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Hi! This turned into a general analysis of (parts of) SH's math/*.out results. Also, perhaps there's a testsuite harness oddity -- seach for Âverbose in the following text if you want to skip the (probably) SH-specific bits. On Thu, 17 May 2012 10:07:00 +0900, Kaz Kojima <kkojima@rr.iij4u.or.jp> wrote: > Thomas Schwinge <thomas@codesourcery.com> wrote: > > With these patches applied, while there is also some improvement visible > > in the test results, I'm seeing a lot more failures in the math/* > > testsuites than without them. I just re-confirmed this in the current > > source tree with the patches reverted. As I have no knowledge about math > > exception handling but you evidently do -- would it be possible for you > > to review that situation? > > > > For example, diff of current source tree vs. current source tree with > > these four patches reverted: > > I haven't seen any differences in test results for those > patches. Surely I did something wrong when testing them. Ho, likewise there might be something wrong in my setup, too. :-) If you want, you could send me your math/*.out files, and I could compare with mine. > It looks that almost new failures come from fraiseexcpt change: > > http://sourceware.org/ml/libc-alpha/2012-04/msg00165.html > > It seems that now instructions to raise execptions clear old > exception flag fields. A quick fix maybe > > --- ORIG/libc/sysdeps/sh/sh4/fpu/fraiseexcpt.c 2012-05-17 09:50:58.000000000 +0900 > +++ libc/sysdeps/sh/sh4/fpu/fraiseexcpt.c 2012-05-17 09:50:34.000000000 +0900 > @@ -60,6 +60,14 @@ feraiseexcept (int excepts) > __asm__ __volatile__ ("fmul %1, %0" : "+d" (d) : "d" (x)); > } > > + /* Restore flag fields. */ > + { > + fexcept_t temp; > + _FPU_GETCW (temp); > + temp |= (excepts & FE_ALL_EXCEPT); > + _FPU_SETCW (temp); > + } > + > return 0; > } > libm_hidden_def (feraiseexcept) Yes, that indeed helps, thanks! math/test-fenv.out: [...] -61 errors occurred. +6 errors occurred. Similarly, a lot of failures disappear from math/test-float.out: [...] Test suite completed: 3832 test cases plus 3388 tests for exception flags executed. - 520 errors occurred. + 420 errors occurred. In the following, [old] means that this was already present without Kaz' recent patch. When I say new, this is a recent tree including both Nobuhiro's patches and Kaz' recent patch. [old] Several exception-realated issues remain in math/test-float.out (but some of these (didn't compare all) were not present before Nobuhiro's patches went in): Failure: cos (inf) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: cos (-inf) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: sin (inf) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: sin (-inf) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: sincos (inf, &sin_res, &cos_res) puts NaN in sin_res plus invalid exception: Exception "Invalid operation" not set Failure: sincos (-inf, &sin_res, &cos_res) puts NaN in sin_res plus invalid exception: Exception "Invalid operation" not set Failure: tan (inf) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: tan (-inf) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: acosh (-inf) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: acosh (-1.125) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: acosh (-max_value) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: atanh (1) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: atanh (-1) == -inf plus division by zero exception: Exception "Divide by zero" not set Failure: atanh (1.125) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: atanh (-1.125) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: atanh (max_value) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: atanh (-max_value) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: exp (710) == inf plus overflow exception: Exception "Overflow" not set Failure: exp (1e5) == inf plus overflow exception: Exception "Overflow" not set Failure: exp (max_value) == inf plus overflow exception: Exception "Overflow" not set Failure: exp2 (1e6) == inf plus overflow exception: Exception "Overflow" not set Failure: exp2 (max_value) == inf plus overflow exception: Exception "Overflow" not set Failure: expm1 (100000.0) == inf plus overflow exception: Exception "Overflow" not set Failure: expm1 (max_value) == inf