Count floating-point operations in Python code & benchmark relative flop costs.

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counted-float

This Python package provides functionality for...

counting floating point operations (FLOPs) of numerical algorithms implemented in plain Python, optionally weighted by their relative cost of execution
running benchmarks to estimate the relative cost of executing various floating-point operations (requires numba optional dependency for achieving accurate results)

The target application area is evaluation of research prototypes of numerical algorithms where (weighted) flop counting can be useful for estimating total computational cost, in cases where benchmarking a compiled version (C, Rust, ...) is not feasible or desirable.

Flop weights are computed using a highly curated dataset spanning a wide range of modern CPUs:

19 benchmarks, 16 spec sheets, 12 third party measurements (Agner Fog, uops.info)
covering x86 (Intel, AMD) and ARM (Apple, AWS, Azure) architectures

1. Installation

Use you favorite package manager such as uv or pip:

pip install counted-float           # install without numba optional dependency
pip install counted-float[numba]    # install with numba optional dependency

Numba is optional due to its relatively large size (40-50MB, including llvmlite), but without it, benchmarks will not be reliable (but will still run, but not in jit-compiled form).

NOTE: the cli optional dependency is only useful when installing the code as a tool using e.g. uv or pipx (see below)

2. Counting Flops

2.1. CountedFloat class

In order to instrument all floating point operations with counting functionality, the CountedFloat class was implemented, which is a drop-in replacement for the built-in float type. The CountedFloat class is a subclass of float and is "contagious", meaning that it will automatically ensure results of math operations where at least one operand is a CountedFloat will also be a CountedFloat. This way we ensure flop counting is a 'closed system'.

On top of this, we monkey-patch the math module to ensure that all math operations that require counting (sqrt, log2, pow, ...) are also instrumented.

Example 1:

from counted_float import CountedFloat

cf = CountedFloat(1.3)
f = 2.8

result = cf + f  # result = CountedFloat(4.1)

is_float_1 = isinstance(cf, float)  # True
is_float_2 = isinstance(result, float)  # True

Example 2:

import math
from counted_float import CountedFloat

cf1 = CountedFloat(0.81)

s = math.sqrt(cf1)  # s = CountedFloat(0.9)
is_float = isinstance(s, float)  # True

The counting model: what gets counted and why

The counting model is a contract with two sides:

Your side: wrap every runtime input of the algorithm you want to measure in CountedFloat at its boundary. Contagion does the rest — everything derived from those inputs stays counted automatically.
The library's side: count every FLOP that a compiled (C/Rust/...) port of your algorithm would execute on data derived from those inputs.

From this contract follows a clean rule for everything else: constants are free. Any plain float encountered mid-computation is, by the contract, not an input — so it must be a constant of the algorithm (a literal, a coefficient, a tolerance), and operations purely among constants are work a compiled port would fold at compile time or precompute. This is why e.g. math.sqrt(3) counts nothing: the port ships sqrt(3) as a precomputed constant.

The library detects constants through two mechanisms, applying the same rule:

Unwrapped values (plain floats): constants by the wrapping contract, as above.
int operands: evidence of a hardcoded constant — ints don't fall out of floating-point computations, so an int operand almost certainly appears literally in your source. This enables counting the strength reductions a compiled port would apply: x**2 counts MUL (i.e. x*x), 2**x counts EXP2, math.log(x, 10) counts LOG10 — while x**2.0, with a float that could be a runtime value, conservatively counts a generic POW.

The flip side: an unwrapped runtime input is invisible to the counter — that is a wrapping error at your algorithm's boundary, not something the library can detect. When in doubt, wrap.

Once we use the CountedFloat class, we can use the available context managers to count the number of flops performed by CountedFloat objects.

Example 1: basic usage

from counted_float import CountedFloat, FlopCountingContext

cf1 = CountedFloat(1.73)
cf2 = CountedFloat(2.94)

with FlopCountingContext() as ctx:
    _ = cf1 * cf2
    _ = cf1 + cf2

counts = ctx.flop_counts()   # {FlopType.MUL: 1, FlopType.ADD: 1}
counts.total_count()         # 2

Example 2: pause counting 1

from counted_float import CountedFloat, FlopCountingContext

cf1 = CountedFloat(1.73)
cf2 = CountedFloat(2.94)

with FlopCountingContext() as ctx:
    _ = cf1 * cf2
    ctx.pause()
    _ = cf1 + cf2   # will be executed but not counted
    ctx.resume()
    _ = cf1 - cf2

counts = ctx.flop_counts()   # {FlopType.MUL: 1, FlopType.SUB: 1}
counts.total_count()         # 2

Example 3: pause counting 2

from counted_float import CountedFloat, FlopCountingContext, PauseFlopCounting

cf1 = CountedFloat(1.73)
cf2 = CountedFloat(2.94)

with FlopCountingContext() as ctx:
    _ = cf1 * cf2
    with PauseFlopCounting():
        _ = cf1 + cf2   # will be executed but not counted
    _ = cf1 - cf2

counts = ctx.flop_counts()   # {FlopType.MUL: 1, FlopType.SUB: 1}
counts.total_count()         # 2

2.3. Weighted FLOP counting

The counted_float package contains a set of default, built-in FLOP weights, based on both empirical measurements and theoretical estimates of the relative cost of different floating point operations.

See fpu_data_sources.md for rationale behind choice of data sources and methodology.

>>> from counted_float.config import get_active_flop_weights
>>> get_active_flop_weights().show()

{
    FlopType.MINUS      [-x]            :   0.45000
    FlopType.ABS        [abs(x)]        :   0.70000
    FlopType.ADD        [x+y]           :   1.00000
    FlopType.COMP       [x<=y]          :   1.00000
    FlopType.SUB        [x-y]           :   1.00000
    FlopType.MUL        [x*y]           :   1.40000
    FlopType.RND        [round]         :   1.80000
    FlopType.F2I        [float->int]    :   2.00000
    FlopType.I2F        [int->float]    :   2.00000
    FlopType.DIV        [x/y]           :   5.50000
    FlopType.SQRT       [sqrt(x)]       :   7.50000
    FlopType.EXP2       [2^x]           :  16.00000
    FlopType.EXP        [e^x]           :  18.00000
    FlopType.LOG        [log(x)]        :  18.00000
    FlopType.EXP10      [10^x]          :  22.00000
    FlopType.LOG2       [log2(x)]       :  22.00000
    FlopType.LOG10      [log10(x)]      :  24.00000
    FlopType.COS        [cos(x)]        :  30.00000
    FlopType.SIN        [sin(x)]        :  30.00000
    FlopType.POW        [x^y]           :  40.00000
    FlopType.TAN        [tan(x)]        :  40.00000
    FlopType.CBRT       [cbrt(x)]       :  45.00000
}

Note that these weights are rounded up to the ~10% closest semi-round number, reflecting a balance between accuracy and readability, while conveying the message that these weights should be used as approximations only. See further down for the different rounding modes.

