def _write_float(f, x):
import math
if x < 0:
sign = 32768
x = x * -1
else:
sign = 0
if x == 0:
expon = 0
himant = 0
lomant = 0
else:
fmant, expon = math.frexp(x)
if expon > 16384 or fmant >= 1 or fmant != fmant:
expon = sign | 32767
himant = 0
lomant = 0
else:
expon = expon + 16382
if expon < 0:
fmant = math.ldexp(fmant, expon)
expon = 0
expon = expon | sign
fmant = math.ldexp(fmant, 32)
fsmant = math.floor(fmant)
himant = long(fsmant)
fmant = math.ldexp(fmant - fsmant, 32)
fsmant = math.floor(fmant)
lomant = long(fsmant)
_write_ushort(f, expon)
_write_ulong(f, himant)
_write_ulong(f, lomant)
def set_ref(self, refval):
x = self.teach()
m,e = math.frexp(refval / 5e-9)
if m < 0:
s = 0x80
m = -m
else:
s = 0
m = math.ldexp(m, -1)
for i in range(14,20):
m = math.ldexp(m, 8)
h = int(m)
m -= h
x[i] = s | h
s = 0
e -= 31
if e < 0:
e += 256
x[20] = e
y=bytearray("LN")
for i in x:
if i == 10 or i == 27 or i == 13 or i == 43:
y.append(27)
y.append(i)
d.wr(y)
def __init__(self, pj, lo):
super(float70, self).__init__(pj, lo, lo + 7)
x = pj.m.rd(self.lo)
if x & 0x80:
s = -1
x ^= 0x80
else:
s = 1
o = -7
m = 0
for i in range(6):
m += math.ldexp(x, o)
o -= 8
x = pj.m.rd(self.lo + 1 + i)
e = pj.m.s8(self.lo + 6)
self.lcmt = "m %g e %g" % (m, e)
v = s * math.ldexp(m, e)
self.val = v
x = "%.9e" % v
if x.find(".") == -1 and x.find("e") == -1:
x += "."
self.fmt = x
self.typ = ".FLOAT"
self.compact = False
pj.set_label(lo, "c_" + x)
print(self, self.fmt)
def sqrt(x):
sqrt_special = [
[inf-infj, 0-infj, 0-infj, infj, infj, inf+infj, nan+infj],
[inf-infj, None, None, None, None, inf+infj, nan+nanj],
[inf-infj, None, 0-0j, 0+0j, None, inf+infj, nan+nanj],
[inf-infj, None, 0-0j, 0+0j, None, inf+infj, nan+nanj],
[inf-infj, None, None, None, None, inf+infj, nan+nanj],
[inf-infj, complex(float("inf"), -0.0), complex(float("inf"), -0.0), inf, inf, inf+infj, inf+nanj],
[inf-infj, nan+nanj, nan+nanj, nan+nanj, nan+nanj, inf+infj, nan+nanj]
]
z = _make_complex(x)
if math.isinf(z.real) or math.isinf(z.imag):
return sqrt_special[_special_type(z.real)][_special_type(z.imag)]
abs_x, abs_y = abs(z.real), abs(z.imag)
if abs_x < _DBL_MIN and abs_y < _DBL_MIN:
if abs_x > 0 or abs_y > 0:
abs_x = math.ldexp(abs_x, _CM_SCALE_UP)
s = math.ldexp(math.sqrt(abs_x +
math.hypot(abs_x,
math.ldexp(abs_y,
_CM_SCALE_UP))),
_CM_SCALE_DOWN)
else:
return complex(0, z.imag)
else:
abs_x /= 8
s = 2 * math.sqrt(abs_x + math.hypot(abs_x, abs_y/8))
if z.real >= 0:
return complex(s, math.copysign(abs_y/(2*s), z.imag))
return complex(abs_y/(2*s), math.copysign(s, z.imag))
def to_float(s, strict=False):
"""
Convert a raw mpf to a Python float. The result is exact if the
bitcount of s is <= 53 and no underflow/overflow occurs.
If the number is too large or too small to represent as a regular
float, it will be converted to inf or 0.0. Setting strict=True
forces an OverflowError to be raised instead.
"""
sign, man, exp, bc = s
if not man:
if s == fzero: return 0.0
if s == finf: return math_float_inf
if s == fninf: return -math_float_inf
return math_float_inf/math_float_inf
if sign:
man = -man
try:
if bc < 100:
return math.ldexp(man, exp)
# Try resizing the mantissa. Overflow may still happen here.
n = bc - 53
m = man >> n
return math.ldexp(m, exp + n)
except OverflowError:
if strict:
raise
# Overflow to infinity
if exp + bc > 0:
if sign:
return -math_float_inf
else:
return math_float_inf
# Underflow to zero
return 0.0
def test_705836(self):
# SF bug 705836. "<f" and ">f" had a severe rounding bug, where a carry
# from the low-order discarded bits could propagate into the exponent
# field, causing the result to be wrong by a factor of 2.
for base in range(1, 33):
# smaller <- largest representable float less than base.
delta = 0.5
while base - delta / 2.0 != base:
delta /= 2.0
smaller = base - delta
# Packing this rounds away a solid string of trailing 1 bits.
packed = struct.pack("<f", smaller)
unpacked = struct.unpack("<f", packed)[0]
# This failed at base = 2, 4, and 32, with unpacked = 1, 2, and
# 16, respectively.
self.assertEqual(base, unpacked)
bigpacked = struct.pack(">f", smaller)
self.assertEqual(bigpacked, string_reverse(packed))
unpacked = struct.unpack(">f", bigpacked)[0]
self.assertEqual(base, unpacked)
# Largest finite IEEE single.
big = (1 << 24) - 1
big = math.ldexp(big, 127 - 23)
packed = struct.pack(">f", big)
unpacked = struct.unpack(">f", packed)[0]
self.assertEqual(big, unpacked)
# The same, but tack on a 1 bit so it rounds up to infinity.
big = (1 << 25) - 1
big = math.ldexp(big, 127 - 24)
self.assertRaises(OverflowError, struct.pack, ">f", big)
def ldexp(x, y):
# The code below is inspired by uncertainties.wrap(). It is
# simpler because only 1 argument is given, and there is no
# delegation to other functions involved (as for __mul__, etc.).
# Another approach would be to add an additional argument to
# uncertainties.wrap() so that some arguments are automatically
# considered as constants.
aff_func = to_affine_scalar(x) # y must be an integer, for math.ldexp
if aff_func.derivatives:
factor = 2**y
return AffineScalarFunc(
math.ldexp(aff_func.nominal_value, y),
# Chain rule:
dict([(var, factor*deriv)
for (var, deriv) in aff_func.derivatives.iteritems()]))
else:
# This function was not called with an AffineScalarFunc
# argument: there is no need to return numbers with uncertainties:
# aff_func.nominal_value is not passed instead of x, because
# we do not have to care about the type of the return value of
# math.ldexp, this way (aff_func.nominal_value might be the
# value of x coerced to a difference type [int->float, for
# instance]):
return math.ldexp(x, y)
def _write_float(f, x): import math if x < 0: sign = 0x8000 x = x * -1 else: sign = 0 if x == 0: expon = 0 himant = 0 lomant = 0 else: fmant, expon = math.frexp(x) if expon > 16384 or fmant >= 1: # Infinity or NaN expon = sign|0x7FFF himant = 0 lomant = 0 else: # Finite expon = expon + 16382 if expon < 0: # denormalized fmant = math.ldexp(fmant, expon) expon = 0 expon = expon | sign fmant = math.ldexp(fmant, 32) fsmant = math.floor(fmant) himant = long(fsmant) fmant = math.ldexp(fmant - fsmant, 32) fsmant = math.floor(fmant) lomant = long(fsmant) _write_short(f, expon) _write_long(f, himant) _write_long(f, lomant)
def msum(iterable):
"""Full precision summation. Compute sum(iterable) without any
intermediate accumulation of error. Based on the 'lsum' function
at http://code.activestate.com/recipes/393090/
"""
tmant, texp = 0, 0
for x in iterable:
mant, exp = math.frexp(x)
mant, exp = int(math.ldexp(mant, mant_dig)), exp - mant_dig
if texp > exp:
tmant <<= texp-exp
texp = exp
else:
