def run_posit_op(self,
abits=None,
op_str=None,
bbits=None,
ref_cbits=None,
nbits=None,
es=None):
a = PCPosit(abits, nbits=nbits, es=es, mode='bits')
b = PCPosit(bbits, nbits=nbits, es=es, mode='bits')
c = None
if op_str == '+':
c = a + b
elif op_str == '-':
c = a - b
elif op_str == '*':
c = a * b
elif op_str == '/':
c = a / b
elif op_str == 'u-':
c = -a
else:
raise NotImplementedError("op={}".format(op_str))
cbits = coder.encode_posit_binary(c.rep)
self.assertEqual(cbits, ref_cbits)
def __truediv__(self, other):
if self.rep['t'] == 'c' or other.rep['t'] == 'z':
p = PCPosit() # FIXME: Use constructor to directly initialized to posit zero.
p.rep = coder.create_cinf_positrep(nbits=self.rep['nbits'], es=self.rep['es'])
return p
elif self.rep['t'] == 'z' or other.rep['t'] == 'c':
p = PCPosit() # FIXME
p.rep = coder.create_zero_positrep(nbits=self.rep['nbits'], es=self.rep['es'])
return p
assert self.rep['t'] == 'n' and other.rep['t'] == 'n'
xa = ( -1)**self.rep['s'] * ( 2**self.rep['h'] + self.rep['f'])
xb = (-1)**other.rep['s'] * (2**other.rep['h'] + other.rep['f'])
ma = 2**self.rep['es'] * self.rep['k'] + self.rep['e'] - self.rep['h']
mb = 2**other.rep['es'] * other.rep['k'] + other.rep['e'] - other.rep['h']
pc = PCPosit() # FIXME
pc.rep = coder.create_zero_positrep(nbits=self.rep['nbits'], es=self.rep['es'])
pc.rep['t'] = 'n'
if (xa < 0) ^ (xb < 0): pc.rep['s'] = 1
if xa < 0: xa = -xa
if xb < 0: xb = -xb
g = ma - mb + (2**pc.rep['es'])*(pc.rep['nbits']-2) + pc.rep['nbits'] - 1
g = max(0, g)
xc = (xa * 2**g) // xb
mc = ma - mb - g
if xc != 0:
while xc != 0 and xc % 2 == 0:
xc >>= 1
mc += 1
g = 0
x = xc
while x >= 2:
x >>= 1
g -= 1
assert x >= 1 and x < 2, "x={}".format(x)
pc.rep['e'] = (mc - g) % 2**pc.rep['es']
pc.rep['k'] = (mc - g) // 2**pc.rep['es']
pc.rep['h'] = -g
pc.rep['f'] = xc - 2**pc.rep['h']
else:
pc.rep = coder.create_zero_positrep(nbits=self.rep['nbits'], es=self.rep['es'])
bits = coder.encode_posit_binary(pc.rep)
pc.rep = coder.decode_posit_binary(bits, nbits=pc.rep['nbits'], es=pc.rep['es'])
return pc
def __add__(self, other):
if self.rep['t'] == 'z':
return PCPosit(other)
elif other.rep['t'] == 'z':
return PCPosit(self)
elif self.rep['t'] == 'c' or other.rep['t'] == 'c':
ret = PCPosit(2**(self.rep['nbits']-1), mode='bits', nbits=self.rep['nbits'], es=self.rep['es'])
return ret
assert self.rep['t'] == 'n' and other.rep['t'] == 'n'
xa = ( -1)**self.rep['s'] * ( 2**self.rep['h'] + self.rep['f'])
xb = (-1)**other.rep['s'] * (2**other.rep['h'] + other.rep['f'])
ma = 2**self.rep['es'] * self.rep['k'] + self.rep['e'] - self.rep['h']
mb = 2**other.rep['es'] * other.rep['k'] + other.rep['e'] - other.rep['h']
m = max(ma, mb)
xc = xa*2**(m-mb) + xb*2**(m-ma)
mc = ma + mb - m
pc = PCPosit(self, nbits=self.rep['nbits'], es=self.rep['es'])
pc.rep = coder.create_positrep(nbits=self.rep['nbits'], es=self.rep['es'])
if xc == 0:
pc.rep['t'] = 'z'
return pc
elif xc < 0:
xc = -xc
pc.rep['s'] = 1
while xc != 0 and xc % 2 == 0:
xc >>= 1
mc += 1
g = 0
x = xc
while x >= 2:
x >>= 1
g -= 1
assert x >= 1 and x < 2, "x={}".format(x)
pc.rep['e'] = (mc - g) % 2**pc.rep['es']
pc.rep['k'] = (mc - g) // 2**pc.rep['es']
pc.rep['h'] = -g
pc.rep['f'] = xc - 2**pc.rep['h']
bits = coder.encode_posit_binary(pc.rep)
pc.rep = coder.decode_posit_binary(bits, nbits=pc.rep['nbits'], es=pc.rep['es'])
return pc
def __mul__(self, other):
if self.rep['t'] == 'c' or other.rep['t'] == 'c':
p = PCPosit() # FIXME: Use constructor to directly initialized to posit zero.