These weights will be used by default when extracting total weighted flop costs:

import math
from counted_float import CountedFloat, FlopCountingContext


cf1 = CountedFloat(1.73)
cf2 = CountedFloat(2.94)

with FlopCountingContext() as ctx:
    _ = cf1 + cf2
    _ = cf1 ** cf2
    _ = math.log2(cf2)
    
flop_counts = ctx.flop_counts()
total_cost = flop_counts.total_weighted_cost()  # 1 + 40 + 22 = 63

Note that the total_weighted_cost method will use the default flop weights as returned by get_flop_weights(). This can be overridden by either configuring different flop weights (see next section) or by setting the weights argument of the total_weighted_cost() method.

2.4. Configuring FLOP weights

We showed earlier that the get_flop_weights() function returns the default FLOP weights. We can change this by using the set_flop_weights() function, which takes a FlopWeights object as an argument. This way we can configure flop weights that might be obtained using benchmarks run on the target hardware (see later sections).

from counted_float.config import set_active_flop_weights
from counted_float import FlopWeights

set_active_flop_weights(weights=FlopWeights(...))  # insert own weights here

2.5. Inspecting built-in data

2.5.1. Default, pre-aggregated flop weights

Built-in flop weights can be inspected using the following functions:

from counted_float.config import get_default_consensus_flop_weights

>>> get_default_consensus_flop_weights(rounding_mode=None).show()

{
    FlopType.MINUS      [-x]            :   0.43688
    FlopType.ABS        [abs(x)]        :   0.71585
    FlopType.COMP       [x<=y]          :   0.97866
    FlopType.SUB        [x-y]           :   0.99565
    FlopType.ADD        [x+y]           :   1.00000
    FlopType.MUL        [x*y]           :   1.39506
    FlopType.RND        [round]         :   1.78130
    FlopType.F2I        [float->int]    :   1.91125
    FlopType.I2F        [int->float]    :   1.91839
    FlopType.DIV        [x/y]           :   5.53385
    FlopType.SQRT       [sqrt(x)]       :   7.37309
    FlopType.EXP2       [2^x]           :  15.79616
    FlopType.EXP        [e^x]           :  17.45201
    FlopType.LOG        [log(x)]        :  18.93143
    FlopType.LOG2       [log2(x)]       :  22.29433
    FlopType.EXP10      [10^x]          :  22.93876
    FlopType.LOG10      [log10(x)]      :  24.56277
    FlopType.SIN        [sin(x)]        :  30.28970
    FlopType.COS        [cos(x)]        :  31.27413
    FlopType.POW        [x^y]           :  41.65022
    FlopType.TAN        [tan(x)]        :  41.99495
    FlopType.CBRT       [cbrt(x)]       :  44.15405
}

There are 3 rounding modes:

None -> no rounding
"nearest_int" -> round up/down to nearest integer, with a minimum of 1
"10%" -> round to nearest semi-round number within ~10% (default)

The default weights that are configured out-of-the-box in the package are the integer-rounded consensus weights.

2.5.2. Custom-aggregated flop weights

We can retrieve built-in flop weights in a more fine-grained manner, by custom filtering and the aggregating them with the geometric mean.

from counted_float.config import get_builtin_flop_weights

>>> get_builtin_flop_weights(key_filter="arm").show()

{
    FlopType.COMP       [x<=y]          :   0.65000
    FlopType.MINUS      [-x]            :   0.90000
    FlopType.ADD        [x+y]           :   1.00000
    FlopType.SUB        [x-y]           :   1.00000
    FlopType.ABS        [abs(x)]        :   1.10000
    FlopType.F2I        [float->int]    :   1.50000
    FlopType.MUL        [x*y]           :   1.50000
    FlopType.I2F        [int->float]    :   1.60000
    FlopType.RND        [round]         :   1.60000
    FlopType.DIV        [x/y]           :   6.00000
    FlopType.SQRT       [sqrt(x)]       :   7.50000
    FlopType.EXP2       [2^x]           :  16.00000
    FlopType.EXP        [e^x]           :  18.00000
    FlopType.LOG        [log(x)]        :  20.00000
    FlopType.LOG2       [log2(x)]       :  20.00000
    FlopType.EXP10      [10^x]          :  24.00000
    FlopType.LOG10      [log10(x)]      :  24.00000
    FlopType.COS        [cos(x)]        :  33.00000
    FlopType.SIN        [sin(x)]        :  33.00000
    FlopType.POW        [x^y]           :  40.00000
    FlopType.CBRT       [cbrt(x)]       :  45.00000
    FlopType.TAN        [tan(x)]        :  45.00000
}

3. Benchmarking

If the package is installed with the optional numba dependency, it provides the ability to micro-benchmark floating point operations as follows:

>>> from counted_float.benchmarking import run_flops_benchmark
>>> results = run_flops_benchmark()

