diff options
| -rw-r--r-- | Doc/library/stdtypes.rst | 65 | ||||
| -rw-r--r-- | Doc/whatsnew/2.6.rst | 5 | ||||
| -rw-r--r-- | Lib/test/test_float.py | 386 | ||||
| -rw-r--r-- | Misc/NEWS | 4 | ||||
| -rw-r--r-- | Objects/floatobject.c | 408 |
5 files changed, 867 insertions, 1 deletions
diff --git a/Doc/library/stdtypes.rst b/Doc/library/stdtypes.rst index a97a519..586770a 100644 --- a/Doc/library/stdtypes.rst +++ b/Doc/library/stdtypes.rst @@ -423,6 +423,71 @@ Notes: .. _typeiter: + +Additional Methods on Float +--------------------------- + +The float type has some additional methods to support conversion to +and from hexadecimal strings. Since Python's floats are stored +internally as binary numbers, converting a float to or from a +*decimal* string usually involves a small rounding error. In +contrast, hexadecimal strings allow exact representation and +specification of floating-point numbers. This can be useful when +debugging, and in numerical work. + + +.. method:: float.hex() + + Return a representation of a floating-point number as a hexadecimal + string. For finite floating-point numbers, this representation + will always include a leading ``0x`` and a trailing ``p`` and + exponent. + + +.. method:: float.fromhex(s) + + Class method to return the float represented by a hexadecimal + string *s*. The string *s* may have leading and trailing + whitespace. + + +Note that :meth:`float.hex` is an instance method, while +:meth:`float.fromhex` is a class method. + +A hexadecimal string takes the form:: + + [sign] ['0x'] integer ['.' fraction] ['p' exponent] + +where the optional ``sign`` may by either ``+`` or ``-``, ``integer`` +and ``fraction`` are strings of hexadecimal digits, and ``exponent`` +is a decimal integer with an optional leading sign. Case is not +significant, and there must be at least one hexadecimal digit in +either the integer or the fraction. This syntax is similar to the +syntax specified in section 6.4.4.2 of the C99 standard, and also to +the syntax used in Java 1.5 onwards. In particular, the output of +:meth:`float.hex` is usable as a hexadecimal floating-point literal in +C or Java code, and hexadecimal strings produced by C's ``%a`` format +character or Java's ``Double.toHexString`` are accepted by +:meth:`float.fromhex`. + + +Note that the exponent is written in decimal rather than hexadecimal, +and that it gives the power of 2 by which to multiply the coefficient. +For example, the hexadecimal string ``0x3.a7p10`` represents the +floating-point number ``(3 + 10./16 + 7./16**2) * 2.0**10``, or +``3740.0``:: + + >>> float.fromhex('0x3.a7p10') + 3740.0 + + +Applying the reverse conversion to ``3740.0`` gives a different +hexadecimal string representing the same number:: + + >>> float.hex(3740.0) + '0x1.d380000000000p+11' + + Iterator Types ============== diff --git a/Doc/whatsnew/2.6.rst b/Doc/whatsnew/2.6.rst index df5ccb6..264ec2e 100644 --- a/Doc/whatsnew/2.6.rst +++ b/Doc/whatsnew/2.6.rst @@ -1397,6 +1397,11 @@ Here are all of the changes that Python 2.6 makes to the core Python language. :func:`isnan`, return true if their floating-point argument is infinite or Not A Number. (:issue:`1640`) + The float type has a new instance method :meth:`float.hex` and a + corresponding new class method :meth:`float.fromhex` to convert + floating-point numbers to and from hexadecimal strings, + respectively. (:issue:`3008`) + * The :mod:`math` module has a number of new functions, and the existing functions have been improved to give more consistent behaviour across platforms, especially with respect to handling of diff --git a/Lib/test/test_float.py b/Lib/test/test_float.py index 4078973..9b84531 100644 --- a/Lib/test/test_float.py +++ b/Lib/test/test_float.py @@ -3,7 +3,7 @@ import unittest, struct