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Fix pow overflow in non-default rounding modes (bug 16315).
This patch fixes bug 16315, bad pow handling of overflow/underflow in non-default rounding modes. Tests of pow are duly converted to ALL_RM_TEST to run all tests in all rounding modes. There are two main issues here. First, various implementations compute a negative result by negating a positive result, but this yields inappropriate overflow / underflow values for directed rounding, so either overflow / underflow results need recomputing in the correct sign, or the relevant overflowing / underflowing operation needs to be made to have a result of the correct sign. Second, the dbl-64 implementation sets FE_TONEAREST internally; in the overflow / underflow case, the result needs recomputing in the original rounding mode. Tested x86_64 and x86 and ulps updated accordingly. [BZ #16315] * sysdeps/i386/fpu/e_pow.S (__ieee754_pow): Ensure possibly overflowing or underflowing operations take place with sign of result. * sysdeps/i386/fpu/e_powf.S (__ieee754_powf): Likewise. * sysdeps/i386/fpu/e_powl.S (__ieee754_powl): Likewise. * sysdeps/ieee754/dbl-64/e_pow.c: Include <math.h>. (__ieee754_pow): Recompute overflowing and underflowing results in original rounding mode. * sysdeps/x86/fpu/powl_helper.c: Include <stdbool.h>. (__powl_helper): Allow negative argument X and scale negated value as needed. Avoid passing value outside [-1, 1] to f2xm1. * sysdeps/x86_64/fpu/e_powl.S (__ieee754_powl): Ensure possibly overflowing or underflowing operations take place with sign of result. * sysdeps/x86_64/fpu/multiarch/e_pow.c [HAVE_FMA4_SUPPORT]: Include <math.h>. * math/auto-libm-test-in: Add more tests of pow. * math/auto-libm-test-out: Regenerated. * math/libm-test.inc (pow_test): Use ALL_RM_TEST. (pow_tonearest_test_data): Remove. (pow_test_tonearest): Likewise. (pow_towardzero_test_data): Likewise. (pow_test_towardzero): Likewise. (pow_downward_test_data): Likewise. (pow_test_downward): Likewise. (pow_upward_test_data): Likewise. (pow_test_upward): Likewise. (main): Don't call removed functions. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
This commit is contained in:
Joseph Myers
parent
5686b236cc
commit
4da6db5188
34
ChangeLog
34
ChangeLog
@ -1,3 +1,37 @@
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2014-06-23 Joseph Myers <joseph@codesourcery.com>
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[BZ #16315]
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* sysdeps/i386/fpu/e_pow.S (__ieee754_pow): Ensure possibly
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overflowing or underflowing operations take place with sign of
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result.
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* sysdeps/i386/fpu/e_powf.S (__ieee754_powf): Likewise.
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* sysdeps/i386/fpu/e_powl.S (__ieee754_powl): Likewise.
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* sysdeps/ieee754/dbl-64/e_pow.c: Include <math.h>.
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(__ieee754_pow): Recompute overflowing and underflowing results in
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original rounding mode.
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* sysdeps/x86/fpu/powl_helper.c: Include <stdbool.h>.
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(__powl_helper): Allow negative argument X and scale negated value
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as needed. Avoid passing value outside [-1, 1] to f2xm1.
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* sysdeps/x86_64/fpu/e_powl.S (__ieee754_powl): Ensure possibly
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overflowing or underflowing operations take place with sign of
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result.
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* sysdeps/x86_64/fpu/multiarch/e_pow.c [HAVE_FMA4_SUPPORT]:
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Include <math.h>.
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* math/auto-libm-test-in: Add more tests of pow.
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* math/auto-libm-test-out: Regenerated.
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* math/libm-test.inc (pow_test): Use ALL_RM_TEST.
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(pow_tonearest_test_data): Remove.
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(pow_test_tonearest): Likewise.
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(pow_towardzero_test_data): Likewise.
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(pow_test_towardzero): Likewise.
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(pow_downward_test_data): Likewise.
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(pow_test_downward): Likewise.
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(pow_upward_test_data): Likewise.
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(pow_test_upward): Likewise.
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(main): Don't call removed functions.
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* sysdeps/i386/fpu/libm-test-ulps: Update.
