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Improve argument reduction #4158

Merged
merged 5 commits into from
Jan 7, 2025
Merged

Improve argument reduction #4158

merged 5 commits into from
Jan 7, 2025
+53 −9

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pleroy
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@pleroy pleroy commented Jan 6, 2025

Don't use the roundsd instruction but use an addition and a subtraction to drop the fractional part. This in turn makes it possible to use FMA in two places.

Comparison on Zen 3. Before:

RAW TSC:                         min      1‰      1%      5%     10%     25%     50%
            identity            4.94   +0.00   +0.00   +0.00   +0.38   +0.38   +0.38
    sqrtps_xmm0_xmm0           16.72   +0.38   +0.38   +0.38   +0.38   +0.38   +0.38
     mulsd_xmm0_xmm0            7.60   +0.00   +0.00   +0.00   +0.00   +0.00   +0.00
  mulsd_xmm0_xmm0_4x           15.20   +0.00   +0.00   +0.00   +0.00   +0.00   +0.00
Slope: 1.186186 cycle/TSC
Correlation coefficient: 0.999887
Cycles:             expected     min      1‰      1%      5%     10%     25%     50%
R           identity       0   -0.07   +0.00   +0.00   +0.00   +0.45   +0.45   +0.45
R    mulsd_xmm0_xmm0       3    3.08   +0.00   +0.00   +0.00   +0.00   +0.00   +0.00
R mulsd_xmm0_xmm0_4x      12   12.10   +0.00   +0.00   +0.00   +0.00   +0.00   +0.00
       principia_cos           66.19   +0.00   +0.45   +0.45   +0.45   +0.90   +0.90
       principia_sin           67.09   +0.45   +0.45   +0.45   +0.45   +0.90   +0.90
R   sqrtps_xmm0_xmm0      14   13.90   +0.45   +0.45   +0.45   +0.45   +0.45   +0.45
             std_cos           54.47   +0.45   +0.45   +0.45   +0.45   +0.90   +0.90
             std_sin           63.03   +0.00   +0.00   +0.00   +0.00   +0.00   +0.45

After:

RAW TSC:                         min      1‰      1%      5%     10%     25%     50%
            identity            4.94   +0.00   +0.00   +0.00   +0.38   +0.38   +0.38
    sqrtps_xmm0_xmm0           16.72   +0.38   +0.38   +0.38   +0.38   +0.38   +0.38
     mulsd_xmm0_xmm0            7.60   +0.00   +0.00   +0.00   +0.00   +0.00   +0.00
  mulsd_xmm0_xmm0_4x           15.20   +0.00   +0.00   +0.00   +0.00   +0.00   +0.00
Slope: 1.186186 cycle/TSC
Correlation coefficient: 0.999887
Cycles:             expected     min      1‰      1%      5%     10%     25%     50%
R           identity       0   -0.07   +0.00   +0.00   +0.00   +0.45   +0.45   +0.45
R    mulsd_xmm0_xmm0       3    3.08   +0.00   +0.00   +0.00   +0.00   +0.00   +0.00
R mulsd_xmm0_xmm0_4x      12   12.10   +0.00   +0.00   +0.00   +0.00   +0.00   +0.00
       principia_cos           65.73   +0.00   +0.00   +0.45   +0.45   +0.90   +0.90
       principia_sin           64.83   +1.35   +1.80   +1.80   +1.80   +2.25   +2.25
R   sqrtps_xmm0_xmm0      14   13.90   +0.45   +0.45   +0.45   +0.45   +0.45   +0.45
             std_cos           55.37   +0.45   +0.90   +0.90   +0.90   +0.90   +0.90
             std_sin           63.03   +0.00   +0.00   +0.00   +0.00   +0.00   +0.45

Comparison on Golden Cove. Before:

