import numpy as np
import matplotlib.pyplot as plt
from fixed_point import fixed, W
from fixed_point import ROUND_MODES
format = W(4, 0, 3)
for rm in ROUND_MODES:
xf = np.arange(-1200, 1200) / 1000.
xq, xe = ([], [])
for ff in xf:
fx = float(fixed(ff, format=format, round_mode=rm))
xq.append(fx) # back to float for plotting, preserves value
xe.append(ff - fx) # also plot error
# plot the quantized values
fig, ax = plt.subplots(1)
tax = ax.twinx()
ax.plot(xf, xf, label='real number value')
ax.plot(xf, xq, label='quantized value')
ax.grid(True)
ax.set_xlim(-1.2, 1.2)
ax.set_ylim(-1.2, 1.2)
ax.set_title("Quantization\nfixed(format=W%s,"
"round_mode='%s'"
"overflow_mode='saturate')" % (rm, W.format))
ax.set_ylabel('')
ax.set_xlabel('')
tax.plot(xf, xe, 'm:', alpha=.6, label='error')
xf = np.array(xf)
def test_math():
x = fixed(0.5, format=W(16, 0))
y = fixed(0.25, format=W(16, 0))
w = x + y # typical modeling
print(repr(w), repr(x), repr(y))
# pre-declared
z = fixed(0, format=x + y)
z[:] = x + y # hardware transfer (type is declared)
print(repr(z), repr(x), repr(y))
assert float(w) == 0.75
assert float(z) == 0.75
# test non-aligned additions
x = fixed(0.5, min=-4, max=4, res=.125)
y = fixed(0.25, min=-16, max=16, res=.0625)
print(repr(z), repr(x), repr(y))
z = x + y
print(repr(z), repr(x), repr(y))
assert float(z) == 0.75
# test non-aligned additions and overflow
x = fixed(0.5, min=-4, max=4, res=2**-32)
y = fixed(1.5, min=-16, max=16, res=2**-32)
z = x + y
print(repr(z), repr(x), repr(y))
assert float(z) == 2.0
# @todo: negative iwl and fwl
# test subtraction
x = fixed(0.5, format=W(16, 0))
y = fixed(0.25, format=W(16, 0))
z = x - y
print('S', repr(z), repr(x), repr(y))
assert float(z) == 0.25
x = fixed(0.5, min=-4, max=4, res=.125)
y = fixed(0.25, min=-16, max=16, res=.0625)
z = x - y
print('S', repr(z), repr(x), repr(y))
assert float(z) == 0.25
z = y - x
print('S', repr(z), repr(x), repr(y))
assert float(z) == -0.25
x = fixed(10.33, min=-16, max=16, res=.125)
y = fixed(10.33, min=-16, max=16, res=.125)
z = x - y
print('S', repr(z), repr(x), repr(y))
assert float(z) == 0.
# The resolution of x is .125, it means 0.33 will be
# rounded to .25 or .375 (it should be .375). For
# y the resolution is 2**-8 and the actual value should
# be .328125 or .33203125 (.32 is closer?)
x = fixed(0.33, min=-1, max=1, res=.125)
y = fixed(0.33, min=-1, max=1, res=2**-8)
z = x + y
print('A', repr(z), repr(x), repr(y))
assert float(z) == 0.375 + 0.328125
x = fixed(0.33, min=-1, max=1, res=.125)
y = fixed(0.33, min=-1, max=1, res=2**-8)
z = x - y
print('S', repr(z), repr(x), repr(y))
assert float(z) == 0.375 - 0.328125
x = fixed(-1, format=W(8, 0, 7)) + .5
assert float(x) == -.5
import numpy as np
import matplotlib.pyplot as plt
from fixed_point import fixed, W
from fixed_point import ROUND_MODES
formats = (W(4, 0, 3), W(4, 1, 2), W(4, 2, 1), W(4, 3, 0))
for format in formats:
for rm in ROUND_MODES:
xf = np.arange(-1200, 1200) / 1000.
xq, xe = ([], [])
for ff in xf:
fx = float(fixed(ff, format=format, round_mode=rm))
xq.append(fx) # back to float for plotting, preserves value
xe.append(ff - fx) # also plot error
# plot the quantized values
fig, ax = plt.subplots(1)
tax = ax.twinx()
ax.plot(xf, xf, label='real number value')
ax.plot(xf, xq, label='quantized value')
ax.grid(True)
ax.set_xlim(-1.2, 1.2)
ax.set_ylim(-1.2, 1.2)
ax.set_title("Quantization\nfixed(format=(4,0,3),"
"round_mode='%s'"
"overflow_mode='saturate')" % (rm))
ax.set_ylabel('')
ax.set_xlabel('')
tax.plot(xf, xe, 'm:', alpha=.6, label='error')