Issue #3008: add instance method float.hex and class method float.fromhex
to convert floats to and from hexadecimal strings respectively.
diff --git a/Lib/test/test_float.py b/Lib/test/test_float.py
index bb48df0..254dd37 100644
--- a/Lib/test/test_float.py
+++ b/Lib/test/test_float.py
@@ -3,7 +3,7 @@
import os
from test import test_support
import math
-from math import isinf, isnan
+from math import isinf, isnan, copysign, ldexp
import operator
INF = float("inf")
@@ -343,6 +343,390 @@
self.failIf(NAN.is_inf())
self.failIf((0.).is_inf())
+fromHex = float.fromhex
+toHex = float.hex
+class HexFloatTestCase(unittest.TestCase):
+ MAX = fromHex('0x.fffffffffffff8p+1024') # max normal
+ MIN = fromHex('0x1p-1022') # min normal
+ TINY = fromHex('0x0.0000000000001p-1022') # min subnormal
+ EPS = fromHex('0x0.0000000000001p0') # diff between 1.0 and next float up
+
+ def identical(self, x, y):
+ # check that floats x and y are identical, or that both
+ # are NaNs
+ if isnan(x) or isnan(y):
+ if isnan(x) == isnan(y):
+ return
+ elif x == y and (x != 0.0 or copysign(1.0, x) == copysign(1.0, y)):
+ return
+ self.fail('%r not identical to %r' % (x, y))
+
+ def test_ends(self):
+ self.identical(self.MIN, 2.**-1022)
+ self.identical(self.TINY, 2.**-1074)
+ self.identical(self.EPS, 2.**-52)
+ self.identical(self.MAX, 2.*(2.**1023 - 2.**970))
+
+ def test_invalid_inputs(self):
+ invalid_inputs = [
+ 'infi', # misspelt infinities and nans
+ '-Infinit',
+ '++inf',
+ '-+Inf',
+ '--nan',
+ '+-NaN',
+ 'snan',
+ 'NaNs',
+ 'nna',
+ '0xnan',
+ '',
+ ' ',
+ 'x1.0p0',
+ '0xX1.0p0',
+ '+ 0x1.0p0', # internal whitespace
+ '- 0x1.0p0',
+ '0 x1.0p0',
+ '0x 1.0p0',
+ '0x1 2.0p0',
+ '+0x1 .0p0',
+ '0x1. 0p0',
+ '-0x1.0 1p0',
+ '-0x1.0 p0',
+ '+0x1.0p +0',
+ '0x1.0p -0',
+ '0x1.0p 0',
+ '+0x1.0p+ 0',
+ '-0x1.0p- 0',
+ '++0x1.0p-0', # double signs
+ '--0x1.0p0',
+ '+-0x1.0p+0',
+ '-+0x1.0p0',
+ '0x1.0p++0',
+ '+0x1.0p+-0',
+ '-0x1.0p-+0',
+ '0x1.0p--0',
+ '0x1.0.p0',
+ '0x.p0', # no hex digits before or after point
+ '0x1,p0', # wrong decimal point character
+ '0x1pa',
+ u'0x1p\uff10', # fullwidth Unicode digits
+ u'\uff10x1p0',
+ u'0x\uff11p0',
+ u'0x1.\uff10p0',
+ '0x1p0 \n 0x2p0',
+ '0x1p0\0 0x1p0', # embedded null byte is not end of string
+ ]
+ for x in invalid_inputs:
+ self.assertRaises(ValueError, fromHex, x)
+
+
+ def test_from_hex(self):
+ MIN = self.MIN;
+ MAX = self.MAX;
+ TINY = self.TINY;
+ EPS = self.EPS;
+
+ # two spellings of infinity, with optional signs; case-insensitive
+ self.identical(fromHex('inf'), INF)
+ self.identical(fromHex('+Inf'), INF)
+ self.identical(fromHex('-INF'), -INF)
+ self.identical(fromHex('iNf'), INF)
+ self.identical(fromHex('Infinity'), INF)
+ self.identical(fromHex('+INFINITY'), INF)
+ self.identical(fromHex('-infinity'), -INF)
+ self.identical(fromHex('-iNFiNitY'), -INF)
+
+ # nans with optional sign; case insensitive
+ self.identical(fromHex('nan'), NAN)
+ self.identical(fromHex('+NaN'), NAN)
+ self.identical(fromHex('-NaN'), NAN)
+ self.identical(fromHex('-nAN'), NAN)
