Does casting double to float always return same value?

Question

Does casting double to float always produce same result, or can there be some \"rounding differences\"?

For example, is x in

Answer 1

If you downcast a double to a float, you are losing precision and data. Upcasting a float to a double is a widening conversion; no data is lost if it is then round-tripped...that is, unless you do something to the value prior to downcasting it back to a float.

Floating-point numbers sacrifice precision and accuracy for range. Single-precision floats give you 32-bits of precision; double-precision give you 64-bits. But they can represent values way outside the bounds that the underlying precision would indicate.

C# float and double are IEEE 754 floating point values.

• float is a single-precision IEEE 754 value (32 bits) and consists of a

  • 1-bit sign
  • 8-bit exponent
  • 23-bit mantissa/significand

• double is double-precision IEEE 754 value (64 bits) and consists of a

  • 1-bit sign
  • 11-bit exponent
  • 52-bit mantissa/significand

The effective precision of the mantissa is 1-bit more than its apparent size (floating point magick).

Some CLR floating point resources for you:

• http://csharpindepth.com/Articles/General/FloatingPoint.aspx
• http://www.extremeoptimization.com/resources/Articles/FPDotNetConceptsAndFormats.aspx

This paper is probably the canonical paper on the perils and pitfalls of floating point arithmetic. If you're not a member of the ACM, click the link on the title to find public downloads of the article:

• David Goldberg. 1991. What every computer scientist should know about floating-point arithmetic. ACM Comput. Surv. 23, 1 (March 1991), 5-48. DOI=10.1145/103162.103163 http://doi.acm.org/10.1145/103162.103163

  Abstract
  Floating-point arithmetic is considered as esoteric subject by many people. This is rather surprising, because floating-point is ubiquitous in computer systems: Almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow. This paper presents a tutorial on the aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating point standard, and concludes with examples of how computer system builders can better support floating point.