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* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
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2014-06-23 Roland McGrath <roland@hack.frob.com>
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* sysdeps/unix/sysv/linux/powerpc/powerpc32/nofpu/nptl/c++-types.data:
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22
NEWS
22
NEWS
@ -10,17 +10,17 @@ Version 2.20
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* The following bugs are resolved with this release:
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6804, 9894, 12994, 13347, 13651, 14308, 14770, 15119, 15132, 15347, 15514,
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15698, 15804, 15894, 15946, 16002, 16064, 16095, 16198, 16284, 16348,
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16349, 16357, 16362, 16447, 16516, 16532, 16545, 16564, 16574, 16599,
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16600, 16609, 16610, 16611, 16613, 16619, 16623, 16629, 16632, 16634,
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16639, 16642, 16648, 16649, 16670, 16674, 16677, 16680, 16681, 16683,
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16689, 16695, 16701, 16706, 16707, 16712, 16713, 16714, 16724, 16731,
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16739, 16740, 16743, 16754, 16758, 16759, 16760, 16770, 16786, 16789,
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16791, 16796, 16799, 16800, 16815, 16823, 16824, 16831, 16838, 16849,
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16854, 16876, 16877, 16878, 16882, 16885, 16888, 16890, 16912, 16915,
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16916, 16917, 16922, 16927, 16928, 16932, 16943, 16958, 16965, 16966,
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16967, 16977, 16978, 16984, 16990, 16996, 17009, 17022, 17031, 17042,
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17048, 17058, 17062, 17069, 17075, 17079.
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15698, 15804, 15894, 15946, 16002, 16064, 16095, 16198, 16284, 16315,
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16348, 16349, 16357, 16362, 16447, 16516, 16532, 16545, 16564, 16574,
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16599, 16600, 16609, 16610, 16611, 16613, 16619, 16623, 16629, 16632,
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16634, 16639, 16642, 16648, 16649, 16670, 16674, 16677, 16680, 16681,
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16683, 16689, 16695, 16701, 16706, 16707, 16712, 16713, 16714, 16724,
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16731, 16739, 16740, 16743, 16754, 16758, 16759, 16760, 16770, 16786,
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16789, 16791, 16796, 16799, 16800, 16815, 16823, 16824, 16831, 16838,
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16849, 16854, 16876, 16877, 16878, 16882, 16885, 16888, 16890, 16912,
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16915, 16916, 16917, 16922, 16927, 16928, 16932, 16943, 16958, 16965,
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16966, 16967, 16977, 16978, 16984, 16990, 16996, 17009, 17022, 17031,
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17042, 17048, 17058, 17062, 17069, 17075, 17079.
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* Optimized strchr implementation for AArch64. Contributed by ARM Ltd.
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@ -1613,6 +1613,71 @@ pow -max 0x1.ffffffffffffffffffffffffffffp+112
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pow -max 0x1.ffffffffffffffffffffffffffffp+113
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pow -max max
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pow -0x1p65 2
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pow -0x1p65 3
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pow -0x1p65 4
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pow -0x1p65 5
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pow -0x1p43 3
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pow -0x1p43 4
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pow -0x1p43 5
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pow -0x1p33 4
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pow -0x1p33 5
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pow -0x1p26 5
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pow -0x1p-65 -2
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pow -0x1p-65 -3
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pow -0x1p-65 -4
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pow -0x1p-65 -5
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pow -0x1p-43 -3
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pow -0x1p-43 -4
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pow -0x1p-43 -5
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pow -0x1p-33 -4
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pow -0x1p-33 -5
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pow -0x1p-26 -5
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pow -0x1p513 2
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pow -0x1p513 3
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pow -0x1p513 4
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pow -0x1p513 5
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pow -0x1p342 3
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pow -0x1p342 4
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pow -0x1p342 5
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pow -0x1p257 4
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pow -0x1p257 5
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pow -0x1p205 5
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pow -0x1p-513 -2
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pow -0x1p-513 -3
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pow -0x1p-513 -4
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pow -0x1p-513 -5
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pow -0x1p-342 -3
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pow -0x1p-342 -4
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pow -0x1p-342 -5
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pow -0x1p-257 -4
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pow -0x1p-257 -5
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pow -0x1p-205 -5
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pow -0x1p8192 2
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pow -0x1p8192 3
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pow -0x1p8192 4
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pow -0x1p8192 5
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pow -0x1p5462 3
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pow -0x1p5462 4
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pow -0x1p5462 5
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pow -0x1p4097 4
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pow -0x1p4097 5
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pow -0x1p3277 5
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pow -0x1p64 257
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pow -0x1p-8192 -2
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pow -0x1p-8192 -3
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pow -0x1p-8192 -4
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pow -0x1p-8192 -5
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pow -0x1p-5462 -3
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pow -0x1p-5462 -4
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pow -0x1p-5462 -5
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pow -0x1p-4097 -4
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pow -0x1p-4097 -5
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pow -0x1p-3277 -5