+
+ # variations in input format
+ self.identical(fromHex('1'), 1.0)
+ self.identical(fromHex('+1'), 1.0)
+ self.identical(fromHex('1.'), 1.0)
+ self.identical(fromHex('1.0'), 1.0)
+ self.identical(fromHex('1.0p0'), 1.0)
+ self.identical(fromHex('01'), 1.0)
+ self.identical(fromHex('01.'), 1.0)
+ self.identical(fromHex('0x1'), 1.0)
+ self.identical(fromHex('0x1.'), 1.0)
+ self.identical(fromHex('0x1.0'), 1.0)
+ self.identical(fromHex('+0x1.0'), 1.0)
+ self.identical(fromHex('0x1p0'), 1.0)
+ self.identical(fromHex('0X1p0'), 1.0)
+ self.identical(fromHex('0X1P0'), 1.0)
+ self.identical(fromHex('0x1P0'), 1.0)
+ self.identical(fromHex('0x1.p0'), 1.0)
+ self.identical(fromHex('0x1.0p0'), 1.0)
+ self.identical(fromHex('0x.1p4'), 1.0)
+ self.identical(fromHex('0x.1p04'), 1.0)
+ self.identical(fromHex('0x.1p004'), 1.0)
+ self.identical(fromHex('0x1p+0'), 1.0)
+ self.identical(fromHex('0x1P-0'), 1.0)
+ self.identical(fromHex('+0x1p0'), 1.0)
+ self.identical(fromHex('0x01p0'), 1.0)
+ self.identical(fromHex('0x1p00'), 1.0)
+ self.identical(fromHex(u'0x1p0'), 1.0)
+ self.identical(fromHex(' 0x1p0 '), 1.0)
+ self.identical(fromHex('\n 0x1p0'), 1.0)
+ self.identical(fromHex('0x1p0 \t'), 1.0)
+ self.identical(fromHex('0xap0'), 10.0)
+ self.identical(fromHex('0xAp0'), 10.0)
+ self.identical(fromHex('0xaP0'), 10.0)
+ self.identical(fromHex('0xAP0'), 10.0)
+ self.identical(fromHex('0xbep0'), 190.0)
+ self.identical(fromHex('0xBep0'), 190.0)
+ self.identical(fromHex('0xbEp0'), 190.0)
+ self.identical(fromHex('0XBE0P-4'), 190.0)
+ self.identical(fromHex('0xBEp0'), 190.0)
+ self.identical(fromHex('0xB.Ep4'), 190.0)
+ self.identical(fromHex('0x.BEp8'), 190.0)
+ self.identical(fromHex('0x.0BEp12'), 190.0)
+
+ # moving the point around
+ pi = fromHex('0x1.921fb54442d18p1')
+ self.identical(fromHex('0x.006487ed5110b46p11'), pi)
+ self.identical(fromHex('0x.00c90fdaa22168cp10'), pi)
+ self.identical(fromHex('0x.01921fb54442d18p9'), pi)
+ self.identical(fromHex('0x.03243f6a8885a3p8'), pi)
+ self.identical(fromHex('0x.06487ed5110b46p7'), pi)
+ self.identical(fromHex('0x.0c90fdaa22168cp6'), pi)
+ self.identical(fromHex('0x.1921fb54442d18p5'), pi)
+ self.identical(fromHex('0x.3243f6a8885a3p4'), pi)
+ self.identical(fromHex('0x.6487ed5110b46p3'), pi)
+ self.identical(fromHex('0x.c90fdaa22168cp2'), pi)
+ self.identical(fromHex('0x1.921fb54442d18p1'), pi)
+ self.identical(fromHex('0x3.243f6a8885a3p0'), pi)
+ self.identical(fromHex('0x6.487ed5110b46p-1'), pi)
+ self.identical(fromHex('0xc.90fdaa22168cp-2'), pi)
+ self.identical(fromHex('0x19.21fb54442d18p-3'), pi)
+ self.identical(fromHex('0x32.43f6a8885a3p-4'), pi)
+ self.identical(fromHex('0x64.87ed5110b46p-5'), pi)
+ self.identical(fromHex('0xc9.0fdaa22168cp-6'), pi)
+ self.identical(fromHex('0x192.1fb54442d18p-7'), pi)
+ self.identical(fromHex('0x324.3f6a8885a3p-8'), pi)
+ self.identical(fromHex('0x648.7ed5110b46p-9'), pi)
+ self.identical(fromHex('0xc90.fdaa22168cp-10'), pi)
+ self.identical(fromHex('0x1921.fb54442d18p-11'), pi)
+ # ...
