Arithmetic

Fixnum and flonum arithmetic is already supported by many systems,
mainly for efficiency. Standardization of fixnum and flonum arithmetic
increases the portability of code that uses it. Standardizing the
precision of fixnum and flonum arithmetic would make it inefficient on
some systems, which would defeat its purpose. Therefore, R^{6}RS
specifies the syntax and much of the semantics of fixnum and flonum
arithmetic, but makes the precision implementation-dependent.

Existing implementations employ different implementation strategies
for fixnums: Some implement the model specified by R^{6}RS (overflows
cause exceptions), some implement modular arithmetic (overflows “wrap
around”), and others do not handle arithmetic overflows at all. The
latter model violates the safety requirement of R^{6}RS. In programs
that use fixnums instead of generic arithmetic, overflows are
typically programming mistakes. The model chosen for R^{6}RS has the
advantage that such overflows do not get silently converted into
meaningless number objects, and that the programs gets notified of the
violation through the exception system.

The bitwise operations have been adapted from the operations described in SRFIs 33 [31] and 60 [20].

`fx+`and`fx*`- These procedures are restricted to two arguments, because their generalizations to three or more arguments would require precision proportional to the number of arguments.
`real->flonum`- This procedure is necessary, because not all real number objects are inexact, and because some inexact real number objects may not be flonums.
`flround`-
The
`flround`procedure rounds to even for consistency with the default rounding mode specified by the IEEE floating-point standard. `flsqrt`-
The behavior of
`flsqrt`on −0.0 is consistent with the IEEE floating-point standard.