Running FLOPS benchmarks using counted-float 0.9.5 ...
(Expected duration: ~87.8 seconds)

baseline                           : wwwwwwwwwwwwwww.........................   [  74.43 ns ±  2.6% |   302 cpu cycles ±  2.6% ]  /  1000 iterations
add                                : wwwwwwwwwwwwwww.........................   [ 662.35 ns ±  0.2% | 2.69K cpu cycles ±  0.2% ]  /  1000 iterations
add_minus                          : wwwwwwwwwwwwwww.........................   [   1.23 µs ±  0.2% | 4.98K cpu cycles ±  0.2% ]  /  1000 iterations
add_abs                            : wwwwwwwwwwwwwww.........................   [   1.23 µs ±  0.4% | 4.99K cpu cycles ±  0.4% ]  /  1000 iterations
add_add                            : wwwwwwwwwwwwwww.........................   [   1.29 µs ±  0.2% | 5.23K cpu cycles ±  0.2% ]  /  1000 iterations
add_sub                            : wwwwwwwwwwwwwww.........................   [   1.29 µs ±  0.2% | 5.23K cpu cycles ±  0.2% ]  /  1000 iterations
add_round                          : wwwwwwwwwwwwwww.........................   [   1.44 µs ±  0.1% | 5.84K cpu cycles ±  0.1% ]  /  1000 iterations
add_sqrt                           : wwwwwwwwwwwwwww.........................   [   3.96 µs ±  0.2% | 16.1K cpu cycles ±  0.2% ]  /  1000 iterations
add_cbrt                           : wwwwwwwwwwwwwww.........................   [  25.42 µs ±  0.2% |  103K cpu cycles ±  0.2% ]  /  1000 iterations
add_log                            : wwwwwwwwwwwwwww.........................   [  11.69 µs ±  0.3% | 47.4K cpu cycles ±  0.3% ]  /  1000 iterations
add_log_exp                        : wwwwwwwwwwwwwww.........................   [  22.57 µs ±  0.1% | 91.5K cpu cycles ±  0.1% ]  /  1000 iterations
add_log2                           : wwwwwwwwwwwwwww.........................   [  12.00 µs ±  0.2% | 48.7K cpu cycles ±  0.2% ]  /  1000 iterations
add_log2_exp2                      : wwwwwwwwwwwwwww.........................   [  22.48 µs ±  0.2% | 91.2K cpu cycles ±  0.2% ]  /  1000 iterations
add_log10                          : wwwwwwwwwwwwwww.........................   [  11.50 µs ±  0.2% | 46.6K cpu cycles ±  0.2% ]  /  1000 iterations
add_log10_exp10                    : wwwwwwwwwwwwwww.........................   [  24.68 µs ±  0.2% |  100K cpu cycles ±  0.2% ]  /  1000 iterations
add_sin                            : wwwwwwwwwwwwwww.........................   [  18.64 µs ±  0.3% | 75.6K cpu cycles ±  0.3% ]  /  1000 iterations
add_cos                            : wwwwwwwwwwwwwww.........................   [  18.92 µs ±  0.3% | 76.7K cpu cycles ±  0.3% ]  /  1000 iterations
add_tan                            : wwwwwwwwwwwwwww.........................   [  20.91 µs ±  0.2% | 84.8K cpu cycles ±  0.2% ]  /  1000 iterations
pow                                : wwwwwwwwwwwwwww.........................   [  24.12 µs ±  0.3% | 97.8K cpu cycles ±  0.3% ]  /  1000 iterations
pow_pow                            : wwwwwwwwwwwwwww.........................   [  48.15 µs ±  0.2% |  195K cpu cycles ±  0.2% ]  /  1000 iterations
sub                                : wwwwwwwwwwwwwww.........................   [ 661.55 ns ±  0.2% | 2.68K cpu cycles ±  0.2% ]  /  1000 iterations
sub_sub                            : wwwwwwwwwwwwwww.........................   [   1.29 µs ±  0.2% | 5.24K cpu cycles ±  0.2% ]  /  1000 iterations
mul                                : wwwwwwwwwwwwwww.........................   [ 961.78 ns ±  0.2% | 3.90K cpu cycles ±  0.2% ]  /  1000 iterations
mul_mul                            : wwwwwwwwwwwwwww.........................   [   1.92 µs ±  0.2% | 7.78K cpu cycles ±  0.2% ]  /  1000 iterations
div                                : wwwwwwwwwwwwwww.........................   [   2.45 µs ±  0.2% | 9.92K cpu cycles ±  0.2% ]  /  1000 iterations
div_div                            : wwwwwwwwwwwwwww.........................   [   5.00 µs ±  0.2% | 20.3K cpu cycles ±  0.2% ]  /  1000 iterations
lte_addsub                         : wwwwwwwwwwwwwww.........................   [   1.71 µs ±  0.2% | 6.94K cpu cycles ±  0.2% ]  /  1000 iterations

>>> results.flop_weights().show() 

{
    FlopType.ABS        [abs(x)]        :   0.89904
    FlopType.MINUS      [-x]            :   0.90935
    FlopType.SUB        [x-y]           :   0.99676
    FlopType.ADD        [x+y]           :   1.00000
    FlopType.RND        [round]         :   1.24397
    FlopType.MUL        [x*y]           :   1.55516
    FlopType.COMP       [x<=y]          :   1.69018
    FlopType.DIV        [x/y]           :   4.12333
    FlopType.SQRT       [sqrt(x)]       :   5.42419
    FlopType.EXP2       [2^x]           :  16.95266
    FlopType.LOG10      [log10(x)]      :  17.60079
    FlopType.EXP        [e^x]           :  17.76250
    FlopType.LOG        [log(x)]        :  17.86149
    FlopType.LOG2       [log2(x)]       :  18.42380
    FlopType.EXP10      [10^x]          :  21.50729
    FlopType.SIN        [sin(x)]        :  29.31571
    FlopType.COS        [cos(x)]        :  29.56218
    FlopType.TAN        [tan(x)]        :  32.88570
    FlopType.POW        [x^y]           :  39.35018
    FlopType.CBRT       [cbrt(x)]       :  40.16857
    FlopType.F2I        [float->int]    :       nan
    FlopType.I2F        [int->float]    :       nan
}

4. Installing the package as a command-line tool

An alternative way of using (parts) of the functionality is installing the package as a stand-alone command-line tool using uv or pipx:

uv tool install git+https://github.com/bertpl/counted-float@main[numba,cli]         # latest official release
uv tool install git+https://github.com/bertpl/counted-float@develop[numba,cli]      # or latest develop version

This installs the counted_float command-line tool, which can be used to e.g. run flops benchmarks.

4.1. Running benchmarks

counted_float benchmark

after which the results will be shown as .json.

