Known Floating-point Bugs Detected by TestFloat
John R. Hauser
1997 December 15
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Introduction
Several popular systems have bugs that TestFloat is very likely to run
across. The ones I know of are documented here. First off, TestFloat finds
no errors in the following processors/machines:
AMD 486 DX4's
Sun UltraSPARC 1's and 2's
On the other hand, bugs are found in these processors/machines:
Older Intel Pentiums (with the divide bug)
Intel Pentium Pros
Sun SPARCstation 1's and IPX's
Sun SPARCstation 10's
HP Precision Architecture processors, with HP-UX prior to version 10.10
For some reason, most of the bugs found involve conversions from floating-
point to integer formats.
The bugs are shown as actual TestFloat error lines, along with a brief
explanation. The error lines given are not necessarily exhaustive and were
not necessarily output in the order shown.
This document does not pretend to be an authoritative bug listing for all
commercial processors. The vast majority of processors are absent from this
list because I have never run TestFloat on such machines and I thus have no
knowledge of what bugs TestFloat might find in them.
The latest version of this file can be found at the Web page `http://
http.cs.berkeley.edu/~jhauser/arithmetic/testfloat.html'.
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Older Intel Pentiums (with the divide bug)
The following conversion problems are found on Pentiums that also suffer
from the infamous floating-point divide bug. These bugs have been fixed on
newer Pentiums. (TestFloat does not find the divide bug.)
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floatx80_to_int32
-- A few small fractions are treated as though they were zero.
Errors found in floatx80_to_int32, rounding nearest_even:
3FFB.8000000000000000 soft: 00000000 ....x syst: 00000000 .....
3FFC.8000000000000000 soft: 00000000 ....x syst: 00000000 .....
3FFC.C000000000000000 soft: 00000000 ....x syst: 00000000 .....
BFFB.8000000000000000 soft: 00000000 ....x syst: 00000000 .....
BFFC.8000000000000000 soft: 00000000 ....x syst: 00000000 .....
Errors found in floatx80_to_int32, rounding to_zero:
3FFB.8000000000000000 soft: 00000000 ....x syst: 00000000 .....
3FFC.8000000000000000 soft: 00000000 ....x syst: 00000000 .....
3FFC.C000000000000000 soft: 00000000 ....x syst: 00000000 .....
BFFB.8000000000000000 soft: 00000000 ....x syst: 00000000 .....
BFFC.8000000000000000 soft: 00000000 ....x syst: 00000000 .....
BFFC.C000000000000000 soft: 00000000 ....x syst: 00000000 .....
Errors found in floatx80_to_int32, rounding down:
3FFB.8000000000000000 soft: 00000000 ....x syst: 00000000 .....
3FFC.8000000000000000 soft: 00000000 ....x syst: 00000000 .....
3FFC.C000000000000000 soft: 00000000 ....x syst: 00000000 .....
BFFB.8000000000000000 soft: FFFFFFFF ....x syst: 00000000 .....
BFFC.8000000000000000 soft: FFFFFFFF ....x syst: 00000000 .....
BFFC.C000000000000000 soft: FFFFFFFF ....x syst: 00000000 .....
Errors found in floatx80_to_int32, rounding up:
3FFB.8000000000000000 soft: 00000001 ....x syst: 00000000 .....
3FFC.8000000000000000 soft: 00000001 ....x syst: 00000000 .....
3FFC.C000000000000000 soft: 00000001 ....x syst: 00000000 .....
BFFB.8000000000000000 soft: 00000000 ....x syst: 00000000 .....
BFFC.8000000000000000 soft: 00000000 ....x syst: 00000000 .....
3FFB.8000000000000000 is the fraction 1/16; 3FFC.8000000000000000 is 1/8;
and 3FFC.C000000000000000 is 3/16. Both positive and negative inputs are
affected.
-- Some (all?) positive floating-point values between 2^32 - 1/2
(401E.FFFFFFFF00000000) and 2^32 (401F.0000000000000000) are rounded to
zero when the rounding mode is nearest/even or up.
