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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Module: test.py
This module contains a suite of tests for the `simsimd` package.
It compares various SIMD kernels (like Dot-products, squared Euclidean, and Cosine distances)
with their NumPy or baseline counterparts, testing accuracy for different data types including
floating-point, integer, and complex numbers.
The tests cover:
- **Dense Vector Operations**: Tests for `float64`, `float32`, `float16` data types using metrics like `inner`, `sqeuclidean`, and `cosine`.
- **Brain Floating-Point Format (bfloat16)**: Tests for operations with the brain floating-point format not natively supported by NumPy.
- **Integer Operations**: Tests for `int8` data type, ensuring accuracy without overflow.
- **Bitwise Operations**: Tests for Hamming and Jaccard distances using bit arrays.
- **Complex Numbers**: Tests for complex dot products and vector dot products.
- **Batch Operations and Cross-Distance Computations**: Tests for batch processing and cross-distance computations using `cdist`.
- **Hardware Capabilities Verification**: Checks the availability of hardware capabilities and function pointers.
**Dependencies**:
- Python 3.x
- `numpy`
- `scipy`
- `pytest`
- `tabulate`
- `simsimd` package
**Usage**:
Run the tests using pytest:
pytest test.py
Or run the script directly:
python test.py
"""
import os
import math
import time
import platform
import collections
from typing import Dict, List
import tabulate
import pytest
import simsimd as simd
# NumPy is available on most platforms and is required for most tests.
# When using PyPy on some platforms NumPy has internal issues, that will
# raise a weird error, not an `ImportError`. That's why we intentionally
# use a naked `except:`. Necessary evil!
try:
import numpy as np
numpy_available = True
baseline_inner = np.inner
baseline_intersect = lambda x, y: len(np.intersect1d(x, y))
baseline_bilinear = lambda x, y, z: x @ z @ y
def baseline_fma(x, y, z, alpha, beta):
xy_scaled = np.multiply((alpha * x), y)
z_scaled = beta * z
r = xy_scaled + z_scaled
if np.issubdtype(x.dtype, np.integer):
r = np.round(r)
#! We need non-overflowing saturating addition for small integers, that NumPy lacks:
#! https://stackoverflow.com/questions/29611185/avoid-overflow-when-adding-numpy-arrays
if x.dtype == np.uint8:
r = np.clip(r, 0, 255, out=r)
elif x.dtype == np.int8:
r = np.clip(r, -128, 127, out=r)
return r.astype(x.dtype)
def baseline_wsum(x, y, alpha, beta):
x_scaled = alpha * x
y_scaled = beta * y
r = x_scaled + y_scaled
if np.issubdtype(x.dtype, np.integer):
r = np.round(r)
#! We need non-overflowing saturating addition for small integers, that NumPy lacks:
#! https://stackoverflow.com/questions/29611185/avoid-overflow-when-adding-numpy-arrays
if x.dtype == np.uint8:
r = np.clip(r, 0, 255, out=r)
elif x.dtype == np.int8:
r = np.clip(r, -128, 127, out=r)
return r.astype(x.dtype)
except:
# NumPy is not installed, most tests will be skipped
numpy_available = False
baseline_inner = lambda x, y: sum(x[i] * y[i] for i in range(len(x)))
baseline_intersect = lambda x, y: len(set(x).intersection(y))
def baseline_bilinear(x, y, z):
result = 0
for i in range(len(x)):
for j in range(len(y)):
result += x[i] * z[i][j] * y[j]
return result
def baseline_fma(x, y, z, alpha, beta):
return [(alpha * xi) * yi + beta * zi for xi, yi, zi in zip(x, y, z)]
def baseline_wsum(x, y, alpha, beta):
return [(alpha * xi) + beta * yi for xi, yi in zip(x, y)]
# At the time of Python 3.12, SciPy doesn't support 32-bit Windows on any CPU,
# or 64-bit Windows on Arm. It also doesn't support `musllinux` distributions,
# like CentOS, RedHat OS, and many others.
try:
import scipy.spatial.distance as spd
scipy_available = True
baseline_euclidean = lambda x, y: np.array(spd.euclidean(x, y)) #! SciPy returns a scalar
baseline_sqeuclidean = spd.sqeuclidean
baseline_cosine = spd.cosine
baseline_jensenshannon = lambda x, y: spd.jensenshannon(x, y) ** 2
baseline_hamming = lambda x, y: spd.hamming(x, y) * len(x)
baseline_jaccard = spd.jaccard
def baseline_mahalanobis(x, y, z):
