From: jacob@jacob.remcomp.fr   
      
   Le 11/01/2021 à 15:39, jacob navia a écrit :   
   > Hi math wizards!   
   >   
   > I have developed an extended precision math package with 448 bits. The   
   > basic operations are written all in assembly, and I am now approx twice   
   > as fast as MPFR.   
   >   
   > BUT...   
   >   
   > (yes there is always a "but" :-)   
   >   
   > MPFR does more square roots than me per millisecond!   
   >   
   > Surely MPFR has a better algo than my pathetic newton iteration... I was   
   > at 1720 square roots/ms, and MPFR is at 6899. I have tried to improve it   
   > with Halley's method and now I am at 2200/ms, still MUCH TOO SLOW.   
   >   
   > Can you point me to some method that would be more appropiate?   
   >   
   > Thanks in advance!   
   >   
   > P.S.   
   > Here are the timings for the 4 operations:   
   >   
   > MPFR   
   > The four operations with    5000000 iterations. Mon Jan 11 15:32:50 2021   
   > Addition      :     2.2837e-05 ms. (43788.58869) per ms   
   > Subtraction   :    1.39152e-05 ms. (71863.86110) per ms   
   > Multiplication:     4.5159e-05 ms. (22143.98016) per ms   
   > Mult. (int)   :    1.59318e-05 ms. (62767.54667) per ms   
   > Division      :     0.00011619 ms. (8606.57784) per ms   
   > Division(int) :     4.0373e-05 ms. (24769.02881) per ms   
   >   
   > My software:   
   > The four operations with    5000000 iterations. Mon Jan 11 15:35:28 2021   
   > Addition      :    1.00136e-05 ms. (99864.18471) per ms   
   > Subtraction   :      9.862e-06 ms. (101399.31048) per ms   
   > Multiplication:    2.06244e-05 ms. (48486.25899) per ms   
   > Mult. (int)   :    6.87133e-06 ms. (145532.16261) per ms   
   > Squaring      :    2.18158e-05 ms. (45838.33735) per ms   
   > Division      :    0.000120662 ms. (8287.59960) per ms   
   > Division(int) :     4.5838e-05 ms. (21815.96056) per ms   
   >   
   > Note that I also use newton iteration for division... I am almost as   
   > slow as MPFR...   
      
   Sorry forgot to tell: all timings were done in an Apple M1 chip   
   (mac-mini, ARM64 architecture)   
      
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