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Posted 12 Jan 2018

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What is the Lower Limit of Floating Point?

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12 Jan 2018CPOL2 min read
Microsoft Versus Google: Who is correct?

Microsoft Versus Google: Who is Correct?

Microsoft Floating Point Range in C# Documentation

Microsoft Floating Point Range

Image 1

Google Floating Point Range Returned from its Search

Google Floating Point Range

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While their higher float point limit tallied, Microsoft and Google are giving different values for lower limit! What is going on? One of them has to be correct! Make a guess before the answer is unveiled!


Both Microsoft and Google are correct! Google answer is correct from normalized number perspective while Microsoft lower range takes into account subnormal numbers (also known as denormalized numbers).

As you may recollect from your computer science school days, IEEE 754 floating point format consists of 3 components: a sign bit, mantissa and exponent. The actual value is derived from multiplying mantissa by base number raised to power of exponent.

Normal Floating Point

In a normal floating point number, its mantissa always implies a leading binary one on left side of decimal point. Since it is always present, mantissa does not store this leading one.


Since the left side of decimal point is always one, how do you store, say 0.5?

0.5 can be derived from multiplying 1(mantissa) with 2 raised to power of -1(exponent).
Note: Mantissa and exponent values are stored in base 2, not base 10, so we raise 2 to power of exponent.

1 * 2^(-1) = 0.5

Subnormal Floating Point

In a subnormal floating point number, its mantissa has a leading binary zero on the left side of decimal point.


But but... didn't I just tell you the left leading one is always there? So how is a subnormal number defined? To give you a definitive answer, we have to go through every nook and cranny of floating point format which is, frankly speaking, too long to fit into this short tip. As promised, the floating-point guide is finally here!


This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)


About the Author

Shao Voon Wong
Software Developer (Senior)
Singapore Singapore
Shao Voon is from Singapore. CodeProject awarded him a MVP in recognition of his article contributions in 2019. In his spare time, he prefers to writing applications based on 3rd party libraries than rolling out his own. His interest lies primarily in computer graphics, software optimization, concurrency, security and Agile methodologies.

You can reach him by sending a message on CodeProject or at his Coding Tidbit Blog!

Comments and Discussions

Questiondifference is ~0.0 and negative infinity Pin
Member 1070168315-Jan-18 20:47
professionalMember 1070168315-Jan-18 20:47 
AnswerRe: difference is ~0.0 and negative infinity Pin
Luis Perez Garcia15-Jan-18 22:00
MemberLuis Perez Garcia15-Jan-18 22:00 
QuestionSlightly relevant: The precision of trigonometric functions Pin
Member 798912215-Jan-18 10:58
MemberMember 798912215-Jan-18 10:58 
QuestionDid you really say anything about Google's lower limit? Pin
Member 798912215-Jan-18 10:29
MemberMember 798912215-Jan-18 10:29 
As far as I can see, everything you quote from Google agrees with what MS says.

Then MS adds some information that is neiter contradicted nor confirmed by Google.
Fair enough. But there is no conflict of any sort.
Generalvery good review Pin
Southmountain13-Jan-18 9:22
MemberSouthmountain13-Jan-18 9:22 

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