plus overflow exception: Exception "Overflow" not set Failure: log1p (-1) == -inf plus division by zero exception: Exception "Divide by zero" not set Failure: log1p (-2) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: log1p (-max_value) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: log1p (-inf) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: logb (0) == -inf plus division by zero exception: Exception "Divide by zero" not set Failure: logb (-0) == -inf plus division by zero exception: Exception "Divide by zero" not set Failure: scalb (0, inf) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: scalb (-0, inf) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: scalb (inf, -inf) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: scalb (-inf, -inf) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: scalbn (1, INT_MAX) == inf plus overflow exception: Exception "Overflow" not set Failure: scalbn (max_value, INT_MAX) == inf plus overflow exception: Exception "Overflow" not set Failure: scalbn (min_value, INT_MAX) == inf plus overflow exception: Exception "Overflow" not set Failure: scalbn (min_value / 4, INT_MAX) == inf plus overflow exception: Exception "Overflow" not set Failure: scalbln (1, INT_MAX) == inf plus overflow exception: Exception "Overflow" not set Failure: scalbln (max_value, INT_MAX) == inf plus overflow exception: Exception "Overflow" not set Failure: scalbln (min_value, INT_MAX) == inf plus overflow exception: Exception "Overflow" not set Failure: scalbln (min_value / 4, INT_MAX) == inf plus overflow exception: Exception "Overflow" not set Failure: scalbln (1, LONG_MAX) == inf plus overflow exception: Exception "Overflow" not set Failure: scalbln (max_value, LONG_MAX) == inf plus overflow exception: Exception "Overflow" not set Failure: scalbln (min_value, LONG_MAX) == inf plus overflow exception: Exception "Overflow" not set Failure: scalbln (min_value / 4, LONG_MAX) == inf plus overflow exception: Exception "Overflow" not set Failure: pow (-0.1, 1.1) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: pow (-0.1, -1.1) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: pow (-10.1, 1.1) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: pow (-10.1, -1.1) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: pow (0, -1) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (0, -11) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (0, -0xffffff) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (-0, -1) == -inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (-0, -11) == -inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (-0, -0xffffff) == -inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (-0, -0x1fffffe) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (0, -2) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (0, -11.1) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (0, -0x1p24) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (0, -0x1p127) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (0, -max_value) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (-0, -2) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (-0, -11.1) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (-0, -0x1p24) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (-0, -0x1p127) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (-0, -max_value) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: pow (0x1p72, 0x1p72) == inf plus overflow exception: Exception "Overflow" not set Failure: pow (max_value, max_value) == inf plus overflow exception: Exception "Overflow" not set Failure: pow (-2.0, 0xffffff) == -inf plus overflow exception: Exception "Overflow" not set Failure: pow (-2.0, 0x1fffffe) == inf plus overflow exception: Exception "Overflow" not set Failure: pow (-2.0, max_value) == inf plus overflow exception: Exception "Overflow" not set Failure: pow (-max_value, 0.5) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: pow (-max_value, 1.5) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: pow (-max_value, 1000.5) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: pow (-max_value, 2) == inf plus overflow exception: Exception "Overflow" not set Failure: pow (-max_value, 3) == -inf plus overflow exception: Exception "Overflow" not set Failure: pow (-max_value, 0xffffff) == -inf plus overflow exception: Exception "Overflow" not