mant <<= exp-texp
tmant += mant
# Round tmant * 2**texp to a float. The original recipe
# used float(str(tmant)) * 2.0**texp for this, but that's
# a little unsafe because str -> float conversion can't be
# relied upon to do correct rounding on all platforms.
tail = max(len(bin(abs(tmant)))-2 - mant_dig, etiny - texp)
if tail > 0:
h = 1 << (tail-1)
tmant = tmant // (2*h) + bool(tmant & h and tmant & 3*h-1)
texp += tail
return math.ldexp(tmant, texp)
def get_heavy_correction(beta, heavytype):
m = get_heavyq_mass(beta, heavytype)
def prop(p):
W = 1-np.cos(p)
Weplus = W + 1./2 + np.sqrt(W + 1./4)
Wemins = W + 1./2 - np.sqrt(W + 1./4)
num = np.sin(p) * np.sin(p*t) + m*(1-Wemins) * np.cos(p*t)
#num = 2*np.sin(p) * np.sin(p*t) #+ m*(1-Wemins) * np.cos(p*t)
den = - (1-Weplus) + m**2*(1-Wemins)
return num/den /(2*np.pi)
Q = ((1+m**2)/(1-m**2))**2
T = (1-Q)/2 + np.sqrt(3*Q+Q**2)/2
W0 = (1+Q)/2 - np.sqrt(3*Q+Q**2)/2
m1 = np.log(T+np.sqrt(T**2-1))
K = 2.0/((1-m**2)*(1.0+np.sqrt(Q/(1.0+4*W0))))
Nt = 65
it = np.arange(Nt)
Ct = np.empty(Nt)
R = {}
minDouble = math.ldexp(1.0, -1022)
smallEpsilon = math.ldexp(1.0, -1074)
epsilon = math.ldexp(1.0, -53)
for t in it:
Ct[t], err = integrate.quad(prop,-np.pi,np.pi)
if Ct[t] < err or (K*np.exp(-m1*t)) < err:
R[t] = 1.
else:
R[t] = Ct[t] / (K*np.exp(-m1*t))
return R
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 c_log(x, y):
# The usual formula for the real part is log(hypot(z.real, z.imag)).
# There are four situations where this formula is potentially
# problematic:
#
# (1) the absolute value of z is subnormal. Then hypot is subnormal,
# so has fewer than the usual number of bits of accuracy, hence may
# have large relative error. This then gives a large absolute error
# in the log. This can be solved by rescaling z by a suitable power
# of 2.
#
# (2) the absolute value of z is greater than DBL_MAX (e.g. when both
# z.real and z.imag are within a factor of 1/sqrt(2) of DBL_MAX)
# Again, rescaling solves this.
#
# (3) the absolute value of z is close to 1. In this case it's
# difficult to achieve good accuracy, at least in part because a
# change of 1ulp in the real or imaginary part of z can result in a
# change of billions of ulps in the correctly rounded answer.
#
# (4) z = 0. The simplest thing to do here is to call the
# floating-point log with an argument of 0, and let its behaviour
# (returning -infinity, signaling a floating-point exception, setting
# errno, or whatever) determine that of c_log. So the usual formula
# is fine here.
# XXX the following two lines seem unnecessary at least on Linux;
# the tests pass fine without them
if not isfinite(x) or not isfinite(y):
return log_special_values[special_type(x)][special_type(y)]
ax = fabs(x)
ay = fabs(y)
if ax > CM_LARGE_DOUBLE or ay > CM_LARGE_DOUBLE:
real = math.log(math.hypot(ax/2., ay/2.)) + M_LN2
elif ax < DBL_MIN and ay < DBL_MIN:
if ax > 0. or ay > 0.:
# catch cases where hypot(ax, ay) is subnormal
real = math.log(math.hypot(math.ldexp(ax, DBL_MANT_DIG),
math.ldexp(ay, DBL_MANT_DIG)))
real -= DBL_MANT_DIG*M_LN2
else:
# log(+/-0. +/- 0i)
raise ValueError("math domain error")
#real = -INF
#imag = atan2(y, x)
else:
h = math.hypot(ax, ay)
if 0.71 <= h and h <= 1.73:
am = max(ax, ay)
an = min(ax, ay)
real = log1p((am-1)*(am+1) + an*an) / 2.
else:
real = math.log(h)
imag = math.atan2(y, x)
return (real, imag)
def sqrt(x):
"""
Return the square root of x.
This has the same branch cut as log().
"""
