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This duplicates a bunch of the implementation over in #3405, so will make some suggestions/comments on that one and then rebase this once that PR lands |
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I guess we should coordinate more as I also was preparing PR for std_normal and normal |
Jenkins Console Log Machine informationDistributor ID: Ubuntu Description: Ubuntu 20.04.3 LTS Release: 20.04 Codename: focal CPU: Architecture: x86_64 CPU op-mode(s): 32-bit, 64-bit Byte Order: Little Endian Address sizes: 52 bits physical, 57 bits virtual CPU(s): 192 On-line CPU(s) list: 0-191 Thread(s) per core: 2 Core(s) per socket: 48 Socket(s): 2 NUMA node(s): 2 Vendor ID: AuthenticAMD CPU family: 25 Model: 17 Model name: AMD EPYC 9474F 48-Core Processor Stepping: 1 Frequency boost: enabled CPU MHz: 1497.515 CPU max MHz: 4114.4229 CPU min MHz: 1500.0000 BogoMIPS: 7189.39 Virtualization: AMD-V L1d cache: 3 MiB L1i cache: 3 MiB L2 cache: 96 MiB L3 cache: 512 MiB NUMA node0 CPU(s): 0-47,96-143 NUMA node1 CPU(s): 48-95,144-191 Vulnerability Gather data sampling: Not affected Vulnerability Indirect target selection: Not affected Vulnerability Itlb multihit: Not affected Vulnerability L1tf: Not affected Vulnerability Mds: Not affected Vulnerability Meltdown: Not affected Vulnerability Mmio stale data: Not affected Vulnerability Old microcode: Not affected Vulnerability Reg file data sampling: Not affected Vulnerability Retbleed: Not affected Vulnerability Spec rstack overflow: Mitigation; Safe RET Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization Vulnerability Spectre v2: Mitigation; Enhanced / Automatic IBRS; IBPB conditional; STIBP always-on; PBRSB-eIBRS Not affected; BHI Not affected Vulnerability Srbds: Not affected Vulnerability Tsa: Mitigation; Clear CPU buffers Vulnerability Tsx async abort: Not affected Vulnerability Vmscape: Mitigation; IBPB before exit to userspace Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx mmxext fxsr_opt pdpe1gb rdtscp lm constant_tsc rep_good amd_lbr_v2 nopl xtopology nonstop_tsc cpuid extd_apicid aperfmperf rapl pni pclmulqdq monitor ssse3 fma cx16 pcid sse4_1 sse4_2 x2apic movbe popcnt aes xsave avx f16c rdrand lahf_lm cmp_legacy svm extapic cr8_legacy abm sse4a misalignsse 3dnowprefetch osvw ibs skinit wdt tce topoext perfctr_core perfctr_nb bpext perfctr_llc mwaitx cpb cat_l3 cdp_l3 hw_pstate ssbd mba perfmon_v2 ibrs ibpb stibp ibrs_enhanced vmmcall fsgsbase bmi1 avx2 smep bmi2 erms invpcid cqm rdt_a avx512f avx512dq rdseed adx smap avx512ifma clflushopt clwb avx512cd sha_ni avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local user_shstk avx512_bf16 clzero irperf xsaveerptr rdpru wbnoinvd amd_ppin cppc arat npt lbrv svm_lock nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold avic v_vmsave_vmload vgif x2avic v_spec_ctrl vnmi avx512vbmi umip pku ospke avx512_vbmi2 gfni vaes vpclmulqdq avx512_vnni avx512_bitalg avx512_vpopcntdq la57 rdpid overflow_recov succor smca fsrm flush_l1d debug_swap G++: g++ (Ubuntu 9.4.0-1ubuntu1~20.04) 9.4.0 Copyright (C) 2019 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. Clang: clang version 10.0.0-4ubuntu1 Target: x86_64-pc-linux-gnu Thread model: posix InstalledDir: /usr/bin |
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I reviewed this PR (with help from Claude). Looks great Accuracy against mpmathWorst ulp over 601 points per range:
For comparison, develop's worst in-range relative error is 7.6e-06 to 5.6e-05, which is 3.4e+10 to 2.5e+11 ulp, across every branch except the far Mills tail. So this PR improves the gradient by about ten orders of magnitude. One suggestion: recover the rounding error of
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| range | value now | value with fma | gradient now | gradient with fma |
|---|---|---|---|---|
| [0.6, 4] | 6.7 | 4.8 | 4.8 | 2.2 |
| [4, 10] | 30.1 | 3.5 | 30.3 | 2.6 |
| [10, 20] | 115.2 | 2.8 | 120.9 | 2.7 |
| [20, 37] | 494.4 | 3.1 | 503.2 | 2.2 |
The cost is 3 to 4 percent on a Xeon E5-2680 v3 and 2 to 5 percent on a Tesla V100, measured with the value and gradient computed together.