set Failure: pow (-max_value, 0x1fffffe) == inf plus overflow exception: Exception "Overflow" not set Failure: pow (-max_value, max_value) == inf plus overflow exception: Exception "Overflow" not set Failure: pow (-0.5, -0xffffff) == -inf plus overflow exception: Exception "Overflow" not set Failure: pow (-0.5, -0x1fffffe) == inf plus overflow exception: Exception "Overflow" not set Failure: pow (-0.5, -max_value) == inf plus overflow exception: Exception "Overflow" not set Failure: pow (-min_value, 0.5) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: pow (-min_value, 1.5) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: pow (-min_value, 1000.5) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: pow (-min_value, -2) == inf plus overflow exception: Exception "Overflow" not set Failure: pow (-min_value, -3) == -inf plus overflow exception: Exception "Overflow" not set Failure: pow (-min_value, -0xffffff) == -inf plus overflow exception: Exception "Overflow" not set Failure: pow (-min_value, -0x1fffffe) == inf plus overflow exception: Exception "Overflow" not set Failure: pow (-min_value, -max_value) == inf plus overflow exception: Exception "Overflow" not set Failure: sqrt (-1) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: sqrt (-max_value) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: sqrt (-inf) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: gamma (0) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: gamma (-3) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: lgamma (0) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: lgamma (-0) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: lgamma (-3) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: lgamma (-max_value) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: lgamma (max_value) == inf plus overflow exception: Exception "Overflow" not set Failure: tgamma (max_value) == inf plus overflow exception: Exception "Overflow" not set Failure: tgamma (0) == inf plus division by zero exception: Exception "Divide by zero" not set Failure: tgamma (-0) == -inf plus division by zero exception: Exception "Divide by zero" not set Failure: tgamma (-2) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: tgamma (-max_value) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: tgamma (-inf) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: fmod (inf, 3) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: fmod (-inf, 3) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: fmod (3, 0) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: fmod (3, -0) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: remainder (1, 0) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: remainder (1, -0) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: remainder (inf, 1) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: remainder (-inf, 1) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: remquo (1, 0, &x) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: remquo (1, -0, &x) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: remquo (inf, 1, &x) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: remquo (-inf, 1, &x) == NaN plus invalid exception: Exception "Invalid operation" not set Failure: nextafter (fltmax, inf) == inf plus overflow exception: Exception "Overflow" not set Failure: nextafter (-fltmax, -inf) == -inf plus overflow exception: Exception "Overflow" not set Failure: Real part of: cexp (180 + 0x1p-149 i) == inf + 2.087071793345235105931967606907855310664e33 i plus overflow exception: Exception "Overflow" not set Failure: Real part of: cexp (1e6 + 0 i) == inf + 0 i plus overflow exception: Exception "Overflow" not set Failure: Real part of: cexp (1e6 + min_value i) == inf + inf i plus overflow exception: Exception "Overflow" not set Failure: Real part of: cexp (1e6 - min_value i) == inf - inf i plus overflow exception: Exception "Overflow" not set Failure: Real part of: clog10 (-0 + 0 i) == -inf + pi i plus division by zero exception: Exception "Divide by zero" not set Failure: Real part of: clog10 (-0 - 0 i) == -inf - pi i plus division by zero exception: Exception "Divide by zero" not set Failure: Real part of: clog10 (0 + 0 i) == -inf + 0.0 i plus division by zero exception: Exception "Divide by zero" not set Failure: Real part of: clog10 (0 - 0 i) == -inf - 0 i plus division by