dist/src/sub1.c

39   mp_limb_t carry, bb, cc;
472         cc = cp[cn];
474         cc = 0;
478         cmp_low = (bb < cc) ? -2+k : (bb > cc) ? 1 : 0;
481          1a: bb > cc + half
482          1b: bb = cc + half
483          1c: 0 < bb - cc < half
484          1d: bb = cc
485          1e: -half < bb - cc < 0
486          1f: bb - cc = -half
487          1g: bb - cc < -half
490          2a: bb > cc
491          2b: bb = cc
492          2c: bb < cc
495          3a: bb > cc
496          3b: bb = cc
497          3c: bb < cc
506           /* add one ulp if bb > cc + half
507              truncate if cc - half < bb < cc + half
508              sub one ulp if bb < cc - half
511           if (cmp_low < 0) /* bb < cc: -1 ulp < low(b) - low(c) < 0,
514               if (cc >= half)
515                 cc -= half;
516               else /* since bb < cc < half, bb+half < 2*half */
518               /* now we have bb < cc + half:
519                  we have to subtract one ulp if bb < cc,
520                  and truncate if bb > cc */
522           else if (cmp_low >= 0) /* bb >= cc, cases 1a to 1d */
524               if (cc < half)
525                 cc += half;
526               else /* since bb >= cc >= half, bb - half >= 0 */
528               /* now we have bb > cc - half: we have to add one ulp if bb > cc,
529                  and truncate if bb < cc */
536       MPFR_LOG_MSG (("k=%d bb=%Mu cc=%Mu cmp_low=%d\n", k, bb, cc, cmp_low));
551               /* If cmp_low < 0 and bb > cc, then -0.5 ulp < low(b)-low(c) < 0,
557                  limbs bb and cc were equal (thus cmp_low was 0 for k=0),
558                  or we had bb - cc = -0.5 ulp or 0.5 ulp.
565               if (bb > cc || sh > 0 || cmp_low == -1)
567                       bb > cc corresponds to cases 1e and 1f1
573               else if (bb < cc) /* here sh = 0 and low(b)-low(c) < -0.5 ulp,
576               /* the only case where we can't conclude is sh=0 and bb=cc,
595               if (bb > cc)
597                   /* if sh=0, then bb>cc means that low(b)-low(c) > 0.5 ulp,
611               else if (bb < cc) /* 0 < low(b) - low(c) < 0.5 ulp, cases 1c,
617               /* the only case where we can't conclude is bb=cc, i.e.,
623          according to the values of bb and cc for k=1:
624          1b. sh=0 and cmp_low = 1 and bb-cc = half [around 0.5 ulp]
625              1b1. bb > cc: add one ulp, inex = 1
626              1b2: bb = cc: cannot conclude
627              1b3: bb < cc: truncate, inex = -1
628          1d. sh=0 and cmp_low = 0 and bb-cc = 0 [around 0]
629              1d1: bb > cc: truncate, inex = -1
630              1d2: bb = cc: cannot conclude
631              1d3: bb < cc: truncate, inex = +1
632          1f. sh=0 and cmp_low = -1 and bb-cc = -half [around -0.5 ulp]
633              1f1: bb > cc: truncate, inex = +1
634              1f2: bb = cc: cannot conclude
635              1f3: bb < cc: sub one ulp, inex = -1
636          2b. sh > 0 and cmp_low = 2 and bb=cc [around 0.5 ulp]
637              2b1. bb > cc: add one ulp, inex = 1
638              2b2: bb = cc: cannot conclude
639              2b3: bb < cc: truncate, inex = -1
641              3b1. bb > cc: truncate, inex = -1
642              3b2: bb = cc: cannot conclude
643              3b3: bb < cc: truncate, inex = +1