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"""
Packing and unpacking of floats in the IEEE 32-bit and 64-bit formats.
"""
import math
from rpython.rlib import rarithmetic, rfloat, objectmodel, jit
from rpython.rtyper.lltypesystem.rffi import r_ulonglong, r_longlong, LONGLONG, ULONGLONG, cast
from rpython.rlib.longlong2float import longlong2float, float2longlong
def round_to_nearest(x):
"""Python 3 style round: round a float x to the nearest int, but
unlike the builtin Python 2.x round function:
- return an int, not a float
- do round-half-to-even, not round-half-away-from-zero.
We assume that x is finite and nonnegative; expect wrong results
if you use this for negative x.
"""
int_part = r_ulonglong(x)
frac_part = x - int_part
if frac_part > 0.5 or frac_part == 0.5 and int_part & 1:
int_part += 1
return int_part
def float_unpack(Q, size):
"""Convert a 16-bit, 32-bit, or 64-bit integer created
by float_pack into a Python float."""
if size == 8:
MIN_EXP = -1021 # = sys.float_info.min_exp
MAX_EXP = 1024 # = sys.float_info.max_exp
MANT_DIG = 53 # = sys.float_info.mant_dig
BITS = 64
elif size == 4:
MIN_EXP = -125 # C's FLT_MIN_EXP
MAX_EXP = 128 # FLT_MAX_EXP
MANT_DIG = 24 # FLT_MANT_DIG
BITS = 32
elif size == 2:
MIN_EXP = -13
MAX_EXP = 16
MANT_DIG = 11
BITS = 16
else:
raise ValueError("invalid size value")
if not objectmodel.we_are_translated():
# This tests generates wrong code when translated:
# with gcc, shifting a 64bit int by 64 bits does
# not change the value.
if Q >> BITS:
raise ValueError("input '%r' out of range '%r'" % (Q, Q>>BITS))
# extract pieces with assumed 1.mant values
one = r_ulonglong(1)
sign = rarithmetic.intmask(Q >> BITS - 1)
exp = rarithmetic.intmask((Q & ((one << BITS - 1) - (one << MANT_DIG - 1))) >> MANT_DIG - 1)
mant = Q & ((one << MANT_DIG - 1) - 1)
if exp == MAX_EXP - MIN_EXP + 2:
# nan or infinity
if mant == 0:
result = rfloat.INFINITY
else:
# preserve at most 52 bits of mant value, but pad w/zeros
exp = r_ulonglong(0x7ff) << 52
sign = r_ulonglong(sign) << 63
if MANT_DIG < 53:
mant = r_ulonglong(mant) << (53 - MANT_DIG)
if mant == 0:
result = rfloat.NAN
else:
uint = exp | mant | sign
result = longlong2float(cast(LONGLONG, uint))
return result
elif exp == 0:
# subnormal or zero
result = math.ldexp(mant, MIN_EXP - MANT_DIG)
else:
# normal: add implicit one value
mant += one << MANT_DIG - 1
result = math.ldexp(mant, exp + MIN_EXP - MANT_DIG - 1)
return -result if sign else result
def float_unpack80(QQ, size):
'''Unpack a (mant, exp) tuple of r_ulonglong in 80-bit extended format
into a python float (a double)
'''
if size == 10 or size == 12 or size == 16:
MIN_EXP = -16381
MAX_EXP = 16384
MANT_DIG = 64
TOP_BITS = 80 - 64
else:
raise ValueError("invalid size value")
if len(QQ) != 2:
raise ValueError("QQ must be two 64 bit uints")
if not objectmodel.we_are_translated():
# This tests generates wrong code when translated:
# with gcc, shifting a 64bit int by 64 bits does
# not change the value.
if QQ[1] >> TOP_BITS:
raise ValueError("input '%r' out of range '%r'" % (QQ, QQ[1]>>TOP_BITS))
# extract pieces with explicit one in MANT_DIG
one = r_ulonglong(1)
sign = rarithmetic.intmask(QQ[1] >> TOP_BITS - 1)
exp = rarithmetic.intmask((QQ[1] & ((one << TOP_BITS - 1) - 1)))
mant = QQ[0]
if exp == MAX_EXP - MIN_EXP + 2:
# nan or infinity
if mant == 0:
result = rfloat.INFINITY
else:
exp = r_ulonglong(0x7ff) << 52
mant = r_ulonglong(mant) >> size + 1
if mant == 0:
result = rfloat.NAN
else:
uint = exp | r_ulonglong(mant) | r_ulonglong(sign)
result = longlong2float(cast(LONGLONG, uint))
return result
else:
# normal
result = math.ldexp(mant, exp + MIN_EXP - MANT_DIG - 1)
return -result if sign else result
def float_pack(x, size):
"""Convert a Python float x into a 64-bit unsigned integer
with the same byte representation."""