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pow -0x1p-64 -257
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pow -0.5 126
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pow -0.5 127
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pow -0.5 -126
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File diff suppressed because it is too large
Load Diff
@ -8697,69 +8697,7 @@ static const struct test_ff_f_data pow_test_data[] =
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static void
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pow_test (void)
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{
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START (pow, 0);
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RUN_TEST_LOOP_ff_f (pow, pow_test_data, );
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END;
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}
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static const struct test_ff_f_data pow_tonearest_test_data[] =
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{
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AUTO_TESTS_ff_f (pow),
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};
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static void
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pow_test_tonearest (void)
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{
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START (pow_tonearest, 0);
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RUN_TEST_LOOP_ff_f (pow, pow_tonearest_test_data, FE_TONEAREST);
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END;
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}
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static const struct test_ff_f_data pow_towardzero_test_data[] =
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{
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TEST_ff_f (pow, 1.0625L, 1.125L, 1.070582293028761362162622578677070098674L),
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TEST_ff_f (pow, 1.5L, 1.03125L, 1.519127098714743184071644334163037684948L),
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};
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static void
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pow_test_towardzero (void)
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{
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START (pow_towardzero, 0);
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RUN_TEST_LOOP_ff_f (pow, pow_towardzero_test_data, FE_TOWARDZERO);
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END;
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}
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static const struct test_ff_f_data pow_downward_test_data[] =
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{
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TEST_ff_f (pow, 1.0625L, 1.125L, 1.070582293028761362162622578677070098674L),
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TEST_ff_f (pow, 1.5L, 1.03125L, 1.519127098714743184071644334163037684948L),
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};
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static void
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pow_test_downward (void)
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{
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START (pow_downward, 0);
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RUN_TEST_LOOP_ff_f (pow, pow_downward_test_data, FE_DOWNWARD);
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END;
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}
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static const struct test_ff_f_data pow_upward_test_data[] =
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{
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TEST_ff_f (pow, 1.0625L, 1.125L, 1.070582293028761362162622578677070098674L),
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TEST_ff_f (pow, 1.5L, 1.03125L, 1.519127098714743184071644334163037684948L),
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};
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static void
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pow_test_upward (void)
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{
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START (pow_upward, 0);
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RUN_TEST_LOOP_ff_f (pow, pow_upward_test_data, FE_UPWARD);
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END;
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ALL_RM_TEST (pow, 0, pow_test_data, RUN_TEST_LOOP_ff_f, END);
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}
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@ -9946,10 +9884,6 @@ main (int argc, char **argv)
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fabs_test ();
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hypot_test ();
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pow_test ();
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pow_test_tonearest ();
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pow_test_towardzero ();
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pow_test_downward ();
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pow_test_upward ();
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sqrt_test ();
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/* Error and gamma functions: */
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@ -144,12 +144,22 @@ ENTRY(__ieee754_pow)
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4: fldl MO(one) // 1 : x
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fxch
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/* If y is even, take the absolute value of x. Otherwise,
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ensure all intermediate values that might overflow have the
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sign of x. */
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testb $1, %al
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jnz 6f
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fabs
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6: shrdl $1, %edx, %eax
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jnc 5f
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fxch
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fabs
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fmul %st(1) // x : ST*x
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fxch
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5: fmul %st(0), %st // x*x : ST*x
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5: fld %st // x : x : ST*x
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fabs // |x| : x : ST*x
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fmulp // |x|*x : ST*x
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shrl $1, %edx
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movl %eax, %ecx
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orl %edx, %ecx
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@ -207,27 +217,28 @@ ENTRY(__ieee754_pow)
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fxch // fract(y*log2(x)) : int(y*log2(x))
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f2xm1 // 2^fract(y*log2(x))-1 : int(y*log2(x))
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faddl MO(one) // 2^fract(y*log2(x)) : int(y*log2(x))
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fscale // 2^fract(y*log2(x))*2^int(y*log2(x)) : int(y*log2(x))
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fstp %st(1) // 2^fract(y*log2(x))*2^int(y*log2(x))
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// Before scaling, we must negate if x is negative and y is an
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// odd integer.
