(42, all flavours) Integer Division - how?
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12-15-2020, 02:51 PM
(This post was last modified: 12-16-2020 08:30 PM by Albert Chan.)
Post: #31
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RE: (42, all flavours) Integer Division - how?
(12-15-2020 12:43 PM)Werner Wrote: Yes, but that is only with binary floating point, not with decimal, as in HP calcs ;-) Not true. When floor-mod "fix" sign, subtraction cancellation may occur, binary or decimal. But, the fix is easy. (your code already fixed this, by using IP) The trick is to start with q = ceil(a/b), or IP(a/b) For a<0, |a|<b: min(a/b) = min(ulp(b)-b)/b) = min(ulp(b)/b) - 1 > -1 Confirm: Free42 Binary: 2 53 X^Y 1 - 1/X 1 - → -9.999999999999999e-1 Free42 Decimal: 1E34 1 - 1/X 1 - → -9.999999999999999999999999999999999e-1 This guaranteed q start with 0, for negative tiny a. (12-15-2020 10:37 AM)Albert Chan Wrote: For negative tiny a = -ε If error = 0, this always work, nothing to fix. If error ≠ 0, and q = 0, we get this: a1 == b1 test : -1 + error == 0 → error == 1 a1==b1-c test: -1 + error == -c → error == -b Since error is tiny, error(b-ε) ≤ ½ulp(b), error(c-ε) ≤ ½ulp(c), both tests failed. This force correction, returning corrected q-1 = -1 This is revised idiv3 should work with non-integer inputs, if c = b+1 is exact. I also added a fast-path, to speed things up. PHP Code: function idiv3c(a,b) -- assumed b > 0 |
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