p.rep = coder.create_cinf_positrep(nbits=self.rep['nbits'], es=self.rep['es'])
return p
elif self.rep['t'] == 'z' or other.rep['t'] == 'z':
p = PCPosit() # FIXME
p.rep = coder.create_zero_positrep(nbits=self.rep['nbits'], es=self.rep['es'])
return p
assert self.rep['t'] == 'n' and other.rep['t'] == 'n'
xa = ( -1)**self.rep['s'] * ( 2**self.rep['h'] + self.rep['f'])
xb = (-1)**other.rep['s'] * (2**other.rep['h'] + other.rep['f'])
ma = 2**self.rep['es'] * self.rep['k'] + self.rep['e'] - self.rep['h']
mb = 2**other.rep['es'] * other.rep['k'] + other.rep['e'] - other.rep['h']
xc = xa * xb
mc = ma + mb
pc = PCPosit() # FIXME
pc.rep = coder.create_zero_positrep(nbits=self.rep['nbits'], es=self.rep['es'])
pc.rep['t'] = 'n'
if xc < 0:
xc = -xc
pc.rep['s'] = 1
while xc != 0 and xc % 2 == 0:
xc >>= 1
mc += 1
g = 0
x = xc
while x >= 2:
x >>= 1
g -= 1
assert x >= 1 and x < 2, "x={}".format(x)
pc.rep['e'] = (mc - g) % 2**pc.rep['es']
pc.rep['k'] = (mc - g) // 2**pc.rep['es']
pc.rep['h'] = -g
pc.rep['f'] = xc - 2**pc.rep['h']
bits = coder.encode_posit_binary(pc.rep)
pc.rep = coder.decode_posit_binary(bits, nbits=pc.rep['nbits'], es=pc.rep['es'])
return pc
def _fixedpoint_to_posit(cls, x, m, nbits=None, es=None):
assert nbits is not None
assert es is not None
if x == 0:
return PCPosit('0', nbits=nbits, es=es)
p = PCPosit(nbits=nbits, es=es)
p.rep['t'] = 'n'
p.rep['s'] = 0
if x < 0:
x = -x
p.rep['s'] = 1
assert x != 0
while x != 0 and x % 2 == 0:
x >>= 1
m += 1
g = 0
y = x
while y >= 2:
y >>= 1
g -= 1
assert y >= 1 and y < 2, "y={}".format(y)
p.rep['e'] = (m - g) % 2**es
p.rep['k'] = (m - g) // 2**es
p.rep['h'] = -g
p.rep['f'] = x - 2**p.rep['h']
bits = coder.encode_posit_binary(p.rep)
p.rep = coder.decode_posit_binary(bits, nbits=nbits, es=es)
return p
def run_posit_2op_exhaustive(self,
op_str=None,
nbits_range=None,
es_range=None):
op = None
mpop = None
if op_str == '+':
op = PCPosit.__add__
mpop = mp.mpf.__add__
elif op_str == '-':
op = PCPosit.__sub__
mpop = mp.mpf.__sub__
elif op_str == '*':
op = PCPosit.__mul__
mpop = mp.mpf.__mul__
elif op_str == '/':
op = PCPosit.__truediv__
mpop = mp.mpf.__truediv__
else:
raise NotImplementedError("op={}".format(op_str))
if nbits_range is None:
nbits_range = self.nbits_range
if es_range is None:
es_range = self.es_range
for nbits in nbits_range:
mask = bitops.create_mask(nbits)
cinf_bits = 1 << (nbits - 1)
is_special = lambda bits: bits == 0 or bits == cinf_bits
is_normal = lambda bits: not is_special(bits)
for es in es_range:
