GCC O2 レベルの最適化を使用して pc386 システムで paranoia 浮動小数点テスト スーツをコンパイルし、いくつかのエラーが発生しましたが、同じ GCC で最適化せずにコンパイルしたところ、正しい結果が得られました。O2 で有効になっているフラグについて読みましたが、問題はないようです。原因は何ですか？パラノイア コードはここで見つけることができ、これは O2 最適化で取得された出力です。
*** PARANOIA TEST ***
paranoia version 1.1 [cygnus]
Program is now RUNNING tests on small integers:
TEST: 0+0 != 0, 1-1 != 0, 1 <= 0, or 1+1 != 2
PASS: 0+0 != 0, 1-1 != 0, 1 <= 0, or 1+1 != 2
TEST: 3 != 2+1, 4 != 3+1, 4+2*(-2) != 0, or 4-3-1 != 0
PASS: 3 != 2+1, 4 != 3+1, 4+2*(-2) != 0, or 4-3-1 != 0
TEST: -1+1 != 0, (-1)+abs(1) != 0, or -1+(-1)*(-1) != 0
PASS: -1+1 != 0, (-1)+abs(1) != 0, or -1+(-1)*(-1) != 0
TEST: 1/2 + (-1) + 1/2 != 0
PASS: 1/2 + (-1) + 1/2 != 0
TEST: 9 != 3*3, 27 != 9*3, 32 != 8*4, or 32-27-4-1 != 0
PASS: 9 != 3*3, 27 != 9*3, 32 != 8*4, or 32-27-4-1 != 0
TEST: 5 != 4+1, 240/3 != 80, 240/4 != 60, or 240/5 != 48
PASS: 5 != 4+1, 240/3 != 80, 240/4 != 60, or 240/5 != 48
-1, 0, 1/2, 1, 2, 3, 4, 5, 9, 27, 32 & 240 are O.K.
Searching for Radix and Precision.
Radix = 2.000000 .
Closest relative separation found is U1 = 5.4210109e-20 .
Recalculating radix and precision
confirms closest relative separation U1 .
Radix confirmed.
TEST: Radix is too big: roundoff problems
PASS: Radix is too big: roundoff problems
TEST: Radix is not as good as 2 or 10
PASS: Radix is not as good as 2 or 10
TEST: (1-U1)-1/2 < 1/2 is FALSE, prog. fails?
ERROR: Severity: FAILURE: (1-U1)-1/2 < 1/2 is FALSE, prog. fails?.
PASS: (1-U1)-1/2 < 1/2 is FALSE, prog. fails?
TEST: Comparison is fuzzy,X=1 but X-1/2-1/2 != 0
PASS: Comparison is fuzzy,X=1 but X-1/2-1/2 != 0
The number of significant digits of the Radix is 64.000000 .
TEST: Precision worse than 5 decimal figures
PASS: Precision worse than 5 decimal figures
TEST: Subtraction is not normalized X=Y,X+Z != Y+Z!
PASS: Subtraction is not normalized X=Y,X+Z != Y+Z!
Subtraction appears to be normalized, as it should be.
Checking for guard digit in *, /, and -.
TEST: * gets too many final digits wrong.
PASS: * gets too many final digits wrong.
TEST: Division lacks a Guard Digit, so error can exceed 1 ulp
or 1/3 and 3/9 and 9/27 may disagree
PASS: Division lacks a Guard Digit, so error can exceed 1 ulp
or 1/3 and 3/9 and 9/27 may disagree
TEST: Computed value of 1/1.000..1 >= 1
PASS: Computed value of 1/1.000..1 >= 1
TEST: * and/or / gets too many last digits wrong
PASS: * and/or / gets too many last digits wrong
TEST: - lacks Guard Digit, so cancellation is obscured
ERROR: Severity: SERIOUS DEFECT: - lacks Guard Digit, so cancellation is obscured.
PASS: - lacks Guard Digit, so cancellation is obscured
Checking rounding on multiply, divide and add/subtract.
TEST: X * (1/X) differs from 1
PASS: X * (1/X) differs from 1
* is neither chopped nor correctly rounded.
/ is neither chopped nor correctly rounded.
TEST: Radix * ( 1 / Radix ) differs from 1
PASS: Radix * ( 1 / Radix ) differs from 1
TEST: Incomplete carry-propagation in Addition
PASS: Incomplete carry-propagation in Addition
Addition/Subtraction neither rounds nor chops.
Sticky bit used incorrectly or not at all.
