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