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testb $2, %dh
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jz 292f
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jz 291f
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// x is negative. If y is an odd integer, negate the result.
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fldl 20(%esp) // y : abs(result)
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fld %st // y : y : abs(result)
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fabs // |y| : y : abs(result)
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fcompl MO(p63) // y : abs(result)
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fldl 20(%esp) // y : 2^fract(y*log2(x)) : int(y*log2(x))
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fld %st // y : y : 2^fract(y*log2(x)) : int(y*log2(x))
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fabs // |y| : y : 2^fract(y*log2(x)) : int(y*log2(x))
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fcompl MO(p63) // y : 2^fract(y*log2(x)) : int(y*log2(x))
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fnstsw
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sahf
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jnc 291f
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jnc 290f
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// We must find out whether y is an odd integer.
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fld %st // y : y : abs(result)
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fistpll (%esp) // y : abs(result)
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fildll (%esp) // int(y) : y : abs(result)
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fucompp // abs(result)
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fld %st // y : y : 2^fract(y*log2(x)) : int(y*log2(x))
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fistpll (%esp) // y : 2^fract(y*log2(x)) : int(y*log2(x))
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fildll (%esp) // int(y) : y : 2^fract(y*log2(x)) : int(y*log2(x))
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fucompp // 2^fract(y*log2(x)) : int(y*log2(x))
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fnstsw
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sahf
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jne 292f
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jne 291f
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// OK, the value is an integer, but is it odd?
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popl %eax
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@ -235,14 +246,17 @@ ENTRY(__ieee754_pow)
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popl %edx
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cfi_adjust_cfa_offset (-4)
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andb $1, %al
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jz 290f // jump if not odd
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jz 292f // jump if not odd
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// It's an odd integer.
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fchs
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290: ret
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jmp 292f
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cfi_adjust_cfa_offset (8)
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291: fstp %st(0) // abs(result)
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292: addl $8, %esp
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290: fstp %st(0) // 2^fract(y*log2(x)) : int(y*log2(x))
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291: addl $8, %esp
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cfi_adjust_cfa_offset (-8)
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292: fscale // +/- 2^fract(y*log2(x))*2^int(y*log2(x)) : int(y*log2(x))
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fstp %st(1) // +/- 2^fract(y*log2(x))*2^int(y*log2(x))
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ret
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@ -129,12 +129,22 @@ ENTRY(__ieee754_powf)
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4: fldl MO(one) // 1 : x
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fxch
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/* If y is even, take the absolute value of x. Otherwise,
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ensure all intermediate values that might overflow have the
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sign of x. */
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testb $1, %dl
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jnz 6f
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fabs
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6: shrl $1, %edx
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jnc 5f
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fxch
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fabs
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fmul %st(1) // x : ST*x
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fxch
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5: fmul %st(0), %st // x*x : ST*x
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5: fld %st // x : x : ST*x
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fabs // |x| : x : ST*x
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fmulp // |x|*x : ST*x
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testl %edx, %edx
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jnz 6b
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fstp %st(0) // ST*x
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@ -151,7 +151,7 @@ ENTRY(__ieee754_powl)
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fcompl MO(p3) // y : x
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fnstsw
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sahf
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jnc 2f
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jnc 3f
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popl %eax
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cfi_adjust_cfa_offset (-4)
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popl %edx
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@ -166,12 +166,22 @@ ENTRY(__ieee754_powl)
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4: fldl MO(one) // 1 : x
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fxch
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/* If y is even, take the absolute value of x. Otherwise,
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ensure all intermediate values that might overflow have the
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sign of x. */
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testb $1, %al
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jnz 6f
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fabs
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6: shrdl $1, %edx, %eax
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jnc 5f
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fxch
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fabs
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fmul %st(1) // x : ST*x
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fxch
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5: fmul %st(0), %st // x*x : ST*x
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5: fld %st // x : x : ST*x
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fabs // |x| : x : ST*x
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fmulp // |x|*x : ST*x
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shrl $1, %edx
|
||||
movl %eax, %ecx
|
||||
orl %edx, %ecx
|
||||
@ -198,79 +208,31 @@ ENTRY(__ieee754_powl)
|
||||
|
||||
cfi_adjust_cfa_offset (8)
|
||||
.align ALIGNARG(4)
|
||||
2: // y is a large integer (absolute value at least 8), but
|
||||
// may be odd unless at least 1L<<64. So it may be necessary
|
||||
// to adjust the sign of a negative result afterwards.