# If there was an error, or the value is NaN, we skip the test.
try:
result = spd.mahalanobis(x, y, z).astype(np.float64)
if not np.isnan(result):
return result
except:
pass
pytest.skip(f"SciPy Mahalanobis distance returned {result} due to `sqrt` of a negative number")
except:
# SciPy is not installed, some tests will be skipped
scipy_available = False
baseline_cosine = lambda x, y: 1.0 - np.dot(x, y) / (np.linalg.norm(x) * np.linalg.norm(y))
baseline_euclidean = lambda x, y: np.array([np.sqrt(np.sum((x - y) ** 2))])
baseline_sqeuclidean = lambda x, y: np.sum((x - y) ** 2)
baseline_jensenshannon = lambda p, q: (np.sum((np.sqrt(p) - np.sqrt(q)) ** 2)) / 2
baseline_hamming = lambda x, y: np.logical_xor(x, y).sum()
def baseline_mahalanobis(x, y, z):
diff = x - y
return np.sqrt(diff @ z @ diff)
def baseline_jaccard(x, y):
intersection = np.logical_and(x, y).sum()
union = np.logical_or(x, y).sum()
return 0.0 if union == 0 else 1.0 - float(intersection) / float(union)
def baseline_intersect(arr1, arr2):
i, j, intersection = 0, 0, 0
while i < len(arr1) and j < len(arr2):
if arr1[i] == arr2[j]:
intersection += 1
i += 1
j += 1
elif arr1[i] < arr2[j]:
i += 1
else:
j += 1
return intersection
def is_running_under_qemu():
return "SIMSIMD_IN_QEMU" in os.environ
def profile(callable, *args, **kwargs) -> tuple:
before = time.perf_counter_ns()
result = callable(*args, **kwargs)
after = time.perf_counter_ns()
return after - before, result
@pytest.fixture(scope="session")
def stats_fixture():
"""Session-scoped fixture that collects errors during tests."""
results = dict()
results["metric"] = []
results["ndim"] = []
results["dtype"] = []
results["absolute_baseline_error"] = []
results["relative_baseline_error"] = []
results["absolute_simsimd_error"] = []
results["relative_simsimd_error"] = []
results["accurate_duration"] = []
results["baseline_duration"] = []
results["simsimd_duration"] = []
results["warnings"] = []
yield results
# Group the errors by (metric, ndim, dtype) to calculate the mean and std error.
grouped_errors = collections.defaultdict(
lambda: {
"absolute_baseline_error": [],
"relative_baseline_error": [],
"absolute_simsimd_error": [],
"relative_simsimd_error": [],
"accurate_duration": [],
"baseline_duration": [],
"simsimd_duration": [],
}
)
for (
metric,
ndim,
dtype,
absolute_baseline_error,
relative_baseline_error,
absolute_simsimd_error,
relative_simsimd_error,
accurate_duration,
baseline_duration,
simsimd_duration,
) in zip(
results["metric"],
results["ndim"],
results["dtype"],
results["absolute_baseline_error"],
results["relative_baseline_error"],
results["absolute_simsimd_error"],
results["relative_simsimd_error"],
results["accurate_duration"],
results["baseline_duration"],
results["simsimd_duration"],
):
key = (metric, ndim, dtype)
grouped_errors[key]["absolute_baseline_error"].append(absolute_baseline_error)
grouped_errors[key]["relative_baseline_error"].append(relative_baseline_error)
grouped_errors[key]["absolute_simsimd_error"].append(absolute_simsimd_error)
grouped_errors[key]["relative_simsimd_error"].append(relative_simsimd_error)
grouped_errors[key]["accurate_duration"].append(accurate_duration)
grouped_errors[key]["baseline_duration"].append(baseline_duration)
grouped_errors[key]["simsimd_duration"].append(simsimd_duration)
# Compute mean and the standard deviation for each task error
final_results = []
for key, errors in grouped_errors.items():
n = len(errors["simsimd_duration"])
# Mean and the standard deviation for errors
baseline_errors = errors["relative_baseline_error"]
simsimd_errors = errors["relative_simsimd_error"]
#! On some platforms (like `cp312-musllinux_aarch64`) without casting via `float(x)`
#! the subsequent `:.2e` string formatting code will fail due to:
#! `TypeError: unsupported format string passed to numpy.ndarray.__format__`.
baseline_mean = float(sum(baseline_errors)) / n
simsimd_mean = float(sum(simsimd_errors)) / n
baseline_std = math.sqrt(sum((x - baseline_mean) ** 2 for x in baseline_errors) / n)
simsimd_std = math.sqrt(sum((x - simsimd_mean) ** 2 for x in simsimd_errors) / n)
baseline_error_formatted = f"{baseline_mean:.2e} ± {baseline_std:.2e}"
simsimd_error_formatted = f"{simsimd_mean:.2e} ± {simsimd_std:.2e}"
# Log durations
accurate_durations = errors["accurate_duration"]
baseline_durations = errors["baseline_duration"]
simsimd_durations = errors["simsimd_duration"]
accurate_mean_duration = sum(accurate_durations) / n
baseline_mean_duration = sum(baseline_durations) / n
simsimd_mean_duration = sum(simsimd_durations) / n
accurate_std_duration = math.sqrt(sum((x - accurate_mean_duration) ** 2 for x in accurate_durations) / n)
baseline_std_duration = math.sqrt(sum((x - baseline_mean_duration) ** 2 for x in baseline_durations) / n)
simsimd_std_duration = math.sqrt(sum((x - simsimd_mean_duration) ** 2 for x in simsimd_durations) / n)
accurate_duration = f"{accurate_mean_duration:.2e} ± {accurate_std_duration:.2e}"
baseline_duration = f"{baseline_mean_duration:.2e} ± {baseline_std_duration:.2e}"
simsimd_duration = f"{simsimd_mean_duration:.2e} ± {simsimd_std_duration:.2e}"
# Measure time improvement
improvements = [baseline / simsimd for baseline, simsimd in zip(baseline_durations, simsimd_durations)]
improvements_mean = sum(improvements) / n
improvements_std = math.sqrt(sum((x - improvements_mean) ** 2 for x in improvements) / n)
simsimd_speedup = f"{improvements_mean:.2f}x ± {improvements_std:.2f}x"
# Calculate Improvement
# improvement = abs(baseline_mean - simsimd_mean) / min(simsimd_mean, baseline_mean)
# if baseline_mean < simsimd_mean:
# improvement *= -1
# improvement_formatted = f"{improvement:+.2}x" if improvement != float("inf") else "N/A"
final_results.append(
(
*key,
baseline_error_formatted,
simsimd_error_formatted,
accurate_duration,
baseline_duration,
simsimd_duration,
simsimd_speedup,
)
)
# Sort results for consistent presentation
final_results.sort(key=lambda x: (x[0], x[1], x[2]))
# Output the final table after all tests are completed
print("\n")
print("Numerical Error Aggregation Report:")
headers = [
"Metric",
"NDim",
"DType",
"Baseline Error", # Printed as mean ± std deviation
"SimSIMD Error", # Printed as mean ± std deviation
"Accurate Duration", # Printed as mean ± std deviation
"Baseline Duration", # Printed as mean ± std deviation
"SimSIMD Duration", # Printed as mean ± std deviation
"SimSIMD Speedup",
]
print(tabulate.tabulate(final_results, headers=headers, tablefmt="pretty", showindex=True))
# Show the additional grouped warnings
warnings = results.get("warnings", [])
warnings = sorted(warnings)
warnings = [f"{name}: {message}" for name, message in warnings]
if len(warnings) != 0:
print("\nWarnings:")
unique_warnings, warning_counts = np.unique(warnings, return_counts=True)
for warning, count in zip(unique_warnings, warning_counts):
print(f"- {count}x times: {warning}")
@pytest.hookimpl(tryfirst=True)
def pytest_runtest_makereport(item, call):
"""Custom hook to ensure that the error aggregator runs even for failed tests."""
