dtoa.c contains two main functions: dtoa(), which converts a double to string, and strtod(), which converts a string to a double. It also contains a lot of support functions, most of which are for its own implementation of arbitrary-precision arithmetic. dtoa.c’s claim to fame is getting these conversions right, and that can only be done, … Read more
Parameters of functions that correspond to … are promoted before passing to your variadic function. char and short are promoted to int, float is promoted to double, etc. 6.5.2.2.7 The ellipsis notation in a function prototype declarator causes argument type conversion to stop after the last declared parameter. The default argument promotions are performed on … Read more
In Python 3, number / 10 will try to return a float. However, floating point values can’t be of arbitrarily large size in Python and if number is large an OverflowError will be raised. You can find the maximum that Python floating point values can take on your system using the sys module: >>> import … 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
The rule can be summed up as this: A number can be represented exactly in binary if the prime factorization of the denominator contains only 2. (i.e. the denominator is a power-of-two) So 1/(32 + 16) is not representable in binary because it has a factor of 3 in the denominator. But 1/32 + 1/16 … 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 other answers don’t exactly explain what’s going on here, so this is the basic problem: When you write blackKey.center.x, the blackKey.center and center.x both look like struct member accesses, but they’re actually completely different things. blackKey.center is a property access, which desugars to something like [blackKey center], which in turn desugars to something like … Read more