diff options
Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/tanh.c')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/tanh.c | 88 |
1 files changed, 50 insertions, 38 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/tanh.c b/Build/source/libs/mpfr/mpfr-src/src/tanh.c index f220321ff75..5459ecfa4d7 100644 --- a/Build/source/libs/mpfr/mpfr-src/src/tanh.c +++ b/Build/source/libs/mpfr/mpfr-src/src/tanh.c @@ -84,7 +84,7 @@ mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode) For x > 0, exp(2*x) > 2^(2*x) If 2 ^(2*x) > 2^emax or x>emax/2, there is an overflow */ if (MPFR_UNLIKELY (mpfr_cmp_si (x, __gmpfr_emax/2) >= 0)) { - /* initialise of intermediary variables + /* initialize of intermediary variables since 'set_one' label assumes the variables have been initialize */ MPFR_GROUP_INIT_2 (group, MPFR_PREC_MIN, t, te); @@ -98,50 +98,62 @@ mpfr_tanh (mpfr_ptr y, mpfr_srcptr xt , mpfr_rnd_t rnd_mode) if (MPFR_GET_EXP (x) < 0) Nt += -MPFR_GET_EXP (x); - /* initialise of intermediary variable */ + /* 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 */ - /* since x > 0, we can only have an overflow */ - mpfr_exp (te, te, MPFR_RNDN); /* exp(2x) */ - if (MPFR_UNLIKELY (MPFR_IS_INF (te))) { - set_one: - inexact = MPFR_FROM_SIGN_TO_INT (sign); - mpfr_set4 (y, __gmpfr_one, MPFR_RNDN, sign); - if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG_SIGN (sign))) + for (;;) + { + /* tanh = (exp(2x)-1)/(exp(2x)+1) */ + 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))) { - inexact = -inexact; - mpfr_nexttozero (y); + set_one: + inexact = MPFR_FROM_SIGN_TO_INT (sign); + mpfr_set4 (y, __gmpfr_one, MPFR_RNDN, sign); + if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG_SIGN (sign))) + { + inexact = -inexact; + mpfr_nexttozero (y); + } + 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 */ + d = d - MPFR_GET_EXP (te); + mpfr_div (t, te, t, MPFR_RNDN); /* (exp(2x)-1)/(exp(2x)+1) */ + + /* Calculation of the error, see algorithms.tex; the current value + of d is k in algorithms.tex. */ + d = MAX(3, d + 1); /* d = exponent in 2^(max(3,k+1)) */ + err = Nt - (d + 1); + + /* The inequality is the condition max(3,k+1) <= floor(p/2). */ + if (MPFR_LIKELY (d <= Nt / 2 && + MPFR_CAN_ROUND (t, err, Ny, rnd_mode))) + { + inexact = mpfr_set4 (y, t, rnd_mode, sign); + break; } - 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*/ - d = d - MPFR_GET_EXP (te); - mpfr_div (t, te, t, MPFR_RNDN); /* (exp(2x)-1)/(exp(2x)+1)*/ - - /* Calculation of the error */ - d = MAX(3, d + 1); - err = Nt - (d + 1); - - if (MPFR_LIKELY ((d <= Nt / 2) && MPFR_CAN_ROUND (t, err, Ny, rnd_mode))) - { - inexact = mpfr_set4 (y, t, rnd_mode, sign); - break; - } - /* if t=1, we still can round since |sinh(x)| < 1 */ - if (MPFR_GET_EXP (t) == 1) - goto set_one; + /* if t=1, we still can round since |sinh(x)| < 1 */ + if (MPFR_GET_EXP (t) == 1) + goto set_one; - /* Actualisation of the precision */ - MPFR_ZIV_NEXT (loop, Nt); - MPFR_GROUP_REPREC_2 (group, Nt, t, te); - } + /* Actualisation of the precision */ + MPFR_ZIV_NEXT (loop, Nt); + MPFR_GROUP_REPREC_2 (group, Nt, t, te); + } MPFR_ZIV_FREE (loop); MPFR_GROUP_CLEAR (group); } |