4.2. Show built-in data

[~] counted_float show-data
                                                                        MINUS       ABS      COMP       SUB       ADD       MUL       RND       F2I       I2F       DIV      SQRT      EXP2       EXP       LOG      LOG2     EXP10     LOG10       SIN       COS       POW       TAN      CBRT
ALL                                                                      0.44      0.72      0.98      1.00      1.00      1.40      1.78      1.91      1.92      5.53      7.37     15.80     17.45     18.93     22.29     22.94     24.56     30.29     31.27     41.65     41.99     44.15
 ├─arm                                                                   0.89      1.05      0.64      1.01      1.00      1.50      1.61      1.49      1.59      6.15      7.60     15.98     18.57     19.60     20.86     23.30     24.26     32.32     34.08     42.28     42.85     44.97
 │  ├─v8_x                                                               0.83      1.00      0.67      1.01      1.00      1.48      1.50      1.56      1.91      5.90      7.42     15.45     17.86     19.06     20.80     22.92     22.90     32.43     33.47     41.19     42.99     44.71
 │  │  ├─benchmarks                                                      0.70      1.01      0.45      1.01      1.00      1.46      1.50        /         /       4.65      6.68     13.93     16.10     17.18     18.75     20.66     20.65     29.23     30.17     37.13     38.76     40.30
 │  │  │  ├─apple_m1_github_actions                                      0.86      0.86      1.73      1.06      1.00      1.48      1.22        /         /       4.07      5.70     15.50     16.98     17.33     20.52     19.61     17.95     29.86     31.59     38.67     38.97     41.44
 │  │  │  ├─apple_m3_max_mbp16                                           0.90      0.90      1.64      1.00      1.00      1.40      1.25        /         /       4.00      5.28     16.69     17.42     17.59     18.15     21.06     17.31     28.77     29.17     37.93     39.04     39.48
 │  │  │  ├─apple_m3_mba15                                               0.90      0.90      1.68      1.00      1.00      1.53      1.24        /         /       4.06      5.27     16.68     17.43     17.56     18.09     21.07     17.29     28.63     29.06     38.46     32.32     39.43
 │  │  │  ├─aws_graviton_2_neoverse_n1_ec2_m6g_xlarge                    0.46      1.47      0.38      1.00      1.00      1.38      2.01        /         /       5.42      8.76     10.21     14.17     15.98     17.91     22.65     25.25     28.68     29.63     33.95     41.90     40.25
 │  │  │  └─aws_graviton_3_neoverse_v1_ec2_m7g_xlarge                    0.51      1.00      0.01      1.00      1.00      1.50      1.99        /         /       6.03      9.58     11.89     14.81     17.49     19.20     19.09     27.67     30.26     31.49     36.85     42.45     40.96
 │  │  └─specs                                                           1.00      1.00      1.00      1.00      1.00      1.50      1.50      1.73      2.12      7.50      8.25        /         /         /         /         /         /         /         /         /         /         / 
 │  │     ├─arm_cortex_a76                                               1.00      1.00      1.00      1.00      1.00      1.50      1.50      2.00      3.00      7.50      8.50        /         /         /         /         /         /         /         /         /         /         / 
 │  │     ├─arm_cortex_x1                                                1.00      1.00      1.00      1.00      1.00      1.50      1.50      1.50      1.50      7.50      8.00        /         /         /         /         /         /         /         /         /         /         / 
 │  │     ├─arm_neoverse_n1                                              1.00      1.00      1.00      1.00      1.00      1.50      1.50      2.00      3.00      7.50      8.50        /         /         /         /         /         /         /         /         /         /         / 
 │  │     └─arm_neoverse_v1                                              1.00      1.00      1.00      1.00      1.00      1.50      1.50      1.50      1.50      7.50      8.00        /         /         /         /         /         /         /         /         /         /         / 
 │  ├─v9_0                                                               0.74      1.00      0.25      1.00      1.00      1.51      1.80      1.27      1.27      6.78      8.83     14.32     17.90     20.66     22.09     24.04     32.41     35.53     37.31     44.86     52.70     48.30
 │  │  ├─benchmarks                                                      0.54      1.00      0.06      1.00      1.00      1.52      2.16        /         /       6.14      9.75     12.12     15.15     17.49     18.70     20.35     27.44     30.08     31.59     37.98     44.62     40.89
 │  │  │  ├─aws_graviton_4_neoverse_v2_ec2_m8g_xlarge                    0.52      1.00      0.01      1.00      1.00      1.50      2.05        /         /       6.04      9.49     12.66     14.40     17.66     18.54     19.86     27.12     28.76     30.11     36.90     42.70     38.65
 │  │  │  └─azure_cobalt_100_neoverse_n2_github_actions                  0.57      1.00      0.33      1.00      1.00      1.53      2.28        /         /       6.23     10.02     11.61     15.94     17.33     18.87     20.85     27.76     31.46     33.15     39.09     46.62     43.26
 │  │  └─specs                                                           1.00      1.00      1.00      1.00      1.00      1.50      1.50      1.50      1.50      7.50      8.00        /         /         /         /         /         /         /         /         /         /         / 
 │  │     ├─arm_cortex_x2                                                1.00      1.00      1.00      1.00      1.00      1.50      1.50      1.50      1.50      7.50      8.00        /         /         /         /         /         /         /         /         /         /         / 
 │  │     ├─arm_cortex_x3                                                1.00      1.00      1.00      1.00      1.00      1.50      1.50      1.50      1.50      7.50      8.00        /         /         /         /         /         /         /         /         /         /         / 
 │  │     ├─arm_neoverse_n2                                              1.00      1.00      1.00      1.00      1.00      1.50      1.50      1.50      1.50      7.50      8.00        /         /         /         /         /         /         /         /         /         /         / 
 │  │     └─arm_neoverse_v2                                              1.00      1.00      1.00      1.00      1.00      1.50      1.50      1.50      1.50      7.50      8.00        /         /         /         /         /         /         /         /         /         /         / 
 │  └─v9_2                                                               1.16      1.16      1.55      1.02      1.00      1.51      1.55      1.66      1.66      5.80      6.70     18.44     20.04     19.11     19.75     22.96     19.23     29.29     31.69     40.89     34.73     42.11
 │     ├─benchmarks                                                      1.35      1.35      2.40      1.03      1.00      1.51      1.84        /         /       5.32      7.10     20.38     22.15     21.13     21.83     25.38     21.25     32.38     35.03     45.20     38.39     46.55
 │     │  └─apple_m4_pro_mbp16                                           1.35      1.35      2.40      1.03      1.00      1.51      1.84        /         /       5.32      7.10     20.38     22.15     21.13     21.83     25.38     21.25     32.38     35.03     45.20     38.39     46.55
 │     └─specs                                                           1.00      1.00      1.00      1.00      1.00      1.50      1.31      1.50      1.50      6.33      6.33        /         /         /         /         /         /         /         /         /         /         / 
 │        ├─arm_cortex_x4                                                1.00      1.00      1.00      1.00      1.00      1.50      1.50      1.50      1.50      6.50      6.50        /         /         /         /         /         /         /         /         /         /         / 
 │        ├─arm_cortex_x925                                              1.00      1.00      1.00      1.00      1.00      1.50      1.00      1.50      1.50      6.00      6.00        /         /         /         /         /         /         /         /         /         /         / 