Errors found in floatx80_to_int32, rounding nearest_even:
401E.FFFFFFFF80000000 soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFC00001FE soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFF8000000 soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFFEC00000 soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFFF002000 soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFFFC00000 soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFFFE00000 soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFFFFD7FFE soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFFFFFFFFE soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFFFFFFFFF soft: 7FFFFFFF v.... syst: 00000000 ....x
Errors found in floatx80_to_int32, rounding up:
401E.FFFFFFFF00800000 soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFF80000000 soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFEFFFC000 soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFFC000000 soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFFE7FFFFF soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFFFF00000 soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFFFFE0800 soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFFFFF7FFB soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFFFFFFFFE soft: 7FFFFFFF v.... syst: 00000000 ....x
401E.FFFFFFFFFFFFFFFF soft: 7FFFFFFF v.... syst: 00000000 ....x
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-------------------------------------------------------------------------------
Intel Pentium Pros
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floatx80_to_int32
-- The inexact flag is sometimes raised instead of the invalid flag for
floating-point inputs under -(2^32) (C01F.0000000000000000). This bug is
sporadic. It appears to be deterministic but dependent on the sequence
of operations executed.
Errors found in floatx80_to_int32, rounding nearest_even:
C01F.C000000000000002 soft: 80000000 v.... syst: 80000000 ....x
C021.F00000000000003F soft: 80000000 v.... syst: 80000000 ....x
Errors found in floatx80_to_int32, rounding to_zero:
C021.F00000000000003F soft: 80000000 v.... syst: 80000000 ....x
Errors found in floatx80_to_int32, rounding up:
C01F.C000000000000007 soft: 80000000 v.... syst: 80000000 ....x
C01F.C000000000001000 soft: 80000000 v.... syst: 80000000 ....x
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Sun SPARCstation 1's and IPX's
Some older SPARCstations appear confused about whether underflow tininess is
detected before or after rounding. For conversions from double precision
to single precision, tininess is detected after rounding, while for all
quadruple-precision operations it is detected before rounding. Single- and
double-precision multipies go both ways:
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float32_mul, float64_mul
-- For multiplies, underflow tininess is detected _before_ rounding if one
of the inputs is subnormal, and _after_ rounding otherwise. If tininess
is assumed to be detected before rounding, the following errors are
generated:
Errors found in float32_mul, rounding nearest_even:
001.000001 07E.7FFFFE soft: 001.000000 ...ux syst: 001.000000 ....x
001.000001 87E.7FFFFE soft: 801.000000 ...ux syst: 801.000000 ....x
001.000002 07E.7FFFFC soft: 001.000000 ...ux syst: 001.000000 ....x
001.000002 87E.7FFFFC soft: 801.000000 ...ux syst: 801.000000 ....x
001.000004 07E.7FFFF8 soft: 001.000000 ...ux syst: 001.000000 ....x
Errors found in float32_mul, rounding down:
001.000001 87E.7FFFFE soft: 801.000000 ...ux syst: 801.000000 ....x
001.000002 87E.7FFFFC soft: 801.000000 ...ux syst: 801.000000 ....x
001.000004 87E.7FFFF8 soft: 801.000000 ...ux syst: 801.000000 ....x