RAW TSC:                         min      1‰      1%      5%     10%     25%     50%
            identity            6.82   +0.16   +0.18   +0.20   +0.22   +0.24   +1.72
    sqrtps_xmm0_xmm0           27.04   +0.22   +0.26   +0.26   +0.28   +0.32   +0.36
     mulsd_xmm0_xmm0           14.04   +0.14   +0.18   +0.62   +0.64   +0.66   +0.70
  mulsd_xmm0_xmm0_4x           32.34   +0.12   +0.20   +1.30   +1.32   +1.36   +1.42
Slope: 0.623174 cycle/TSC
Correlation coefficient: 0.998850
Cycles:             expected     min      1‰      1%      5%     10%     25%     50%
R           identity       0   -0.26   +0.10   +0.11   +0.12   +0.14   +0.15   +0.16
R    mulsd_xmm0_xmm0       4    4.26   +0.34   +0.36   +0.37   +0.39   +0.40   +0.42
R mulsd_xmm0_xmm0_4x      16   15.65   +0.10   +0.79   +0.82   +0.82   +0.85   +0.88
       principia_cos           71.20   +0.90   +1.45   +2.18   +2.58   +3.10   +3.60
       principia_sin           75.37   +0.70   +0.91   +1.11   +1.21   +1.41   +1.65
R   sqrtps_xmm0_xmm0      12   12.39   +0.10   +0.12   +0.14   +0.15   +0.17   +0.20
             std_cos           54.51   +1.10   +1.27   +1.38   +1.43   +1.53   +1.66
             std_sin           64.19   +0.14   +0.20   +0.26   +0.30   +0.37   +0.46

After:

RAW TSC:                         min      1‰      1%      5%     10%     25%     50%
            identity            6.74   +0.22   +0.24   +0.26   +0.28   +0.30   +0.32
    sqrtps_xmm0_xmm0           26.94   +0.32   +0.34   +0.36   +0.38   +0.42   +0.46
     mulsd_xmm0_xmm0           14.04   +0.14   +0.58   +0.62   +0.64   +0.66   +0.70
  mulsd_xmm0_xmm0_4x           32.36   +0.10   +1.22   +1.28   +1.30   +1.34   +1.40
Slope: 0.622294 cycle/TSC
Correlation coefficient: 0.998924
Cycles:             expected     min      1‰      1%      5%     10%     25%     50%
R           identity       0   -0.23   +0.11   +0.11   +0.12   +0.14   +0.15   +0.16
R    mulsd_xmm0_xmm0       4    4.30   +0.06   +0.09   +0.36   +0.37   +0.39   +0.41
R mulsd_xmm0_xmm0_4x      16   15.64   +0.10   +0.19   +0.83   +0.85   +0.87   +0.91
       principia_cos           69.40   +0.35   +0.54   +0.71   +0.80   +0.97   +1.17
       principia_sin           70.49   +0.41   +0.58   +0.73   +0.82   +0.97   +1.15
R   sqrtps_xmm0_xmm0      12   12.44   +0.06   +0.09   +0.10   +0.11   +0.12   +0.15
             std_cos           55.23   +0.42   +0.52   +0.62   +0.68   +0.77   +0.88
             std_sin           64.13   +0.12   +0.20   +0.26   +0.30   +0.37   +0.46

pleroy added 5 commits January 1, 2025 02:32
@pleroy
Improved reduction is actually horribly bad.
f9a2ec4
@pleroy
Merge remote-tracking branch 'mockingbirdnest/master' into TresVieux
ad832e5
@pleroy
An argument reduction that doesn’t use roundsd. On Zen3 is is probabl…
87a767b 
…y pessimizing.

Numbers on Golden Cove.  Before:
       principia_cos           71.25   +0.67   +1.17   +1.83   +2.27   +2.80   +3.29
       principia_sin           75.37   +0.66   +0.92   +1.18   +1.36   +9.97  +10.21
After:
       principia_cos           69.01   +0.47   +0.66   +0.82   +0.92   +1.07   +1.25
       principia_sin           70.20   +0.37   +0.56   +0.71   +0.81   +0.95   +1.17

Unfortunately, on Zen3 this is pessimizing.  Before:
       principia_cos           65.73   +0.45   +0.90   +0.90   +0.90   +1.35   +1.35
       principia_sin           66.19   +1.35   +1.35   +1.35   +1.35   +1.80   +1.80
After:
       principia_cos           68.44   +0.45   +0.45   +0.45   +0.45   +0.90   +0.90
       principia_sin           67.99   +1.35   +1.35   +1.35   +1.80   +1.80   +2.25
@pleroy
Merge remote-tracking branch 'mockingbirdnest/master' into TresVieux
1458ada
@pleroy
Cleanup.
bbad4e6
@eggrobin eggrobin added the LGTM label Jan 7, 2025
@pleroy pleroy merged commit 535e54c into mockingbirdnest:master Jan 7, 2025
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@pleroy @eggrobin