zero exception: Exception "Divide by zero" not set Failure: Real part of: clog (-0 + 0 i) == -inf + pi i plus division by zero exception: Exception "Divide by zero" not set Failure: Real part of: clog (-0 - 0 i) == -inf - pi i plus division by zero exception: Exception "Divide by zero" not set Failure: Real part of: clog (0 + 0 i) == -inf + 0.0 i plus division by zero exception: Exception "Divide by zero" not set Failure: Real part of: clog (0 - 0 i) == -inf - 0 i plus division by zero exception: Exception "Divide by zero" not set math/test-float.out: [old] The rint_downward, rint_upward, lrint_downward, lrint_upward, llrint_downward, llrint_upward functions round towards the wrong end. math/test-float.out: There are now also new failures showing up -- having Âexp10 (x) == x surely must be a cheap operation -- but I have no idea off-hand how that could be due to Kaz' exception handling change? (Perhaps there are exceptions involved in intermediate computations, and then things go wrong?) Failure: Test: exp10 (3) == 1000 Result: is: 3.00000000000000000000e+00 0x1.80000000000000000000p+1 should be: 1.00000000000000000000e+03 0x1.f4000000000000000000p+9 difference: 9.97000000000000000000e+02 0x1.f2800000000000000000p+9 ulp : 16334848.0000 max.ulp : 2.0000 Failure: Test: exp10 (-1) == 0.1 Result: is: -1.00000000000000000000e+00 -0x1.00000000000000000000p+0 should be: 1.00000001490116119385e-01 0x1.99999a00000000000000p-4 difference: 1.10000002384185791016e+00 0x1.19999a00000000000000p+0 ulp : 147639504.0000 max.ulp : 1.0000 Failure: Test: exp10 (36) == 1.0e36 Result: is: 3.60000000000000000000e+01 0x1.20000000000000000000p+5 should be: 9.99999961690316245365e+35 0x1.812f9c00000000000000p+119 difference: 9.99999961690316245365e+35 0x1.812f9c00000000000000p+119 ulp : 12621774.0000 max.ulp : 0.0000 Failure: Test: exp10 (-36) == 1.0e-36 Result: is: -3.60000000000000000000e+01 -0x1.20000000000000000000p+5 should be: 1.00000003593912982384e-36 0x1.54484a00000000000000p-120 difference: 3.60000000000000000000e+01 0x1.20000000000000000000p+5 ulp : inf max.ulp : 0.0000 Failure: Test: exp10 (1e6) == inf plus overflow exception Result: is: 1.00000000000000000000e+06 0x1.e8480000000000000000p+19 should be: inf inf Failure: Test: exp10 (-1e6) == 0 Result: is: -1.00000000000000000000e+06 -0x1.e8480000000000000000p+19 should be: 0.00000000000000000000e+00 0x0.00000000000000000000p+0 difference: 1.00000000000000000000e+06 0x1.e8480000000000000000p+19 ulp : 8388608000000.0000 max.ulp : 0.0000 Failure: Test: exp10 (max_value) == inf plus overflow exception Result: is: 3.40282346638528859812e+38 0x1.fffffe00000000000000p+127 should be: inf inf Failure: Test: exp10 (-max_value) == 0 Result: is: -3.40282346638528859812e+38 -0x1.fffffe00000000000000p+127 should be: 0.00000000000000000000e+00 0x0.00000000000000000000p+0 difference: 3.40282346638528859812e+38 0x1.fffffe00000000000000p+127 ulp : inf max.ulp : 0.0000 Failure: Test: exp10 (0.75) == 5.62341325190349080394951039776481231 Result: is: 7.50000000000000000000e-01 0x1.80000000000000000000p-1 should be: 5.62341308593750000000e+00 0x1.67e60000000000000000p+2 difference: 4.87341308593750000000e+00 0x1.37e60000000000000000p+2 ulp : 10220288.0000 max.ulp : 0.0000 Maximal error of `exp10' is : inf ulp accepted: 2 ulp Failure: Test: fma (inf, inf, -inf) == NaN plus invalid exception Result: is: -inf -inf should be: nan nan Failure: Test: fma (-inf, inf, inf) == NaN plus invalid exception Result: is: inf inf should be: nan nan Failure: Test: fma (inf, -inf, inf) == NaN plus invalid exception Result: is: inf inf should be: nan nan Failure: Test: fma (-inf, -inf, -inf) == NaN plus invalid exception Result: is: -inf -inf should be: nan nan Failure: Test: fma (inf, 3.5, -inf) == NaN plus invalid exception Result: is: -inf -inf should be: nan nan Failure: Test: fma (-inf, -7.5, -inf) == NaN plus invalid exception Result: is: -inf -inf should be: nan nan Failure: Test: fma (-13.5, inf, inf) == NaN plus invalid exception Result: is: inf inf should be: nan nan Failure: Test: fma (-inf, 7.5, inf) == NaN plus invalid exception Result: is: inf inf should be: nan nan Failure: Test: fma (0x1.7ff8p+13, 0x1.000002p+0, 0x1.ffffp-24) == 0x1.7ff802p+13 Result: is: 1.19208380056079477072e-07 0x1.ffff0000000000000000p-24 should be: 1.22870009765625000000e+04 0x1.7ff80200000000000000p+13 difference: 