+ self.identical(fromHex('0x1921fb54442d1.8p-47'), pi)
+ self.identical(fromHex('0x3243f6a8885a3p-48'), pi)
+ self.identical(fromHex('0x6487ed5110b46p-49'), pi)
+ self.identical(fromHex('0xc90fdaa22168cp-50'), pi)
+ self.identical(fromHex('0x1921fb54442d18p-51'), pi)
+ self.identical(fromHex('0x3243f6a8885a30p-52'), pi)
+ self.identical(fromHex('0x6487ed5110b460p-53'), pi)
+ self.identical(fromHex('0xc90fdaa22168c0p-54'), pi)
+ self.identical(fromHex('0x1921fb54442d180p-55'), pi)
+
+
+ # results that should overflow...
+ self.assertRaises(OverflowError, fromHex, '-0x1p1024')
+ self.assertRaises(OverflowError, fromHex, '0x1p+1025')
+ self.assertRaises(OverflowError, fromHex, '+0X1p1030')
+ self.assertRaises(OverflowError, fromHex, '-0x1p+1100')
+ self.assertRaises(OverflowError, fromHex, '0X1p123456789123456789')
+ self.assertRaises(OverflowError, fromHex, '+0X.8p+1025')
+ self.assertRaises(OverflowError, fromHex, '+0x0.8p1025')
+ self.assertRaises(OverflowError, fromHex, '-0x0.4p1026')
+ self.assertRaises(OverflowError, fromHex, '0X2p+1023')
+ self.assertRaises(OverflowError, fromHex, '0x2.p1023')
+ self.assertRaises(OverflowError, fromHex, '-0x2.0p+1023')
+ self.assertRaises(OverflowError, fromHex, '+0X4p+1022')
+ self.assertRaises(OverflowError, fromHex, '0x1.ffffffffffffffp+1023')
+ self.assertRaises(OverflowError, fromHex, '-0X1.fffffffffffff9p1023')
+ self.assertRaises(OverflowError, fromHex, '0X1.fffffffffffff8p1023')
+ self.assertRaises(OverflowError, fromHex, '+0x3.fffffffffffffp1022')
+ self.assertRaises(OverflowError, fromHex, '0x3fffffffffffffp+970')
+ self.assertRaises(OverflowError, fromHex, '0x10000000000000000p960')
+ self.assertRaises(OverflowError, fromHex, '-0Xffffffffffffffffp960')
+
+ # ...and those that round to +-max float
+ self.identical(fromHex('+0x1.fffffffffffffp+1023'), MAX)
+ self.identical(fromHex('-0X1.fffffffffffff7p1023'), -MAX)
+ self.identical(fromHex('0X1.fffffffffffff7fffffffffffffp1023'), MAX)
+
+ # zeros
+ self.identical(fromHex('0x0p0'), 0.0)
+ self.identical(fromHex('0x0p1000'), 0.0)
+ self.identical(fromHex('-0x0p1023'), -0.0)
+ self.identical(fromHex('0X0p1024'), 0.0)
+ self.identical(fromHex('-0x0p1025'), -0.0)
+ self.identical(fromHex('0X0p2000'), 0.0)
+ self.identical(fromHex('0x0p123456789123456789'), 0.0)
+ self.identical(fromHex('-0X0p-0'), -0.0)
+ self.identical(fromHex('-0X0p-1000'), -0.0)
+ self.identical(fromHex('0x0p-1023'), 0.0)