|
||||
fxch // x : y
|
||||
fabs // |x| : y
|
||||
fxch // y : |x|
|
||||
2: // y is a large integer (absolute value at least 1L<<63).
|
||||
// If y has absolute value at least 1L<<78, then any finite
|
||||
// nonzero x will result in 0 (underflow), 1 or infinity (overflow).
|
||||
// Saturate y to those bounds to avoid overflow in the calculation
|
||||
// of y*log2(x).
|
||||
fld %st // y : y : |x|
|
||||
fabs // |y| : y : |x|
|
||||
fcompl MO(p78) // y : |x|
|
||||
fld %st // y : y : x
|
||||
fabs // |y| : y : x
|
||||
fcompl MO(p78) // y : x
|
||||
fnstsw
|
||||
sahf
|
||||
jc 3f
|
||||
fstp %st(0) // pop y
|
||||
fldl MO(p78) // 1L<<78 : |x|
|
||||
fldl MO(p78) // 1L<<78 : x
|
||||
testb $2, %dl
|
||||
jz 3f // y > 0
|
||||
fchs // -(1L<<78) : |x|
|
||||
fchs // -(1L<<78) : x
|
||||
.align ALIGNARG(4)
|
||||
3: /* y is a real number. */
|
||||
subl $28, %esp
|
||||
cfi_adjust_cfa_offset (28)
|
||||
fstpt 12(%esp) // x
|
||||
fstpt (%esp) // <empty>
|
||||
mov %edx, 24(%esp)
|
||||
call HIDDEN_JUMPTARGET (__powl_helper) // <result>
|
||||
mov 24(%esp), %edx
|
||||
addl $28, %esp
|
||||
cfi_adjust_cfa_offset (-28)
|
||||
testb $2, %dh
|
||||
jz 292f
|
||||
// x is negative. If y is an odd integer, negate the result.
|
||||
#ifdef PIC
|
||||
LOAD_PIC_REG (cx)
|
||||
#endif
|
||||
fldt 24(%esp) // y : abs(result)
|
||||
fld %st // y : y : abs(result)
|
||||
fabs // |y| : y : abs(result)
|
||||
fcompl MO(p64) // y : abs(result)
|
||||
fnstsw
|
||||
sahf
|
||||
jnc 291f
|
||||
fldl MO(p63) // p63 : y : abs(result)
|
||||
fxch // y : p63 : abs(result)
|
||||
fprem // y%p63 : p63 : abs(result)
|
||||
fstp %st(1) // y%p63 : abs(result)
|
||||
|
||||
// We must find out whether y is an odd integer.
|
||||
fld %st // y : y : abs(result)
|
||||
fistpll (%esp) // y : abs(result)
|
||||
fildll (%esp) // int(y) : y : abs(result)
|
||||
fucompp // abs(result)
|
||||
fnstsw
|
||||
sahf
|
||||
jne 292f
|
||||
|
||||
// OK, the value is an integer, but is it odd?
|
||||
popl %eax
|
||||
cfi_adjust_cfa_offset (-4)
|
||||
popl %edx
|
||||
cfi_adjust_cfa_offset (-4)
|
||||
andb $1, %al
|
||||
jz 290f // jump if not odd
|
||||
// It's an odd integer.