for abits in range(2**nbits):
for bbits in range(2**nbits):
a = PCPosit(abits, nbits=nbits, es=es, mode='bits')
b = PCPosit(bbits, nbits=nbits, es=es, mode='bits')
c = op(a, b)
cbits = coder.encode_posit_binary(c.rep)
test_info = {
'nbits': nbits,
'es': es,
'a': str(a),
'b': str(b),
'c': str(c),
'abits': abits,
'bbits': bbits,
'cbits': cbits,
'arep': a.rep,
'brep': b.rep,
'crep': c.rep,
}
if is_normal(abits) and is_normal(
bbits) and cbits == 0:
self.assertTrue(op_str in ['+', '-'])
if op_str == '+':
self.assertEqual(abits, -bbits & mask)
else: # '-'
self.assertEqual(abits, bbits)
elif is_normal(abits) and is_normal(bbits):
self.assertNotEqual(cbits, 0)
self.assertNotEqual(cbits, cinf_bits)
amp = mp.mpf(
eval(coder.positrep_to_rational_str(a.rep)))
bmp = mp.mpf(
eval(coder.positrep_to_rational_str(b.rep)))
c2mp = mpop(amp, bmp)
c0bits = (cbits - 1) & mask
while c0bits == 0 or c0bits == cinf_bits:
c0bits = (c0bits - 1) & mask
c1bits = (cbits + 1) & mask
while c1bits == 0 or c1bits == cinf_bits:
c1bits = (c1bits + 1) & mask
c0 = PCPosit(c0bits,
nbits=nbits,
es=es,
mode='bits')
c1 = PCPosit(c1bits,
nbits=nbits,
es=es,
mode='bits')
test_info['c0'] = str(c0)
test_info['c1'] = str(c1)
test_info['c0bits'] = c0bits
test_info['c1bits'] = c1bits
test_info['c0rep'] = c0.rep
test_info['c1rep'] = c1.rep
rcmp = mp.mpf(
eval(coder.positrep_to_rational_str(c.rep)))
cratiodiffmp = mp.fabs(mp.log(
rcmp / c2mp)) if c2mp != 0 else mp.fabs(rcmp -
c2mp)
cabsdiffmp = mp.fabs(rcmp - c2mp)
c0mp = mp.mpf(
eval(coder.positrep_to_rational_str(c0.rep)))
c0ratiodiffmp = mp.fabs(mp.log(
c0mp / c2mp)) if c2mp != 0 else mp.fabs(c0mp -
c2mp)
c0absdiffmp = mp.fabs(c0mp - c2mp)
self.assertTrue(
cratiodiffmp <= c0ratiodiffmp
or cabsdiffmp <= c0absdiffmp, test_info)
c1mp = mp.mpf(
eval(coder.positrep_to_rational_str(c1.rep)))
c1ratiodiffmp = mp.fabs(mp.log(
c1mp / c2mp)) if c2mp != 0 else mp.fabs(c1mp -
c2mp)
c1absdiffmp = mp.fabs(c1mp - c2mp)
self.assertTrue(
cratiodiffmp <= c1ratiodiffmp
or cabsdiffmp <= c1absdiffmp, test_info)
elif abits == cinf_bits:
self.assertTrue(op_str in ['+', '-', '*', '/'])
self.assertEqual(cbits, cinf_bits)
elif abits != cinf_bits and bbits == cinf_bits:
self.assertTrue(op_str in ['+', '-', '*', '/'])
if op_str == '/':
self.assertEqual(cbits, 0)
else:
self.assertEqual(cbits, cinf_bits)
elif abits == 0 and bbits == 0:
self.assertTrue(op_str in ['+', '-', '*', '/'])
if op_str == '/':
self.assertEqual(cbits, cinf_bits)
else:
self.assertEqual(cbits, 0)
elif is_normal(abits) and bbits == 0:
