Benchmark: Lossy Floating Point Preprocessing Turbo Razor vs Granular bitround vs libroundfast
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Quantization of the floating point mantissa by zeroing the rightmost bits according to a maximum allowed pointwise relative error.
- Floating point datasets:
+Float Compression dataset : description
+Datasets for Benchmarking Floating-Point Compressors
+Scientific IEEE 754 32-Bit Single-Precision Floating-Point Datasets
Rounding algorithm benchmark:
- Turbo Razor from TurboPFor-Integer-Compression - pointwise relative error bound (percentage of each value)
- Granular bitround/bitgroom - number of significat digits
- libround fast - number of significat digits
Turbo Razor is the fastest (2-10 times) rounding algorithm with better precision according to the maximum allowed relative error. It's the only rounding algorithm supporting the pointwise relative error bound. Other algorithms are simply shaving the mantissa bits even if the values are very small.
option -G3 : Number of significant digits for Granular bitround and libround fast.
option -z : maximum relative error bound allowed for Turbo razor
PSNR: Peak Signal-to-Noise Ratio
NRMSE: Normalized Root Mean Square Error
CTZ: Ratio of mantissa bits set to zero by the rounding algorithm.
libroundfast is setting some mantissa bits to 1 (ctz negative) resulting in worse compression when used in conjunction with general purpose compressors (see iccodec.c)
- 64-bits:
icapp *.f64 -I15 -e149,150,152 -Fd -v1 -z.005 -G3 E MB/s size ratio relat. err PSNR NRMSE CTZ 5258.78 548458560 100.00% 0.005 148 4.18161e-08 2.4% 149:fprazor Turbo razor astro_mhd130x514x1026.f64 579.05 548458560 100.00% 0.00497256 102 8.20064e-06 2.5% 150:gb granular bitround astro_mhd130x514x1026.f64 690.77 548458560 100.00% 0.00485313 103 7.15003e-06 -14.2% 152:libdroundfast float fast round astro_mhd130x514x1026.f64 1218.58 671088640 100.00% 0.005 76 0.000151481 69.7% 149:fprazor Turbo razor astro_pt512x256x640.f64 580.57 671088640 100.00% 0.00487795 82 7.62695e-05 68.2% 150:gb granular bitround astro_pt512x256x640.f64 672.15 671088640 100.00% 0.00431012 83 7.42398e-05 64.7% 152:libdroundfast float fast round astro_pt512x256x640.f64 1000.58 188563456 100.00% 0.005 191 2.79912e-10 52.0% 149:fprazor Turbo razor rsim2048x11509.f64 748.38 188563456 100.00% 0.00496792 113 2.24649e-06 51.0% 150:gb granular bitround rsim2048x11509.f64 617.11 188563456 100.00% 0.00485028 113 2.25849e-06 44.5% 152:libdroundfast float fast round rsim2048x11509.f64 919.95 1073741824 100.00% 0.005 68 0.00040705 69.9% 149:fprazor Turbo razor wave512x512x512.f64 577.63 1073741824 100.00% 0.00487804 78 0.000120339 68.5% 150:gb granular bitround wave512x512x512.f64 668.71 1073741824 100.00% 0.00431019 79 0.000117616 65.1% 152:libdroundfast float fast round wave512x512x512.f64
- 32 bits
icapp *.f32 -I15 -e149,150,152 -Ff -v1 -z.005 -G3 E MB/s size ratio relat. err PSNR NRMSE CTZ 2772.92 268435456 100.00% 0.005 148 3.88992e-08 1.3% 149:fprazor Turbo razor astro_mhd128x512x1024.f32 282.54 268435456 100.00% 0.00497253 102 8.21992e-06 1.5% 150:gb granular bitround astro_mhd128x512x1024.f32 341.38 268435456 100.00% 0.0048531 103 7.15148e-06 -32.2% 152:libdroundfast float fast round astro_mhd128x512x1024.f32 619.29 335544320 100.00% 0.005 76 0.000151478 48.9% 149:fprazor Turbo razor astro_pt512x256x640.f32 284.69 335544320 100.00% 0.00487797 82 7.62695e-05 45.9% 150:gb granular bitround astro_pt512x256x640.f32 330.96 335544320 100.00% 0.00431015 83 7.42398e-05 38.8% 152:libdroundfast float fast round astro_pt512x256x640.f32 608.86 3722080 100.00% 0.00499997 62 0.000792645 31.6% 149:fprazor Turbo razor float232630x4.f32 389.60 3722080 100.00% 0.00467482 82 8.09473e-05 31.3% 150:gb granular bitround