Skip to content

FP-Analysis/atomic-condition

master
Switch branches/tags
Code

Latest commit

 

Git stats

Files

Permalink
Failed to load latest commit information.
Type
Name
Latest commit message
Commit time
 
 
lib
 
 
 
 
 
 
src
 
 
 
 
 
 
 
 

Detecting Floating-Point Errors via Atomic Conditions

Setup

Install the docker. Here are some guides for install docker for Ubuntu and docker for MacOS

Clone this repo to your local workspace:

$ git clone https://github.com/FP-Analysis/atomic-condition.git

The docker folder contains a Dockerfile that can be used to build our implementation. If an error about permission denied occurs, try to run docker in root sudo docker ....

$ cd atomic-condition/docker
$ docker build -t atomic .

It may takes a few minutes (5 minutes approx) for installing necessary packages and compiling the whole GSL Library.

Usage

Run this docker's container with interactive mode, the working directory is at /atom.

$ docker run -it atomic /bin/bash

Play with the Motivation Example

The small example foo in src/targetExample.c computes the motivation example in our paper: y = (1 - cos(x)) / (x * x)

Run on the small example foo, defined in src/targetExample.c:

( In docker's container: /atom )
$ make
$ bin/gslSolver.out example

The result shows:

...
Most suspicious input first:
-1.6006806510433069e-08         Output: 4.3331212264181757e-01
1.5707963267949008e+00          Output: 4.0528473456935066e-01
End of suspicious input list.
...

Then we use mpmath to calculate the accurate result of this two inputs:

(In python3)
>>> import mpmath
>>> mpmath.mp.prec=256
>>> def foo_h(x):
...     x = mpmath.mpf(x)
...     return (1-mpmath.cos(x))/(x*x)
...
>>> y1 = foo_h(-1.6006806510433069e-08)
>>> print(y1)
0.49999999999999998932425...
>>> y2 = foo_h(1.5707963267949008e+00)
>>> print(y2)
0.40528473456935062536197...

We can see that there is a significant error when x=-1.6006806510433069e-08, the first of our reported inputs.

If you want to play with your own function, just modify the foo function in src/targetExample.c, then

$ make
$ bin/gslSolver.out example

Run on GSL Functions

$ make
$ bin/gslSolver.out gsl <function_index>

Compute Relative Error (Only support GSL functions for now)

Using the oracle from mpmath to compute the relative error:

$ make
$ bin/gslSolver.out gsl <function_index> && python3 script/oracleMpmath.py

Example: GSL function gsl_sf_lngamma has the index 73,

$ bin/gslSolver.out gsl 73 && python3 script/oracleMpmath.py
...
Function Index: 73
Max Relative Error:
  Input:  -2.457024738220797e+00
  Output: 3.552713678800501e-15
  Oracle: 4.767633887335327e-15
        Relative Error: 2.54827e-01

Reproduce the Results in Paper

Getting the relative errors of GSL functions (Table 4 and Table 5)

You can check GSL functions one by one as mentioned in above section. You can also check all of the results in single run with:

$ make
$ bin/gslSolver.out gsl all
$ python3 script/oracleMpmath.py

Getting the statistics of the relative errors (Figure 3) and the ranking results (Figure 4)

(If you have already run these 3 commands, you don't need to run them again)
$ make
$ bin/gslSolver.out gsl all
$ python3 script/oracleMpmath.py

(Please do not insert other commands between this one and the above 3 ones, otherwise you need to run them once again to get the necessary intermediate results.)
$ python3 script/reproduce.py

Data sources for LSGA and DEMC

The data of LSGA's running time are collected from the LSGA paper, which claims (the running time)

... are approximately equal to 60 seconds.

The data of DEMC's running time are collected from the DEMC's data repository.

