diff options
Diffstat (limited to 'src/sqr.c')
| -rw-r--r-- | src/sqr.c | 8 |
1 files changed, 8 insertions, 0 deletions
@@ -65,6 +65,14 @@ mpfr_sqr_1 (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode, mpfr_prec_t p) a >= 0.111...111[1]*2^(emin-1), there is no underflow. */ if (MPFR_UNLIKELY(ax < __gmpfr_emin)) { + /* Note: for emin=2*k+1, a >= 0.111...111*2^(emin-1) is not possible, + i.e., a >= (1 - 2^(-p))*2^(2k), since we need a = b^2 with EXP(b)=k, + and the largest such b is (1 - 2^(-p))*2^k satisfies + b^2 < (1 - 2^(-p))*2^(2k). + For emin=2*k, it is only possible for some values of p: it is not + possible for p=53, because the largest significand is 6369051672525772 + but its square has only 52 leading ones. For p=24 it is possible, + with b = 11863283, whose square has 24 leading ones. */ if ((ax == __gmpfr_emin - 1) && (ap[0] == ~mask) && ((rnd_mode == MPFR_RNDN && rb) || (MPFR_IS_LIKE_RNDA(rnd_mode, MPFR_IS_NEG (a)) && (rb | sb)))) |