# Method: use symmetries to reduce to the case when x = z.real and y
# = z.imag are nonnegative. Then the real part of the result is
# given by
#
# s = sqrt((x + hypot(x, y))/2)
#
# and the imaginary part is
#
# d = (y/2)/s
#
# If either x or y is very large then there's a risk of overflow in
# computation of the expression x + hypot(x, y). We can avoid this
# by rewriting the formula for s as:
#
# s = 2*sqrt(x/8 + hypot(x/8, y/8))
#
# This costs us two extra multiplications/divisions, but avoids the
# overhead of checking for x and y large.
# If both x and y are subnormal then hypot(x, y) may also be
# subnormal, so will lack full precision. We solve this by rescaling
# x and y by a sufficiently large power of 2 to ensure that x and y
# are normal.
s, d, ax, ay = .0, .0, math.fabs(x.real), math.fabs(x.imag)
ret = _SPECIAL_VALUE(x, _sqrt_special_values)
if ret is not None:
return ret
if x.real == .0 and x.imag == .0:
_real = .0
_imag = x.imag
return complex(_real,_imag)
if ax < sys.float_info.min and ay < sys.float_info.min and (ax > 0. or ay > 0.):
#here we catch cases where hypot(ax, ay) is subnormal
ax = math.ldexp(ax, _CM_SCALE_UP);
s = math.ldexp(math.sqrt(ax + math.hypot(ax, math.ldexp(ay, _CM_SCALE_UP))),_CM_SCALE_DOWN)
else:
ax /= 8.0;
s = 2.0*math.sqrt(ax + math.hypot(ax, ay/8.0));
d = ay/(2.0*s)
if x.real >= .0:
_real = s;
_imag = math.copysign(d, x.imag)
else:
_real = d;
_imag = math.copysign(s, x.imag)
return complex(_real,_imag)
def TakeData():
t0 = time.clock();
result = "Test started at " + str(datetime.now()) + "\n";
LIA1.write("STRT");
#LIA1.write("STRD"); #start scan after 0.5 sec
t = time.clock() - t0;
result += "Scan started at t = " + str(t) + "\n";
time.sleep(0.5); #32s max
LIA1.write("PAUS"); #pause
t = time.clock() - t0;
result += "Scan ended at t = " + str(t) + "\n";
LIA1.ask("SPTS ?");
num = LIA1.ask("SPTS ?"); #number of points
result += "There are " + num + " points\n";
t = time.clock() - t0;
result += "Transfer started at t = " + str(t) + "\n";
#LIA1.term_chars = "\0";
CH1 = LIA1.ask_for_values("TRCA ? 1,0," + num);
CH2 = LIA1.ask_for_values("TRCA ? 2,0," + num);
LIA1.values_format = visa.single;
BIN1 = LIA1.ask("TRCL ? 1,0," + num);
BIN2 = LIA1.ask("TRCL ? 2,0," + num);
t = time.clock() - t0;
result += "Transfer ended at t = " + str(t) + "\n";
BIN1 = list(BIN1);
BIN2 = list(BIN2);
CONV1 = list(CH1);
CONV2 = list(CH2);
if len(BIN1) != 4*int(num) or len(BIN2) != 4*int(num):
print "ERROR in num!" + num + "\t" + str(len(BIN1));
for i in range(0,int(num)):
mantissa = ord(BIN1[4*i+1])*256+ord(BIN1[4*i]);
if mantissa >= 32768:
mantissa -= 65536;
CONV1[i] = math.ldexp(mantissa, ord(BIN1[4*i+2])-124);
mantissa = ord(BIN2[4*i+1])*256+ord(BIN2[4*i]);
if mantissa >= 32768:
mantissa -= 65536;
CONV2[i] = math.ldexp(mantissa, ord(BIN2[4*i+2])-124);
show = str(CH1[i]) + "\t" + str(CONV1[i]) + \
"\t" + str(CH2[i]) + "\t" + str(CONV2[i]);
print show;
result += show + "\n";
t = time.clock() - t0;
result += "Evrything ended at t = " + str(t) + "\n";
output.write(result);
def __float__(s):
"""Convert s to a Python float. OverflowError will be raised
if the magnitude of s is too large."""
try:
return math.ldexp(s.man, s.exp)
# Handle case when mantissa has too many bits (will still
# overflow if exp is too large)
except OverflowError:
n = s.bc - 64
m = s.man >> n
return math.ldexp(m, s.exp + n)
def getBoundingBox(x, y, z, dimension, projection): #pixel location of the center of the metatile x0 = x * TILE_SIZE y0 = (y + dimension) * TILE_SIZE x1 = (x + dimension) * TILE_SIZE y1 = y * TILE_SIZE #from pixels to WGS 84, comes back as (lng, lat) ul = projection.from_pixels((x0, y0), z) lr = projection.from_pixels((x1, y1), z) #using ldexp for performant floating point division by 2 to get center pixel location center = (int(math.ldexp(x0 + x1, -1) + .5) , int(math.ldexp(y0 + y1, -1) + .5)) center = projection.from_pixels(center, z) return ((ul[1], ul[0]), (lr[1], lr[0])), (center[1], center[0])
def c_sqrt(x, y):
'''
Method: use symmetries to reduce to the case when x = z.real and y
= z.imag are nonnegative. Then the real part of the result is
given by
s = sqrt((x + hypot(x, y))/2)
and the imaginary part is
d = (y/2)/s
If either x or y is very large then there's a risk of overflow in
computation of the expression x + hypot(x, y). We can avoid this
by rewriting the formula for s as:
s = 2*sqrt(x/8 + hypot(x/8, y/8))
This costs us two extra multiplications/divisions, but avoids the
overhead of checking for x and y large.
If both x and y are subnormal then hypot(x, y) may also be
subnormal, so will lack full precision. We solve this by rescaling
x and y by a sufficiently large power of 2 to ensure that x and y
are normal.
'''
if not isfinite(x) or not isfinite(y):
return sqrt_special_values[special_type(x)][special_type(y)]
if x == 0. and y == 0.:
return (0., y)
ax = fabs(x)
ay = fabs(y)
if ax < DBL_MIN and ay < DBL_MIN and (ax > 0. or ay > 0.):
# here we catch cases where hypot(ax, ay) is subnormal
ax = math.ldexp(ax, CM_SCALE_UP)
ay1= math.ldexp(ay, CM_SCALE_UP)
s = math.ldexp(math.sqrt(ax + math.hypot(ax, ay1)),
CM_SCALE_DOWN)
else:
ax /= 8.
s = 2.*math.sqrt(ax + math.hypot(ax, ay/8.))
d = ay/(2.*s)
if x >= 0.:
return (s, copysign(d, y))
else:
return (d, copysign(s, y))
def read_float(s, length):
t = read(s, length)
i = byte2num(t)
if length == 4:
f = ldexp((i & 0x7fffff) + (1 << 23), (i >> 23 & 0xff) - 150)
if i & (1 << 31):
f = -f
elif length == 8:
f = ldexp((i & ((1 << 52) - 1)) + (1 << 52), (i >> 52 & 0x7ff) - 1075)
if i & (1 << 63):
f = -f
else:
raise SyntaxError
return f
def calc(self, args, irc):
'''(calc <math expression>) -- Lifted from supybot.
'''
expr = ' '.join(args)
try:
expr = str(expr)
except UnicodeEncodeError:
return 'No Unicode allowed in math expressions.'
if self.forbidden.match(expr):
return 'No underscores or brackets allowed in math expressions.'
if 'lambda' in expr:
return 'lambda is not allowed in math expressions.'
expr = self._mathRe.sub(Math.handleMatch, expr.lower())
try:
log.msg('evaluating %q from %s', expr, irc.sender)
x = complex(eval(expr, self._mathSafeEnv, self._mathSafeEnv))
return self._complexToString(x)
except OverflowError:
maxFloat = math.ldexp(0.9999999999999999, 1024)
return 'The answer exceeded %s or so.' % maxFloat
except TypeError:
return 'Something in there wasn\'t a valid number.'
except NameError as e:
return '%s is not a defined function.' % str(e).split()[1]
except Exception as e:
return str(e)
def calc(self, irc, msg, args, text):
"""<math expression>
Returns the value of the evaluated <math expression>. The syntax is
Python syntax; the type of arithmetic is floating point. Floating
point arithmetic is used in order to prevent a user from being able to
crash to the bot with something like '10**10**10**10'. One consequence
is that large values such as '10**24' might not be exact.
"""
try:
text = str(text)
except UnicodeEncodeError:
irc.error(_("There's no reason you should have fancy non-ASCII "
"characters in your mathematical expression. "
"Please remove them."))
return
if self._calc_match_forbidden_chars.match(text):
irc.error(_('There\'s really no reason why you should have '
'underscores or brackets in your mathematical '
'expression. Please remove them.'))
return
text = self._calc_remover(text)
if 'lambda' in text:
irc.error(_('You can\'t use lambda in this command.'))
return
text = text.lower()
def handleMatch(m):
s = m.group(1)
if s.startswith('0x'):
i = int(s, 16)
elif s.startswith('0') and '.' not in s:
try:
i = int(s, 8)
except ValueError:
i = int(s)
else:
i = float(s)
x = complex(i)
if x.imag == 0:
x = x.real
# Need to use string-formatting here instead of str() because
# use of str() on large numbers loses information:
# str(float(33333333333333)) => '3.33333333333e+13'
# float('3.33333333333e+13') => 33333333333300.0
return '%.16f' % x
return str(x)
text = self._mathRe.sub(handleMatch, text)
try:
self.log.info('evaluating %q from %s', text, msg.prefix)
x = complex(eval(text, self._mathSafeEnv, self._mathSafeEnv))
irc.reply(self._complexToString(x))
except OverflowError:
maxFloat = math.ldexp(0.9999999999999999, 1024)
irc.error(_('The answer exceeded %s or so.') % maxFloat)
except TypeError:
irc.error(_('Something in there wasn\'t a valid number.'))
