To use Kahan-Ozawa summation, pass the string 'ozawa' as the last argument to the function. `unt` with non-integral arguments by default now uses Kahan-Babuska autocorrection which is more accurate than the Kahan-Ozawa algorithm used before, with a performance loss of just one percent. `math.accu` did not work correctly with the 'kbn' option. Just pass the string 'raw' as the last argument. `math.accu` now has a `raw` mode with no auto-correction at all.
While this may produce much more accurate iteration values, the speed loss is 20 percent. Numeric `for` loops with fractional step sizes can now alternatively use enhanced Kahan-Babuska summation instead of the default Kahan summation, by the explicit setting: This release has been Valgrind-checked on x86 and amd64 Linux to ensure there are no internal errors or memory leaks. This has all been fixed and the functions have been sped up a little bit on all platforms. In OS/2 and DOS and with complex arguments, `hypot`, `hypot2`, `hypot3` and `hypot4` returned `undefined` instead of a complex result if either the real or the imaginary unit of an argument was zero. `math.ndigits` can now also count the number of decimal places (number of digits after the dot) in a number of base 10. `bytes.arshift32` now accepts negative values to be arithmetically shifted. This behaviour is the defacto-standard for most C compilers. Starting with this release, Agena behaves the same on all platforms when shifting negative values to the right with the `>` operator: it performs an arithmetic shift, thus preserving the sign of the value shifted. On older Intel Apple platforms and on ARM- and PowerPC-based systems and in unsigned bits mode, if you tried to left-shift a value x >= 2^32, with the ` environ.kernel(foradjust=false) Also hardened the internal set creation process. Hardened `reduce`, `countitems`, `map`, `select`, `selectremove` and `remove` against internal stack corruption. You can now apply the unary minus operator to Booleans, converting them to either 0 or -1: The new function `hashes.jnumber` maps a number to one or two unsigned 4 byte integers, Julia-style. The current setting of `math.hEps` can be queried by: You can entirely switch off these new features by setting `math.Eps` to zero, but only by calling `environ.kernel`: If a you pass a step size that is equals or less then `math.hEps`, Agena now issues an error.
By default, numeric for loops with fractional step sizes now automatically increase the stop limit by the value of the constant `math.hEps` so that it is made sure that they iterate until the limit has actually been reached. The new constant `math.hEps` represents the value 1.4901161193847656e-12, an epsilon value more or less in the middle of `Eps` and `DoubleEps`.
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