if call.when == "call":
item.test_result = call.excinfo is None
def collect_errors(
metric: str,
ndim: int,
dtype: str,
accurate_result: float,
accurate_duration: float,
baseline_result: float,
baseline_duration: float,
simsimd_result: float,
simsimd_duration: float,
stats,
):
"""Calculates and aggregates errors for a given test.
What we want to know in the end of the day is:
- How much SimSIMD implementation is more/less accurate than baseline,
when compared against the accurate result?
- TODO: How much faster is SimSIMD than the baseline kernel?
- TODO: How much faster is SimSIMD than the accurate kernel?
"""
eps = np.finfo(accurate_result.dtype).resolution
absolute_baseline_error = np.max(np.abs(baseline_result - accurate_result))
relative_baseline_error = np.max(np.abs(baseline_result - accurate_result) / (np.abs(accurate_result) + eps))
absolute_simsimd_error = np.max(np.abs(simsimd_result - accurate_result))
relative_simsimd_error = np.max(np.abs(simsimd_result - accurate_result) / (np.abs(accurate_result) + eps))
stats["metric"].append(metric)
stats["ndim"].append(ndim)
stats["dtype"].append(dtype)
stats["absolute_baseline_error"].append(absolute_baseline_error)
stats["relative_baseline_error"].append(relative_baseline_error)
stats["absolute_simsimd_error"].append(absolute_simsimd_error)
stats["relative_simsimd_error"].append(relative_simsimd_error)
stats["accurate_duration"].append(accurate_duration)
stats["baseline_duration"].append(baseline_duration)
stats["simsimd_duration"].append(simsimd_duration)
def get_current_test():
"""Get's the current test filename, test name, and function name.
Similar metadata can be obtained from the `request` fixture, but this
solution uses environment variables."""
full_name = os.environ.get("PYTEST_CURRENT_TEST").split(" ")[0]
test_file = full_name.split("::")[0].split("/")[-1].split(".py")[0]
test_name = full_name.split("::")[1]
# The `test_name` may look like: "test_dense_i8[cosine-1536-24-50]"
function_name = test_name.split("[")[0]
return test_file, test_name, function_name
def collect_warnings(message: str, stats: dict):
"""Collects warnings for the final report."""
_, _, function_name = get_current_test()
stats["warnings"].append((function_name, message))
# For normalized distances we use the absolute tolerance, because the result is close to zero.
# For unnormalized ones (like squared Euclidean or Jaccard), we use the relative.
SIMSIMD_RTOL = 0.1
SIMSIMD_ATOL = 0.1
# We will run all the tests many times using different instruction sets under the hood.
available_capabilities: Dict[str, str] = simd.get_capabilities()
possible_x86_capabilities: List[str] = ["haswell", "ice", "skylake", "sapphire", "turin", "genoa", "sierra"]
possible_arm_capabilities: List[str] = [
"neon",
"neon_f16",
"neon_bf16",
"neon_i8",
"sve",
"sve_f16",
"sve_bf16",
"sve_i8",
]
possible_x86_capabilities: List[str] = [c for c in possible_x86_capabilities if available_capabilities[c]]
possible_arm_capabilities: List[str] = [c for c in possible_arm_capabilities if available_capabilities[c]]
possible_capabilities: List[str] = (
possible_x86_capabilities if platform.machine() == "x86_64" else possible_arm_capabilities
)
def keep_one_capability(cap: str):
assert cap in possible_capabilities
for c in possible_capabilities:
if c != cap:
simd.disable_capability(c)
simd.enable_capability(c)
def name_to_kernels(name: str):
"""
Having a separate "helper" function to convert the kernel name is handy for PyTest decorators,
that can't generally print non-trivial object (like function pointers) well.