except NameError as e:
irc.error(_('%s is not a defined function.') % str(e).split()[1])
except Exception as e:
irc.error(str(e))
def truediv(a, b):
"""Correctly-rounded true division for integers."""
negative = a^b < 0
a, b = abs(a), abs(b)
# exceptions: division by zero, overflow
if not b:
raise ZeroDivisionError("division by zero")
if a >= DBL_MIN_OVERFLOW * b:
raise OverflowError("int/int too large to represent as a float")
# find integer d satisfying 2**(d - 1) <= a/b < 2**d
d = a.bit_length() - b.bit_length()
if d >= 0 and a >= 2**d * b or d < 0 and a * 2**-d >= b:
d += 1
# compute 2**-exp * a / b for suitable exp
exp = max(d, DBL_MIN_EXP) - DBL_MANT_DIG
a, b = a << max(-exp, 0), b << max(exp, 0)
q, r = divmod(a, b)
# round-half-to-even: fractional part is r/b, which is > 0.5 iff
# 2*r > b, and == 0.5 iff 2*r == b.
if 2*r > b or 2*r == b and q % 2 == 1:
q += 1
result = math.ldexp(float(q), exp)
return -result if negative else result
def icalc(self, irc, msg, args, text):
"""<math expression>
This is the same as the calc command except that it allows integer
math, and can thus cause the bot to suck up CPU. Hence it requires
the 'trusted' capability to use.
"""
if self._calc_match_forbidden_chars.match(text):
irc.error(
_(
"There's really no reason why you should have "
"underscores or brackets in your mathematical "
"expression. Please remove them."
)
)
return
# This removes spaces, too, but we'll leave the removal of _[] for
# safety's sake.
text = self._calc_remover(text)
if "lambda" in text:
irc.error(_("You can't use lambda in this command."))
return
text = text.replace("lambda", "")
try:
self.log.info("evaluating %q from %s", text, msg.prefix)
irc.reply(str(eval(text, self._mathEnv, self._mathEnv)))
except OverflowError:
maxFloat = math.ldexp(0.9999999999999999, 1024)
irc.error(_("The answer exceeded %s or so.") % maxFloat)
except TypeError:
irc.error(_("Something in there wasn't a valid number."))
except NameError, e:
irc.error(_("%s is not a defined function.") % str(e).split()[1])
def icalc(self, irc, msg, args, text):
"""<math expression>
This is the same as the calc command except that it allows integer
math, and can thus cause the bot to suck up CPU. Hence it requires
the 'trusted' capability to use.
"""
if text != text.translate(utils.str.chars, '_[]'):
irc.error(_('There\'s really no reason why you should have '
'underscores or brackets in your mathematical '
'expression. Please remove them.'))
return
# This removes spaces, too, but we'll leave the removal of _[] for
# safety's sake.
text = text.translate(utils.str.chars, '_[] \t')
if 'lambda' in text:
irc.error(_('You can\'t use lambda in this command.'))
return
text = text.replace('lambda', '')
try:
self.log.info('evaluating %q from %s', text, msg.prefix)
irc.reply(str(eval(text, self._mathEnv, self._mathEnv)))
except OverflowError:
maxFloat = math.ldexp(0.9999999999999999, 1024)
irc.error(_('The answer exceeded %s or so.') % maxFloat)
except TypeError:
irc.error(_('Something in there wasn\'t a valid number.'))
except NameError, e:
irc.error(_('%s is not a defined function.') % str(e).split()[1])
def PyNextAfter(x, y):
"""returns the next float after x in the direction of y if possible, else returns x"""
# if x or y is Nan, we don't do much
if IsNaN(x) or IsNaN(y):
return x
# we can't progress if x == y
if x == y:
return x
# similarly if x is infinity
if x >= infinity or x <= -infinity:
return x
# return small numbers for x very close to 0.0
if -minFloat < x < minFloat:
if y > x:
return x + smallEpsilon
else:
return x - smallEpsilon # we know x != y
# it looks like we have a normalized number
# break x down into a mantissa and exponent
m, e = math.frexp(x)
# all the special cases have been handled
if y > x:
m += epsilon
else:
m -= epsilon
return math.ldexp(m, e)
def descr_hex(self, space):
TOHEX_NBITS = rfloat.DBL_MANT_DIG + 3 - (rfloat.DBL_MANT_DIG + 2) % 4
value = self.floatval
if not isfinite(value):
return self.descr_str(space)
if value == 0.0:
if copysign(1., value) == -1.:
return space.wrap("-0x0.0p+0")
else:
return space.wrap("0x0.0p+0")
mant, exp = math.frexp(value)
shift = 1 - max(rfloat.DBL_MIN_EXP - exp, 0)
mant = math.ldexp(mant, shift)
mant = abs(mant)
exp -= shift
result = ['\0'] * ((TOHEX_NBITS - 1) // 4 + 2)
result[0] = _char_from_hex(int(mant))
mant -= int(mant)
result[1] = "."
for i in range((TOHEX_NBITS - 1) // 4):
mant *= 16.0
result[i + 2] = _char_from_hex(int(mant))
mant -= int(mant)
if exp < 0:
sign = "-"
else:
sign = "+"
exp = abs(exp)
s = ''.join(result)
if value < 0.0:
return space.wrap("-0x%sp%s%d" % (s, sign, exp))
else:
return space.wrap("0x%sp%s%d" % (s, sign, exp))
def _float_or_double(self, x, nmbits, nebits, suffix, nanfmt):
nbits = nmbits + nebits + 1
assert nbits % 32 == 0
sbit, ebits, mbits = x >> (nbits - 1), (x >> nmbits) % (1 << nebits), x % (1 << nmbits)
if ebits == (1 << nebits) - 1:
result = "NaN" if mbits else "Infinity"
if self.roundtrip and mbits:
result += nanfmt.format(x)
elif ebits == 0 and mbits == 0:
result = "0.0"
else:
ebias = (1 << (nebits - 1)) - 1
exponent = ebits - ebias - nmbits
mantissa = mbits
if ebits > 0:
mantissa += 1 << nmbits
else:
exponent += 1
if self.roundtrip:
result = "0x{:X}p{}".format(mantissa, exponent)
else:
result = repr(math.ldexp(mantissa, exponent))
return "+-"[sbit] + result + suffix
def unpack_float(data,index,size,le):
bytes = [ord(b) for b in data[index:index+size]]
if len(bytes) != size:
raise StructError,"Not enough data to unpack"
if max(bytes) == 0:
return 0.0
if le == 'big':
bytes.reverse()
if size == 4:
bias = 127
exp = 8
prec = 23
else:
bias = 1023
exp = 11
prec = 52
mantissa = long(bytes[size-2] & (2**(15-exp)-1))
for b in bytes[size-3::-1]:
mantissa = mantissa << 8 | b
mantissa = 1 + (1.0*mantissa)/(2**(prec))
mantissa /= 2
e = (bytes[-1] & 0x7f) << (exp - 7)
e += (bytes[size-2] >> (15 - exp)) & (2**(exp - 7) -1)
e -= bias
e += 1
sign = bytes[-1] & 0x80
if e == bias + 2:
if mantissa == 0.5:
number = INFINITY
else:
return NAN
else:
number = math.ldexp(mantissa,e)
if sign : number *= -1
return number
def bytes2float(bytes):
""" Convert four bytes to a string. """
# the first 23 bits (0-22) define the mantissa
# the next 8 bits (23-30) the exponent,
# the last bit (31) defines the sign
b0, b1, b2, b3 = bytes
mantissa = ((b2 % 128) << 16) + (b1 << 8) + b0