Two notes on this. It stays applicable after the rebase onto #3405, because it concerns the exp(-z^2/2) factor and not erfcx.
The same expression appears in std_normal_lcdf_impl in the OpenCL device function, so the change belongs in both places.
erfcx looks slightly faster on the lower tail
Beyond removing the duplicated Cody coefficients, #3405 may improve speed. Comparing your internal std_normal_erfcx path against calling erfcx directly, value and gradient computed together:
| range (scaled) | CPU | GPU |
|---|---|---|
| far tail [-40, -10] | 1.16 | 1.35 |
| Cody [-10, -4] | 1.10 | 2.21 |
| Cody edge [-4, -2.5] | 1.06 | 1.03 |
| interior [-2.5, -0.1] | 1.11 | 1.93 |
Ratios above 1 mean the direct erfcx call is faster.
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awesome! thanks @andrjohns for putting this together, it's much needed |
Two more functions get the benefit with no extra workTwo functions that benefit from this
One function benefits from erfcx directly and is not covered here
return std_normal_lcdf(-x) - std_normal_lpdf(x);It calls
The loss grows without bound. |
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@andrjohns this is very cool! Because of how tied in this and #3405 are do you want to handle the #3405 review and then I'll review this once that is in? |
Yep sounds like a plan to me! |
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@andrjohns ping me when this is ready for review |
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@andrjohns is this ready for me to look at? |
Jenkins Console Log Machine informationDistributor ID: Ubuntu Description: Ubuntu 20.04.3 LTS Release: 20.04 Codename: focal CPU: Architecture: x86_64 CPU op-mode(s): 32-bit, 64-bit Byte Order: Little Endian Address sizes: 43 bits physical, 48 bits virtual CPU(s): 256 On-line CPU(s) list: 0-255 Thread(s) per core: 2 Core(s) per socket: 64 Socket(s): 2 NUMA node(s): 2 Vendor ID: AuthenticAMD CPU family: 23 Model: 49 Model name: AMD EPYC 7742 64-Core Processor Stepping: 0 Frequency boost: enabled CPU MHz: 1496.992 CPU max MHz: 3416.0681 CPU min MHz: 1500.0000 BogoMIPS: 4491.85 Virtualization: AMD-V L1d cache: 4 MiB L1i cache: 4 MiB L2 cache: 64 MiB L3 cache: 512 MiB NUMA node0 CPU(s): 0-63,128-191 NUMA node1 CPU(s): 64-127,192-255 Vulnerability Gather data sampling: Not affected Vulnerability Indirect target selection: Not affected Vulnerability Itlb multihit: Not affected Vulnerability L1tf: Not affected Vulnerability Mds: Not affected Vulnerability Meltdown: Not affected Vulnerability Mmio stale data: Not affected Vulnerability Old microcode: Not affected Vulnerability Reg file data sampling: Not affected Vulnerability Retbleed: Mitigation; untrained return thunk; SMT enabled with STIBP protection Vulnerability Spec rstack overflow: Mitigation; Safe RET Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization Vulnerability Spectre v2: Mitigation; Retpolines; IBPB conditional; STIBP always-on; RSB filling; PBRSB-eIBRS Not affected; BHI Not affected Vulnerability Srbds: Not affected Vulnerability Tsa: Not affected Vulnerability Tsx async abort: Not affected Vulnerability Vmscape: Mitigation; IBPB before exit to userspace Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ht syscall nx mmxext fxsr_opt pdpe1gb rdtscp lm constant_tsc rep_good nopl xtopology nonstop_tsc cpuid extd_apicid aperfmperf rapl pni pclmulqdq monitor ssse3 fma cx16 sse4_1 sse4_2 x2apic movbe popcnt aes xsave avx f16c rdrand lahf_lm cmp_legacy svm extapic cr8_legacy abm sse4a misalignsse 3dnowprefetch osvw ibs skinit wdt tce topoext perfctr_core perfctr_nb bpext perfctr_llc mwaitx cpb cat_l3 cdp_l3 hw_pstate ssbd mba ibrs ibpb stibp vmmcall fsgsbase bmi1 