"""
if name == "inner":
return baseline_inner, simd.inner
elif name == "euclidean":
return baseline_euclidean, simd.euclidean
elif name == "sqeuclidean":
return baseline_sqeuclidean, simd.sqeuclidean
elif name == "cosine":
return baseline_cosine, simd.cosine
elif name == "bilinear":
return baseline_bilinear, simd.bilinear
elif name == "mahalanobis":
return baseline_mahalanobis, simd.mahalanobis
elif name == "jaccard":
return baseline_jaccard, simd.jaccard
elif name == "hamming":
return baseline_hamming, simd.hamming
elif name == "intersect":
return baseline_intersect, simd.intersect
elif name == "fma":
return baseline_fma, simd.fma
elif name == "wsum":
return baseline_wsum, simd.wsum
else:
raise ValueError(f"Unknown kernel name: {name}")
def f32_downcast_to_bf16(array):
"""Converts an array of 32-bit floats into 16-bit brain-floats."""
array = np.asarray(array, dtype=np.float32)
# NumPy doesn't natively support brain-float, so we need a trick!
# Luckily, it's very easy to reduce the representation accuracy
# by simply masking the low 16-bits of our 32-bit single-precision
# numbers. We can also add `0x8000` to round the numbers.
array_f32_rounded = ((array.view(np.uint32) + 0x8000) & 0xFFFF0000).view(np.float32)
# To represent them as brain-floats, we need to drop the second halves.
array_bf16 = np.right_shift(array_f32_rounded.view(np.uint32), 16).astype(np.uint16)
return array_f32_rounded, array_bf16
def i8_downcast_to_i4(array):
"""Converts an array of 8-bit integers into 4-bit integers, packing 2 per byte."""
array = np.asarray(array, dtype=np.int8)
assert np.all(array >= -8) and np.all(array <= 7), "Input array must be in the range [-8, 7]"
def hex_array(arr):
"""Converts numerical array into a string of comma-separated hexadecimal values for debugging.
Supports 1D and 2D arrays.
"""
printer = np.vectorize(hex)
strings = printer(arr)
if strings.ndim == 1:
return ", ".join(strings)
else:
return "\n".join(", ".join(row) for row in strings)
def test_pointers_availability():
"""Tests the availability of pre-compiled functions for compatibility with USearch."""
assert simd.pointer_to_sqeuclidean("float64") != 0
assert simd.pointer_to_cosine("float64") != 0
assert simd.pointer_to_inner("float64") != 0
assert simd.pointer_to_sqeuclidean("float32") != 0
assert simd.pointer_to_cosine("float32") != 0
assert simd.pointer_to_inner("float32") != 0
assert simd.pointer_to_sqeuclidean("float16") != 0
assert simd.pointer_to_cosine("float16") != 0
assert simd.pointer_to_inner("float16") != 0
assert simd.pointer_to_sqeuclidean("int8") != 0
assert simd.pointer_to_cosine("int8") != 0
assert simd.pointer_to_inner("int8") != 0
assert simd.pointer_to_sqeuclidean("uint8") != 0
assert simd.pointer_to_cosine("uint8") != 0
assert simd.pointer_to_inner("uint8") != 0
def test_capabilities_list():
"""Tests the visibility of hardware capabilities."""
assert "serial" in simd.get_capabilities()
assert "neon" in simd.get_capabilities()
assert "neon_f16" in simd.get_capabilities()
assert "neon_bf16" in simd.get_capabilities()
assert "neon_i8" in simd.get_capabilities()
assert "sve" in simd.get_capabilities()
assert "sve_f16" in simd.get_capabilities()
assert "sve_bf16" in simd.get_capabilities()
assert "sve_i8" in simd.get_capabilities()
assert "haswell" in simd.get_capabilities()
assert "ice" in simd.get_capabilities()
assert "skylake" in simd.get_capabilities()
assert "genoa" in simd.get_capabilities()
assert "sapphire" in simd.get_capabilities()
assert "turin" in simd.get_capabilities()
assert simd.get_capabilities().get("serial") == 1
# Check the toggle:
previous_value = simd.get_capabilities().get("neon")
simd.enable_capability("neon")
assert simd.get_capabilities().get("neon") == 1
if not previous_value:
simd.disable_capability("neon")
def to_array(x, dtype=None):
if numpy_available:
y = np.array(x)
if dtype is not None:
y = y.astype(dtype)
return y
@pytest.mark.skipif(not numpy_available, reason="NumPy is not installed")
@pytest.mark.parametrize(
"function, expected_error, args, kwargs",
[
# Test missing positional arguments
(simd.sqeuclidean, TypeError, (), {}), # No arguments provided
(simd.sqeuclidean, TypeError, (to_array([1.0]),), {}), # Only one positional argument
# Try missing type name
(simd.sqeuclidean, ValueError, (to_array([1.0]), to_array([1.0]), "missing_dtype"), {}),
# Test incorrect argument type
(simd.sqeuclidean, TypeError, (to_array([1.0]), "invalid"), {}), # Wrong type for second argument
# Test invalid keyword argument name
(simd.sqeuclidean, TypeError, (to_array([1.0]), to_array([1.0])), {"invalid_kwarg": "value"}),
# Test wrong argument type for SIMD capability toggle
(simd.enable_capability, TypeError, (123,), {}), # Should expect a string
(simd.disable_capability, TypeError, ([],), {}), # Should expect a string
# Test missing required argument for Mahalanobis
(simd.mahalanobis, TypeError, (to_array([1.0]), to_array([1.0])), {}), # Missing covariance matrix
# Test missing required arguments for bilinear
(simd.bilinear, TypeError, (to_array([1.0]),), {}), # Missing second vector and metric tensor
# Test passing too many arguments to a method
(simd.cosine, TypeError, (to_array([1.0]), to_array([1.0]), to_array([1.0])), {}), # Too many arguments
(simd.cdist, TypeError, (to_array([[1.0]]), to_array([[1.0]]), "cos", "dos"), {}), # Too many arguments
# Same argument as both positional and keyword
(simd.cdist, TypeError, (to_array([[1.0]]), to_array([[1.0]]), "cos"), {"metric": "cos"}),
# Applying real metric to complex numbers - missing kernel
(simd.cosine, LookupError, (to_array([1 + 2j]), to_array([1 + 2j])), {}),
# Test incompatible vectors for cosine
(simd.cosine, ValueError, (to_array([1.0]), to_array([1.0, 2.0])), {}), # Different number of dimensions
(simd.cosine, TypeError, (to_array([1.0]), to_array([1], "uint32")), {}), # Floats and integers
(simd.cosine, TypeError, (to_array([1]), to_array([1], "float16")), {}), # Different floats
],
)
def test_invalid_argument_handling(function, expected_error, args, kwargs):
"""Test that functions raise TypeError when called with invalid arguments."""