GSL Function List and mpmath Support

GSL Function Name Index mpmath support?
gsl_sf_airy_Ai 0 ✔️
gsl_sf_airy_Bi 1 ✔️
gsl_sf_airy_Ai_scaled 2 ✔️
gsl_sf_airy_Bi_scaled 3 ✔️
gsl_sf_airy_Ai_deriv 4 ✔️
gsl_sf_airy_Bi_deriv 5 ✔️
gsl_sf_airy_Ai_deriv_scaled 6 ✔️
gsl_sf_airy_Bi_deriv_scaled 7 ✔️
gsl_sf_bessel_J0 8 ✔️
gsl_sf_bessel_J1 9 ✔️
gsl_sf_bessel_Y0 10 ✔️
gsl_sf_bessel_Y1 11 ✔️
gsl_sf_bessel_I0 12 ✔️
gsl_sf_bessel_I1 13 ✔️
gsl_sf_bessel_I0_scaled 14 ✔️
gsl_sf_bessel_I1_scaled 15 ✔️
gsl_sf_bessel_K0 16 ✔️
gsl_sf_bessel_K1 17 ✔️
gsl_sf_bessel_K0_scaled 18 ✔️
gsl_sf_bessel_K1_scaled 19 ✔️
gsl_sf_bessel_j0 20 ✔️
gsl_sf_bessel_j1 21 ✔️
gsl_sf_bessel_j2 22 ✔️
gsl_sf_bessel_y0 23 ✔️
gsl_sf_bessel_y1 24 ✔️
gsl_sf_bessel_y2 25 ✔️
gsl_sf_bessel_i0_scaled 26 ✔️
gsl_sf_bessel_i1_scaled 27 ✔️
gsl_sf_bessel_i2_scaled 28 ✔️
gsl_sf_bessel_k0_scaled 29 ✔️
gsl_sf_bessel_k1_scaled 30 ✔️
gsl_sf_bessel_k2_scaled 31 ✔️
gsl_sf_clausen 32 ✔️
gsl_sf_dawson 33
gsl_sf_debye_1 34
gsl_sf_debye_2 35
gsl_sf_debye_3 36
gsl_sf_debye_4 37
gsl_sf_debye_5 38
gsl_sf_debye_6 39
gsl_sf_dilog 40 ✔️
gsl_sf_ellint_Kcomp 41 ✔️
gsl_sf_ellint_Ecomp 42 ✔️
gsl_sf_ellint_Dcomp 43
gsl_sf_erfc 44 ✔️
gsl_sf_log_erfc 45 ✔️
gsl_sf_erf 46 ✔️
gsl_sf_erf_Z 47 ✔️
gsl_sf_erf_Q 48 ✔️
gsl_sf_hazard 49 ✔️
gsl_sf_exp 50 ✔️
gsl_sf_expm1 51 ✔️
gsl_sf_exprel 52 ✔️
gsl_sf_exprel_2 53 ✔️
gsl_sf_expint_E1 54 ✔️
gsl_sf_expint_E2 55 ✔️
gsl_sf_expint_E1_scaled 56 ✔️
gsl_sf_expint_E2_scaled 57 ✔️
gsl_sf_expint_Ei 58 ✔️
gsl_sf_expint_Ei_scaled 59 ✔️
gsl_sf_Shi 60 ✔️
gsl_sf_Chi 61 ✔️
gsl_sf_expint_3 62
gsl_sf_Si 63 ✔️
gsl_sf_Ci 64 ✔️
gsl_sf_atanint 65
gsl_sf_fermi_dirac_m1 66 ✔️
gsl_sf_fermi_dirac_0 67 ✔️
gsl_sf_fermi_dirac_1 68 ✔️
gsl_sf_fermi_dirac_2 69 ✔️
gsl_sf_fermi_dirac_mhalf 70 ✔️
gsl_sf_fermi_dirac_half 71 ✔️
gsl_sf_fermi_dirac_3half 72 ✔️
gsl_sf_lngamma 73 ✔️
gsl_sf_gamma 74 ✔️
gsl_sf_gammastar 75
gsl_sf_gammainv 76 ✔️
gsl_sf_lambert_W0 77 ✔️
gsl_sf_lambert_Wm1 78 ✔️
gsl_sf_legendre_P1 79 ✔️
gsl_sf_legendre_P2 80 ✔️
gsl_sf_legendre_P3 81 ✔️
gsl_sf_legendre_Q0 82 ✔️
gsl_sf_legendre_Q1 83 ✔️
gsl_sf_log 84 ✔️
gsl_sf_log_abs 85 ✔️
gsl_sf_log_1plusx 86 ✔️
gsl_sf_log_1plusx_mx 87 ✔️
gsl_sf_psi 88 ✔️
gsl_sf_psi_1piy 89
gsl_sf_psi_1 90 ✔️
gsl_sf_sin_pi 91
gsl_sf_cos_pi 92
gsl_sf_synchrotron_1 93
gsl_sf_synchrotron_2 94 ✔️
gsl_sf_transport_2 95
gsl_sf_transport_3 96
gsl_sf_transport_4 97
gsl_sf_transport_5 98
gsl_sf_sin 99 ✔️
gsl_sf_cos 100 ✔️
gsl_sf_sinc 101 ✔️
gsl_sf_lnsinh 102 ✔️
gsl_sf_lncosh 103 ✔️
gsl_sf_zeta 104 ✔️
gsl_sf_zetam1 105 ✔️
gsl_sf_eta 106 ✔️

About

No description, website, or topics provided.

Resources

Stars

Watchers

Forks

Releases

No releases published

Packages

No packages published