initiating leading zeros prediction.
+        Takes 'predict_in_layout' as argument
+        Returns shift amount as 'predict_out_layout'
+    """
+
+    def __init__(self, *, fpu_params: FPUParams):
+
+        self.lza_params = fpu_params
+        self.method_layouts = LZAMethodLayout(fpu_params=self.lza_params)
+        self.predict_request = Method(
+            i=self.method_layouts.predict_in_layout,
+            o=self.method_layouts.predict_out_layout,
+        )
+
+    def elaborate(self, platform):
+        m = TModule()
+
+        @def_method(m, self.predict_request)
+        def _(sig_a, sig_b, carry):
+            f_size = 2 ** ceil_log2(self.lza_params.sig_width)
+            filler_size = f_size - self.lza_params.sig_width
+            lower_ones = Const((2**filler_size) - 1, f_size)
+
+            t = Signal(self.lza_params.sig_width + 1)
+            g = Signal(self.lza_params.sig_width + 1)
+            z = Signal(self.lza_params.sig_width + 1)
+            f = Signal(f_size)
+            shift_amount = Signal(range(self.lza_params.sig_width))
+            is_zero = Signal(1)
+
+            m.d.av_comb += t.eq((sig_a ^ sig_b) << 1)
+            m.d.av_comb += g.eq((sig_a & sig_b) << 1)
+            m.d.av_comb += z.eq(((sig_a | sig_b) << 1))
+            with m.If(carry):
+                m.d.av_comb += g[0].eq(1)
+                m.d.av_comb += z[0].eq(1)
+
+            for i in reversed(range(1, self.lza_params.sig_width + 1)):
+                m.d.av_comb += f[i + filler_size - 1].eq((t[i] ^ z[i - 1]))
+
+            m.d.av_comb += shift_amount.eq(0)
+            m.d.av_comp += f.eq(f | lower_ones)
+            m.d.av_comb += shift_amount.eq(count_leading_zeros(f))
+
+            m.d.av_comb += is_zero.eq((carry & t[1 : self.lza_params.sig_width].all()))
+
+            return {
+                "shift_amount": shift_amount,
+                "is_zero": is_zero,
+            }
+
+        return m

test/func_blocks/fu/fpu/test_lza.py

@@ -0,0 +1,112 @@
+import random
+from coreblocks.func_blocks.fu.fpu.lza import *
+from coreblocks.func_blocks.fu.fpu.fpu_common import FPUParams
+from transactron import TModule
+from transactron.lib import AdapterTrans
+from transactron.testing import *
+from amaranth import *
+
+
+def clz(sig_a, sig_b, carry, sig_width):
+    zeros = 0
+    msb_bit_mask = 1 << (sig_width - 1)
+    sum = sig_a + sig_b + carry
+    while 1:
+        if not (sum & msb_bit_mask):
+            zeros += 1
+            sum = sum << 1
+        else:
+            return zeros
+
+
+class TestLZA(TestCaseWithSimulator):
+    class LZAModuleTest(Elaboratable):
+        def __init__(self, params: FPUParams):
+            self.params = params
+
+        def elaborate(self, platform):
+            m = TModule()
+            m.submodules.lza = lza = self.lza_module = LZAModule(fpu_params=self.params)
+            m.submodules.predict = self.predict_request_adapter = TestbenchIO(AdapterTrans(lza.predict_request))
+            return m
+
+    def test_manual(self):
+        params = FPUParams(sig_width=24, exp_width=8)
+        lza = TestLZA.LZAModuleTest(params)
+
+        async def random_test(sim: TestbenchContext, seed: int, iters: int):
+            xor_mask = (2**params.sig_width) - 1
+            random.seed(seed)
+            for _ in range(iters):
+                sig_a = random.randint(1 << (params.sig_width - 1), (2**params.sig_width) - 1)
+                sig_b = random.randint(1 << (params.sig_width - 1), sig_a)
+                sig_b = (sig_b ^ xor_mask) | (1 << params.sig_width)
+                resp = await lza.predict_request_adapter.call(sim, {"sig_a": sig_a, "sig_b": sig_b, "carry": 0})
+                pred_lz = resp["shift_amount"]
+                true_lz = clz(sig_a, sig_b, 0, params.sig_width)
+                assert pred_lz == true_lz or (pred_lz + 1) == true_lz
+
+        async def lza_test(sim: TestbenchContext):
+            test_cases = [
+                {
+                    "sig_a": 16368512,
+                    "sig_b": 409600,
+                    "carry": 0,
+                },
+                {
+                    "sig_a": 0,
+                    "sig_b": (2**24) - 1,
+                    "carry": 0,
+                },
+                {
+                    "sig_a": (2**24) // 2,
+                    "sig_b": (2**24) // 2,
+                    "carry": 0,
+                },
+                {
+                    "sig_a": 12582912,
+                    "sig_b": 12550144,
+                    "carry": 0,
+                },
+                {
+                    "sig_a": 16744448,
+                    "sig_b": 12615680,
+                    "carry": 0,
+                },
+                {
+                    "sig_a": 8421376,
+                    "sig_b": 8421376,
+                    "carry": 0,
+                },
+            ]
+            expected_results = [
+                {"shift_amount": 13, "is_zero": 0},
+                {"shift_amount": 13, "is_zero": 0},
+                {"shift_amount": 23, "is_zero": 0},
+                {"shift_amount": 0, "is_zero": 1},
+                {"shift_amount": 0, "is_zero": 0},
+                {"shift_amount": 23, "is_zero": 0},
+                {"shift_amount": 0, "is_zero": 0},
+                {"shift_amount": 0, "is_zero": 0},
+                {"shift_amount": 0, "is_zero": 0},
+                {"shift_amount": 0, "is_zero": 0},
+                {"shift_amount": 7, "is_zero": 0},
+                {"shift_amount": 7, "is_zero": 0},
+            ]
+            for i in range(len(test_cases)):
+
+                resp = await lza.predict_request_adapter.call(sim, test_cases[i])
+                assert resp["shift_amount"] == expected_results[2 * i]["shift_amount"]
+                assert resp["is_zero"] == expected_results[2 * i]["is_zero"]
+
+                test_cases[i]["carry"] = 1
+                resp = await lza.predict_request_adapter.call(sim, test_cases[i])
+                assert resp["shift_amount"] == expected_results[2 * i + 1]["shift_amount"]
+                assert resp["is_zero"] == expected_results[2 * i + 1]["is_zero"]
+
+        async def test_process(sim: TestbenchContext):
+            await lza_test(sim)
+            await random_test(sim, 2024, 20)
+
+        with self.run_simulation(lza) as sim:
+            sim.add_testbench(test_process)