if op_str == '+' or op_str == '-':
self.assertEqual(cbits, abits)
elif op_str == '*':
self.assertEqual(cbits, 0)
elif op_str == '/':
self.assertEqual(cbits, cinf_bits)
else:
self.assertTrue(False)
elif abits == 0 and is_normal(bbits):
self.assertTrue(op_str in ['+', '-', '*', '/'])
if op_str == '+':
self.assertEqual(cbits, bbits)
elif op_str == '-':
self.assertEqual(cbits, -bbits & mask)
else:
self.assertEqual(cbits, 0)
else:
self.assertTrue(False)
def __repr__(self):
nbits, es = self.rep['nbits'], self.rep['es']
bits = coder.encode_posit_binary(self.rep)
template = "PCPosit({}, mode='bits', nbits={}, es={})"
return template.format(hex(bits), nbits, es)
def run_posit_2op_exhaustive(self,
op_str=None,
nbits_range=None,
es_range=None):
op = None
mpop = None
if op_str == '+':
op = PCPosit.__add__
mpop = mp.mpf.__add__
elif op_str == '-':
op = PCPosit.__sub__
mpop = mp.mpf.__sub__
elif op_str == '*':
op = PCPosit.__mul__
mpop = mp.mpf.__mul__
elif op_str == '/':
op = PCPosit.__truediv__
mpop = mp.mpf.__truediv__
else:
raise NotImplementedError("op={}".format(op_str))
for nbits in nbits_range:
mask = bitops.create_mask(nbits)
for es in es_range:
for abits in range(2**nbits):
for bbits in range(2**nbits):
a = PCPosit(abits, nbits=nbits, es=es, mode='bits')
b = PCPosit(bbits, nbits=nbits, es=es, mode='bits')
c = op(a, b)
if a.rep['t'] == 'n' and b.rep['t'] == 'n':
amp = mp.mpf(
eval(coder.positrep_to_rational_str(a.rep)))
bmp = mp.mpf(
eval(coder.positrep_to_rational_str(b.rep)))
c2mp = mpop(amp, bmp)
c0 = PCPosit((bbits - 1) & mask,
nbits=nbits,
es=es,
mode='bits')
c1 = PCPosit((bbits + 1) & mask,
nbits=nbits,
es=es,
mode='bits')
cbits = coder.encode_posit_binary(c.rep)
roundedc = coder.decode_posit_binary(cbits,
nbits=nbits,
es=es)
rcmp = mp.mpf(
eval(coder.positrep_to_rational_str(roundedc)))
cratiodiffmp = mp.fabs(mp.log(
rcmp / c2mp)) if c2mp != 0 else mp.fabs(rcmp -
c2mp)
cabsdiffmp = mp.fabs(rcmp - c2mp)
if c0.rep['t'] != 'c':
c0mp = mp.mpf(
eval(coder.positrep_to_rational_str(
c0.rep)))
c0ratiodiffmp = mp.fabs(mp.log(
c0mp /
c2mp)) if c2mp != 0 else mp.fabs(c0mp -
c2mp)
c0absdiffmp = mp.fabs(c0mp - c2mp)
self.assertTrue(cratiodiffmp <= c0ratiodiffmp
or cabsdiffmp <= c0absdiffmp)
if c1.rep['t'] != 'c':
c1mp = mp.mpf(
eval(coder.positrep_to_rational_str(
c1.rep)))
c1ratiodiffmp = mp.fabs(mp.log(
c1mp /
c2mp)) if c2mp != 0 else mp.fabs(c1mp -
c2mp)
c1absdiffmp = mp.fabs(c1mp - c2mp)
self.assertTrue(cratiodiffmp <= c1ratiodiffmp
or cabsdiffmp <= c1absdiffmp)