NumPy frexp() – Find Mantissa and Exponent of Each Element in Array

NumPy frexp()

The numpy.frexp() function decomposes each element of an input array into its mantissa and exponent. It expresses the number in the form:

x = mantissa × 2**exponent

The mantissa will always lie in the range (-1, 1), and the exponent is an integer.

Syntax

numpy.frexp(x, [out1, out2, ]/, [out=(None, None), ]*, where=True, casting='same_kind', order='K', dtype=None, subok=True)

Parameters

Parameter	Type	Description
x	array_like	Array of numbers to be decomposed into mantissa and exponent.
out1	ndarray, optional	Optional output array for the mantissa. Must have the same shape as x.
out2	ndarray, optional	Optional output array for the exponent. Must have the same shape as x.
out	ndarray, None, or tuple of ndarray and None, optional	A location to store the result. If None, a new array is created.
where	array_like, optional	Boolean mask specifying elements to process. Elements where where=False retain their original value.
casting	str, optional	Defines the casting behavior for computation.
order	str, optional	Memory layout order of the output array.
dtype	data-type, optional	Defines the data type of the output array.
subok	bool, optional	Determines if subclasses of ndarray are preserved in the output.

Return Value

Returns a tuple (mantissa, exponent), where:

• mantissa: An array with floating-point values in the range (-1, 1).
• exponent: An array of integer exponents.

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Examples

1. Decomposing a Single Number

We decompose a single floating-point number into its mantissa and exponent.

import numpy as np

# Define a number
num = 16.0

# Decompose into mantissa and exponent
mantissa, exponent = np.frexp(num)

# Print the results
print("Mantissa:", mantissa)
print("Exponent:", exponent)

Output:

Mantissa: 0.5
Exponent: 5

The result shows that 16.0 = 0.5 × 2⁵.

2. Decomposing an Array of Numbers

Here, we decompose multiple numbers in an array.

import numpy as np

# Define an array of numbers
nums = np.array([4.0, 8.0, 32.0, 64.0])

# Compute the mantissa and exponent
mantissa, exponent = np.frexp(nums)

# Print the results
print("Numbers:", nums)
print("Mantissas:", mantissa)
print("Exponents:", exponent)

Output:

Numbers: [ 4.  8. 32. 64.]
Mantissas: [0.5 0.5 0.5 0.5]
Exponents: [3 4 6 7]

Each number is represented in the form x = mantissa × 2**exponent.

3. Using the out Parameter

We store the mantissa and exponent in preallocated output arrays.

import numpy as np

# Define an array of numbers
nums = np.array([10.0, 20.0, 40.0])

# Preallocate output arrays
mantissa_out = np.empty_like(nums)
exponent_out = np.empty_like(nums, dtype=int)

# Compute frexp and store results in output arrays
np.frexp(nums, out=(mantissa_out, exponent_out))

# Print the results
print("Mantissas:", mantissa_out)
print("Exponents:", exponent_out)

Output:

Mantissas: [0.625 0.625 0.625]
Exponents: [4 5 6]

4. Using the where Parameter

We use a condition to compute frexp only for selected elements.

import numpy as np

# Define an array of numbers
nums = np.array([10.0, 20.0, 40.0, 80.0])

# Define a condition mask (apply frexp only where True)
mask = np.array([True, False, True, False])

# Compute mantissa and exponent where mask is True
mantissa, exponent = np.frexp(nums, where=mask)

# Print the results
print("Mantissas:", mantissa)
print("Exponents:", exponent)

Output:

Mantissas: [0.625 0.    0.625 0.   ]
Exponents: [4 0 6 0]

Only elements where mask=True are processed; other values remain unchanged.