From: robert@nospicedham.prino.org   
      
   On 2018-03-12 19:50, Terje Mathisen wrote:   
   > Robert Prins wrote:   
   >> On 2018-03-12 09:05, Terje Mathisen wrote:   
   >>> The reason for this extra stuff is that you need n+1 bits of actual   
   >>> precision   
   >>> in order to get exact results when emulating an n-bit division.   
   >>   
   >> Which is what Agner Fog attributes to you in his manuals.   
   >>   
   >> So many things are "too trivial" to require online tools, what's the   
   >> harm in one more?   
   >>   
   >> Anyway, am I correct in finding that for limited range dividends, you   
   >> can get away with, as if it matters, smaller shifts?   
   >>   
   >> I use 301036/8 for division by 3652425, 1881437/4 for division by 36525,   
   >> 14035840/0 for division by 306, and 429496729/0 for division by 10, and   
   >> for the JDN's I'm working with (1980-06-16 to now+) that works.   
   >   
   > The accuracy of the reciprocal must be higher than both the divisor and the   
   > dividend, so for division of the full 32-bit range you always need an   
   > effectively 33 bit reciprocal.   
   >   
   > For smaller values like I neded for calendar operations, i.e. calculating the   
   > century number given a (julian) day number which is known to be inside a   
   > 400-year period I could approximate j/100 with 41/4096. This works because   
   that   
   > fraction just happens to be very close to the exact (1/100) reciprocal. :-)   
   >   
   > Multiplication by 41 can be done in several ways:   
   >   
   >    imul eax,edx        ;; *41   
   >   
   >    lea edx,[eax+eax*4] ;; *5   
   >    lea eax,[eax+edx*8] ;; *41   
   >   
   >    lea edx,[eax+eax*8]     ;; *9   
   >    shl eax,5        ;; *32   
   >    add eax,edx   
   >   
   > On a cpu where LEA takes two cycles the last version can run in three cycles   
   > while the dual-LEA version would take four.   
      
   But that takes me back to my earlier question, given that fact that multiplies   
   are very fast nowadays, how useful are the above LEA sequences?   
      
   The 41/4096 is neat, but do you know what you can do with these six digits, 1,   
   1, 3, 3, 5, and 5?   
      
      
   Well, quite remarkably, 1 / (113 / 355) is, for two (relatively) tiny numbers,   
   amazingly close to pi!   
      
   Robert   
   --   
   Robert AH Prins   
   robert(a)prino(d)org   
      
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