def test_fixed_point(self):
for wl, fl in [(5, 4), (3, 2)]:
for rounding in ["nearest"]:
for device in [("cuda:%d" % d)
for d in range(torch.cuda.device_count())]:
t_max = 1 - (2**(-fl))
to_quantize_cuda = torch.linspace(
-t_max, t_max, steps=1200, device=torch.device(device))
to_quantize_cpu = to_quantize_cuda.clone().to("cpu")
fixed_quantized_cuda = fixed_point_quantize(
to_quantize_cuda, wl=wl, fl=fl, rounding=rounding)
fixed_quantized_cpu = fixed_point_quantize(
to_quantize_cpu, wl=wl, fl=fl, rounding=rounding)
mse = self.error(fixed_quantized_cuda, fixed_quantized_cpu)
self.assertTrue(mse < 1e-15,
msg="%.2e MSE on device '%s'" %
(mse, device))
def QG(x, bits_G, bits_R, lr, mode="nearest"):
x = shift(x)
grad_number = FixedPoint(wl=bits_G,
fl=bits_G - 1,
clamp=False,
symmetric=True)
norm = fixed_point_quantize(lr * x, grad_number, rounding=mode)
return norm / (2.**((bits_G - 1)))
def QG(x, max_entry=None, bits_G=8, fl_mode="ceil", mode="nearest"):
x, max_entry = shift(x, max_entry)
norm = fixed_point_quantize(x,
wl=bits_G,
fl=bits_G - 1,
clamp=True,
symmetric=True,
rounding=mode)
output = rebase(norm, max_entry)
return output
def QG(x, bits_G, bits_R, lr, mode="nearest"):
x = shift(x)
lr = lr / (2.0**(bits_G - 1))
norm = fixed_point_quantize(lr * x,
wl=bits_G,
fl=bits_G - 1,
clamp=False,
symmetric=True,
rounding=mode)
return norm
def test_fixed_point(self):
for wl, fl in [(5, 4), (3, 2)]:
for rounding in ["nearest"]:
t_max = 1 - (2**(-fl))
to_quantize_cuda = torch.linspace(-t_max,
t_max,
steps=20,
device='cuda')
to_quantize_cpu = to_quantize_cuda.clone().to("cpu")
fixed_quantized_cuda = fixed_point_quantize(to_quantize_cuda,
wl=wl,
fl=fl,
rounding=rounding)
fixed_quantized_cpu = fixed_point_quantize(to_quantize_cpu,
wl=wl,
fl=fl,
rounding=rounding)
mse = self.error(fixed_quantized_cuda, fixed_quantized_cpu)
self.assertTrue(mse < 1e-15)
def QW(x, bits, scale=1.0, mode="nearest"):
y = fixed_point_quantize(x,
wl=bits,
fl=bits - 1,
clamp=True,
symmetric=True,
rounding=mode)
# per layer scaling
if scale > 1.8: y /= scale
return y
def test_fixed_block_zero_exponent(self):
"""
invariant: when the max exponent of a block is zero, block floating point behaves similar to
a fixed point where fl = wl -1, without the lowest number of the fixed point (-1).
"""
for wl, fl in [(3,2), (5,4)]:
t_max = 1-(2**(-fl))
to_quantize = torch.linspace(-t_max, t_max, steps=1000, device='cuda')
fixed_quantized = fixed_point_quantize(to_quantize, wl=wl, fl=fl, rounding='nearest')
block_quantized = block_quantize(to_quantize, wl=wl, rounding='nearest')
self.assertTrue(torch.eq(fixed_quantized, block_quantized).all().item())
