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Optimisation progress for libzahl, compared to other big integer
libraries. These comparisons are for 152-bit integers. Functions
in parenthesis the right column are functions that needs
optimisation to improve the peformance of the function in the
left column. Double-parenthesis means there may be a better way
to do it.
zset .................... fastest
zseti ................... tomsfastmath is faster, otherwise fastest
zsetu ................... tomsfastmath is faster, otherwise fastest
zneg(a, b) .............. fastest
zneg(a, a) .............. fastest
zabs(a, b) .............. fastest
zabs(a, a) .............. tomsfastmath is faster, otherwise fastest
zadd_unsigned ........... fastest
zsub_unsigned ........... fastest
zadd .................... 98 % of libtommath, otherwise fastest
zsub .................... 74 % of tomsfastmath, otherwise fastest
zand .................... 69 % of tomsfastmath, otherwise fastest
zor ..................... 39 % of tomsfastmath, otherwise fastest
zxor .................... 52 % of tomsfastmath, otherwise fastest
znot .................... fastest
zeven ................... fastest
zodd .................... fastest
zeven_nonzero ........... fastest
zodd_nonzero ............ fastest
zzero ................... fastest
zsignum ................. fastest
zbits ................... gmp is faster, because of bug in libzahl
zlsb .................... fastest
zswap ................... fastest
zlsh .................... fastest
zrsh .................... fastest
ztrunc(a, b, c) ......... fastest
ztrunc(a, a, b) ......... fastest
zsplit .................. fastest
zcmpmag ................. gmp is faster, otherwise fastest
zcmp .................... 80 % of hebimath, gmp is even faster (zcmpmag)
zcmpi ................... fastest
zcmpu ................... fastest
zbset(a, b, 1) .......... fastest
zbset(a, a, 1) .......... fastest
zbset(a, b, 0) .......... fastest
zbset(a, a, 0) .......... fastest
zbset(a, b, -1) ......... fastest
zbset(a, a, -1) ......... fastest
zbtest .................. fastest
zgcd .................... 26 % of gmp, otherwise fastest (zcmpmag)
zmul .................... slowest
zsqr .................... slowest (zmul)
zmodmul(big mod) ........ slowest ((zmul, zmod))
zmodsqr(big mod) ........ slowest ((zmul, zmod))
zmodmul(tiny mod) ....... slowest ((zmul))
zmodsqr(tiny mod) ....... slowest ((zmul))
zpow .................... slowest (zmul, zsqr)
zpowu ................... slowest (zmul, zsqr)
zmodpow ................. slowest (zmul, zsqr. zmod)
zmodpowu ................ slowest (zmul, zsqr, zmod)
zsets ................... 14 % of gmp, otherwise fastest
zstr_length(a, 10) ...... gmp is faster, otherwise fastest (zdiv, zsqr)
zstr(a, b, n) ........... 10 % of gmp, otherwise fastest
zrand(default uniform) .. gmp and tomsfastmath are faster
zptest .................. slowest (zrand, zmodpow, zsqr, zmod)
zsave ................... fastest
zload ................... fastest
zdiv(big denum) ......... slowest (zdivmod)
zmod(big denum) ......... slowest (zdivmod)
zdivmod(big denum) ...... slowest (excluding hebimath)
zdiv(tiny denum) ........ fastest
zmod(tiny denum) ........ fastest
zdivmod(tiny denum) ..... fastest
Note, some corresponding functions are not implemented in
some other libraries. In such cases, they have been implemented
in the translation layers (found under bench/). Those
implementations are often suboptimal, but probably in style
with what you would write if you need that functionality.
Note further, that if, for example, you want do perform
addition and you know that your operands are non-negative,
you would choose zadd_unsigned in libzahl, but if you are
using a library that does not have the corrsponding function,
you are better of with the regular addition (zadd).
Also note, TomsFastMath does not allow arbitrarily large
integers, which gives is a significant performance advantage.
Furthermore, not failure check is done with GMP. Additionally,
hebimath is some functions that are not working correctly;
those have been excluded from the comparison.
Also note, NOT does not mean the same thing in all libraries,
for example in GMP it means (-x - 1), thus, znot does not
use GMP's NOT in the translations layer.
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