 │        └─arm_neoverse_v3                                              1.00      1.00      1.00      1.00      1.00      1.50      1.50      1.50      1.50      6.50      6.50        /         /         /         /         /         /         /         /         /         /         / 
 └─x86                                                                   0.21      0.49      1.50      0.98      1.00      1.30      1.97      2.46      2.31      4.98      7.15     15.62     16.40     18.29     23.83     22.58     24.87     28.39     28.70     41.03     41.15     43.35
    ├─amd                                                                0.25      0.45      1.52      0.99      1.00      1.17      1.22      2.39      2.51      4.74      7.38     18.22     16.50     17.98     24.59     23.73     24.13     28.04     28.30     42.41     40.31     45.11
    │  ├─2017_zen1                                                       0.34      0.34      1.16      1.00      1.00      1.29      1.34      3.07      3.07      4.18      6.44     63.95     19.71     17.05     32.24     43.83     18.79     30.58     30.27     57.99     39.24     66.55
    │  │  ├─benchmarks                                                   0.35      0.35      0.58      1.01      1.00      1.24      1.34        /         /       4.03      6.23     58.90     18.16     15.70     29.69     40.37     17.30     28.16     27.88     53.41     36.14     61.29
    │  │  │  └─amd_ryzen_1700x                                           0.35      0.35      0.58      1.01      1.00      1.24      1.34        /         /       4.03      6.23     58.90     18.16     15.70     29.69     40.37     17.30     28.16     27.88     53.41     36.14     61.29
    │  │  └─other                                                        0.33      0.33      2.33      1.00      1.00      1.33      1.33      3.33      3.33      4.33      6.67        /         /         /         /         /         /         /         /         /         /         / 
    │  │     └─analysis_uops_info_zen1+                                  0.33      0.33      2.33      1.00      1.00      1.33      1.33      3.33      3.33      4.33      6.67        /         /         /         /         /         /         /         /         /         /         / 
    │  ├─2020_zen3                                                       0.18      0.34      1.16      1.00      1.00      0.98      1.00      2.17      2.34      4.36      6.76     11.69     15.85     16.99     22.46     19.32     21.13     24.05     24.07     38.13     38.04     39.06
    │  │  ├─benchmark                                                    0.10      0.34      0.68      1.00      1.00      1.00      1.00        /         /       4.30      6.86     10.33     14.01     15.02     19.86     17.08     18.69     21.26     21.28     33.72     33.63     34.54
    │  │  │  ├─amd_epyc_7763_linux_github                                0.10      0.34      0.68      1.00      1.00      1.00      1.00        /         /       4.31      6.86     10.35     11.79     15.35     14.36     14.53     22.21     22.45     22.86     30.57     33.34     31.25
    │  │  │  └─amd_epyc_7763_windows_github                              0.10      0.34      0.68      1.00      1.00      1.00      1.00        /         /       4.28      6.86     10.32     16.65     14.70     27.48     20.08     15.72     20.14     19.82     37.19     33.92     38.17
    │  │  └─other                                                        0.33      0.33      1.97      1.00      1.00      0.95      1.00      2.45      2.65      4.42      6.67        /         /         /         /         /         /         /         /         /         /         / 
    │  │     ├─analysis_agner_fog_r7_5800x                               0.33      0.33      1.67      1.00      1.00        /       1.00      2.00      2.33      4.50      6.67        /         /         /         /         /         /         /         /         /         /         / 
    │  │     └─analysis_uops_info_zen3                                   0.33      0.33      2.33      1.00      1.00      1.00      1.00      3.00      3.00      4.33      6.67        /         /         /         /         /         /         /         /         /         /         / 
    │  ├─2022_zen4                                                       0.15      0.33      1.41      0.99      1.00      0.99      1.00      1.85      1.78      4.41      6.92     10.77     12.47     17.12     20.49     15.83     25.03     24.11     24.56     32.21     35.99     33.32
    │  │  ├─benchmark                                                    0.07      0.33      1.57      0.97      1.00      0.98      0.99        /         /       4.49      6.95      9.97     11.55     15.86     18.98     14.66     23.19     22.34     22.75     29.84     33.34     30.87
    │  │  │  └─amd_epyc_9r14_ec2_m7a_xlarge                              0.07      0.33      1.57      0.97      1.00      0.98      0.99        /         /       4.49      6.95      9.97     11.55     15.86     18.98     14.66     23.19     22.34     22.75     29.84     33.34     30.87
    │  │  └─other                                                        0.33      0.33      1.28      1.00      1.00      1.01      1.00      2.00      1.92      4.33      6.89        /         /         /         /         /         /         /         /         /         /         / 
    │  │     ├─analysis_agner_fog_r9_7900x                               0.33      0.33      1.33      1.00      1.00        /       1.00      2.00      2.00      4.33      7.00        /         /         /         /         /         /         /         /         /         /         / 
    │  │     ├─analysis_uops_info_zen4                                   0.33      0.33      2.33      1.00      1.00      1.00      1.00      3.00      2.67      4.33      7.00        /         /         /         /         /         /         /         /         /         /         / 
    │  │     └─specs_amd                                                 0.33      0.33      0.67      1.00      1.00      1.00      1.00      1.33      1.33      4.33      6.67        /         /         /         /         /         /         /         /         /         /         / 
    │  └─2024_zen5                                                       0.39      1.04      2.83      0.95      1.00      1.50      1.68      2.64      3.08      6.31      9.84     13.71     19.04     21.09     24.62     23.64     34.12     34.84     35.83     45.40     49.16     47.78
    │     ├─benchmark                                                    0.21      1.53      2.95      0.91      1.00      1.36      1.87        /         /       6.12      9.69     13.33     18.50     20.50     23.94     22.98     33.17     33.87     34.83     44.14     47.79     46.45
    │     │  └─amd_epyc_9r45_ec2_m8a_xlarge                              0.21      1.53      2.95      0.91      1.00      1.36      1.87        /         /       6.12      9.69     13.33     18.50     20.50     23.94     22.98     33.17     33.87     34.83     44.14     47.79     46.45
    │     └─other                                                        0.71      0.71      2.72      1.00      1.00      1.66      1.50      2.72      3.17      6.50     10.00        /         /         /         /         /         /         /         /         /         /         / 
    │        ├─analysis_agner_fog_r7_9800x3d                             1.00      1.00      3.00      1.00      1.00        /       1.50      3.00      3.50      6.50     10.00        /         /         /         /         /         /         /         /         /         /         / 
    │        └─specs_amd                                                 0.50      0.50        /       1.00      1.00      1.50      1.50        /         /       6.50     10.00        /         /         /         /         /         /         /         /         /         /         / 
    └─intel                                                              0.18      0.53      1.47      0.98      1.00      1.45      3.17      2.53      2.14      5.23      6.93     13.38     16.30     18.60     23.09     21.50     25.64     28.75     29.11     39.70     42.01     41.67