with pytest.raises(expected_error):
function(*args, **kwargs)
@pytest.mark.skipif(not numpy_available, reason="NumPy is not installed")
@pytest.mark.repeat(50)
@pytest.mark.parametrize("ndim", [11, 97, 1536])
@pytest.mark.parametrize("dtype", ["float64", "float32", "float16"])
@pytest.mark.parametrize("metric", ["inner", "euclidean", "sqeuclidean", "cosine"])
@pytest.mark.parametrize("capability", possible_capabilities)
def test_dense(ndim, dtype, metric, capability, stats_fixture):
"""Compares various SIMD kernels (like Dot-products, squared Euclidean, and Cosine distances)
with their NumPy or baseline counterparts, testing accuracy for IEEE standard floating-point types."""
if dtype == "float16" and is_running_under_qemu():
pytest.skip("Testing low-precision math isn't reliable in QEMU")
np.random.seed()
a = np.random.randn(ndim).astype(dtype)
b = np.random.randn(ndim).astype(dtype)
keep_one_capability(capability)
baseline_kernel, simd_kernel = name_to_kernels(metric)
accurate_dt, accurate = profile(baseline_kernel, a.astype(np.float64), b.astype(np.float64))
expected_dt, expected = profile(baseline_kernel, a, b)
result_dt, result = profile(simd_kernel, a, b)
result = np.array(result)
np.testing.assert_allclose(result, expected.astype(np.float64), atol=SIMSIMD_ATOL, rtol=SIMSIMD_RTOL)
collect_errors(metric, ndim, dtype, accurate, accurate_dt, expected, expected_dt, result, result_dt, stats_fixture)
@pytest.mark.skipif(not numpy_available, reason="NumPy is not installed")
@pytest.mark.repeat(50)
@pytest.mark.parametrize("ndim", [11, 97])
@pytest.mark.parametrize(
"dtypes", # representation datatype and compute precision
[
("float64", "float64"),
("float32", "float32"),
("float16", "float32"), # otherwise NumPy keeps aggregating too much error
],
)
@pytest.mark.parametrize("metric", ["bilinear", "mahalanobis"])
@pytest.mark.parametrize("capability", possible_capabilities)
def test_curved(ndim, dtypes, metric, capability, stats_fixture):
"""Compares various SIMD kernels (like Bilinear Forms and Mahalanobis distances) for curved spaces
with their NumPy or baseline counterparts, testing accuracy for IEEE standard floating-point types."""
dtype, compute_dtype = dtypes
if dtype == "float16" and is_running_under_qemu():
pytest.skip("Testing low-precision math isn't reliable in QEMU")
np.random.seed()
# Let's generate some non-negative probability distributions
a = np.abs(np.random.randn(ndim).astype(dtype))
b = np.abs(np.random.randn(ndim).astype(dtype))
a /= np.sum(a)
b /= np.sum(b)
# Let's compute the inverse of the covariance matrix, otherwise in the SciPy
# implementation of the Mahalanobis we may face `sqrt` of a negative number.
# We multiply the matrix by its transpose to get a positive-semi-definite matrix.
c = np.abs(np.random.randn(ndim, ndim).astype(dtype))
c = np.dot(c, c.T)
keep_one_capability(capability)
baseline_kernel, simd_kernel = name_to_kernels(metric)
accurate_dt, accurate = profile(
baseline_kernel,
a.astype(np.float64),
b.astype(np.float64),
c.astype(np.float64),
)
expected_dt, expected = profile(
baseline_kernel,
a.astype(compute_dtype),
b.astype(compute_dtype),
c.astype(compute_dtype),
)
result_dt, result = profile(simd_kernel, a, b, c)
result = np.array(result)
np.testing.assert_allclose(result, expected, atol=SIMSIMD_ATOL, rtol=SIMSIMD_RTOL)
collect_errors(metric, ndim, dtype, accurate, accurate_dt, expected, expected_dt, result, result_dt, stats_fixture)
@pytest.mark.skipif(not numpy_available, reason="NumPy is not installed")
@pytest.mark.repeat(50)
@pytest.mark.parametrize("ndim", [11, 97, 1536])
@pytest.mark.parametrize("metric", ["inner", "euclidean", "sqeuclidean", "cosine"])
@pytest.mark.parametrize("capability", possible_capabilities)
def test_dense_bf16(ndim, metric, capability, stats_fixture):
"""Compares various SIMD kernels (like Dot-products, squared Euclidean, and Cosine distances)
with their NumPy or baseline counterparts, testing accuracy for the Brain-float format not
natively supported by NumPy."""