float232630x4.f32 291.57 3722080 100.00% 0.00431034 76 0.000167833 17.0% 152:libdroundfast float fast round float232630x4.f32 2901.84 11437608 100.00% 0.0049975 130 3.15258e-07 21.4% 149:fprazor Turbo razor float953134x3.f32 284.50 11437608 100.00% 0.00496978 79 0.000110678 46.9% 150:gb granular bitround float953134x3.f32 320.09 11437608 100.00% 0.00479505 79 0.00011031 40.5% 152:libdroundfast float fast round float953134x3.f32 1228.49 139497932 100.00% 0.00499999 72 0.000254028 33.9% 149:fprazor Turbo razor msg_sppm.f32 317.21 139497932 100.00% 0.00466576 89 3.35241e-05 34.9% 150:gb granular bitround msg_sppm.f32 326.94 139497932 100.00% 0.00430519 75 0.000171811 22.0% 152:libdroundfast float fast round msg_sppm.f32 429.15 62865612 100.00% 0.005 76 0.000160812 48.6% 149:fprazor Turbo razor msg_sweep3d.f32 288.06 62865612 100.00% 0.00482618 85 5.33581e-05 45.3% 150:gb granular bitround msg_sweep3d.f32 320.19 62865612 100.00% 0.00426642 82 7.65017e-05 38.3% 152:libdroundfast float fast round msg_sweep3d.f32 503.95 94281728 100.00% 0.005 191 2.79382e-10 36.6% 149:fprazor Turbo razor rsim2048x11509.f32 371.42 94281728 100.00% 0.00496795 113 2.24649e-06 34.5% 150:gb granular bitround rsim2048x11509.f32 299.93 94281728 100.00% 0.00485031 113 2.25849e-06 23.9% 152:libdroundfast float fast round rsim2048x11509.f32 2561.73 16777216 100.00% 0.00499999 147 4.47113e-08 2.3% 149:fprazor Turbo razor sq1024x1024x4.f32 858.54 16777216 100.00% 0.00479316 73 0.00023009 12.4% 150:gb granular bitround sq1024x1024x4.f32 356.91 16777216 100.00% 0.00424078 73 0.000217539 -5.6% 152:libdroundfast float fast round sq1024x1024x4.f32 1267.69 67108864 100.00% 0.005 117 1.41099e-06 16.1% 149:fprazor Turbo razor sq2048x2048x4.f32 264.77 67108864 100.00% 0.00497512 79 0.000118169 19.3% 150:gb granular bitround sq2048x2048x4.f32 349.99 67108864 100.00% 0.00485415 79 0.000111484 4.4% 152:libdroundfast float fast round sq2048x2048x4.f32 464.65 536870912 100.00% 0.005 68 0.000407049 49.4% 149:fprazor Turbo razor wave512x512x512.f32 283.51 536870912 100.00% 0.00487805 78 0.000120339 46.5% 150:gb granular bitround wave512x512x512.f32 325.72 536870912 100.00% 0.00431021 79 0.000117616 39.8% 152:libdroundfast float fast round wave512x512x512.f32
how floating point rounding algorithms work using the PI value
Algo NSD Error bound value Difference to PI trailling zeros PI exact 3.141592653589793116 3 Turbo Razor 5.000000e-01 3 0.1415926536 51 Granular bitround 1 3 0.1415926536 51 Bit Grooming 0 3 0.1415926536 51 Turbo Razor 5.000000e-02 3.125 0.01659265359 48 Granular bitround 2 3.125 0.01659265359 48 Bit Grooming 1 3.125 0.01659265359 48 Turbo Razor 5.000000e-03 3.140625 0.0009676535898 45 Granular bitround 3 3.140625 0.0009676535898 45 Bit Grooming 2 3.140625 0.0009676535898 45 Turbo Razor 5.000000e-04 3.140625 0.0009676535898 45 Granular bitround 4 3.141601562 -8.908910207e-06 41 Bit Grooming 3 3.140625 0.0009676535898 45 Turbo Razor 5.000000e-05 3.141540527 5.212624604e-05 37 Granular bitround 5 3.141601562 -8.908910207e-06 41 Bit Grooming 4 3.141540527 5.212624604e-05 37 Turbo Razor 5.000000e-06 3.141586304 6.349878856e-06 35 Granular bitround 6 3.141593933 -1.279515676e-06 34 Bit Grooming 5 3.141586304 6.349878856e-06 35 Turbo Razor 5.000000e-07 3.141592026 6.278329572e-07 32 Granular bitround 7 3.141592979 -3.258413592e-07 31 Bit Grooming 6 3.141592026 6.278329572e-07 32 Turbo Razor 5.000000e-08 3.141592622 3.178650942e-08 28 Granular bitround 8 3.141592681 -2.781813535e-08 27 Bit Grooming 7 3.141592622 3.178650942e-08 28 Turbo Razor 5.000000e-09 3.141592652 1.984187037e-09 26 Granular bitround 9 3.141592652 1.984187037e-09 26 Bit Grooming 8 3.141592652 1.984187037e-09 26
Turbo Razor is using the rel. error. NSD is used by Granular bitround and Bit Grooming