This file defines a few very basic functions which I feel should
really be part of the standard C++. Nevertheless I have placed all
definitions inside the namespace CoCoA. Here is a summary:
round(x) -- round x (of type double) to nearest integer value (of type double); halves round towards +infinity.
ULongDiff(hi,lo) -- computes hi-lo as unsigned long (assumes hi>=lo)
LongRange(lo,hi) -- returns a vector<long> filled with lo,lo+1,...,hi (useful for submat)
IsDecimal(strm) -- returns true is i/o stream strm is in decimal mode, o/w returns false
MaxSquarableInteger<T>() -- returns largest integer whose square fits in type T
fold(str, n) -- make a copy of the string str inserting a newline every n chars
len(v) -- same as v.size() except that result is long
rather than size_t
Everything is in utils.H;
the functions are all so simple that they can be implemented inline.
Impl of template fn MaxSquarableInteger uses GMP to compute the
memorized values. A table of constants would be faster but potentially
less portable (given that CoCoALib requires GMP anyway). I haven't yet
found a neat way of ensuring that the type T is integral & bounded.
A possibly better idea for MaxSquarableInteger: precompute 2^63*sqrt(2) as
unsigned long, then simply right shift this value for integral types with
less than 127 bits. This suggestion presupposes a binary computer.
2017