Basic demonstrator for mem-mode heatmap/op flagging.

[Mittagskogel]

Revive tracking for individual floating-point errors in mem-mode.

[Mittagskogel]

@lucasmnd this is the basic proof-of-concept for tracing errors to individual operations and building a heatmap of errors. In this state, the idea is quite primitive: compute the error of the truncated operation results compared to double-precision. Then, divide by the result to get a relative error. See Mpfr.cpp lines 435-450. I've added a few extra print statements here to show what's going on; you will want to remove them if you plan to use this code with any more than a few tens of operations.

Calling __raptor_fprt_op_dump_status(unsigned n) will print the top n instances where the relative error was large than the threshold defined in Mpfr.cpp line 281.

I've added a quick example in examples/heatmap/heatmap.cpp for you to play around with. After re-building (and re-installing) Raptor, you can build it with raptor-clang++ ./heatmap.cpp -O3 -g -o heatmap. Then try something like ./heatmap 5.0 and you should see the following:

fmul: trunc = 1.500000e+01 err = 0.000000e+00 err/trunc = 0.000000e+00
fmul: trunc = 4.997253e-04 err = 2.746582e-07 err/trunc = 5.496183e-04 (flagged)
fadd: trunc = 5.000000e+00 err = 5.000000e-04 err/trunc = 1.000000e-04
fadd: trunc = 2.000000e+01 err = 5.000000e-04 err/trunc = 2.500000e-05
Exact: 20.0005
Truncated: 20
Information about top 4 operations.
./heatmap.cpp:17:23: 1xfmul L1 Error Norm: 2.74658e-07 Number of violations: 1 Ignored 0 times.
./heatmap.cpp:18:24: 1xfadd L1 Error Norm: 0.0005 Number of violations: 0 Ignored 0 times.
./heatmap.cpp:16:21: 1xfmul L1 Error Norm: 0 Number of violations: 0 Ignored 0 times.
./heatmap.cpp:20:16: 1xfadd L1 Error Norm: 0.0005 Number of violations: 0 Ignored 0 times.
4 ops were truncated.

So you can see that the multiplication in * frac in line 17 of heatmap.cpp got flagged for a large relative error. The bad addition (large+small fp) in line 18 doesn't get flagged because the overall relative error stays small.

A few more details:

• It only works in mem-mode because it exploits the __raptor_fp struct defined in Trace.cpp.
• RAPTOR_FPRT_ENABLE_SHADOW_RESIDUALS needs to be enabled in Mpfr.cpp (For this demo, I've turned it on permanently in line 276)
• The code snippet to calculate and flag the error is currently duplicated for each operation type (__RAPTOR_MPFR_SINGOP, __RAPTOR_MPFR_BIN, etc.)
• Statistics are grouped by debug location (-g). If you call foo() twice, you will see that the number of "violations" increases.

This is very much a prototype. I'm looking forward to getting some insights into your use-case and building on your feedback to turn this into a proper feature.