At Wednesday 17/1/2007 03:36, shellon wrote:

>I'm sorry I mistake the function name, the function is

floatToRawIntBits(), it convert ieee 754 floating point number to

integer, e.g. if f1>f2 then floatToRawBits(f1) floatToRawBits(f1)

I want convert floating point number to sortable string to index in

Lucene, so I want first to conver the floating point number to integer

first, and than convert the integer to sortable string?

The following two functions may be useful; they do more-or-less the

same thing, but returning a string instead of an integer.

Note that this property: f1>f2 =floatToRawBits(f1) >

floatToRawBits(f2), only holds for nonnegative numbers; this code

has the same restriction.

The code assumes a few things: float(repr(x))==x for 0.5<=x<1 (that

is, repr(x) is exact in that range); the maximum double value has an

exponent (as given by frexp) less than 5000; the minimum positive

value has an exponent greater than -5000; 0 is the only number having

mantissa==0; and surely I'm assuming many more but I'm not aware of

them. I think it's not dependent on a particular FP hardware or representation.

Beasts like denormals, INFs and NaNs are not considered at all. It

appears to work OK for "normal" numbers, but I've not checked all

corner cases. It was only tested on Windows XP.

After such long disclaimer... I hope it's useful :)

--- begin fpsrepr.py ---

import math

def float2srepr(f):

"""Convert a floating point number into a string representation

which can be sorted lexicographically maintaining the original

numerical order (only for numbers >= 0).

That is, given f1,f2 >= 0, f1<f2 <=float2srepr(f1)<float2srepr(f2)

Denormals, INFs, NaNs are not handled at all!

format: Seeeem*

S : sign, "0" for +, else "-"

eeee: exponent + 5000 (never negative)

m* : mantissa, one or more chars as needed,

0.5<=mantissa<1, without the leading "0."

"""

try: m, e = math.frexp(f)

except ValueError,E:

E.args = list(E.args) + [repr(f)]

raise

if m < 0:

sign = '-'

m = -m

else:

sign = '0'

e = e+5000

if m==0.0: e = 0

return "%s%04.4d%s" % (sign, e, repr(m)[2:])

def srepr2float(s):

"""Convert a string in the format used by float2srepr

into a floating point number.

srepr2float(float2srepr(x)) == x

"""

sign, e, m = s[0], s[1:5], s[5:]

neg = sign == '-'

e = int(e)

e = e-5000

m = float('0.'+m)

if m==0: f = 0

else: f = math.ldexp(m, e)

if neg: f = -f

return f

# test

def find_eps(): # smallest x such 1+x!=1

prev, curr = 1.0, 0.5

while 1.0+curr 1.0 and curr < prev:

prev = curr

curr /= 2.0

return prev

def find_minf(): # smallest x such x>0

prev, curr = 1.0, 0.5

while curr 0.0 and curr < prev:

prev = curr

curr /= 2

return prev

eps = find_eps()

print "eps=%r %r" % (eps, 1.0+eps)

minf = find_minf()

print "minf=%r %r" % (minf, -minf)

values = [0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,

1.0,1.0+eps,1.0+2*eps,1.0-eps,1.0-2*eps,

2,3,10,10.0000001,10.00000000001,

123.456,1234.567,12345.678,123456.789,1.234e10,

123412341234,123412341234123412341234.0,1.234e20,

1e100,1e200,1e300,math.pi,math.e]

values += [1.0/x for x in values if x>0] + [eps, minf]

values += [-x for x in values]

values = sorted(values)

for x in values:

s = float2srepr(x)

xr = srepr2float(s)

print '%-30r %s' % (x, s)

assert x==xr, '%r!=%r' % (x, xr)

f2svalues = [float2srepr(x) for x in values if x>=0]

s2fvalues = [srepr2float(x) for x in sorted(f2svalues)]

assert s2fvalues == sorted(s2fvalues), s2fvalues

--- end fpsrepr.py ---

--

Gabriel Genellina

Softlab SRL

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