import os from test import support import math -from math import isinf, isnan +from math import isinf, isnan, copysign, ldexp import operator INF = float("inf") @@ -358,6 +358,389 @@ class InfNanTest(unittest.TestCase): 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', + '0x1p\uff10', # fullwidth Unicode digits + '\uff10x1p0', + '0x\uff11p0', + '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(' 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 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))) + def test_main(): support.run_unittest( @@ -367,6 +750,7 @@ def test_main(): FormatTestCase, ReprTestCase, InfNanTest, + HexFloatTestCase, ) if __name__ == '__main__': @@ -12,6 +12,10 @@ What's new in Python 3.0b2? Core and Builtins ----------------- +- Issue #3008: the float type has a new instance method 'float.hex' + and a new class method 'float.fromhex' to convert floating-point + numbers to and from hexadecimal strings, respectively. + - Issue #3083: Add alternate (#) formatting for bin, oct, hex output for str.format(). This adds the prefix 0b, 0o, or 0x, respectively. diff --git a/Objects/floatobject.c b/Objects/floatobject.c index db1c99f..f18e7dd 100644 --- a/Objects/floatobject.c +++ b/Objects/floatobject.c @@ -10,6 +10,11 @@ #include <ctype.h> #include <float.h> +#undef MAX +#undef MIN +#define MAX(x, y) ((x) < (y) ? (y) : (x)) +#define MIN(x, y) ((x) < (y) ? (x) : (y)) + #ifdef HAVE_IEEEFP_H #include <ieeefp.h> #endif @@ -1015,6 +1020,405 @@ float_float(PyObject *v) return v; } +/* turn ASCII hex characters into integer values and vice versa */ + +static char +char_from_hex(int x) +{ + assert(0 <= x && x < 16); + return "0123456789abcdef"[x]; +} + +static int +hex_from_char(char c) { + int x; + assert(isxdigit(c)); + switch(c) { + case '0': + x = 0; + break; + case '1': + x = 1; + break; + case '2': + x = 2; + break; + case '3': + x = 3; + break; + case '4': + x = 4; + break; + case '5': + x = 5; + break; + case '6': + x = 6; + break; + case '7': + x = 7; + break; + case '8': + x = 8; + break; + case '9': + x = 9; + break; + case 'a': + case 'A': + x = 10; + break; + case 'b': + case 'B': + x = 11; + break; + case 'c': + case 'C': + x = 12; + break; + case 'd': + case 'D': + x = 13; + break; + case 'e': + case 'E': + x = 14; + break; + case 'f': + case 'F': + x = 15; + break; + default: + x = -1; + break; + } + return x; +} + +/* convert a float to a hexadecimal string */ + +/* TOHEX_NBITS is DBL_MANT_DIG rounded up to the next integer + of the form 4k+1. */ +#define TOHEX_NBITS DBL_MANT_DIG + 3 - (DBL_MANT_DIG+2)%4 + +static PyObject * +float_hex(PyObject *v) +{ + double x, m; + int e, shift, i, si, esign; + /* Space for 1+(TOHEX_NBITS-1)/4 digits, a decimal point, and the + trailing NUL byte. */ + char s[(TOHEX_NBITS-1)/4+3]; + + CONVERT_TO_DOUBLE(v, x); + + if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) + return float_str((PyFloatObject *)v); + + if (x == 0.0) { + if(copysign(1.0, x) == -1.0) + return PyUnicode_FromString("-0x0.0p+0"); + else + return PyUnicode_FromString("0x0.0p+0"); + } + + m = frexp(fabs(x), &e); + shift = 1 - MAX(DBL_MIN_EXP - e, 0); + m = ldexp(m, shift); + e -= shift; + + si = 0; + s[si] = char_from_hex((int)m); + si++; + m -= (int)m; + s[si] = '.'; + si++; + for (i=0; i < (TOHEX_NBITS-1)/4; i++) { + m *= 16.0; + s[si] = char_from_hex((int)m); + si++; + m -= (int)m; + } + s[si] = '\0'; + + if (e < 0) { + esign = (int)'-'; + e = -e; + } + else + esign = (int)'+'; + + if (x < 0.0) + return PyUnicode_FromFormat("-0x%sp%c%d", s, esign, e); + else + return PyUnicode_FromFormat("0x%sp%c%d", s, esign, e); +} + +PyDoc_STRVAR(float_hex_doc, +"float.hex() -> string\n\ +\n\ +Return a hexadecimal representation of a floating-point number.