np.random.seed()
a = np.random.randn(ndim).astype(np.float32)
b = np.random.randn(ndim).astype(np.float32)
a_f32_rounded, a_bf16 = f32_downcast_to_bf16(a)
b_f32_rounded, b_bf16 = f32_downcast_to_bf16(b)
keep_one_capability(capability)
baseline_kernel, simd_kernel = name_to_kernels(metric)
accurate_dt, accurate = profile(baseline_kernel, a_f32_rounded.astype(np.float64), b_f32_rounded.astype(np.float64))
expected_dt, expected = profile(baseline_kernel, a_f32_rounded, b_f32_rounded)
result_dt, result = profile(simd_kernel, a_bf16, b_bf16, "bf16")
result = np.array(result)
np.testing.assert_allclose(
result,
expected,
atol=SIMSIMD_ATOL,
rtol=SIMSIMD_RTOL,
err_msg=f"""
First `f32` operand in hex: {hex_array(a_f32_rounded.view(np.uint32))}
Second `f32` operand in hex: {hex_array(b_f32_rounded.view(np.uint32))}
First `bf16` operand in hex: {hex_array(a_bf16)}
Second `bf16` operand in hex: {hex_array(b_bf16)}
""",
)
collect_errors(
metric, ndim, "bfloat16", accurate, accurate_dt, expected, expected_dt, result, result_dt, stats_fixture
)
@pytest.mark.skipif(not numpy_available, reason="NumPy is not installed")
@pytest.mark.repeat(50)
@pytest.mark.parametrize("ndim", [11, 16, 33])
@pytest.mark.parametrize("metric", ["bilinear", "mahalanobis"])
@pytest.mark.parametrize("capability", possible_capabilities)
def test_curved_bf16(ndim, metric, capability, stats_fixture):
"""Compares various SIMD kernels (like Bilinear Forms and Mahalanobis distances) for curved spaces
with their NumPy or baseline counterparts, testing accuracy for the Brain-float format not
natively supported by NumPy."""
np.random.seed()
# Let's generate some non-negative probability distributions
a = np.abs(np.random.randn(ndim).astype(np.float32))
b = np.abs(np.random.randn(ndim).astype(np.float32))
a /= np.sum(a)
b /= np.sum(b)
# Let's compute the inverse of the covariance matrix, otherwise in the SciPy
# implementation of the Mahalanobis we may face `sqrt` of a negative number.
# We multiply the matrix by its transpose to get a positive-semi-definite matrix.
c = np.abs(np.random.randn(ndim, ndim).astype(np.float32))
c = np.dot(c, c.T)
a_f32_rounded, a_bf16 = f32_downcast_to_bf16(a)
b_f32_rounded, b_bf16 = f32_downcast_to_bf16(b)
c_f32_rounded, c_bf16 = f32_downcast_to_bf16(c)
keep_one_capability(capability)
baseline_kernel, simd_kernel = name_to_kernels(metric)
accurate_dt, accurate = profile(
baseline_kernel,
a_f32_rounded.astype(np.float64),
b_f32_rounded.astype(np.float64),
c_f32_rounded.astype(np.float64),
)
expected_dt, expected = profile(baseline_kernel, a_f32_rounded, b_f32_rounded, c_f32_rounded)
result_dt, result = profile(simd_kernel, a_bf16, b_bf16, c_bf16, "bf16")
result = np.array(result)
np.testing.assert_allclose(
result,
expected,
atol=SIMSIMD_ATOL,
rtol=SIMSIMD_RTOL,
err_msg=f"""
First `f32` operand in hex: {hex_array(a_f32_rounded.view(np.uint32))}
Second `f32` operand in hex: {hex_array(b_f32_rounded.view(np.uint32))}
First `bf16` operand in hex: {hex_array(a_bf16)}
Second `bf16` operand in hex: {hex_array(b_bf16)}
Matrix `bf16` operand in hex: {hex_array(c_bf16)}
Matrix `bf16` operand in hex: {hex_array(c_bf16)}
""",
)
collect_errors(
metric, ndim, "bfloat16", accurate, accurate_dt, expected, expected_dt, result, result_dt, stats_fixture
)
@pytest.mark.skipif(not numpy_available, reason="NumPy is not installed")
@pytest.mark.repeat(50)
@pytest.mark.parametrize("ndim", [11, 97, 1536])
@pytest.mark.parametrize("dtype", ["int8", "uint8"])
@pytest.mark.parametrize("metric", ["inner", "euclidean", "sqeuclidean", "cosine"])
@pytest.mark.parametrize("capability", possible_capabilities)
def test_dense_i8(ndim, dtype, metric, capability, stats_fixture):
"""Compares various SIMD kernels (like Dot-products, squared Euclidean, and Cosine distances)
with their NumPy or baseline counterparts, testing accuracy for small integer types, that can't
be directly processed with other tools without overflowing."""
