diff options
Diffstat (limited to 'src/log_ui.c')
| -rw-r--r-- | src/log_ui.c | 12 |
1 files changed, 10 insertions, 2 deletions
diff --git a/src/log_ui.c b/src/log_ui.c index b544e0d64..4acaf20a6 100644 --- a/src/log_ui.c +++ b/src/log_ui.c @@ -120,8 +120,16 @@ mpfr_log_ui (mpfr_ptr x, unsigned long n, mpfr_rnd_t rnd_mode) /* here n >= 3 */ - /* argument reduction: compute k such that 2/3 <= n/2^k < 4/3, - i.e., 2^(k+1) <= 3n < 2^(k+2) */ + /* Argument reduction: compute k such that 2/3 <= n/2^k < 4/3, + i.e., 2^(k+1) <= 3n < 2^(k+2). + + FIXME: we could do better by considering n/(2^k*3^i*5^j), + which reduces the maximal distance to 1 from 1/3 to 1/8, + thus needing about 1.89 less terms in the Taylor expansion of + the reduced argument. Then log(2^k*3^i*5^j) can be computed + using a combination of log(16/15), log(25/24) and log(81/80), + see Section 6.5 of "A Fortran Multiple-Precision Arithmetic Package", + Richard P. Brent, ACM Transactions on Mathematical Software, 1978. */ mpz_init_set_ui (three_n, n); mpz_mul_ui (three_n, three_n, 3); |