if size == 8:
MIN_EXP = -1021 # = sys.float_info.min_exp
MAX_EXP = 1024 # = sys.float_info.max_exp
MANT_DIG = 53 # = sys.float_info.mant_dig
BITS = 64
elif size == 4:
MIN_EXP = -125 # C's FLT_MIN_EXP
MAX_EXP = 128 # FLT_MAX_EXP
MANT_DIG = 24 # FLT_MANT_DIG
BITS = 32
elif size == 2:
MIN_EXP = -13
MAX_EXP = 16
MANT_DIG = 11
BITS = 16
else:
raise ValueError("invalid size value")
sign = rfloat.copysign(1.0, x) < 0.0
if rfloat.isinf(x):
mant = r_ulonglong(0)
exp = MAX_EXP - MIN_EXP + 2
elif rfloat.isnan(x):
asint = cast(ULONGLONG, float2longlong(x))
sign = asint >> 63
# shift off lower bits, perhaps losing data
mant = asint & ((r_ulonglong(1) << 52) - 1)
if MANT_DIG < 53:
mant = mant >> (53 - MANT_DIG)
if mant == 0:
mant = r_ulonglong(1) << (MANT_DIG - 1) - 1
exp = MAX_EXP - MIN_EXP + 2
elif x == 0.0:
mant = r_ulonglong(0)
exp = 0
else:
m, e = math.frexp(abs(x)) # abs(x) == m * 2**e
exp = e - (MIN_EXP - 1)
if exp > 0:
# Normal case.
mant = round_to_nearest(m * (r_ulonglong(1) << MANT_DIG))
mant -= r_ulonglong(1) << MANT_DIG - 1
else:
# Subnormal case.
if exp + MANT_DIG - 1 >= 0:
mant = round_to_nearest(m * (r_ulonglong(1) << exp + MANT_DIG - 1))
else:
mant = r_ulonglong(0)
exp = 0
# Special case: rounding produced a MANT_DIG-bit mantissa.
if not objectmodel.we_are_translated():
assert 0 <= mant <= 1 << MANT_DIG - 1
if mant == r_ulonglong(1) << MANT_DIG - 1:
mant = r_ulonglong(0)
exp += 1
# Raise on overflow (in some circumstances, may want to return
# infinity instead).
if exp >= MAX_EXP - MIN_EXP + 2:
raise OverflowError("float too large to pack in this format")
# check constraints
if not objectmodel.we_are_translated():
assert 0 <= mant <= (1 << MANT_DIG) - 1
assert 0 <= exp <= MAX_EXP - MIN_EXP + 2
assert 0 <= sign <= 1
exp = r_ulonglong(exp)
sign = r_ulonglong(sign)
return ((sign << BITS - 1) | (exp << MANT_DIG - 1)) | mant
def float_pack80(x, size):
"""Convert a Python float or longfloat x into two 64-bit unsigned integers
with 80 bit extended representation."""
x = float(x) # longfloat not really supported
if size == 10 or size == 12 or size == 16:
MIN_EXP = -16381
MAX_EXP = 16384
MANT_DIG = 64
BITS = 80
else:
raise ValueError("invalid size value")
sign = rfloat.copysign(1.0, x) < 0.0
if rfloat.isinf(x):
mant = r_ulonglong(0)
exp = MAX_EXP - MIN_EXP + 2
elif rfloat.isnan(x): # rfloat.isnan(x):
asint = cast(ULONGLONG, float2longlong(x))
mant = asint & ((r_ulonglong(1) << 51) - 1)
if mant == 0:
mant = r_ulonglong(1) << (MANT_DIG - 1) - 1
sign = asint < 0
exp = MAX_EXP - MIN_EXP + 2
elif x == 0.0:
mant = r_ulonglong(0)
exp = 0
else:
m, e = math.frexp(abs(x)) # abs(x) == m * 2**e
exp = e - (MIN_EXP - 1)
if exp > 0:
# Normal case. Avoid uint64 overflow by using MANT_DIG-1
mant = round_to_nearest(m * (r_ulonglong(1) << MANT_DIG - 1))
else:
# Subnormal case.
if exp + MANT_DIG - 1 >= 0:
mant = round_to_nearest(m * (r_ulonglong(1) << exp + MANT_DIG - 1))
else:
mant = r_ulonglong(0)
exp = 0
# Special case: rounding produced a MANT_DIG-bit mantissa.
if mant == r_ulonglong(1) << MANT_DIG - 1:
mant = r_ulonglong(0)
exp += 1
# Raise on overflow (in some circumstances, may want to return
# infinity instead).
if exp >= MAX_EXP - MIN_EXP + 2:
raise OverflowError("float too large to pack in this format")
mant = mant << 1
# check constraints
if not objectmodel.we_are_translated():
assert 0 <= mant <= (1 << MANT_DIG) - 1
assert 0 <= exp <= MAX_EXP - MIN_EXP + 2
assert 0 <= sign <= 1
exp = r_ulonglong(exp)
sign = r_ulonglong(sign)
return (mant, (sign << BITS - MANT_DIG - 1) | exp)
@jit.unroll_safe
def pack_float(result, x, size, be):
l = []
unsigned = float_pack(x, size)
for i in range(size):
l.append(chr((unsigned >> (i * 8)) & 0xFF))
if be:
l.reverse()
result.append("".join(l))
@jit.unroll_safe
def pack_float80(result, x, size, be):
l = []
unsigned = float_pack80(x, size)
for i in range(8):
l.append(chr((unsigned[0] >> (i * 8)) & 0xFF))
for i in range(2):
l.append(chr((unsigned[1] >> (i * 8)) & 0xFF))
for i in range(size - 10):
l.append('\x00')
if be:
l.reverse()
result.append("".join(l))
@jit.unroll_safe
def unpack_float(s, be):
unsigned = r_ulonglong(0)
for i in range(min(len(s), 8)):
c = ord(s[-i - 1 if be else i])
unsigned |= r_ulonglong(c) << (i * 8)
return float_unpack(unsigned, len(s))
@jit.unroll_safe
def unpack_float80(s, be):
QQ = [r_ulonglong(0), r_ulonglong(0)]
for i in range(8):
c = ord(s[-i - 1 if be else i])
QQ[0] |= r_ulonglong(c) << (i * 8)
for i in range(8, 10):
c = ord(s[-i - 1 if be else i])
QQ[1] |= r_ulonglong(c) << ((i - 8) * 8)
return float_unpack80(QQ, len(s))
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