+ self.identical(fromHex('-0X0p-1024'), -0.0)
+ self.identical(fromHex('-0x0p-1025'), -0.0)
+ self.identical(fromHex('-0x0p-1072'), -0.0)
+ self.identical(fromHex('0X0p-1073'), 0.0)
+ self.identical(fromHex('-0x0p-1074'), -0.0)
+ self.identical(fromHex('0x0p-1075'), 0.0)
+ self.identical(fromHex('0X0p-1076'), 0.0)
+ self.identical(fromHex('-0X0p-2000'), -0.0)
+ self.identical(fromHex('-0x0p-123456789123456789'), -0.0)
+
+ # values that should underflow to 0
+ self.identical(fromHex('0X1p-1075'), 0.0)
+ self.identical(fromHex('-0X1p-1075'), -0.0)
+ self.identical(fromHex('-0x1p-123456789123456789'), -0.0)
+ self.identical(fromHex('0x1.00000000000000001p-1075'), TINY)
+ self.identical(fromHex('-0x1.1p-1075'), -TINY)
+ self.identical(fromHex('0x1.fffffffffffffffffp-1075'), TINY)
+
+ # check round-half-even is working correctly near 0 ...
+ self.identical(fromHex('0x1p-1076'), 0.0)
+ self.identical(fromHex('0X2p-1076'), 0.0)
+ self.identical(fromHex('0X3p-1076'), TINY)
+ self.identical(fromHex('0x4p-1076'), TINY)
+ self.identical(fromHex('0X5p-1076'), TINY)
+ self.identical(fromHex('0X6p-1076'), 2*TINY)
+ self.identical(fromHex('0x7p-1076'), 2*TINY)
+ self.identical(fromHex('0X8p-1076'), 2*TINY)
+ self.identical(fromHex('0X9p-1076'), 2*TINY)
+ self.identical(fromHex('0xap-1076'), 2*TINY)
+ self.identical(fromHex('0Xbp-1076'), 3*TINY)
+ self.identical(fromHex('0xcp-1076'), 3*TINY)
+ self.identical(fromHex('0Xdp-1076'), 3*TINY)
+ self.identical(fromHex('0Xep-1076'), 4*TINY)
+ self.identical(fromHex('0xfp-1076'), 4*TINY)
+ self.identical(fromHex('0x10p-1076'), 4*TINY)
+ self.identical(fromHex('-0x1p-1076'), -0.0)
+ self.identical(fromHex('-0X2p-1076'), -0.0)
+ self.identical(fromHex('-0x3p-1076'), -TINY)
+ self.identical(fromHex('-0X4p-1076'), -TINY)
+ self.identical(fromHex('-0x5p-1076'), -TINY)
+ self.identical(fromHex('-0x6p-1076'), -2*TINY)
+ self.identical(fromHex('-0X7p-1076'), -2*TINY)
+ self.identical(fromHex('-0X8p-1076'), -2*TINY)
+ self.identical(fromHex('-0X9p-1076'), -2*TINY)
+ self.identical(fromHex('-0Xap-1076'), -2*TINY)
+ self.identical(fromHex('-0xbp-1076'), -3*TINY)
+ self.identical(fromHex('-0xcp-1076'), -3*TINY)
+ self.identical(fromHex('-0Xdp-1076'), -3*TINY)
+ self.identical(fromHex('-0xep-1076'), -4*TINY)
+ self.identical(fromHex('-0Xfp-1076'), -4*TINY)
+ self.identical(fromHex('-0X10p-1076'), -4*TINY)
+
+ # ... and near MIN ...