|
||||
fchs
|
||||
290: ret
|
||||
cfi_adjust_cfa_offset (8)
|
||||
291: fstp %st(0) // abs(result)
|
||||
292: addl $8, %esp
|
||||
cfi_adjust_cfa_offset (-8)
|
||||
addl $36, %esp
|
||||
cfi_adjust_cfa_offset (-36)
|
||||
ret
|
||||
|
||||
// pow(x,±0) = 1
|
||||
|
||||
@ -1653,6 +1653,8 @@ double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 4
|
||||
ldouble: 4
|
||||
|
||||
Function: "pow_tonearest":
|
||||
ildouble: 1
|
||||
@ -1663,14 +1665,16 @@ double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "pow_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: "sin":
|
||||
ildouble: 1
|
||||
|
||||
@ -34,6 +34,7 @@
|
||||
/* round to nearest mode of IEEE 754 standard. */
|
||||
/* */
|
||||
/***************************************************************************/
|
||||
#include <math.h>
|
||||
#include "endian.h"
|
||||
#include "upow.h"
|
||||
#include <dla.h>
|
||||
@ -91,27 +92,33 @@ __ieee754_pow (double x, double y)
|
||||
{ /* if y<-1 or y>1 */
|
||||
double retval;
|
||||
|
||||
SET_RESTORE_ROUND (FE_TONEAREST);
|
||||
{
|
||||
SET_RESTORE_ROUND (FE_TONEAREST);
|
||||
|
||||
/* Avoid internal underflow for tiny y. The exact value of y does
|
||||
not matter if |y| <= 2**-64. */
|
||||
if (ABS (y) < 0x1p-64)
|
||||
y = y < 0 ? -0x1p-64 : 0x1p-64;
|
||||
z = log1 (x, &aa, &error); /* x^y =e^(y log (X)) */
|
||||
t = y * CN;
|
||||
y1 = t - (t - y);
|
||||
y2 = y - y1;
|
||||
t = z * CN;
|
||||
a1 = t - (t - z);
|
||||
a2 = (z - a1) + aa;
|
||||
a = y1 * a1;
|
||||
aa = y2 * a1 + y * a2;
|
||||
a1 = a + aa;
|
||||
a2 = (a - a1) + aa;
|
||||
error = error * ABS (y);
|
||||
t = __exp1 (a1, a2, 1.9e16 * error); /* return -10 or 0 if wasn't computed exactly */
|
||||
retval = (t > 0) ? t : power1 (x, y);
|
||||
/* Avoid internal underflow for tiny y. The exact value of y does
|
||||
not matter if |y| <= 2**-64. */
|
||||
if (ABS (y) < 0x1p-64)
|
||||
y = y < 0 ? -0x1p-64 : 0x1p-64;
|
||||
z = log1 (x, &aa, &error); /* x^y =e^(y log (X)) */
|
||||
t = y * CN;
|
||||
y1 = t - (t - y);
|
||||
y2 = y - y1;
|
||||
t = z * CN;
|
||||
a1 = t - (t - z);
|
||||
a2 = (z - a1) + aa;
|
||||
a = y1 * a1;
|
||||
aa = y2 * a1 + y * a2;
|
||||
a1 = a + aa;
|
||||
a2 = (a - a1) + aa;
|
||||
error = error * ABS (y);
|
||||
t = __exp1 (a1, a2, 1.9e16 * error); /* return -10 or 0 if wasn't computed exactly */
|
||||
retval = (t > 0) ? t : power1 (x, y);
|
||||
}
|
||||
|
||||
if (__isinf (retval))
|
||||
retval = huge * huge;
|
||||
else if (retval == 0)
|
||||
retval = tiny * tiny;
|
||||
return retval;
|
||||
}
|
||||
|
||||
@ -164,7 +171,21 @@ __ieee754_pow (double x, double y)
|
||||
return y < 0 ? 0.0 : INF.x;
|
||||
}
|
||||
/* if y even or odd */
|
||||
return (k == 1) ? __ieee754_pow (-x, y) : -__ieee754_pow (-x, y);
|
||||
if (k == 1)
|
||||
return __ieee754_pow (-x, y);
|
||||
else
|
||||
{
|
||||
double retval;
|
||||
{
|
||||
SET_RESTORE_ROUND (FE_TONEAREST);
|
||||
retval = -__ieee754_pow (-x, y);
|
||||
}
|
||||
if (__isinf (retval))
|
||||
retval = -huge * huge;
|
||||
else if (retval == 0)
|
||||
retval = -tiny * tiny;
|
||||
return retval;
|
||||
}
|
||||
}
|
||||
/* x>0 */
|
||||
|
||||
|
||||
@ -18,6 +18,7 @@
|
||||
|
||||
#include <math.h>
|
||||
#include <math_private.h>
|
||||
#include <stdbool.h>
|
||||
|
||||
/* High parts and low parts of -log (k/16), for integer k from 12 to
|
||||
24. */
|
||||
@ -63,15 +64,32 @@ acc_split (long double *rhi, long double *rlo, long double hi, long double lo,