001.000008 87E.7FFFF0 soft: 801.000000 ...ux syst: 801.000000 ....x
001.000010 87E.7FFFE0 soft: 801.000000 ...ux syst: 801.000000 ....x
Errors found in float32_mul, rounding up:
001.000001 07E.7FFFFE soft: 001.000000 ...ux syst: 001.000000 ....x
001.000002 07E.7FFFFC soft: 001.000000 ...ux syst: 001.000000 ....x
001.000004 07E.7FFFF8 soft: 001.000000 ...ux syst: 001.000000 ....x
001.000008 07E.7FFFF0 soft: 001.000000 ...ux syst: 001.000000 ....x
001.000010 07E.7FFFE0 soft: 001.000000 ...ux syst: 001.000000 ....x
Errors found in float64_mul, rounding nearest_even:
001.0000000000001 3FE.FFFFFFFFFFFFE
soft: 001.0000000000000 ...ux syst: 001.0000000000000 ....x
001.0000000000001 BFE.FFFFFFFFFFFFE
soft: 801.0000000000000 ...ux syst: 801.0000000000000 ....x
001.0000000000002 3FE.FFFFFFFFFFFFC
soft: 001.0000000000000 ...ux syst: 001.0000000000000 ....x
001.0000000000002 BFE.FFFFFFFFFFFFC
soft: 801.0000000000000 ...ux syst: 801.0000000000000 ....x
001.0000000000004 3FE.FFFFFFFFFFFF8
soft: 001.0000000000000 ...ux syst: 001.0000000000000 ....x
Errors found in float64_mul, rounding down:
001.0000000000001 BFE.FFFFFFFFFFFFE
soft: 801.0000000000000 ...ux syst: 801.0000000000000 ....x
001.0000000000002 BFE.FFFFFFFFFFFFC
soft: 801.0000000000000 ...ux syst: 801.0000000000000 ....x
001.0000000000004 BFE.FFFFFFFFFFFF8
soft: 801.0000000000000 ...ux syst: 801.0000000000000 ....x
001.0000000000008 BFE.FFFFFFFFFFFF0
soft: 801.0000000000000 ...ux syst: 801.0000000000000 ....x
001.0000000000010 BFE.FFFFFFFFFFFE0
soft: 801.0000000000000 ...ux syst: 801.0000000000000 ....x
Errors found in float64_mul, rounding up:
001.0000000000001 3FE.FFFFFFFFFFFFE
soft: 001.0000000000000 ...ux syst: 001.0000000000000 ....x
001.0000000000002 3FE.FFFFFFFFFFFFC
soft: 001.0000000000000 ...ux syst: 001.0000000000000 ....x
001.0000000000004 3FE.FFFFFFFFFFFF8
soft: 001.0000000000000 ...ux syst: 001.0000000000000 ....x
001.0000000000008 3FE.FFFFFFFFFFFF0
soft: 001.0000000000000 ...ux syst: 001.0000000000000 ....x
001.0000000000010 3FE.FFFFFFFFFFFE0
soft: 001.0000000000000 ...ux syst: 001.0000000000000 ....x
If we assume tininess should be detected after rounding, we get the
following errors:
Errors found in float32_mul, rounding nearest_even:
000.7FFC00 07F.000400 soft: 001.000000 ....x syst: 001.000000 ...ux
000.7FFC00 87F.000400 soft: 801.000000 ....x syst: 801.000000 ...ux
000.7FFE00 07F.000200 soft: 001.000000 ....x syst: 001.000000 ...ux
000.7FFE00 87F.000200 soft: 801.000000 ....x syst: 801.000000 ...ux
000.7FFF00 07F.000100 soft: 001.000000 ....x syst: 001.000000 ...ux
Errors found in float32_mul, rounding down:
000.7FFC00 87F.000400 soft: 801.000000 ....x syst: 801.000000 ...ux
000.7FFE00 87F.000200 soft: 801.000000 ....x syst: 801.000000 ...ux
000.7FFF00 87F.000100 soft: 801.000000 ....x syst: 801.000000 ...ux
000.7FFF80 87F.000080 soft: 801.000000 ....x syst: 801.000000 ...ux
000.7FFFC0 87F.000040 soft: 801.000000 ....x syst: 801.000000 ...ux
Errors found in float32_mul, rounding up:
000.7FFC00 07F.000400 soft: 001.000000 ....x syst: 001.000000 ...ux
000.7FFE00 07F.000200 soft: 001.000000 ....x syst: 001.000000 ...ux
000.7FFF00 07F.000100 soft: 001.000000 ....x syst: 001.000000 ...ux
000.7FFF80 07F.000080 soft: 001.000000 ....x syst: 001.000000 ...ux
000.7FFFC0 07F.000040 soft: 001.000000 ....x syst: 001.000000 ...ux
Errors found in float64_mul, rounding nearest_even:
000.FFFFFFE000000 3FF.0000002000000
soft: 001.0000000000000 ....x syst: 001.0000000000000 ...ux
000.FFFFFFE000000 BFF.0000002000000
soft: 801.0000000000000 ....x syst: 801.0000000000000 ...ux
000.FFFFFFF000000 3FF.0000001000000
soft: 001.0000000000000 ....x syst: 001.0000000000000 ...ux
000.FFFFFFF000000 BFF.0000001000000
soft: 801.0000000000000 ....x syst: 801.0000000000000 ...ux
