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| -rw-r--r-- | src/strtofr.c | 11 |
1 files changed, 11 insertions, 0 deletions
diff --git a/src/strtofr.c b/src/strtofr.c index 703caa7b2..9ac116341 100644 --- a/src/strtofr.c +++ b/src/strtofr.c @@ -512,6 +512,17 @@ parsed_string_to_mpfr (mpfr_t x, struct parsed_string *pstr, mpfr_rnd_t rnd) and ysize_bits = a*Den+b, then ysize_bits * Num/Den = a*Num + (b * Num)/Den, thus ceil(ysize_bits * Num/Den) = a*Num + floor(b * Num + Den - 1)/Den + + Note: denoting m = pstr_size and n = ysize_bits, assuming we have + m = 1 + ceil(n/log2(b)), i.e., b^(m-1) >= 2^n > b^(m-2), then + b^(m-1)/2^n < b, and since we consider m characters of the input, + the corresponding part is less than b^m < b^2*2^n. + This implies that if b^2 < 2^GMP_NUMB_BITS, which for b <= 62 holds + for GMP_NUMB_BITS >= 12, we have real_ysize <= ysize+1 below + (this also imlies that for GMP_NUMB_BITS >= 13, the number of bits + of y[real_ysize-1] below is less than GMP_NUMB_BITS, thus + count < GMP_NUMB_BITS. + Warning: for GMP_NUMB_BITS=8, we can have real_ysize = ysize+2! */ { unsigned long Num = RedInvLog2Table[pstr->base-2][0]; |