avx2 smep bmi2 cqm rdt_a rdseed adx smap clflushopt clwb sha_ni xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local clzero irperf xsaveerptr rdpru wbnoinvd amd_ppin arat npt lbrv svm_lock nrip_save tsc_scale vmcb_clean flushbyasid decodeassists pausefilter pfthreshold avic v_vmsave_vmload vgif v_spec_ctrl umip rdpid overflow_recov succor smca sev sev_es G++: g++ (Ubuntu 9.4.0-1ubuntu1~20.04) 9.4.0 Copyright (C) 2019 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. Clang: clang version 10.0.0-4ubuntu1 Target: x86_64-pc-linux-gnu Thread model: posix InstalledDir: /usr/bin |
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This PR fixes #2881 |
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This PR also implements most of #3364: the |
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Yes I am reviewing this all now. I'm seeing if there is a way to vectorize some of the calculations. Though there is a lot of branching so I'm not sure it is possible in a nice way |
Keep Eigen normal log-CDF evaluation on the scalar kernel, reuse compatible input storage, and return values alone when gradients are not needed. Move the standard normal distribution implementation into its shared header. Construct partials propagators only for autodiff paths, replace summand traits with direct proportional/autodiff conditions, and name shared density expressions for reuse at their final uses. Preserve the eval and log1p improvements and update callers and regression coverage for the return types. Validation: targeted value and nested-autodiff tests pass, along with 256 proportional-density checks. OpenCL test binaries compile; runtime validation is limited by driver kernel creation failures (CL_INVALID_KERNEL).
This branch has not been deployed
6 participants
Summary
This PR extracts the key value and gradient calculations from the
std_normal_lcdfheader into reusable functions that other normal-cdf-related functions can delegate to, removing a lot of duplicated/inconsistent implementations.The value and gradient calculations are also updated to replace the taylor expansions with the Cody rational approximations (previously only used for the tail).
Two other bugs were found & fixed for
var_value<Eigen::VectorXd>handling:as_array_or_scalar()now returns an array unchanged instead of re-wrapping itref_type_ifkeeps an rvaluearena_matrixby value rather than referencing a dead temporaryThe valid ranges of inputs (before over/underflow) across all functions are expanded:
While performance is either unchanged or significantly improved across inputs:
Full timing comparisons
double (values only)
var_value (Eigen::Matrix<var_value> y, var_value parameters, gradient)
var_valueEigen::Matrix (var_valueEigen::VectorXd y, var_value parameters, gradient)
fvar (tangent)
Tests
Additional tests exercising the increased numerical stability are added, as well new
mixtests for the distributionsSide Effects
N/A
Release notes
Increased numerical stability and performance of the
normal,std_normal,lognormalandexp_mod_normal(LC)CDF functionsChecklist
Copyright holder: (fill in copyright holder information)
The copyright holder is typically you or your assignee, such as a university or company. By submitting this pull request, the copyright holder is agreeing to the license the submitted work under the following licenses:
- Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
- Documentation: CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/)
the basic tests are passing
./runTests.py test/unit)make test-headers)make test-math-dependencies)make doxygen)make cpplint)the code is written in idiomatic C++ and changes are documented in the doxygen
the new changes are tested