fastdual 0.2.0

Fast forward-mode automatic differentiation via dual numbers (C extension)

fastdual

Fast forward-mode automatic differentiation via dual numbers, implemented as a CPython C extension.

Computes exact gradients and Jacobians with minimal overhead — no taping, no graph construction, just numbers that carry their derivatives.

Install

pip install fastdual

For development:

pip install -e .[test]

Drop-in Gradients

Any function that works with floats works with Dual — no rewriting, no framework, no JIT warmup:

# your existing code
def my_function(x):
    return x**3 - 2*x + 1

# just swap float for Dual
from fastdual import Dual, der

x = Dual(3.0)
y = my_function(x)      # same function, unchanged
dy_dx = der(y, x)       # 25.0 (exact derivative, for free)

Two lines changed. Exact gradient at 1.3x the cost of a plain float.

Quick Start

from fastdual import Dual, der
import numpy as np

# Create independent variables
x = Dual(3.0)
y = Dual(5.0)

# Compute — gradients propagate automatically
z = x * y + np.sin(x)
print(z.val)        # 15.1411...
print(der(z, x))    # 5.99 (dz/dx = y + cos(x))
print(der(z, y))    # 3.0  (dz/dy = x)

Array Operations

from fastdual import seed_array, val, jac
import numpy as np

# Create array of independent seeds
xs = seed_array([1.0, 2.0, 3.0])

# NumPy ufuncs work directly — dispatched to C, not per-element Python
result = np.sin(xs) + xs ** 2

# Extract values and Jacobian
print(val(result))   # [sin(1)+1, sin(2)+4, sin(3)+9]
print(jac(result, xs))
# [[cos(1)+2,       0,       0],
#  [      0, cos(2)+4,       0],
#  [      0,       0, cos(3)+6]]

Automatic Jacobians

from fastdual import autojac
import numpy as np

@autojac
def f(x, y):
    return np.array([x**2 + y, x * y**2])

result, J = f(2.0, 3.0)
# result = [7.0, 18.0]
# J = [[4.0,  1.0],
#      [9.0, 12.0]]

Supported Operations

Arithmetic: +, -, *, /, **, abs, unary -/+

Transcendentals (25): sin, cos, tan, exp, log, log2, log10, sqrt, arcsin, arccos, arctan, sinh, cosh, tanh, arcsinh, arccosh, arctanh, exp2, log1p, expm1, square, cbrt, sign, conjugate, negative

NumPy integration: All of the above work as np.sin(dual), np.exp(dual), etc. — both on scalars and arrays. Array operations are batch-dispatched to C via DualArray, avoiding per-element Python overhead.

Comparisons: <, <=, ==, !=, >, >= (compare primal values)

API Reference

Function	Description
Dual(value)	Create an independent variable (seed)
Dual(value, seed=False)	Create a constant (no gradient)
der(result, wrt)	Partial derivative of result w.r.t. a seed
seed_array(values)	Array of independent seeds from floats
val(array)	Extract primal values from Dual array
jac(results, seeds)	Full Jacobian matrix
autojac(fn)	Decorator: fn(*floats) -> (values, jacobian)
reset()	Reset variable ID counter

Performance

All hot paths are in C. Overhead vs plain floats:

Operation	Overhead
Scalar arithmetic	1.3-1.5x
Transcendentals	1.2-1.7x
np.sin(arr[10])	~4x
np.sin(arr[100])	~8x
Jacobian (10x10) vs finite diff	10x faster
Jacobian (20x20) vs finite diff	10x faster

Test

pytest tests/ -v