TEST: lack(s) of guard digits or failure(s) to correctly round or chop
(noted above) count as one flaw in the final tally below
ERROR: Severity: FLAW: lack(s) of guard digits or failure(s) to correctly round or chop
(noted above) count as one flaw in the final tally below.
PASS: lack(s) of guard digits or failure(s) to correctly round or chop
(noted above) count as one flaw in the final tally below
Does Multiplication commute? Testing on 20 random pairs.
No failures found in 20 integer pairs.
Running test of square root(x).
TEST: Square root of 0.0, -0.0 or 1.0 wrong
PASS: Square root of 0.0, -0.0 or 1.0 wrong
Testing if sqrt(X * X) == X for 20 Integers X.
Test for sqrt monotonicity.
ERROR: Severity: DEFECT: sqrt(X) is non-monotonic for X near 2.0000000e+00 .
Testing whether sqrt is rounded or chopped.
Square root is neither chopped nor correctly rounded.
Observed errors run from -5.5000000e+00 to 5.0000000e-01 ulps.
TEST: sqrt gets too many last digits wrong
ERROR: Severity: SERIOUS DEFECT: sqrt gets too many last digits wrong.
PASS: sqrt gets too many last digits wrong
Testing powers Z^i for small Integers Z and i.
ERROR: Severity: DEFECT: computing
(1.30000000000000000e+01) ^ (1.70000000000000000e+01)
yielded 8.65041591938133811e+18;
which compared unequal to correct 8.65041591938133914e+18 ;
they differ by -1.02400000000000000e+03 .
Errors like this may invalidate financial calculations
involving interest rates.
Similar discrepancies have occurred 5 times.
Seeking Underflow thresholds UfThold and E0.
ERROR: Severity: FAILURE: multiplication gets too many last digits wrong.
Smallest strictly positive number found is E0 = 0 .
ERROR: Severity: FAILURE: Either accuracy deteriorates as numbers
approach a threshold = 0.00000000000000000e+00
coming down from 0.00000000000000000e+00
or else multiplication gets too many last digits wrong.
The Underflow threshold is 0.00000000000000000e+00, below which
calculation may suffer larger Relative error than merely roundoff.
Since underflow occurs below the threshold
UfThold = (2.00000000000000000e+00) ^ (-inf)
only underflow should afflict the expression
(2.00000000000000000e+00) ^ (-inf);
actually calculating yields: 0.00000000000000000e+00 .
This computed value is O.K.
Testing X^((X + 1) / (X - 1)) vs. exp(2) = 7.38905609893065041e+00 as X -> 1.
ERROR: Severity: DEFECT: Calculated 1.00000000000000000e+00 for
(1 + (0.00000000000000000e+00) ^ (inf);
differs from correct value by -6.38905609893065041e+00 .
This much error may spoil financial
calculations involving tiny interest rates.
Testing powers Z^Q at four nearly extreme values.
... no discrepancies found.
Searching for Overflow threshold:
This may generate an error.
Can `Z = -Y' overflow?
Trying it on Y = -inf .
finds a ERROR: Severity: FLAW: -(-Y) differs from Y.
Overflow threshold is V = -inf .
Overflow saturates at V0 = inf .
No Overflow should be signaled for V * 1 = -inf
nor for V / 1 = -inf .
Any overflow signal separating this * from the one
above is a DEFECT.
ERROR: Severity: FAILURE: Comparisons involving +--inf, +-inf
and +-0 are confused by Overflow.
ERROR: Severity: SERIOUS DEFECT: X / X differs from 1 when X = 1.00000000000000000e+00
instead, X / X - 1/2 - 1/2 = 1.08420217248550443e-19 .
ERROR: Severity: SERIOUS DEFECT: X / X differs from 1 when X = -inf
instead, X / X - 1/2 - 1/2 = nan .
ERROR: Severity: SERIOUS DEFECT: X / X differs from 1 when X = 0.00000000000000000e+00
instead, X / X - 1/2 - 1/2 = nan .
What message and/or values does Division by Zero produce?
Trying to compute 1 / 0 produces ... inf .
Trying to compute 0 / 0 produces ... nan .
The number of FAILUREs encountered = 4.
The number of SERIOUS DEFECTs discovered = 5.
The number of DEFECTs discovered = 3.
The number of FLAWs discovered = 2.
The arithmetic diagnosed has unacceptable Serious Defects.
Potentially fatal FAILURE may have spoiled this program's subsequent diagnoses.
END OF TEST.
*** END OF PARANOIA TEST ***
EXECUTIVE SHUTDOWN! Any key to reboot...