+ self.identical(fromHex('0x0.ffffffffffffd6p-1022'), MIN-3*TINY)
+ self.identical(fromHex('0x0.ffffffffffffd8p-1022'), MIN-2*TINY)
+ self.identical(fromHex('0x0.ffffffffffffdap-1022'), MIN-2*TINY)
+ self.identical(fromHex('0x0.ffffffffffffdcp-1022'), MIN-2*TINY)
+ self.identical(fromHex('0x0.ffffffffffffdep-1022'), MIN-2*TINY)
+ self.identical(fromHex('0x0.ffffffffffffe0p-1022'), MIN-2*TINY)
+ self.identical(fromHex('0x0.ffffffffffffe2p-1022'), MIN-2*TINY)
+ self.identical(fromHex('0x0.ffffffffffffe4p-1022'), MIN-2*TINY)
+ self.identical(fromHex('0x0.ffffffffffffe6p-1022'), MIN-2*TINY)
+ self.identical(fromHex('0x0.ffffffffffffe8p-1022'), MIN-2*TINY)
+ self.identical(fromHex('0x0.ffffffffffffeap-1022'), MIN-TINY)
+ self.identical(fromHex('0x0.ffffffffffffecp-1022'), MIN-TINY)
+ self.identical(fromHex('0x0.ffffffffffffeep-1022'), MIN-TINY)
+ self.identical(fromHex('0x0.fffffffffffff0p-1022'), MIN-TINY)
+ self.identical(fromHex('0x0.fffffffffffff2p-1022'), MIN-TINY)
+ self.identical(fromHex('0x0.fffffffffffff4p-1022'), MIN-TINY)
+ self.identical(fromHex('0x0.fffffffffffff6p-1022'), MIN-TINY)
+ self.identical(fromHex('0x0.fffffffffffff8p-1022'), MIN)
+ self.identical(fromHex('0x0.fffffffffffffap-1022'), MIN)
+ self.identical(fromHex('0x0.fffffffffffffcp-1022'), MIN)
+ self.identical(fromHex('0x0.fffffffffffffep-1022'), MIN)
+ self.identical(fromHex('0x1.00000000000000p-1022'), MIN)
+ self.identical(fromHex('0x1.00000000000002p-1022'), MIN)
+ self.identical(fromHex('0x1.00000000000004p-1022'), MIN)
+ self.identical(fromHex('0x1.00000000000006p-1022'), MIN)
+ self.identical(fromHex('0x1.00000000000008p-1022'), MIN)
+ self.identical(fromHex('0x1.0000000000000ap-1022'), MIN+TINY)
+ self.identical(fromHex('0x1.0000000000000cp-1022'), MIN+TINY)
+ self.identical(fromHex('0x1.0000000000000ep-1022'), MIN+TINY)
+ self.identical(fromHex('0x1.00000000000010p-1022'), MIN+TINY)
+ self.identical(fromHex('0x1.00000000000012p-1022'), MIN+TINY)
+ self.identical(fromHex('0x1.00000000000014p-1022'), MIN+TINY)
+ self.identical(fromHex('0x1.00000000000016p-1022'), MIN+TINY)
+ self.identical(fromHex('0x1.00000000000018p-1022'), MIN+2*TINY)
+
+ # ... and near 1.0.