exponent = (b3 % 128) * 2 + (b2 >= 128) * 1
negative = b3 >= 128
e = exponent - 0x7f
m = np.abs(mantissa) / np.float64(1 << 23)
if negative:
return -math.ldexp(m, e)
return math.ldexp(m, e)
def test_ldexp(self):
"""tests if the ldexp function works"""
a = simplearray.array(test_sample).fill_arange()
b = cumath.ldexp(a,5)
for i in range(test_sample):
self.assert_(math.ldexp(a[i],5) == b[i])
def __getvalue__(self):
"""convert the stored floating-point number into a python native float"""
exponentbias = (2**self.components[1])/2 - 1
value = super(type, self).__getvalue__()
res = bitmap.new(value, sum(self.components))
# extract components
res,sign = bitmap.shift(res, self.components[0])
res,exponent = bitmap.shift(res, self.components[1])
res,mantissa = bitmap.shift(res, self.components[2])
if exponent > 0 and exponent < (2**self.components[1]-1):
# convert to float
s = -1 if sign else +1
e = exponent - exponentbias
m = 1.0 + (float(mantissa) / 2**self.components[2])
# done
return math.ldexp( math.copysign(m,s), e)
if exponent == 2**self.components[1]-1 and mantissa == 0:
return float('-inf') if sign else float('+inf')
elif exponent in (0,2**self.components[1]-1) and mantissa != 0:
return float('-nan') if sign else float('+nan')
elif exponent == 0 and mantissa == 0:
return float('-0') if sign else float('+0')
# FIXME: this should return NaN or something
Log.warn('float_t.__getvalue__ : {:s} : invalid components value : {:d} : {:d} : {:d}'.format(self.instance(), sign, exponent, mantissa))
raise NotImplementedError
def test_strong_reference_implementation(self):
# Like test_referenceImplementation, but checks for exact bit-level
# equality. This should pass on any box where C double contains
# at least 53 bits of precision (the underlying algorithm suffers
# no rounding errors -- all results are exact).
from math import ldexp
expected = [
0x0eab3258d2231f, 0x1b89db315277a5, 0x1db622a5518016,
0x0b7f9af0d575bf, 0x029e4c4db82240, 0x04961892f5d673,
0x02b291598e4589, 0x11388382c15694, 0x02dad977c9e1fe,
0x191d96d4d334c6
]
self.gen.seed(61731 + (24903 << 32) + (614 << 64) + (42143 << 96))
actual = self.randomlist(2000)[-10:]
for a, e in zip(actual, expected):
self.assertEqual(int(ldexp(a, 53)), e)
def unpack_float(input, bigendian):
"""Interpret the 'input' string into a 32-bit or 64-bit
IEEE representation a the number.
"""
size = len(input)
bytes = []
if bigendian:
reverse_mask = size - 1
else:
reverse_mask = 0
nonzero = False
for i in range(size):
x = ord(input[i ^ reverse_mask])
bytes.append(x)
nonzero |= x
if not nonzero:
return 0.0
if size == 4:
bias = 127
exp = 8
prec = 23
else:
bias = 1023
exp = 11
prec = 52
mantissa_scale_factor = 0.5**prec # this is constant-folded if it's
# right after the 'if'
mantissa = r_longlong(bytes[size - 2] & ((1 << (15 - exp)) - 1))
for i in range(size - 3, -1, -1):
mantissa = mantissa << 8 | bytes[i]
mantissa = 1 + mantissa * mantissa_scale_factor
mantissa *= 0.5
e = (bytes[-1] & 0x7f) << (exp - 7)
e += (bytes[size - 2] >> (15 - exp)) & ((1 << (exp - 7)) - 1)
e -= bias
e += 1
sign = bytes[-1] & 0x80
if e == bias + 2:
if mantissa == 0.5:
number = INFINITY
else:
return NAN
else:
number = math.ldexp(mantissa, e)
if sign: number = -number
return number
def convert_to_floating_point(inputVal, exponentOffset, mantissaBits,
exponentBits):
"""
HELPER FUNCTION NOT WRITTEN BY THE AUTHORS
Computes modified floating point value represented by specified
floating point parameters.
fp = gain * mantissa^mantissaExponent * 2^exponentOffset
Returns:
Floating point value corresponding to passed parameters
"""
# Error check largest number that can be represented in specified number of bits
maxExponent = int((1 << exponentBits) - 1)
maxMantissa = np.uint32(((1 << mantissaBits) - 1))
exponent = int(
math.floor(((math.log(inputVal) / math.log(2)) - exponentOffset)))
# mantissa = 0
if exponent > maxExponent:
# Too big to represent
exponent = maxExponent
mantissa = maxMantissa
elif exponent >= 0:
mantissaScale = int((1 << mantissaBits))
effectiveExponent = int(exponentOffset + exponent)
# ldexp(X, Y) is the same as matlab pow2(X, Y) = > X * 2 ^ Y
mantissa = np.uint32(
(((math.ldexp(inputVal, -effectiveExponent) - 1) * mantissaScale) +
0.5))
if mantissa > maxMantissa:
# Handle case where rounding causes the mantissa to overflow
if exponent < maxExponent:
# Still representable
mantissa = 0
exponent += 1
else:
# Handle slightly-too-big to represent case
mantissa = maxMantissa
else:
# Too small to represent
mantissa = 0
exponent = 0
return ((np.uint32(exponent)) << mantissaBits) | mantissa
def run404_03():
"""
x = m * 2 ** e
0.5 <= abs(m) < 1
"""
print('{:^7} {:^7} {:^7}'.format('x', 'm', 'e'))
print('{:-^7} {:-^7} {:-^7}'.format('', '', ''))
for x in [0.1, 0.5, 4.0]:
m, e = math.frexp(x)
print('{:7.2f} {:7.2f} {:7d}'.format(x, m, e))
print('{:^7} {:^7} {:^7}'.format('m', 'e', 'x'))
print('{:-^7} {:-^7} {:-^7}'.format('', '', ''))
for m, e in [(0.8, -3), (0.5, 0), (0.5, 3)]:
x = math.ldexp(m, e)
print('{:7.2f} {:7d} {:7.2f}'.format(m, e, x))
def truediv(a, b):
"""Correctly-rounded true division for integers."""
negative = a ^ b < 0
a, b = abs(a), abs(b)
if not b:
raise ZeroDivisionError('division by zero')
if a >= DBL_MIN_OVERFLOW * b:
raise OverflowError('int/int too large to represent as a float')
d = a.bit_length() - b.bit_length()
if d >= 0 and a >= 2**d * b or d < 0 and a * 2**-d >= b:
d += 1
exp = max(d, DBL_MIN_EXP) - DBL_MANT_DIG
a, b = a << max(-exp, 0), b << max(exp, 0)
q, r = divmod(a, b)
if 2 * r > b or 2 * r == b and q % 2 == 1:
q += 1
result = math.ldexp(q, exp)
return -result if negative else result
def printFloat(x, isSingle):
assert x >= 0.0 and not math.isinf(x)
suffix = 'f' if isSingle else ''
if isSingle and x > 0.0:
# Try to find more compract representation for floats, since repr treats everything as doubles
m, e = math.frexp(x)
half_ulp2 = math.ldexp(
1.0, max(e - 25, -150)
) # don't bother doubling when near the upper range of a given e value
half_ulp1 = (half_ulp2 / 2) if m == 0.5 and e >= -125 else half_ulp2
lbound, ubound = x - half_ulp1, x + half_ulp2
assert lbound < x < ubound
s = '{:g}'.format(x).replace('+', '')
if lbound < float(
s
) < ubound: # strict ineq to avoid potential double rounding issues
return s + suffix
return repr(x) + suffix
def _put01_inf(v):
"""
Convert a value in [0,1] to a full floating point number.
