The Numeric Types section documents this behaviour explicitly: round(x[, n]) x rounded to n digits, rounding half to even. If n is omitted, it defaults to 0. Note the rounding half to even. This is also called bankers rounding; instead of always rounding up or down (compounding rounding errors), by rounding to the nearest even … Read more
Python’s built-in float type has double precision (it’s a C double in CPython, a Java double in Jython). If you need more precision, get NumPy and use its numpy.float128.
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
The reason it is only a suggestion is that you could quite easily write a print function that ignored the options value. The built-in printing and formatting functions do use the options value as a default. As to the second question, since R uses finite precision arithmetic, your answers aren’t accurate beyond 15 or 16 … Read more
The rounding error is not random and the way it is implemented it attempts to minimise the error. This means that sometimes the error is not visible, or there is not error. For example 0.1 is not exactly 0.1 i.e. new BigDecimal(“0.1”) < new BigDecimal(0.1) but 0.5 is exactly 1.0/2 This program shows you the … Read more
toFixed(n) provides n length after the decimal point; toPrecision(x) provides x total length. Ref at w3schools: toFixed and toPrecision EDIT: I learned a while back that w3schools isn’t exactly the best source, but I forgot about this answer until I saw kzh’s, uh, “enthusiastic” comment. Here are additional refs from Mozilla Doc Center for toFixed() … Read more
I know of no way to way to make normal floating points deterministic in .net. The JITter is allowed to create code that behaves differently on different platforms(or between different versions of .net). So using normal floats in deterministic .net code is not possible. The workarounds I considered: Implement FixedPoint32 in C#. While this is … Read more
As others have mentioned, you’ll probably want to use the BigDecimal class, if you want to have an exact representation of 11.4. Now, a little explanation into why this is happening: The float and double primitive types in Java are floating point numbers, where the number is stored as a binary representation of a fraction … Read more
I found the bug. .NET does the following in clr\src\vm\comnumber.cpp: DoubleToNumber(value, DOUBLE_PRECISION, &number); if (number.scale == (int) SCALE_NAN) { gc.refRetVal = gc.numfmt->sNaN; goto lExit; } if (number.scale == SCALE_INF) { gc.refRetVal = (number.sign? gc.numfmt->sNegativeInfinity: gc.numfmt->sPositiveInfinity); goto lExit; } NumberToDouble(&number, &dTest); if (dTest == value) { gc.refRetVal = NumberToString(&number, ‘G’, DOUBLE_PRECISION, gc.numfmt); goto lExit; } DoubleToNumber(value, … Read more
Note: the Nintendo 64 does have a 64-bit processor, however: Many games took advantage of the chip’s 32-bit processing mode as the greater data precision available with 64-bit data types is not typically required by 3D games, as well as the fact that processing 64-bit data uses twice as much RAM, cache, and bandwidth, thereby … Read more