|
||||
extern long double __powl_helper (long double x, long double y);
|
||||
libm_hidden_proto (__powl_helper)
|
||||
|
||||
/* Given X a value that is finite and nonzero, or a NaN, and only
|
||||
negative if Y is not an integer, and Y a finite nonzero value with
|
||||
0x1p-79 <= |Y| <= 0x1p78, compute X to the power Y. */
|
||||
/* Given X a value that is finite and nonzero, or a NaN, and Y a
|
||||
finite nonzero value with 0x1p-79 <= |Y| <= 0x1p78, compute X to
|
||||
the power Y. */
|
||||
|
||||
long double
|
||||
__powl_helper (long double x, long double y)
|
||||
{
|
||||
if (isnan (x) || x < 0)
|
||||
if (isnan (x))
|
||||
return __ieee754_expl (y * __ieee754_logl (x));
|
||||
bool negate;
|
||||
if (x < 0)
|
||||
{
|
||||
long double absy = fabsl (y);
|
||||
if (absy >= 0x1p64L)
|
||||
negate = false;
|
||||
else
|
||||
{
|
||||
unsigned long long yll = absy;
|
||||
if (yll != absy)
|
||||
return __ieee754_expl (y * __ieee754_logl (x));
|
||||
negate = (yll & 1) != 0;
|
||||
}
|
||||
x = fabsl (x);
|
||||
}
|
||||
else
|
||||
negate = false;
|
||||
|
||||
/* We need to compute Y * log2 (X) to at least 64 bits after the
|
||||
point for normal results (that is, to at least 78 bits
|
||||
@ -199,11 +217,17 @@ __powl_helper (long double x, long double y)
|
||||
fractional parts. */
|
||||
long double log2_res_int = __roundl (log2_res_hi);
|
||||
long double log2_res_frac = log2_res_hi - log2_res_int + log2_res_lo;
|
||||
/* If the integer part is very large, the computed fractional part
|
||||
may be outside the valid range for f2xm1. */
|
||||
if (fabsl (log2_res_int) > 16500)
|
||||
log2_res_frac = 0;
|
||||
|
||||
/* Compute the final result. */
|
||||
long double res;
|
||||
asm ("f2xm1" : "=t" (res) : "0" (log2_res_frac));
|
||||
res += 1.0L;
|
||||
if (negate)
|
||||
res = -res;
|
||||
asm ("fscale" : "=t" (res) : "0" (res), "u" (log2_res_int));
|
||||
return res;
|
||||
}
|
||||
|
||||
@ -141,7 +141,7 @@ ENTRY(__ieee754_powl)
|
||||
fabs // |y| : 8 : y : x
|
||||
fcomip %st(1), %st // 8 : y : x
|
||||
fstp %st(0) // y : x
|
||||
jnc 2f
|
||||
jnc 3f
|
||||
mov -8(%rsp),%eax
|
||||
mov -4(%rsp),%edx
|
||||
orl $0, %edx
|
||||
@ -154,12 +154,22 @@ ENTRY(__ieee754_powl)
|
||||
4: fldl MO(one) // 1 : x
|
||||
fxch
|
||||
|
||||
/* If y is even, take the absolute value of x. Otherwise,
|
||||
ensure all intermediate values that might overflow have the
|
||||
sign of x. */
|
||||
testb $1, %al
|
||||
jnz 6f
|
||||
fabs
|
||||
|
||||
6: shrdl $1, %edx, %eax
|
||||
jnc 5f
|
||||
fxch
|
||||
fabs
|
||||
fmul %st(1) // x : ST*x
|
||||
fxch
|
||||
5: fmul %st(0), %st // x*x : ST*x
|
||||
5: fld %st // x : x : ST*x
|
||||
fabs // |x| : x : ST*x
|
||||
fmulp // |x|*x : ST*x
|
||||
shrl $1, %edx
|
||||
movl %eax, %ecx
|
||||
orl %edx, %ecx
|
||||
@ -177,71 +187,32 @@ ENTRY(__ieee754_powl)
|
||||
ret
|
||||
|
||||
.align ALIGNARG(4)
|
||||
2: // y is a large integer (absolute value at least 8), but
|
||||
// may be odd unless at least 1L<<64. So it may be necessary
|
||||
// to adjust the sign of a negative result afterwards.
|
||||
fxch // x : y
|
||||
fabs // |x| : y
|
||||
fxch // y : |x|
|
||||
2: // y is a large integer (absolute value at least 1L<<63).
|
||||
// If y has absolute value at least 1L<<78, then any finite
|
||||
// nonzero x will result in 0 (underflow), 1 or infinity (overflow).
|
||||
// Saturate y to those bounds to avoid overflow in the calculation
|
||||
// of y*log2(x).