Sort order is preserved. Reverses :func:`_get01_inf`, but with fewer
bits of precision.
"""
# Arctan alternative
# return tan(pi*(v-0.5))
v = (v - 0.5) * 4 * _E_MAX
s = math.copysign(1., v)
v *= s
e = int(v)
m = v - e
x = math.ldexp(s * m, e + _E_MIN)
# print "< x,e,m,s,v",x,e+_e_min,s*m,s,v
return x
def _bigint_true_divide(a, b):
ad, aexp = _AsScaledDouble(a)
bd, bexp = _AsScaledDouble(b)
if bd == 0.0:
raise ZeroDivisionError("long division or modulo by zero")
# True value is very close to ad/bd * 2**(SHIFT*(aexp-bexp))
ad /= bd # overflow/underflow impossible here
aexp -= bexp
if aexp > sys.maxint / SHIFT:
raise OverflowError
elif aexp < -(sys.maxint / SHIFT):
return 0.0 # underflow to 0
ad = math.ldexp(ad, aexp * SHIFT)
##if isinf(ad): # ignore underflow to 0.0
## raise OverflowError
# math.ldexp checks and raises
return ad
def from50(theWord):
"""Returns a double from Rep code 0x32, 32bit floating point representation.
Value +153 is 0x00084C80
Value -153 is 0x0008B380"""
#mant = float(theWord & 0xFFFF) / (1 << 15)
#exp = (theWord >> 16 )& 0xFFFF
# Or:
mant = theWord & 0xFFFF
# Only take 10 bits of exponent as significant as IEEE-754
exp = (theWord >> 16) & 0x03FF
# Need to divide mantissa by 1 << 15 or 32768 but
# instead we reduce the exponent by 15
exp -= 15
if theWord & 0x8000:
mant -= 0x10000
if theWord & 0x80000000:
exp -= 0x10000
return math.ldexp(mant, exp)
def descr_hex(self, space):
"""float.hex() -> string
Return a hexadecimal representation of a floating-point
number.
>>> (-0.1).hex()
'-0x1.999999999999ap-4'
>>> 3.14159.hex()
'0x1.921f9f01b866ep+1'
"""
TOHEX_NBITS = rfloat.DBL_MANT_DIG + 3 - (rfloat.DBL_MANT_DIG + 2) % 4
value = self.floatval
if not isfinite(value):
return self.descr_str(space)
if value == 0.0:
if math.copysign(1., value) == -1.:
return space.newtext("-0x0.0p+0")
else:
return space.newtext("0x0.0p+0")
mant, exp = math.frexp(value)
shift = 1 - max(rfloat.DBL_MIN_EXP - exp, 0)
mant = math.ldexp(mant, shift)
mant = abs(mant)
exp -= shift
result = ['\0'] * ((TOHEX_NBITS - 1) // 4 + 2)
result[0] = _char_from_hex(int(mant))
mant -= int(mant)
result[1] = "."
for i in range((TOHEX_NBITS - 1) // 4):
mant *= 16.0
result[i + 2] = _char_from_hex(int(mant))
mant -= int(mant)
if exp < 0:
sign = "-"
else:
sign = "+"
exp = abs(exp)
s = ''.join(result)
if value < 0.0:
return space.newtext("-0x%sp%s%d" % (s, sign, exp))
else:
return space.newtext("0x%sp%s%d" % (s, sign, exp))
def minimum_part_size(size_in_bytes):
# The default part size (4 MB) will be too small for a very large
# archive, as there is a limit of 10,000 parts in a multipart upload.
# This puts the maximum allowed archive size with the default part size
# at 40,000 MB. We need to do a sanity check on the part size, and find
# one that works if the default is too small.
part_size = _MEGABYTE
if (DEFAULT_PART_SIZE * MAXIMUM_NUMBER_OF_PARTS) < size_in_bytes:
if size_in_bytes > (4096 * _MEGABYTE * 10000):
raise ValueError("File size too large: %s" % size_in_bytes)
min_part_size = size_in_bytes / 10000
power = 3
while part_size < min_part_size:
part_size = math.ldexp(_MEGABYTE, power)
power += 1
part_size = int(part_size)
else:
part_size = DEFAULT_PART_SIZE
return part_size
def ceil_pow_2(n):
"""Return the least integer power of 2 that is greater than or equal to n.
>>> ceil_pow_2(128.0)
128.0
>>> ceil_pow_2(0.125)
0.125
>>> ceil_pow_2(129.0)
256.0
>>> ceil_pow_2(0.126)
0.25
>>> ceil_pow_2(1.0)
1.0
"""
# frexp splits floats into mantissa and exponent, ldexp does the opposite.
# For positive numbers, mantissa is in [0.5, 1.).
mantissa, exponent = math.frexp(n)
return math.ldexp(1 if mantissa >= 0 else float('nan'),
exponent - 1 if mantissa == 0.5 else exponent)
def int_to_float(n):
"""
Correctly-rounded integer-to-float conversion.
"""
# Constants, depending only on the floating-point format in use.
# We use an extra 2 bits of precision for rounding purposes.
PRECISION = sys.float_info.mant_dig + 2
SHIFT_MAX = sys.float_info.max_exp - PRECISION
Q_MAX = 1 << PRECISION
ROUND_HALF_TO_EVEN_CORRECTION = [0, -1, -2, 1, 0, -1, 2, 1]
# Reduce to the case where n is positive.
if n == 0:
return 0.0
elif n < 0:
return -int_to_float(-n)
# Convert n to a 'floating-point' number q * 2**shift, where q is an
# integer with 'PRECISION' significant bits. When shifting n to create q,
# the least significant bit of q is treated as 'sticky'. That is, the
# least significant bit of q is set if either the corresponding bit of n
# was already set, or any one of the bits of n lost in the shift was set.
shift = n.bit_length() - PRECISION
q = n << -shift if shift < 0 else (n >> shift) | bool(n & ~(-1 << shift))
# Round half to even (actually rounds to the nearest multiple of 4,
# rounding ties to a multiple of 8).
q += ROUND_HALF_TO_EVEN_CORRECTION[q & 7]
# Detect overflow.
if shift + (q == Q_MAX) > SHIFT_MAX:
raise OverflowError("integer too large to convert to float")
# Checks: q is exactly representable, and q**2**shift doesn't overflow.
assert q % 4 == 0 and q // 4 <= 2**(sys.float_info.mant_dig)