\n\ +>>> (-0.1).hex()\n\ +'-0x1.999999999999ap-4'\n\ +>>> 3.14159.hex()\n\ +'0x1.921f9f01b866ep+1'"); + +/* Convert a hexadecimal string to a float. */ + +static PyObject * +float_fromhex(PyObject *cls, PyObject *arg) +{ + PyObject *result_as_float, *result; + double x; + long exp, top_exp, lsb, key_digit; + char *s, *coeff_start, *s_store, *coeff_end, *exp_start, *s_end; + int half_eps, digit, round_up, sign=1; + Py_ssize_t length, ndigits, fdigits, i; + + /* + * For the sake of simplicity and correctness, we impose an artificial + * limit on ndigits, the total number of hex digits in the coefficient + * The limit is chosen to ensure that, writing exp for the exponent, + * + * (1) if exp > LONG_MAX/2 then the value of the hex string is + * guaranteed to overflow (provided it's nonzero) + * + * (2) if exp < LONG_MIN/2 then the value of the hex string is + * guaranteed to underflow to 0. + * + * (3) if LONG_MIN/2 <= exp <= LONG_MAX/2 then there's no danger of + * overflow in the calculation of exp and top_exp below. + * + * More specifically, ndigits is assumed to satisfy the following + * inequalities: + * + * 4*ndigits <= DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2 + * 4*ndigits <= LONG_MAX/2 + 1 - DBL_MAX_EXP + * + * If either of these inequalities is not satisfied, a ValueError is + * raised. Otherwise, write x for the value of the hex string, and + * assume x is nonzero. Then + * + * 2**(exp-4*ndigits) <= |x| < 2**(exp+4*ndigits). + * + * Now if exp > LONG_MAX/2 then: + * + * exp - 4*ndigits >= LONG_MAX/2 + 1 - (LONG_MAX/2 + 1 - DBL_MAX_EXP) + * = DBL_MAX_EXP + * + * so |x| >= 2**DBL_MAX_EXP, which is too large to be stored in C + * double, so overflows. If exp < LONG_MIN/2, then + * + * exp + 4*ndigits <= LONG_MIN/2 - 1 + ( + * DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2) + * = DBL_MIN_EXP - DBL_MANT_DIG - 1 + * + * and so |x| < 2**(DBL_MIN_EXP-DBL_MANT_DIG-1), hence underflows to 0 + * when converted to a C double. + * + * It's easy to show that if LONG_MIN/2 <= exp <= LONG_MAX/2 then both + * exp+4*ndigits and exp-4*ndigits are within the range of a long. + */ + + s = PyUnicode_AsStringAndSize(arg, &length); + if (s == NULL) + return NULL; + s_end = s + length; + + /******************** + * Parse the string * + ********************/ + + /* leading whitespace and optional sign */ + while (isspace(*s)) + s++; + if (*s == '-') { + s++; + sign = -1; + } + else if (*s == '+') + s++; + + /* infinities and nans */ + if (PyOS_mystrnicmp(s, "nan", 4) == 0) { + x = Py_NAN; + goto finished; + } + if (PyOS_mystrnicmp(s, "inf", 4) == 0 || + PyOS_mystrnicmp(s, "infinity", 9) == 0) { + x = sign*Py_HUGE_VAL; + goto finished; + } + + /* [0x] */ + s_store = s; + if (*s == '0') { + s++; + if (tolower(*s) == (int)'x') + s++; + else + s = s_store; + } + + /* coefficient: <integer> [. <fraction>] */ + coeff_start = s; + while (isxdigit(*s)) + s++; + s_store = s; + if (*s == '.') { + s++; + while (isxdigit(*s)) + s++; + coeff_end = s-1; + } + else + coeff_end = s; + + /* ndigits = total # of hex digits; fdigits = # after point */ + ndigits = coeff_end - coeff_start; + fdigits = coeff_end - s_store; + if (ndigits == 0) + goto parse_error; + if (ndigits > MIN(DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2, + LONG_MAX/2 + 1 - DBL_MAX_EXP)/4) + goto insane_length_error; + + /* [p <exponent>] */ + if (tolower(*s) == (int)'p') { + s++; + exp_start = s; + if (*s == '-' || *s == '+') + s++; + if (!isdigit(*s)) + goto parse_error; + s++; + while (isdigit(*s)) + s++; + exp = strtol(exp_start, NULL, 10); + } + else + exp = 0; + + /* optional trailing whitespace leading to the end of the string */ + while (isspace(*s)) + s++; + if (s != s_end) + goto parse_error; + +/* for 0 <= j < ndigits, HEX_DIGIT(j) gives the jth most significant digit */ +#define HEX_DIGIT(j) hex_from_char(*((j) < fdigits ? \ + coeff_end-(j) : \ + coeff_end-1-(j))) + + /******************************************* + * Compute rounded value of the hex string * + *******************************************/ + + /* Discard leading zeros, and catch extreme overflow and underflow */ + while (ndigits > 0 && HEX_DIGIT(ndigits-1) == 0) + ndigits--; + if (ndigits == 0 || exp < LONG_MIN/2) { + x = sign * 0.0; + goto finished; + } + if (exp > LONG_MAX/2) + goto overflow_error; + + /* Adjust exponent for fractional part. */ + exp = exp - 4*((long)fdigits); + + /* top_exp = 1 more than exponent of most sig. bit of coefficient */ + top_exp = exp + 4*((long)ndigits - 1); + for (digit = HEX_DIGIT(ndigits-1); digit != 0; digit /= 2) + top_exp++; + + /* catch almost all nonextreme cases of overflow and underflow here */ + if (top_exp < DBL_MIN_EXP - DBL_MANT_DIG) { + x = sign * 0.0; + goto finished; + } + if (top_exp > DBL_MAX_EXP) + goto overflow_error; + + /* lsb = exponent of least significant bit of the *rounded* value. + This is top_exp - DBL_MANT_DIG unless result is subnormal. */ + lsb = MAX(top_exp, (long)DBL_MIN_EXP) - DBL_MANT_DIG; + + x = 0.0; + if (exp >= lsb) { + /* no rounding required */ + for (i = ndigits-1; i >= 0; i--) + x = 16.0*x + HEX_DIGIT(i); + x = sign * ldexp(x, (int)(exp)); + goto finished; + } + /* rounding required. key_digit is the index of the hex digit + containing the first bit to be rounded away. */ + half_eps = 1 << (int)((lsb - exp - 1) % 4); + key_digit = (lsb - exp - 1) / 4; + for (i = ndigits-1; i > key_digit; i--) + x = 16.0*x + HEX_DIGIT(i); + digit = HEX_DIGIT(key_digit); + x = 16.0*x + (double)(digit & (16-2*half_eps)); + + /* round-half-even: round up if bit lsb-1 is 1 and at least one of + bits lsb, lsb-2, lsb-3, lsb-4, ... is 1. */ + if ((digit & half_eps) != 0) { + round_up = 0; + if ((digit & (3*half_eps-1)) != 0 || + (half_eps == 8 && (HEX_DIGIT(key_digit+1) & 1) != 0)) + round_up = 1; + else + for (i = key_digit-1; i >= 0; i--) + if (HEX_DIGIT(i) != 0) { + round_up = 1; + break; + } + if (round_up == 1) { + x += 2*half_eps; + if (top_exp == DBL_MAX_EXP && + x == ldexp((double)(2*half_eps), DBL_MANT_DIG)) + /* overflow corner case: pre-rounded value < + 2**DBL_MAX_EXP; rounded=2**DBL_MAX_EXP. */ + goto overflow_error; + } + } + x = sign * ldexp(x, (int)(exp+4*key_digit)); + + finished: + result_as_float = Py_BuildValue("(d)", x); + if (result_as_float == NULL) + return NULL; + result = PyObject_CallObject(cls, result_as_float); + Py_DECREF(result_as_float); + return result; + + overflow_error: + PyErr_SetString(PyExc_OverflowError, + "hexadecimal value too large to represent as a float"); + return NULL; + + parse_error: + PyErr_SetString(PyExc_ValueError, + "invalid hexadecimal floating-point string"); + return NULL; + + insane_length_error: + PyErr_SetString(PyExc_ValueError, + "hexadecimal string too long to convert"); + return NULL; +} + +PyDoc_STRVAR(float_fromhex_doc, +"float.fromhex(string) -> float\n\ +\n\ +Create a floating-point number from a hexadecimal string.\n\ +>>> float.fromhex('0x1.ffffp10')\n\ +2047.984375\n\ +>>> float.fromhex('-0x1p-1074')\n\ +-4.9406564584124654e-324"); + + static PyObject * float_as_integer_ratio(PyObject *v, PyObject *unused) { @@ -1326,6 +1730,10 @@ static PyMethodDef float_methods[] = { "When an argument is passed, works like built-in round(x, ndigits)."}, {"as_integer_ratio", (PyCFunction)float_as_integer_ratio, METH_NOARGS, float_as_integer_ratio_doc}, + {"fromhex", (PyCFunction)float_fromhex, + METH_O|METH_CLASS, float_fromhex_doc}, + {"hex", (PyCFunction)float_hex, + METH_NOARGS, float_hex_doc}, {"is_integer", (PyCFunction)float_is_integer, METH_NOARGS, "Returns True if the float is an integer."}, #if 0 |