       ├─2017_coffee_lake_gen_8                                          0.14      0.40      1.12      0.98      1.00      1.03      1.99      1.69      1.69      3.54      4.56     10.27     16.31     12.42     19.10     21.50     12.84     20.48     20.47     32.65     28.21     35.74
       │  ├─benchmarks                                                   0.08      0.63      1.73      0.96      1.00      1.05      1.99        /         /       3.45      4.78     10.69     16.98     12.92     19.88     22.38     13.37     21.31     21.31     33.99     29.36     37.20
       │  │  ├─intel_i7_8550U_windows                                    0.08      0.44      1.69      1.01      1.00      1.01      2.00        /         /       3.15      4.79      7.02     15.44     11.99     30.07     21.33     13.00     17.80     17.21     32.36     28.09     35.06
       │  │  └─intel_i7_8700B_macos_github_actions                       0.08      0.91      1.77      0.92      1.00      1.10      1.97        /         /       3.78      4.77     16.30     18.68     13.93     13.15     23.47     13.74     25.51     26.38     35.70     30.68     39.48
       │  └─other                                                        0.25      0.25      0.73      1.00      1.00      1.00      2.00      1.62      1.62      3.62      4.36        /         /         /         /         /         /         /         /         /         /         / 
       │     ├─analysis_agner_fog_coffee_lake                            0.25      0.25        /       1.00      1.00      1.00      2.00      1.50      1.50      3.50      4.00        /         /         /         /         /         /         /         /         /         /         / 
       │     └─analysis_uops_info_coffee_lake                            0.25      0.25      0.75      1.00      1.00      1.00      2.00      1.75      1.75      3.75      4.75        /         /         /         /         /         /         /         /         /         /         / 
       ├─2019_sunny_cove_gen_10                                          0.10      0.33      0.92      0.95      1.00      0.98      1.94      1.60      1.60      3.58      4.54     12.27      9.43     14.01     17.18     13.39     20.23     19.23     19.83     28.71     29.72     28.95
       │  ├─benchmarks                                                   0.04      0.44      1.30      0.91      1.00      1.00      1.89        /         /       3.50      4.60     11.82      9.08     13.49     16.55     12.90     19.48     18.52     19.09     27.65     28.63     27.88
       │  │  └─intel_xeon_8375c_ice_lake_ec2_m6i_xlarge                  0.04      0.44      1.30      0.91      1.00      1.00      1.89        /         /       3.50      4.60     11.82      9.08     13.49     16.55     12.90     19.48     18.52     19.09     27.65     28.63     27.88
       │  └─other                                                        0.25      0.25      0.66      1.00      1.00      0.97      2.00      1.66      1.66      3.66      4.49        /         /         /         /         /         /         /         /         /         /         / 
       │     ├─analysis_agner_fog_ice_lake                               0.25      0.25      0.50      1.00      1.00        /       2.00      1.50      1.50      3.50      4.00        /         /         /         /         /         /         /         /         /         /         / 
       │     ├─analysis_uops_info_ice_lake                               0.25      0.25      0.75      1.00      1.00      1.00      2.00      1.75      1.75      3.75      4.75        /         /         /         /         /         /         /         /         /         /         / 
       │     └─analysis_uops_info_tiger_lake                             0.25      0.25      0.75      1.00      1.00      1.00      2.00      1.75      1.75      3.75      4.75        /         /         /         /         /         /         /         /         /         /         / 
       ├─2021_golden_cove_gen_12                                         0.23      0.64      1.76      0.99      1.00      1.80      4.05      3.11      2.63      6.34      8.58     14.98     18.37     21.93     25.63     24.02     32.77     34.73     35.06     44.04     50.72     46.59
       │  ├─benchmarks                                                   0.13      0.99      2.52      0.98      1.00      1.99      5.03        /         /       6.80      9.74     16.28     19.97     23.84     27.86     26.11     35.63     37.76     38.12     47.88     55.14     50.65
       │  │  └─intel_xeon_8488c_sapphire_rapids_ec2_m7i_xlarge           0.13      0.99      2.52      0.98      1.00      1.99      5.03        /         /       6.80      9.74     16.28     19.97     23.84     27.86     26.11     35.63     37.76     38.12     47.88     55.14     50.65
       │  └─other                                                        0.41      0.41      1.22      1.00      1.00      1.63      3.27      2.86      2.42      5.92      7.55        /         /         /         /         /         /         /         /         /         /         / 
       │     ├─analysis_uops_info_alder_lake_p                           0.33      0.33      1.00      1.00      1.00      1.33      2.67      2.33      2.33      5.00      6.33        /         /         /         /         /         /         /         /         /         /         / 
       │     └─specs_intel                                               0.50      0.50      1.50      1.00      1.00      2.00      4.00      3.50      2.50      7.00      9.00        /         /         /         /         /         /         /         /         /         /         / 
       ├─2022_raptor_cove_gen_13_14                                      0.26      0.71      1.96      1.00      1.00      2.00      4.51      3.55      2.53      7.00      9.49     15.73     19.93     24.00     28.64     26.02     35.73     37.86     38.33     49.02     55.79     51.16
       │  ├─benchmarks                                                   0.13      1.00      2.55      1.00      1.00      2.00      5.08        /         /       7.00     10.00     15.95     20.20     24.33     29.03     26.37     36.21     38.37     38.85     49.69     56.55     51.86
       │  │  └─intel_xeon_8559c_emerald_rapids_ec2_i7i_xlarge            0.13      1.00      2.55      1.00      1.00      2.00      5.08        /         /       7.00     10.00     15.95     20.20     24.33     29.03     26.37     36.21     38.37     38.85     49.69     56.55     51.86
       │  └─other                                                        0.50      0.50      1.50      1.00      1.00      2.00      4.00      3.50      2.50      7.00      9.00        /         /         /         /         /         /         /         /         /         /         / 
       │     └─specs_intel                                               0.50      0.50      1.50      1.00      1.00      2.00      4.00      3.50      2.50      7.00      9.00        /         /         /         /         /         /         /         /         /         /         / 
       └─2023_redwood_cove_ultra_1                                       0.24      0.71      1.95      0.99      1.00      1.73      4.51      3.46      2.47      6.97      9.47     14.44     20.41     24.32     27.29     25.53     36.40     37.92     38.32     48.75     55.19     50.95
          ├─benchmarks                                                   0.12      1.01      2.53      0.98      1.00      1.50      5.09        /         /       6.94      9.96     14.28     20.19     24.06     26.99     25.26     36.01     37.51     37.91     48.22     54.60     50.40
          │  └─intel_xeon_6975p_granite_rapids_ec2_m8i_xlarge            0.12      1.01      2.53      0.98      1.00      1.50      5.09        /         /       6.94      9.96     14.28     20.19     24.06     26.99     25.26     36.01     37.51     37.91     48.22     54.60     50.40
          └─other                                                        0.50      0.50      1.50      1.00      1.00      2.00      4.00      3.50      2.50      7.00      9.00        /         /         /         /         /         /         /         /         /         /         / 
             └─specs_intel                                               0.50      0.50      1.50      1.00      1.00      2.00      4.00      3.50      2.50      7.00      9.00        /         /         /         /         /         /         /         /         /         /         /