assert q * 2**shift <= sys.float_info.max
# Some circularity here, since float(q) is doing an int-to-float
# conversion. But here q is of bounded size, and is exactly representable
# as a float. In a low-level C-like language, this operation would be a
# simple cast (e.g., from unsigned long long to double).
return math.ldexp(float(q), shift)
def _cubic_exp2_approx(self, value):
# type: (float) -> float
# Derived from Cardano's formula
exponent = int(math.floor(value))
delta_0 = self.B * self.B - 3 * self.A * self.C
delta_1 = (
2.0 * self.B * self.B * self.B
- 9.0 * self.A * self.B * self.C
- 27.0 * self.A * self.A * (value - exponent)
)
cardano = _cbrt(
(delta_1 - ((delta_1 * delta_1 - 4 * delta_0 * delta_0 * delta_0) ** 0.5))
/ 2.0
)
significand_plus_one = (
-(self.B + cardano + delta_0 / cardano) / (3.0 * self.A) + 1.0
)
mantissa = significand_plus_one / 2
return math.ldexp(mantissa, exponent + 1)
def getpowers(self, times):
x = list(
self._sensors.find(
{
'target': 'system',
'timestamp': {
'$gte': times['begin'],
'$lte': times['end']
}
},
projection=['rapl', 'timestamp']))
conso = pd.DataFrame(x)
sonde = next(iter(x[0]['rapl']['0']))
conso['power'] = conso['rapl'].apply(
lambda row: math.ldexp(row['0'][sonde]['RAPL_ENERGY_PKG'], -32))
warmup = conso[(conso["timestamp"] <= times["execution"])
& (conso["timestamp"] > times["warmup"])]
execution = conso[(conso["timestamp"] > times["execution"])]
return warmup.loc[:, ['timestamp', 'power'
]], execution.loc[:, ['timestamp', 'power']],
def _gen_power_report(self, timestamp, target, counter):
"""
Generate a power report using the given parameters.
:param timestamp: Timestamp of the measurements
:param target: Target name
:param formula: Formula identifier
:param power: Power estimation
:return: Power report filled with the given parameters
"""
metadata = {
'scope': self.config.scope.value,
'socket': self.socket,
}
power = ldexp(counter, -32)
report = PowerReport(timestamp, self.sensor, target, power, metadata)
return report
def test_strong_reference_implementation(self):
# Like test_referenceImplementation, but checks for exact bit-level
# equality. This should pass on any box where C double contains
# at least 53 bits of precision (the underlying algorithm suffers
# no rounding errors -- all results are exact).
from math import ldexp
expected = [
0x0eab3258d2231fL, 0x1b89db315277a5L, 0x1db622a5518016L,
0x0b7f9af0d575bfL, 0x029e4c4db82240L, 0x04961892f5d673L,
0x02b291598e4589L, 0x11388382c15694L, 0x02dad977c9e1feL,
0x191d96d4d334c6L
]
self.gen.seed(61731L + (24903L << 32) + (614L << 64) + (42143L << 96))
actual = self.randomlist(2000)[-10:]
for a, e in zip(actual, expected):
if not test_support.due_to_ironpython_incompatibility(
"http://tkbgitvstfat01:8080/WorkItemTracking/WorkItem.aspx?artifactMoniker=318984"
):
self.assertEqual(long(ldexp(a, 53)), e)
def icalc(self, irc, msg, args, text):
"""<math expression>
This is the same as the calc command except that it allows integer
math, and can thus cause the bot to suck up CPU. Hence it requires
the 'trusted' capability to use.
"""
try:
self.log.info('evaluating %q from %s', text, msg.prefix)
x = safe_eval(text, allow_ints=True)
irc.reply(str(x))
except OverflowError:
maxFloat = math.ldexp(0.9999999999999999, 1024)
irc.error(_('The answer exceeded %s or so.') % maxFloat)
except InvalidNode as e:
irc.error(_('Invalid syntax: %s') % e.args[0])
except NameError as e:
irc.error(_('%s is not a defined function.') % str(e).split()[1])
except Exception as e:
irc.error(utils.exnToString(e))
def __init__(self, value):
if isinstance(value, (int, long)):
self.n = value
self.d = 1
elif isinstance(value, float):
# Convert to exact rational equivalent.
f, e = math.frexp(abs(value))
assert f == 0 or 0.5 <= f < 1.0
# |value| = f * 2**e exactly
# Suck up CHUNK bits at a time; 28 is enough so that we suck
# up all bits in 2 iterations for all known binary double-
# precision formats, and small enough to fit in an int.
CHUNK = 28
top = 0
# invariant: |value| = (top + f) * 2**e exactly
while f:
f = math.ldexp(f, CHUNK)
digit = int(f)
assert digit >> CHUNK == 0
top = (top << CHUNK) | digit
f -= digit
assert 0.0 <= f < 1.0
e -= CHUNK
# Now |value| = top * 2**e exactly.
if e >= 0:
n = top << e
d = 1
else:
n = top
d = 1 << -e
if value < 0:
n = -n
self.n = n
self.d = d
assert float(n) / float(d) == value
else:
raise TypeError("can't deal with %r" % val)
def int_to_float(n):
"""
Correctly-rounded integer-to-float conversion.
"""
PRECISION = sys.float_info.mant_dig + 2
SHIFT_MAX = sys.float_info.max_exp - PRECISION
Q_MAX = 1 << PRECISION
ROUND_HALF_TO_EVEN_CORRECTION = [0, -1, -2, 1, 0, -1, 2, 1]
if n == 0:
return 0.0
elif n < 0:
return -int_to_float(-n)
shift = n.bit_length() - PRECISION
q = n << -shift if shift < 0 else n >> shift | bool(n & ~(-1 << shift))
q += ROUND_HALF_TO_EVEN_CORRECTION[q & 7]
if shift + (q == Q_MAX) > SHIFT_MAX:
raise OverflowError('integer too large to convert to float')
assert q % 4 == 0 and q // 4 <= 2**sys.float_info.mant_dig
assert q * 2**shift <= sys.float_info.max
return math.ldexp(float(q), shift)
def ParseFloat64(self, index: int) -> str:
if self.data[index + 7] == 0:
return 0
exp = self.data[
index +
7] - 184 # -184 = -128 + -56 (56 because the significand is behind a decimal dot)
mantissa = ((self.data[index + 6] | 0x80) << 48) | (self.data[index + 5] << 40) | (self.data[index + 4] << 32) \
| (self.data[index + 3] << 24) | (self.data[index + 2] << 16) | (self.data[index + 1] << 8) | self.data[index]
# We must always output a positive number for doubles,
# because a token for '-' is already added before the negative ones.
number = math.ldexp(mantissa, exp)
# Doubles always get their postfix '#'
# Must round to 16 significant figures (from 17) when displaying
# The exponent sign for doubles is 'D' instead of 'E'
numberStr = self.CanonizeNumber(
'%s' % float('%.16g' % number)).replace('E', 'D') + '#'
return numberStr
def float_to_bin(f):
# NOTE: the implementation closely follows float.hex()
if not isfinite(f):
return repr(f) # inf nan
sign = '-' * (copysign(1.0, f) < 0)
if f == 0: # zero
return sign + '0b0.0p+0'
# f = m * 2**e
m, e = frexp(fabs(f)) # 0.5 <= m < 1.0
shift = 1 - max(sys.float_info.min_exp - e, 0)
m = ldexp(m, shift) # m * (2**shift)
e -= shift
fm, im = modf(m)
assert im == 1.0 or im == 0.0
n, d = fm.as_integer_ratio()
assert d & (d - 1) == 0 # power of two
return '{sign}0b{i}.{frac:0{width}b}p{e:+}'.format(
sign=sign, i=int(im), frac=n, width=d.bit_length() - 1, e=e)
def to_float(s, strict=False, rnd=round_fast):
"""
Convert a raw mpf to a Python float. The result is exact if the
bitcount of s is <= 53 and no underflow/overflow occurs.