000.FFFFFFF800000 3FF.0000000800000
soft: 001.0000000000000 ....x syst: 001.0000000000000 ...ux
Errors found in float64_mul, rounding down:
000.FFFFFFE000000 BFF.0000002000000
soft: 801.0000000000000 ....x syst: 801.0000000000000 ...ux
000.FFFFFFF000000 BFF.0000001000000
soft: 801.0000000000000 ....x syst: 801.0000000000000 ...ux
000.FFFFFFF800000 BFF.0000000800000
soft: 801.0000000000000 ....x syst: 801.0000000000000 ...ux
000.FFFFFFFC00000 BFF.0000000400000
soft: 801.0000000000000 ....x syst: 801.0000000000000 ...ux
000.FFFFFFFE00000 BFF.0000000200000
soft: 801.0000000000000 ....x syst: 801.0000000000000 ...ux
Errors found in float64_mul, rounding up:
000.FFFFFFE000000 3FF.0000002000000
soft: 001.0000000000000 ....x syst: 001.0000000000000 ...ux
000.FFFFFFF000000 3FF.0000001000000
soft: 001.0000000000000 ....x syst: 001.0000000000000 ...ux
000.FFFFFFF800000 3FF.0000000800000
soft: 001.0000000000000 ....x syst: 001.0000000000000 ...ux
000.FFFFFFFC00000 3FF.0000000400000
soft: 001.0000000000000 ....x syst: 001.0000000000000 ...ux
000.FFFFFFFE00000 3FF.0000000200000
soft: 001.0000000000000 ....x syst: 001.0000000000000 ...ux
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Sun SPARCstation 10's
Like other SPARCstations, some SPARCstation 10's are inconsistent regarding
underflow tininess, detecting it after rounding for single- and double-
precision operations and before rounding for quadruple-precision operations.
The following bug has also been observed.
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float32_to_int32_round_to_zero, float64_to_int32_round_to_zero
-- Single- and double-precision NaNs are converted to the integer zero.
(The invalid exception flag is raised correctly.)
Errors found in float32_to_int32_round_to_zero:
8FF.5D36AC soft: 7FFFFFFF v.... syst: 00000000 v....
0FF.7FFFC0 soft: 7FFFFFFF v.... syst: 00000000 v....
8FF.7C0000 soft: 7FFFFFFF v.... syst: 00000000 v....
0FF.2AB7ED soft: 7FFFFFFF v.... syst: 00000000 v....
0FF.03FFFF soft: 7FFFFFFF v.... syst: 00000000 v....
Errors found in float64_to_int32_round_to_zero:
7FF.45AD84DB2524A soft: 7FFFFFFF v.... syst: 00000000 v....
7FF.CFEE063EE0512 soft: 7FFFFFFF v.... syst: 00000000 v....
7FF.89FF03AB7DBA2 soft: 7FFFFFFF v.... syst: 00000000 v....
7FF.FFFFFFFFFF800 soft: 7FFFFFFF v.... syst: 00000000 v....
FFF.68A6410E91BF6 soft: 7FFFFFFF v.... syst: 00000000 v....
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-------------------------------------------------------------------------------
HP Precision Architecture processors, with HP-UX prior to version 10.10
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float32_to_int32_round_to_zero, float64_to_int32_round_to_zero
-- When the floating-point value is too large, the overflow and inexact
exception flags are raised instead of the invalid flag.
Errors found in float32_to_int32_round_to_zero:
89E.000007 soft: 80000000 v.... syst: 80000000 ..o.x
0A2.000020 soft: 7FFFFFFF v.... syst: 7FFFFFFF ..o.x
8FA.7C0000 soft: 80000000 v.... syst: 80000000 ..o.x
Errors found in float64_to_int32_round_to_zero:
7FD.0448700002F1C soft: 7FFFFFFF v.... syst: 7FFFFFFF ..o.x
DAA.F000000000000 soft: 80000000 v.... syst: 80000000 ..o.x
41E.063DA00005E65 soft: 7FFFFFFF v.... syst: 7FFFFFFF ..o.x
47E.FFFF800000000 soft: 7FFFFFFF v.... syst: 7FFFFFFF ..o.x
51F.0000000000004 soft: 7FFFFFFF v.... syst: 7FFFFFFF ..o.x
DDA.0000001FFFFFF soft: 80000000 v.... syst: 80000000 ..o.x
D70.00000000003FF soft: 80000000 v.... syst: 80000000 ..o.x
C7E.0000100000000 soft: 80000000 v.... syst: 80000000 ..o.x
47E.000000000007F soft: 7FFFFFFF v.... syst: 7FFFFFFF ..o.x
D57.000000000FFFF soft: 80000000 v.... syst: 80000000 ..o.x
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