This is what ยง2.3.2 of the JVM 7 spec has to say about it: The elements of the double value set are exactly the values that can be represented using the double floating-point format defined in the IEEE 754 standard, except that there is only one NaN value (IEEE 754 specifies 253-2 distinct NaN values). … Read more
Really not any different than you do it with pencil and paper. Okay a little different 123400 – 5432 = 1.234*10^5 – 5.432*10^3 the bigger number dominates, shift the smaller number’s mantissa off into the bit bucket until the exponents match 1.234*10^5 – 0.05432*10^5 then perform the subtraction with the mantissas 1.234 – 0.05432 = … Read more
First, a paper you should consider reading, if you want to understand floating point foibles better: “What Every Computer Scientist Should Know About Floating Point Arithmetic,” http://www.validlab.com/goldberg/paper.pdf And now to some meat. The following code is bare bones, and attempts to produce an IEEE-754 single precision float from an unsigned int in the range 0 … Read more
From Wikipedia: It is claimed that the inclusion of signed zero in IEEE 754 makes it much easier to achieve numerical accuracy in some critical problems[1], in particular when computing with complex elementary functions[2]. The first reference is “Branch Cuts for Complex Elementary Functions or Much Ado About Nothing’s Sign Bit” by W. Kahan, that … Read more
Essentially all architectures in current non-punch-card use, including embedded architectures and exotic signal processing architectures, offer one of two floating point systems: IEEE-754. IEEE-754 except for blah. That is, they mostly implement 754, but cheap out on some of the more expensive and/or fiddly bits. The most common cheap-outs: Flushing denormals to zero. This invalidates … Read more
I believe __STDC_IEC_559__ relies on some library features and can’t be defined solely by the compiler. See this post for some information. This is not uncommon for C — the compiler and the C library must sometimes cooperate in order to implement the entire standard. What you’re asking depends on the compiler. I think you … Read more
Check out the article on “What every computer scientist should know about floating point arithmetic”
A 32 bit floating point number has 23 + 1 bits of mantissa and an 8 bit exponent (-126 to 127 is used though) so the largest number you can represent is: (1 + 1 / 2 + … 1 / (2 ^ 23)) * (2 ^ 127) = (2 ^ 23 + 2 ^ … Read more
The iPhone can do both single and double precision arithmetic in hardware. On the 1176 (original iPhone and iPhone3G), they operate at approximately the same speed, though you can fit more single-precision data in the caches. On the Cortex-A8 (iPhone3GS, iPhone4 and iPad), single-precision arithmetic is done on the NEON unit instead of VFP, and … Read more