If the number is too large or too small to represent as a regular
float, it will be converted to inf or 0.0. Setting strict=True
forces an OverflowError to be raised instead.
Warning: with a directed rounding mode, the correct nearest representable
floating-point number in the specified direction might not be computed
in case of overflow or (gradual) underflow.
"""
sign, man, exp, bc = s
if not man:
if s == fzero:
return 0.0
if s == finf:
return math_float_inf
if s == fninf:
return -math_float_inf
return math_float_inf / math_float_inf
if bc > 53:
sign, man, exp, bc = normalize1(sign, man, exp, bc, 53, rnd)
if sign:
man = -man
try:
return math.ldexp(man, exp)
except OverflowError:
if strict:
raise
# Overflow to infinity
if exp + bc > 0:
if sign:
return -math_float_inf
else:
return math_float_inf
# Underflow to zero
return 0.0
def _zoomRatio(self, basePoint):
# type: (om.MPoint) -> float
"""Calculate zoom factor as distance from the current view's camera position."""
# FIXME: all views share this value from current one.
# camera distance
cameraPath = omui.M3dView.active3dView().getCamera()
camNode = om.MFnDependencyNode(cameraPath.node())
isOrtho = camNode.findPlug("orthographic", False)
camMat = cameraPath.inclusiveMatrix().homogenize()
camPos = om.MPoint(
camMat.getElement(3, 0),
camMat.getElement(3, 1),
camMat.getElement(3, 2),
)
if isOrtho.asBool():
orthoWidth = camNode.findPlug("orthographicWidth", False).asFloat()
return math.ldexp(orthoWidth, 3) * 0.01
else:
return basePoint.distanceTo(camPos) * 0.1
def _int_to_real(num):
"""
Convert REAL8 from internal integer representation to Python reals.
Zeroes:
>>> print(_int_to_real(0x0))
0.0
>>> print(_int_to_real(0x8000000000000000)) # negative
0.0
>>> print(_int_to_real(0xff00000000000000)) # denormalized
0.0
Others:
>>> print(_int_to_real(0x4110000000000000))
1.0
>>> print(_int_to_real(0xC120000000000000))
-2.0
"""
sgn = -1 if 0x8000000000000000 & num else 1
mant = num & 0x00ffffffffffffff
exp = (num >> 56) & 0x7f
return math.ldexp(sgn * mant, 4 * (exp - 64) - 56)
def _half_to_float(half):
# Half is 16-bit int
single = (half & 0x7fff) << 13 | (half & 0x8000) << 16
if (half & 0x7c00) != 0x7c00:
mant = half & 0x03ff
exp = half & 0x7c00
if mant and exp == 0:
exp = 0x1c400
while (mant & 0x400) == 0:
mant <<= 1
exp -= 0x400
mant &= 0x3ff
single = (half & 0x8000) << 16 | (exp | mant) << 13
return struct.unpack('>f', struct.pack('>I', single))[0]
return math.ldexp(struct.unpack('>f', struct.pack('>I', single))[0], 112)
single |= 0x7f800000
return struct.unpack('>f', struct.pack('>I', single))[0]
def test_handle_hwpc_report_with_one_rapl_event_and_other_groups(state):
"""
handle a HWPC report with a simple RAPL event and events from other
groups
The HWPC report contain one RAPL event and events from a group 'sys'
with two cores
The handle method must return a PowerReport containing only the RAPL event
"""
raw_power = 10
socket_id = '1'
rapl_event_id = 'RAPL_1'
hwpc_report = create_report_root([
create_group_report('rapl', [
create_socket_report(
socket_id, [create_core_report('1', rapl_event_id, raw_power)])
]),
create_group_report('sys', [
create_socket_report(socket_id, [
create_core_report('1', 'e0', 0),
create_core_report('2', 'e0', 0)
])
])
])
validation_report = PowerReport(hwpc_report.timestamp, hwpc_report.sensor,
hwpc_report.target,
math.ldexp(raw_power, -32), {
'socket': socket_id,
'event': rapl_event_id
})
result = RAPLFormulaHWPCReportHandler(get_fake_pusher())._process_report(
hwpc_report, state)
assert [validation_report] == result
def nearest_point_on_curve(self, P, cps):
"""Compute the parameter value fo the point on a Bezier curve
segment closest to some arbitrary, user-input point
Return point on the curve at that parameter value"""
self.maxdepth = 64
self.epsilon = math.ldexp(1.0, -self.maxdepth-1)
rec_depth = 0
w_degree = 5
degree = 3
# Convert point p and bezcurve defined by control points cps into
# a 5th-degree bezier curve form
w = self.convert_to_bezier_form(P, cps)
# Find all possible roots of that 5th degree equation
n_candidates = self.find_roots(w, rec_depth)
t_candidates = self.tvals
# Check distance to beginning of curve, where t = 0
dist = (P - cps[0]).get_length_sqrd()
tval = 0.0
# Compare distances of point p to all candidate points found as roots
for t in t_candidates:
p = self.get_at_t(cps, t)
new_dist = (P - p).get_length_sqrd()
if new_dist < dist:
dist = new_dist
tval = t
# Finally, look at distance to end point, where t = 1.0
new_dist = (P - cps[3]).get_length_sqrd()
if new_dist < dist:
dist = new_dist
tval = 1.0
#print tval, dist, self.tvals
# Return point on curve at parameter value tval
return self.get_at_t(cps, tval)
def minimum_part_size(size_in_bytes, default_part_size=DEFAULT_PART_SIZE):
"""Calculate the minimum part size needed for a multipart upload.
Glacier allows a maximum of 10,000 parts per upload. It also
states that the maximum archive size is 10,000 * 4 GB, which means
the part size can range from 1MB to 4GB (provided it is one 1MB
multiplied by a power of 2).
This function will compute what the minimum part size must be in
order to upload a file of size ``size_in_bytes``.
It will first check if ``default_part_size`` is sufficient for
a part size given the ``size_in_bytes``. If this is not the case,
then the smallest part size than can accomodate a file of size
``size_in_bytes`` will be returned.
If the file size is greater than the maximum allowed archive
size of 10,000 * 4GB, a ``ValueError`` will be raised.
"""
# The default part size (4 MB) will be too small for a very large
# archive, as there is a limit of 10,000 parts in a multipart upload.
# This puts the maximum allowed archive size with the default part size
# at 40,000 MB. We need to do a sanity check on the part size, and find
# one that works if the default is too small.
part_size = _MEGABYTE
if (default_part_size * MAXIMUM_NUMBER_OF_PARTS) < size_in_bytes:
if size_in_bytes > (4096 * _MEGABYTE * 10000):
raise ValueError("File size too large: %s" % size_in_bytes)
min_part_size = size_in_bytes / 10000
power = 3
while part_size < min_part_size:
part_size = math.ldexp(_MEGABYTE, power)
power += 1
part_size = int(part_size)
else:
part_size = default_part_size
return part_size
def test_roundtrip(self):
def roundtrip(x):
return fromHex(toHex(x))
for x in [
NAN, INF, self.MAX, self.MIN, self.MIN - self.TINY, self.TINY,
0.0
]:
self.identical(x, roundtrip(x))
self.identical(-x, roundtrip(-x))
# fromHex(toHex(x)) should exactly recover x, for any non-NaN float x.
import random
for i in range(10000):
e = random.randrange(-1200, 1200)
m = random.random()
s = random.choice([1.0, -1.0])
try:
x = s * ldexp(m, e)
except OverflowError:
pass
else:
self.identical(x, fromHex(toHex(x)))
