diff options
Diffstat (limited to 'doc/sum.txt')
| -rw-r--r-- | doc/sum.txt | 16 |
1 files changed, 8 insertions, 8 deletions
diff --git a/doc/sum.txt b/doc/sum.txt index 408861150..3dc0f048a 100644 --- a/doc/sum.txt +++ b/doc/sum.txt @@ -354,7 +354,7 @@ let e and err denote the exponents of the computed result and of the error bound respectively. While e − err is less than some given bound denoted prec, shift the accumulator, update maxexp and minexp, and reiterate. For the caller, this bound must be large enough in order to -reach some wanted accuracy. However it cannot be too large since the +reach some wanted accuracy. However, it cannot be too large since the accumulator has a limited precision: we will need to make sure that if a reiteration is needed, then the cause is a partial cancellation, so that the shift count is nonzero, otherwise minexp would not change @@ -1163,10 +1163,10 @@ For the moment, let us assume that sq ≥ 2. We distinguish two cases: (this is important because if corr = 2 and the significand has only one limb, the least significant nontrailing bit may be 1), and e is incremented. If corr < 0, then it is −1, so that we - subtract 1 from the significand with mpn_sub_1. In case of - borrow out, meaning a change of binade, the most significant bit - of the significand is set to 1 so that all the (nontrailing) bits - of the significand are 1's, and e is decremented. + subtract 1 from the significand with mpn_sub_1. If the MSB of the + significand becomes 0, meaning a change of binade, then it is set + back to 1 so that all the (nontrailing) bits of the significand + are 1's, and e is decremented. * neg = 1 (negative sum). Contrary to the positive case, where we could do MPN number + limb (with mpn_add_1) or MPN number − limb @@ -1220,8 +1220,8 @@ For the moment, let us assume that sq ≥ 2. We distinguish two cases: Here we want to compute com(x) − 1, but GMP does not provide an operation for that. The fact is that a sequence of low significant bits 1 is invariant, and we need to do the loop - ourselves in C instead of uses an optimized assembly version - from GMP. However this may not be a problem in practice, as + ourselves in C instead of using an optimized assembly version + from GMP. However, this may not be a problem in practice, as the difference is probably not noticeable. When a limb with a zero is reached (there is at least one since the most significant bit of the significand is a 0), we compute its @@ -1370,7 +1370,7 @@ have the minimal precision 2, and the output precision is p: Here long carry propagation will occur for each addition of the initial iteration, so that the complexity will be O(n·p) instead of O(n+p) if we -choose to delay carry propagation (however such a choice may slower the +choose to delay carry propagation (however, such a choice may slower the average case and take more memory, such as around 3p instead of 2p). When a new iteration is needed due to cancellation, a second accumulator |