+ self.identical(fromHex('0x0.fffffffffffff0p0'), 1.0-EPS)
+ self.identical(fromHex('0x0.fffffffffffff1p0'), 1.0-EPS)
+ self.identical(fromHex('0X0.fffffffffffff2p0'), 1.0-EPS)
+ self.identical(fromHex('0x0.fffffffffffff3p0'), 1.0-EPS)
+ self.identical(fromHex('0X0.fffffffffffff4p0'), 1.0-EPS)
+ self.identical(fromHex('0X0.fffffffffffff5p0'), 1.0-EPS/2)
+ self.identical(fromHex('0X0.fffffffffffff6p0'), 1.0-EPS/2)
+ self.identical(fromHex('0x0.fffffffffffff7p0'), 1.0-EPS/2)
+ self.identical(fromHex('0x0.fffffffffffff8p0'), 1.0-EPS/2)
+ self.identical(fromHex('0X0.fffffffffffff9p0'), 1.0-EPS/2)
+ self.identical(fromHex('0X0.fffffffffffffap0'), 1.0-EPS/2)
+ self.identical(fromHex('0x0.fffffffffffffbp0'), 1.0-EPS/2)
+ self.identical(fromHex('0X0.fffffffffffffcp0'), 1.0)
+ self.identical(fromHex('0x0.fffffffffffffdp0'), 1.0)
+ self.identical(fromHex('0X0.fffffffffffffep0'), 1.0)
+ self.identical(fromHex('0x0.ffffffffffffffp0'), 1.0)
+ self.identical(fromHex('0X1.00000000000000p0'), 1.0)
+ self.identical(fromHex('0X1.00000000000001p0'), 1.0)
+ self.identical(fromHex('0x1.00000000000002p0'), 1.0)
+ self.identical(fromHex('0X1.00000000000003p0'), 1.0)
+ self.identical(fromHex('0x1.00000000000004p0'), 1.0)
+ self.identical(fromHex('0X1.00000000000005p0'), 1.0)
+ self.identical(fromHex('0X1.00000000000006p0'), 1.0)
+ self.identical(fromHex('0X1.00000000000007p0'), 1.0)
+ self.identical(fromHex('0x1.00000000000007ffffffffffffffffffffp0'),
+ 1.0)
+ self.identical(fromHex('0x1.00000000000008p0'), 1.0)
+ self.identical(fromHex('0x1.00000000000008000000000000000001p0'),
+ 1+EPS)
+ self.identical(fromHex('0X1.00000000000009p0'), 1.0+EPS)
+ self.identical(fromHex('0x1.0000000000000ap0'), 1.0+EPS)
+ self.identical(fromHex('0x1.0000000000000bp0'), 1.0+EPS)
+ self.identical(fromHex('0X1.0000000000000cp0'), 1.0+EPS)
+ self.identical(fromHex('0x1.0000000000000dp0'), 1.0+EPS)
+ self.identical(fromHex('0x1.0000000000000ep0'), 1.0+EPS)
+ self.identical(fromHex('0X1.0000000000000fp0'), 1.0+EPS)
+ self.identical(fromHex('0x1.00000000000010p0'), 1.0+EPS)
+ self.identical(fromHex('0X1.00000000000011p0'), 1.0+EPS)
+ self.identical(fromHex('0x1.00000000000012p0'), 1.0+EPS)
+ self.identical(fromHex('0X1.00000000000013p0'), 1.0+EPS)
+ self.identical(fromHex('0X1.00000000000014p0'), 1.0+EPS)
+ self.identical(fromHex('0x1.00000000000015p0'), 1.0+EPS)
+ self.identical(fromHex('0x1.00000000000016p0'), 1.0+EPS)
+ self.identical(fromHex('0X1.00000000000017p0'), 1.0+EPS)
+ self.identical(fromHex('0x1.00000000000017ffffffffffffffffffffp0'),
+ 1.0+EPS)
+ self.identical(fromHex('0x1.00000000000018p0'), 1.0+2*EPS)
+ self.identical(fromHex('0X1.00000000000018000000000000000001p0'),
+ 1.0+2*EPS)
+ self.identical(fromHex('0x1.00000000000019p0'), 1.0+2*EPS)
+ self.identical(fromHex('0X1.0000000000001ap0'), 1.0+2*EPS)
+ self.identical(fromHex('0X1.0000000000001bp0'), 1.0+2*EPS)
+ self.identical(fromHex('0x1.0000000000001cp0'), 1.0+2*EPS)
+ self.identical(fromHex('0x1.0000000000001dp0'), 1.0+2*EPS)
+ self.identical(fromHex('0x1.0000000000001ep0'), 1.0+2*EPS)
+ self.identical(fromHex('0X1.0000000000001fp0'), 1.0+2*EPS)
+ self.identical(fromHex('0x1.00000000000020p0'), 1.0+2*EPS)
+
+ 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 xrange(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)))
+
def test_main():
test_support.run_unittest(
@@ -351,6 +735,7 @@
IEEEFormatTestCase,
ReprTestCase,
InfNanTest,
+ HexFloatTestCase,
)
if __name__ == '__main__':