4.2. Test performance of `CountedFloat` vs `float`

[~] counted_float benchmark-counted-float

See next section for results.

5. Performance impact

Obviously, using CountedFloat instead of regular float will have a performance impact due to the overhead of counting operations. It is not advised to use CountedFloat for production code, but just for research code for which you want to estimate the floating-point operation count.

Micro-benchmarking of a bisection algorithm using counted_float benchmark-counted-float teaches us this:

------------------------------------------------------------------------------------------------------------------------
Running CountedFloat benchmark...

float                              : wwwwwwwwwwwwwww...................................   [  12.34 µs ±  1.2% | 50.1K cpu cycles ±  1.2% ]  /  execution
CountedFloat                       : wwwwwwwwwwwwwww...................................   [ 459.95 µs ±  0.2% | 1.87M cpu cycles ±  0.2% ]  /  execution
------------------------------------------------------------------------------------------------------------------------

CountedFloat Benchmark Results:
  Bisection using float        :   12.34 µs / execution
  Bisection using CountedFloat :  459.95 µs / execution

CountedFloat is 37.3x slower than float

6. Known limitations

currently any non-Python-built-in math operations are not counted (e.g. numpy)
not all Python built-in math operations are counted (e.g. hyperbolic functions)
flop weights should be taken with a grain of salt and should only provide relative ballpark estimates w.r.t computational complexity. Production implementations in a compiled language could have vastly differing performance depending on cpu cache sizes, branch prediction misses, compiler optimizations using vector operations (AVX etc...), etc...

Appendix A - Flop counting / analysis details

This appendix provides detailed information about how each floating-point operation (FLOP) type is counted and analyzed in the counted-float package. For each flop type, you will find:

Relevant scalar instructions for ARM (v8+) and x86 (SSE2+)
Python operations that are counted for this flop type
Python operations that are not counted for this flop type

Flop Types

FlopType.ABS (`abs(x)`)

Relevant CPU instructions
- ARM: FABS
- x86: ANDPD
Counted Python operations: abs(x) where x is a CountedFloat
Not counted: numpy.abs, complex abs, abs on non-CountedFloat

FlopType.MINUS (`-x`)

Relevant CPU instructions
- ARM: FNEG
- x86: XORPD
Counted Python operations: Unary minus (-x) for CountedFloat
Not counted: Negation on non-CountedFloat, numpy negation

FlopType.COMP (`x<=y`, `x>y`, `x==y`, `x==0.0`, ...)

Relevant CPU instructions
- ARM: FCMP
- x86: (U)COMISD
Counted Python operations: x == y, x != y, x <= y, ... and min(x,y), max(x,y) for CountedFloat
Not counted: Comparisons on non-CountedFloat, numpy comparisons

FlopType.RND (`round`)

Relevant CPU instructions
- ARM: FRINT
- x86: ROUNDSD
Counted Python operations: round(x, 0) for CountedFloat (returns float)
Not counted: numpy.round, rounding with decimals, rounding on non-CountedFloat

FlopType.F2I (`float->int`)

Relevant CPU instructions
- ARM: FCVTZS
- x86: CVTSD2SI
Counted Python operations: int(x), math.floor(x), math.ceil(x), math.trunc(x), round(x) for CountedFloat (returns int)
Not counted: Conversions on non-CountedFloat, numpy conversions

FlopType.I2F (`int->float`)

Relevant CPU instructions
- ARM: SCVTF
- x86: CVTSI2SD
Counted Python operations: Construction of CountedFloat from int, any binary operation where one operand is an int and the other a CountedFloat (e.g., x + 3, 3 * x, etc.)
Not counted: float(n), unitary operations (e.g. math.sqrt on integers -> convert to CountedFloat first)

FlopType.ADD (`x+y`)

Relevant CPU instructions
- ARM: FADD
- x86: ADDSD
Counted Python operations: x + y or y + x for CountedFloat
Not counted: Addition on non-CountedFloat, numpy addition

FlopType.SUB (`x-y`)

Relevant CPU instructions
- ARM: FSUB
- x86: SUBSD
Counted Python operations: x - y or y - x for CountedFloat
Not counted: Subtraction on non-CountedFloat, numpy subtraction

