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* Fix some regressions caused by the switch from gcc to clang. The fixesdas2013-05-271-6/+3
| | | | | | | | | | are workarounds for various symptoms of the problem described in clang bugs 3929, 8100, 8241, 10409, and 12958. The regression tests did their job: they failed, someone brought it up on the mailing lists, and then the issue got ignored for 6 months. Oops. There may still be some regressions for functions we don't have test coverage for yet.
* Fix exp2*(x) on signaling NaNs by returning x+x as usual.bde2008-02-131-1/+1
| | | | | | | | | | | | | | | This has the side effect of confusing gcc-4.2.1's optimizer into more often doing the right thing. When it does the wrong thing here, it seems to be mainly making too many copies of x with dependency chains. This effect is tiny on amd64, but in some cases on i386 it is enormous. E.g., on i386 (A64) with -O1, the current version of exp2() should take about 50 cycles, but took 83 cycles before this change and 66 cycles after this change. exp2f() with -O1 only speeded up from 51 to 47 cycles. (exp2f() should take about 40 cycles, on an Athlon in either i386 or amd64 mode, and now takes 42 on amd64). exp2l() with -O1 slowed down from 155 cycles to 123 for some args; this is unimportant since the i386 exp2l() is a fake; the wrong thing for it seems to involve branch misprediction.
* Use a better method of scaling by 2**k. Instead of adding to thebde2008-02-071-11/+15
| | | | | | | | | | | | | | | | | | | | | exponent bits of the reduced result, construct 2**k (hopefully in parallel with the construction of the reduced result) and multiply by it. This tends to be much faster if the construction of 2**k is actually in parallel, and might be faster even with no parallelism since adjustment of the exponent requires a read-modify-wrtite at an unfortunate time for pipelines. In some cases involving exp2* on amd64 (A64), this change saves about 40 cycles or 30%. I think it is inherently only about 12 cycles faster in these cases and the rest of the speedup is from partly-accidentally avoiding compiler pessimizations (the construction of 2**k is now manually scheduled for good results, and -O2 doesn't always mess this up). In most cases on amd64 (A64) and i386 (A64) the speedup is about 20 cycles. The worst case that I found is expf on ia64 where this change is a pessimization of about 10 cycles or 5%. The manual scheduling for plain exp[f] is harder and not as tuned. This change ld128/s_exp2l.c has not been tested.
* Implement exp2l(). There is one version for machines with 80-bitdas2008-01-181-0/+426
long doubles (i386, amd64, ia64) and one for machines with 128-bit long doubles (sparc64). Other platforms use the double version. I've only done runtime testing on i386. Thanks to bde@ for helpful discussions and bugfixes.
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