1.22870009765625000000e+04 0x1.7ff80200000000000000p+13 ulp : 12581889.0000 max.ulp : 0.0000 math/test-double.out: [old] The tests for acos, acos_tonearest, acos_towardzero, acos_downward, acos_upward, asin return nonsensical results. (51327489295686790529285095424 ulp, anyone?) ;-) Perhaps related to that: Failure: asin (0x0.ffffffp0) == 1.5704510598101804156437184421571127056013: Exception "Invalid operation" set Failure: asin (0x0.ffffffp0) == 1.5704510598101804156437184421571127056013: Exception "Overflow" set Failure: asin (0x0.ffffffff8p0) == 1.5707810680058339712015850710748035974710: Exception "Invalid operation" set Failure: asin (0x0.ffffffff8p0) == 1.5707810680058339712015850710748035974710: Exception "Overflow" set Failure: asin (0x0.ffffffffffffp0) == 1.5707962425011995974432331617542781977068: Exception "Invalid operation" set Failure: asin (0x0.ffffffffffffp0) == 1.5707962425011995974432331617542781977068: Exception "Overflow" set The math/test-double.out testsuite terminates after printing the first bits of the atan test results. Running it manually, I see the (faulty) results for Âatan (inf) and Âatan (NaN)Â, and then it hangs, eating 100 % CPU time. Specifying Â--verbose=1 makes it complete after 37 s. Strange. That log does *not* show the bugs acos results cited above (huh?), but instead shows several more exception-related failures, and again the issues with exp10 and fma as well as rint_downward et al., and likewise for erf, erfc, ccos including some Âinfinity has wrong sign occurrences. To reiterate, the (successful) run with Â--verbose=1 has this: atan (inf) == pi/2: Exception "Divide by zero" not set atan (inf) == pi/2: Exception "Invalid operation" not set atan (inf) == pi/2: Exception "Overflow" not set Test: atan (inf) == pi/2 Result: is: 1.57079632679489655800e+00 0x1.921fb54442d180000000p+0 should be: 1.57079632679489655800e+00 0x1.921fb54442d180000000p+0 difference: 0.00000000000000000000e+00 0x0.00000000000000000000p+0 ulp : 0.0000 max.ulp : 0.0000 atan (-inf) == -pi/2: Exception "Divide by zero" not set atan (-inf) == -pi/2: Exception "Invalid operation" not set atan (-inf) == -pi/2: Exception "Overflow" not set Test: atan (-inf) == -pi/2 Result: is: -1.57079632679489655800e+00 -0x1.921fb54442d180000000p+0 should be: -1.57079632679489655800e+00 -0x1.921fb54442d180000000p+0 difference: 0.00000000000000000000e+00 0x0.00000000000000000000p+0 ulp : 0.0000 max.ulp : 0.0000 ..., where as the regular run (testsuite or without Â--verbose=1Â) shows: Failure: atan (inf) == pi/2: Exception "Invalid operation" set Failure: Test: atan (inf) == pi/2 Result: is: -1.57079632679489655800e+00 -0x1.921fb54442d180000000p+0 should be: 1.57079632679489655800e+00 0x1.921fb54442d180000000p+0 difference: 4.02123859659493518848e+02 0x1.921fb54442d180000000p+8 ulp : 5963735302941976.0000 max.ulp : 0.0000 ..., then continues with ÂFailure: Test: atan (NaN) == NaNÂ, and then busy-loops. Also, notice the two missing exceptions, and the swapped sign/result of atan (-inf) for atan (inf). Might all be coincidence, or is there something wrong in the test harness itself? math/test-ifloat.out: Also shows the (new) exp10 and fma failures cited before. Also shows the rint_downward, rint_upward, lrint_downward, lrint_upward, llrint_downward, llrint_upward failures cited before. No exception-related failures here, it seems. math/test-idouble.out: New with Kaz' patch: The tests for acos, cos, cos_tonearest, cos_towardzero, cos_downward, cos_upward return nonsensical results. And there is also a ÂBus error after ÂFailure: Test: sin (-pi/6) == -0.5Â, and the test terminates (after 1 min 22 s). Running with Â--verbose=1 the ÂBus error reproducibly occurs after ÂTest: pow (-0, -11.1) == inf plus division by zero exception (after 15 s). Accoding to dmesg, ÂSending SIGBUS to "ld-linux.so.2" due to unaligned access (PC 404d46 PR 404d4a)Â. math/test-dbl-wrap.out used to pass, now times out (testsuite)/doesn't finish (if run with Â--directÂ; I killed it after having eaten 6 min CPU time). math/atest-exp.out: 131071 failures; 0 errors; error rate 0.00% maximum error: efffeffff7fffd5554aaaa888882d82cc error in exp(1): 00000000000000000000000cbffc1f5e9 This is new; used to pass. math/atest-sincos.out now also seems to get stuck in some kind of busy-loop. GrÃÃe, Thomas
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