FlopType.MUL (`x*y`)

Relevant CPU instructions
- ARM: FMUL
- x86: MULSD
Counted Python operations: x * y or y * x for CountedFloat
Not counted: Multiplication on non-CountedFloat, numpy multiplication

FlopType.DIV (`x/y`)

Relevant CPU instructions
- ARM: FDIV
- x86: DIVSD
Counted Python operations: x / y or y / x for CountedFloat
Not counted: Division on non-CountedFloat, numpy division

FlopType.SQRT (`sqrt(x)`)

Relevant CPU instructions
- ARM: FSQRT
- x86: SQRTSD
Counted Python operations: math.sqrt(x) for CountedFloat
Not counted: numpy.sqrt, sqrt on non-CountedFloat

FlopType.CBRT (`cbrt(x)`)

Relevant CPU instructions
- ARM: (software)
- x86: (software)
Counted Python operations: math.cbrt(x) for CountedFloat
Not counted: numpy.cbrt, cbrt on non-CountedFloat

FlopType.EXP (`e^x`)

Relevant CPU instructions
- ARM: (software)
- x86: (software)
Counted Python operations: math.exp(x) for CountedFloat
Not counted: math.exp(x) on non-CountedFloat, numpy.exp, math.expm1, math.e ** x

FlopType.EXP2 (`2^x`)

Relevant CPU instructions
- ARM: (software)
- x86: (software)
Counted Python operations: 2 ** x, pow(2, x) or math.exp2(x) for CountedFloat
Not counted: exp2 on non-CountedFloat, numpy.exp2

FlopType.EXP10 (`10^x`)

Relevant CPU instructions
- ARM: (software)
- x86: (software)
Counted Python operations: 10 ** x, pow(10, x) for CountedFloat
Not counted: 10 ** x on non-CountedFloat

FlopType.LOG (`log(x)`)

Relevant CPU instructions
- ARM: (software)
- x86: (software)
Counted Python operations: math.log(x) for CountedFloat; math.log(x, base) for CountedFloat decomposes per the constant-detection heuristic (int base 2/10 -> LOG2/LOG10; other int base -> LOG+MUL; float base -> LOG per counted operand + DIV)
Not counted: numpy.log, log on non-CountedFloat

FlopType.LOG2 (`log2(x)`)

Relevant CPU instructions
- ARM: (software)
- x86: (software)
Counted Python operations: math.log2(x) for CountedFloat; math.log(x, 2) (int base) for CountedFloat
Not counted: numpy.log2, log2 on non-CountedFloat

FlopType.LOG10 (`log10(x)`)

Relevant CPU instructions
- ARM: (software)
- x86: (software)
Counted Python operations: math.log10(x) for CountedFloat; math.log(x, 10) (int base) for CountedFloat
Not counted: numpy.log10, log10 on non-CountedFloat

FlopType.POW (`x^y`)

Relevant CPU instructions
- ARM: (software)
- x86: (software)
Counted Python operations: x ** y, pow(x, y) for CountedFloat
Not counted: pow on non-CountedFloat, numpy.pow

FlopType.SIN (`sin(x)`)

Relevant CPU instructions
- ARM: (software)
- x86: (software)
Counted Python operations: math.sin(x) for CountedFloat
Not counted: sin on non-CountedFloat, numpy.sin

FlopType.COS (`cos(x)`)

Relevant CPU instructions
- ARM: (software)
- x86: (software)
Counted Python operations: math.cos(x) for CountedFloat
Not counted: cos on non-CountedFloat, numpy.cos

FlopType.TAN (`tan(x)`)

Relevant CPU instructions
- ARM: (software)
- x86: (software)
Counted Python operations: math.tan(x) for CountedFloat
Not counted: tan on non-CountedFloat, `numpy.tan

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counted-float 1.0.4

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counted-float

1. Installation

2. Counting Flops

2.1. CountedFloat class

The counting model: what gets counted and why

2.3. Weighted FLOP counting

2.4. Configuring FLOP weights

2.5. Inspecting built-in data

2.5.1. Default, pre-aggregated flop weights

2.5.2. Custom-aggregated flop weights

3. Benchmarking

4. Installing the package as a command-line tool

4.1. Running benchmarks

4.2. Show built-in data

4.2. Test performance of CountedFloat vs float

5. Performance impact

6. Known limitations

Appendix A - Flop counting / analysis details

Flop Types

FlopType.ABS (abs(x))

FlopType.MINUS (-x)

FlopType.COMP (x<=y, x>y, x==y, x==0.0, ...)

FlopType.RND (round)

FlopType.F2I (float->int)

FlopType.I2F (int->float)

FlopType.ADD (x+y)

FlopType.SUB (x-y)

FlopType.MUL (x*y)

FlopType.DIV (x/y)

FlopType.SQRT (sqrt(x))

FlopType.CBRT (cbrt(x))

FlopType.EXP (e^x)

FlopType.EXP2 (2^x)

FlopType.EXP10 (10^x)

FlopType.LOG (log(x))

FlopType.LOG2 (log2(x))

FlopType.LOG10 (log10(x))

FlopType.POW (x^y)

FlopType.SIN (sin(x))

FlopType.COS (cos(x))

FlopType.TAN (tan(x))

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4.2. Test performance of `CountedFloat` vs `float`

FlopType.ABS (`abs(x)`)

FlopType.MINUS (`-x`)

FlopType.COMP (`x<=y`, `x>y`, `x==y`, `x==0.0`, ...)

FlopType.RND (`round`)

FlopType.F2I (`float->int`)

FlopType.I2F (`int->float`)

FlopType.ADD (`x+y`)

FlopType.SUB (`x-y`)

FlopType.MUL (`x*y`)

FlopType.DIV (`x/y`)

FlopType.SQRT (`sqrt(x)`)

FlopType.CBRT (`cbrt(x)`)

FlopType.EXP (`e^x`)

FlopType.EXP2 (`2^x`)

FlopType.EXP10 (`10^x`)

FlopType.LOG (`log(x)`)

FlopType.LOG2 (`log2(x)`)

FlopType.LOG10 (`log10(x)`)

FlopType.POW (`x^y`)

FlopType.SIN (`sin(x)`)

FlopType.COS (`cos(x)`)

FlopType.TAN (`tan(x)`)