np.random.seed()
if dtype == "int8":
a = np.random.randint(-128, 127, size=(ndim), dtype=np.int8)
b = np.random.randint(-128, 127, size=(ndim), dtype=np.int8)
else:
a = np.random.randint(0, 255, size=(ndim), dtype=np.uint8)
b = np.random.randint(0, 255, size=(ndim), dtype=np.uint8)
keep_one_capability(capability)
baseline_kernel, simd_kernel = name_to_kernels(metric)
accurate_dt, accurate = profile(baseline_kernel, a.astype(np.float64), b.astype(np.float64))
expected_dt, expected = profile(baseline_kernel, a.astype(np.int64), b.astype(np.int64))
result_dt, result = profile(simd_kernel, a, b)
result = np.array(result)
if metric == "inner":
assert round(float(result)) == round(float(expected)), f"Expected {expected}, but got {result}"
else:
np.testing.assert_allclose(
result, expected, atol=SIMSIMD_ATOL, rtol=SIMSIMD_RTOL
), f"Expected {expected}, but got {result}"
collect_errors(metric, ndim, dtype, accurate, accurate_dt, expected, expected_dt, result, result_dt, stats_fixture)
#! Fun fact: SciPy doesn't actually raise an `OverflowError` when overflow happens
#! here, instead it raises `ValueError: math domain error` during the `sqrt` operation.
try:
expected_overflow = baseline_kernel(a, b)
if np.isinf(expected_overflow):
collect_warnings("Couldn't avoid overflow in SciPy", stats_fixture)
except Exception as e:
collect_warnings(f"Arbitrary error raised in SciPy: {e}", stats_fixture)
@pytest.mark.skipif(not numpy_available, reason="NumPy is not installed")
@pytest.mark.skipif(not scipy_available, reason="SciPy is not installed")
@pytest.mark.repeat(50)
@pytest.mark.parametrize("ndim", [11, 97, 1536])
@pytest.mark.parametrize("metric", ["jaccard", "hamming"])
@pytest.mark.parametrize("capability", possible_capabilities)
def test_dense_bits(ndim, metric, capability, stats_fixture):
"""Compares various SIMD kernels (like Hamming and Jaccard/Tanimoto distances) for dense bit arrays
with their NumPy or baseline counterparts, even though, they can't process sub-byte-sized scalars."""
np.random.seed()
a = np.random.randint(2, size=ndim).astype(np.uint8)
b = np.random.randint(2, size=ndim).astype(np.uint8)
keep_one_capability(capability)
baseline_kernel, simd_kernel = name_to_kernels(metric)
accurate_dt, accurate = profile(baseline_kernel, a.astype(np.uint64), b.astype(np.uint64))
expected_dt, expected = profile(baseline_kernel, a, b)
result_dt, result = profile(simd_kernel, np.packbits(a), np.packbits(b), "bin8")
result = np.array(result)
np.testing.assert_allclose(result, expected, atol=SIMSIMD_ATOL, rtol=SIMSIMD_RTOL)
collect_errors(metric, ndim, "bin8", accurate, accurate_dt, expected, expected_dt, result, result_dt, stats_fixture)
@pytest.mark.skip(reason="Problems inferring the tolerance bounds for numerical errors")
@pytest.mark.repeat(50)
@pytest.mark.parametrize("ndim", [11, 97, 1536])
@pytest.mark.parametrize("dtype", ["float32", "float16"])
@pytest.mark.parametrize("capability", possible_capabilities)
def test_jensen_shannon(ndim, dtype, capability):
"""Compares the simd.jensenshannon() function with scipy.spatial.distance.jensenshannon(), measuring the accuracy error for f16, and f32 types."""
np.random.seed()
a = np.abs(np.random.randn(ndim)).astype(dtype)
b = np.abs(np.random.randn(ndim)).astype(dtype)
a /= np.sum(a)
b /= np.sum(b)
keep_one_capability(capability)
baseline_kernel, simd_kernel = name_to_kernels("jensenshannon")
accurate_dt, accurate = profile(baseline_kernel, a.astype(np.float64), b.astype(np.float64))
expected_dt, expected = profile(baseline_kernel, a, b)
result_dt, result = profile(simd_kernel, a, b)
result = np.array(result)
np.testing.assert_allclose(result, expected, atol=SIMSIMD_ATOL, rtol=SIMSIMD_RTOL)
collect_errors(
"jensenshannon", ndim, dtype, accurate, accurate_dt, expected, expected_dt, result, result_dt, stats_fixture
)
@pytest.mark.skipif(not numpy_available, reason="NumPy is not installed")
@pytest.mark.parametrize("ndim", [11, 97, 1536])
@pytest.mark.parametrize("dtype", ["float32", "float16"])
@pytest.mark.parametrize("capability", possible_capabilities)
def test_cosine_zero_vector(ndim, dtype, capability):
"""Tests the simd.cosine() function with zero vectors, to catch division by zero errors."""
a = np.zeros(ndim, dtype=dtype)
b = (np.random.randn(ndim) + 1).astype(dtype)
keep_one_capability(capability)
result = simd.cosine(a, b)
assert result == 1, f"Expected 1, but got {result}"
result = simd.cosine(a, a)
assert result == 0, f"Expected 0 distance from itself, but got {result}"
result = simd.cosine(b, b)
assert abs(result) < SIMSIMD_ATOL, f"Expected 0 distance from itself, but got {result}"
# For the cosine, the output must not be negative!
assert np.all(result >= 0), f"Negative result for cosine distance"
@pytest.mark.skip(reason="Lacks overflow protection: https://github.com/ashvardanian/SimSIMD/issues/206") # TODO
@pytest.mark.skipif(not numpy_available, reason="NumPy is not installed")
@pytest.mark.repeat(50)
@pytest.mark.parametrize("ndim", [11, 97, 1536])
@pytest.mark.parametrize("dtype", ["float64", "float32", "float16"])
@pytest.mark.parametrize("metric", ["inner", "euclidean", "sqeuclidean", "cosine"])
@pytest.mark.parametrize("capability", possible_capabilities)
def test_overflow(ndim, dtype, metric, capability):
"""Tests if the floating-point kernels are capable of detecting overflow yield the same ±inf result."""
