Sarnold Acronym for Multiple Precision Arithmetics. Library in pure Tcl available at : http://sarnold.free.fr/
Released with a BSDish License. The fact is that the floating-point numbers are still experimental, even if it 'works'. (that means, the precision of fp. numbers is a subject i personnaly do not master) I guess it is not obvious to do such computations without losing precision at each step.
What's new : in tcllib there is a bignum implementation that is much faster than mine. For your information it uses lists as an internal representation of bignums.
Version 1.2 dated 12th November 2004 with many performance enhancements
AM (12 november 2004) Do you care to contribute this to Tcllib?
Examples
with a 333MHz PII 100MHz PCI Bus PC with Windows Me.
(mpa-v0.11) 50 % package require mpa
0.11
(mpa-v0.11) 51 % mpa::int::add 111111111111111111111 98237827463784678346478
98348938574895789457589
(mpa-v0.11) 52 % mpa::int::add 1000000000000000000000 99999999999999999
1000099999999999999999
(mpa-v0.11) 53 % mpa::int::mul 1001 9009
9018009
(mpa-v0.11) 54 % mpa::int::mul 10010001 9009009
90180189099009
(mpa-v0.11) 55 % mpa::float::pi 20
# Pi constant with 20 decimals, the result is cached in a namespace variable
3.14159265358979323846
(mpa-v0.11) 56 % time {mpa::float::pi 20};# result is cached in memory
363 microseconds per iteration
(mpa-v0.11) 57 % time {mpa::float::pi 21};# result is now recomputed
90643 microseconds per iteration
(mpa-v0.11) 58 % time {puts [mpa::float::pi 21]};# result is cached
3.141592653589793238462
4962 microseconds per iteration
(mpa-v0.11) 59 % mpa::float::add 1.0 2.0
3.0~2 # the precision with 1.0 ans 2.0 is assumed to be 0.1
# and the precision of the sum is the sum of the precisions
(mpa-v0.11) 60 % mpa::float::add 1.0000 2.0000
3.0000~2
(mpa-v0.11) 62 % mpa::float::format [mpa::float::mul 1.0000000 2.0000000];
# the precision of the product is approximatly A*Pb+B*Pa = 3e-7
2.000000 # now the number is formatted to be put on screen
(mpa-v0.11) 63 % mpa::float::mul 1.0000000 2.0000000
2.0000000~4 # precision is computed to be always the smallest ,
# even if such computations are complex to handle and loss of CPUSarnold This package is especially good when you want it to represent arbitrary floating-point numbers. See also : bignum in pure tcl.