As Livius points out in his comment, this is an issue with R (and in fact, most programming language), with how numbers are represented in binary. To work with extremely large/small floating point numbers, you can use the Rmpfr library: install.packages(“Rmpfr”) library(“Rmpfr”) x <- c(-2.5e+59, -5.6e+60) y <- mpfr(x, 6) # the second number is … Read more
This drove me nuts for a bit until I finally found this bug which points you to this RFC which says Currently json_encode() uses EG(precision) which is set to 14. That means that 14 digits at most are used for displaying (printing) the number. IEEE 754 double supports higher precision and serialize()/var_export() uses PG(serialize_precision) which … Read more
You could implement your own based on .NET 4.0’s BigInteger class. I did this for fun, it does multiplication only: public struct BigDecimal { public BigInteger Integer { get; set; } public BigInteger Scale { get; set; } public BigDecimal(BigInteger integer, BigInteger scale) : this() { Integer = integer; Scale = scale; while (Scale > … Read more
Due to the fact the float and double are internally stored in binary, the literal 7.40200133400 actually stands for the number 7.40200133400000037653398976544849574565887451171875 …so how much precision do you really want? 🙂 #include <iomanip> int main() { double x = 7.40200133400; std::cout << std::setprecision(51) << x << “\n”; } And yes, this program really prints 7.40200133400000037653398976544849574565887451171875!
double-float is a technique that uses pairs of single-precision numbers to achieve almost twice the precision of single precision arithmetic accompanied by a slight reduction of the single precision exponent range (due to intermediate underflow and overflow at the far ends of the range). The basic algorithms were developed by T.J. Dekker and William Kahan … Read more
If you really care about precision, you should use BigDecimal https://docs.oracle.com/javase/8/docs/api/java/math/BigDecimal.html https://docs.oracle.com/en/java/javase/11/docs/api/java.base/java/math/BigDecimal.html
Disclaimer (as suggested by Toby Speight): Although IEEE 754 representations are quite common, an implementation is permitted to use any other representation that satisfies the requirements of the language. The doubles are represented in the form mantissa * 2^exponent, i.e. some of the bits are used for the non-integer part of the double number. bits … Read more
Your instinct is basically right, sorting in ascending order (of magnitude) usually improves things somewhat. Consider the case where we’re adding single-precision (32 bit) floats, and there are 1 billion values equal to 1 / (1 billion), and one value equal to 1. If the 1 comes first, then the sum will come to 1, … Read more
float_num.toFixed(2); Note:toFixed() will round or pad with zeros if necessary to meet the specified length.
The value of a float does not change when converted to a double. There is a difference in the displayed numerals because more digits are required to distinguish a double value from its neighbors, which is required by the Java documentation. That is the documentation for toString, which is referred (through several links) from the … Read more