diff options
Diffstat (limited to 'src/tanh.c')
| -rw-r--r-- | src/tanh.c | 19 |
1 files changed, 13 insertions, 6 deletions
diff --git a/src/tanh.c b/src/tanh.c index 06adf7874..e731f2623 100644 --- a/src/tanh.c +++ b/src/tanh.c @@ -98,13 +98,20 @@ mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode) if (MPFR_GET_EXP (x) < 0) Nt += -MPFR_GET_EXP (x); + /* The error analysis in algorithms.tex assumes that x is exactly + representable with working precision Nt. + FIXME: adapt the error analysis for the case Nt < PREC(x). */ + if (Nt < MPFR_PREC(x)) + Nt = MPFR_PREC(x); + /* initialize of intermediary variable */ MPFR_GROUP_INIT_2 (group, Nt, t, te); MPFR_ZIV_INIT (loop, Nt); for (;;) { /* tanh = (exp(2x)-1)/(exp(2x)+1) */ - mpfr_mul_2ui (te, x, 1, MPFR_RNDN); /* 2x */ + inexact = mpfr_mul_2ui (te, x, 1, MPFR_RNDN); /* 2x */ + MPFR_ASSERTD(inexact == 0); /* see FIXME above */ /* since x > 0, we can only have an overflow */ mpfr_exp (te, te, MPFR_RNDN); /* exp(2x) */ if (MPFR_UNLIKELY (MPFR_IS_INF (te))) { @@ -119,13 +126,13 @@ mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode) break; } d = MPFR_GET_EXP (te); /* For Error calculation */ - mpfr_add_ui (t, te, 1, MPFR_RNDD); /* exp(2x) + 1*/ - mpfr_sub_ui (te, te, 1, MPFR_RNDU); /* exp(2x) - 1*/ + mpfr_add_ui (t, te, 1, MPFR_RNDD); /* exp(2x) + 1 */ + mpfr_sub_ui (te, te, 1, MPFR_RNDU); /* exp(2x) - 1 */ d = d - MPFR_GET_EXP (te); - mpfr_div (t, te, t, MPFR_RNDN); /* (exp(2x)-1)/(exp(2x)+1)*/ + mpfr_div (t, te, t, MPFR_RNDN); /* (exp(2x)-1)/(exp(2x)+1) */ - /* Calculation of the error */ - d = MAX(3, d + 1); + /* Calculation of the error, see algorithms.tex */ + d = MAX(4, d + 2); err = Nt - (d + 1); if (MPFR_LIKELY ((d <= Nt / 2) && MPFR_CAN_ROUND (t, err, Ny, rnd_mode))) |