np.random.seed()
a = np.random.randn(ndim)
b = np.random.randn(ndim)
# Replace scalar at random position with infinity
a[np.random.randint(ndim)] = np.inf
a = a.astype(dtype)
b = b.astype(dtype)
keep_one_capability(capability)
baseline_kernel, simd_kernel = name_to_kernels(metric)
result = simd_kernel(a, b)
assert np.isinf(result), f"Expected ±inf, but got {result}"
#! In the Euclidean (L2) distance, SciPy raises a `ValueError` from the underlying
#! NumPy function: `ValueError: array must not contain infs or NaNs`.
try:
expected_overflow = baseline_kernel(a, b)
if not np.isinf(expected_overflow):
collect_warnings("Overflow not detected in SciPy", stats_fixture)
except Exception as e:
collect_warnings(f"Arbitrary error raised in SciPy: {e}", stats_fixture)
@pytest.mark.skip(reason="Lacks overflow protection: https://github.com/ashvardanian/SimSIMD/issues/206") # TODO
@pytest.mark.skipif(not numpy_available, reason="NumPy is not installed")
@pytest.mark.repeat(50)
@pytest.mark.parametrize("ndim", [131072, 262144])
@pytest.mark.parametrize("metric", ["inner", "euclidean", "sqeuclidean", "cosine"])
@pytest.mark.parametrize("capability", possible_capabilities)
def test_overflow_i8(ndim, metric, capability):
"""Tests if the integral kernels are capable of detecting overflow yield the same ±inf result,
as with 2^16 elements accumulating "u32(u16(u8)*u16(u8))+u32" products should overflow and the
same is true for 2^17 elements with "i32(i15(i8))*i32(i15(i8))" products.
"""
np.random.seed()
a = np.full(ndim, fill_value=-128, dtype=np.int8)
b = np.full(ndim, fill_value=-128, dtype=np.int8)
keep_one_capability(capability)
baseline_kernel, simd_kernel = name_to_kernels(metric)
expected = baseline_kernel(a, b)
result = simd_kernel(a, b)
assert np.isinf(result), f"Expected ±inf, but got {result}"
try:
expected_overflow = baseline_kernel(a, b)
if not np.isinf(expected_overflow):
collect_warnings("Overflow not detected in SciPy", stats_fixture)
except Exception as e:
collect_warnings(f"Arbitrary error raised in SciPy: {e}", stats_fixture)
@pytest.mark.skipif(is_running_under_qemu(), reason="Complex math in QEMU fails")
@pytest.mark.skipif(not numpy_available, reason="NumPy is not installed")
@pytest.mark.repeat(50)
@pytest.mark.parametrize("ndim", [22, 66, 1536])
@pytest.mark.parametrize("dtype", ["float32", "float64"])
@pytest.mark.parametrize("capability", possible_capabilities)
def test_dot_complex(ndim, dtype, capability, stats_fixture):
"""Compares the simd.dot() and simd.vdot() against NumPy for complex numbers."""
np.random.seed()
dtype_view = np.complex64 if dtype == "float32" else np.complex128
a = np.random.randn(ndim).astype(dtype=dtype).view(dtype_view)
b = np.random.randn(ndim).astype(dtype=dtype).view(dtype_view)
keep_one_capability(capability)
accurate_dt, accurate = profile(np.dot, a.astype(np.complex128), b.astype(np.complex128))
expected_dt, expected = profile(np.dot, a, b)
result_dt, result = profile(simd.dot, a, b)
result = np.array(result)
np.testing.assert_allclose(result, expected, atol=SIMSIMD_ATOL, rtol=SIMSIMD_RTOL)
collect_errors(
"dot", ndim, dtype + "c", accurate, accurate_dt, expected, expected_dt, result, result_dt, stats_fixture
)
accurate_dt, accurate = profile(np.vdot, a.astype(np.complex128), b.astype(np.complex128))
expected_dt, expected = profile(np.vdot, a, b)
result_dt, result = profile(simd.vdot, a, b)
result = np.array(result)
np.testing.assert_allclose(result, expected, atol=SIMSIMD_ATOL, rtol=SIMSIMD_RTOL)
collect_errors(
"vdot", ndim, dtype + "c", accurate, accurate_dt, expected, expected_dt, result, result_dt, stats_fixture
)
@pytest.mark.skipif(is_running_under_qemu(), reason="Complex math in QEMU fails")
@pytest.mark.skipif(not numpy_available, reason="NumPy is not installed")
@pytest.mark.repeat(50)
@pytest.mark.parametrize("ndim", [22, 66, 1536])
@pytest.mark.parametrize("capability", possible_capabilities)
def test_dot_complex_explicit(ndim, capability):
"""Compares the simd.dot() and simd.vdot() against NumPy for complex numbers."""
np.random.seed()
a = np.random.randn(ndim).astype(dtype=np.float32)
b = np.random.randn(ndim).astype(dtype=np.float32)
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