|
||||
fldl MO(p78) // 1L<<78 : y : |x|
|
||||
fld %st(1) // y : 1L<<78 : y : |x|
|
||||
fabs // |y| : 1L<<78 : y : |x|
|
||||
fcomip %st(1), %st // 1L<<78 : y : |x|
|
||||
fstp %st(0) // y : |x|
|
||||
fldl MO(p78) // 1L<<78 : y : x
|
||||
fld %st(1) // y : 1L<<78 : y : x
|
||||
fabs // |y| : 1L<<78 : y : x
|
||||
fcomip %st(1), %st // 1L<<78 : y : x
|
||||
fstp %st(0) // y : x
|
||||
jc 3f
|
||||
fstp %st(0) // pop y
|
||||
fldl MO(p78) // 1L<<78 : |x|
|
||||
fldl MO(p78) // 1L<<78 : x
|
||||
testb $2, %dl
|
||||
jz 3f // y > 0
|
||||
fchs // -(1L<<78) : |x|
|
||||
fchs // -(1L<<78) : x
|
||||
.align ALIGNARG(4)
|
||||
3: /* y is a real number. */
|
||||
subq $40, %rsp
|
||||
cfi_adjust_cfa_offset (40)
|
||||
fstpt 16(%rsp) // x
|
||||
fstpt (%rsp) // <empty>
|
||||
mov %edx, 32(%rsp)
|
||||
call HIDDEN_JUMPTARGET (__powl_helper) // <result>
|
||||
mov 32(%rsp), %edx
|
||||
addq $40, %rsp
|
||||
cfi_adjust_cfa_offset (-40)
|
||||
testb $2, %dh
|
||||
jz 292f
|
||||
// x is negative. If y is an odd integer, negate the result.
|
||||
fldt 24(%rsp) // y : abs(result)
|
||||
fldl MO(p64) // 1L<<64 : y : abs(result)
|
||||
fld %st(1) // y : 1L<<64 : y : abs(result)
|
||||
fabs // |y| : 1L<<64 : y : abs(result)
|
||||
fcomip %st(1), %st // 1L<<64 : y : abs(result)
|
||||
fstp %st(0) // y : abs(result)
|
||||
jnc 291f
|
||||
fldl MO(p63) // p63 : y : abs(result)
|
||||
fxch // y : p63 : abs(result)
|
||||
fprem // y%p63 : p63 : abs(result)
|
||||
fstp %st(1) // y%p63 : abs(result)
|
||||
|
||||
// We must find out whether y is an odd integer.
|
||||
fld %st // y : y : abs(result)
|
||||
fistpll -8(%rsp) // y : abs(result)
|
||||
fildll -8(%rsp) // int(y) : y : abs(result)
|
||||
fucomip %st(1),%st // y : abs(result)
|
||||
ffreep %st // abs(result)
|
||||
jne 292f
|
||||
|
||||
// OK, the value is an integer, but is it odd?
|
||||
mov -8(%rsp), %eax
|
||||
mov -4(%rsp), %edx
|
||||
andb $1, %al
|
||||
jz 290f // jump if not odd
|
||||
// It's an odd integer.
|
||||
fchs
|
||||
290: ret
|
||||
291: fstp %st(0) // abs(result)
|
||||
292: ret
|
||||
ret
|
||||
|
||||
// pow(x,±0) = 1
|
||||
.align ALIGNARG(4)
|
||||
|
||||
@ -1736,8 +1736,12 @@ ildouble: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "pow_downward":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 4
|
||||
ldouble: 4
|
||||
|
||||
Function: "pow_tonearest":
|
||||
float: 1
|
||||
@ -1746,15 +1750,21 @@ ildouble: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "pow_towardzero":
|
||||
double: 1
|
||||
float: 1
|
||||
ifloat: 1
|
||||
|
||||
Function: "pow_upward":
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
|
||||
Function: "pow_upward":
|
||||
double: 1
|
||||
float: 1
|
||||
idouble: 1
|
||||
ifloat: 1
|
||||
ildouble: 2
|
||||
ldouble: 2
|
||||
|
||||
Function: "sin":
|
||||
ildouble: 1
|
||||
ldouble: 1
|
||||
|
||||
@ -1,5 +1,6 @@
|
||||
#ifdef HAVE_FMA4_SUPPORT
|
||||
# include <init-arch.h>
|
||||
# include <math.h>
|
||||
# include <math_private.h>
|
||||
|
||||
extern double __ieee754_pow_sse2 (double, double);
|
||||
|
||||
Loading…
Reference in New Issue
Block a user