diff options
Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/log.c')
| -rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/log.c | 44 |
1 files changed, 32 insertions, 12 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/log.c b/Build/source/libs/mpfr/mpfr-src/src/log.c index 866ce86b3b8..7b61280b7c8 100644 --- a/Build/source/libs/mpfr/mpfr-src/src/log.c +++ b/Build/source/libs/mpfr/mpfr-src/src/log.c @@ -44,6 +44,7 @@ mpfr_log (mpfr_ptr r, mpfr_srcptr a, mpfr_rnd_t rnd_mode) int inexact; mpfr_prec_t p, q; mpfr_t tmp1, tmp2; + mpfr_exp_t exp_a; MPFR_SAVE_EXPO_DECL (expo); MPFR_ZIV_DECL (loop); MPFR_GROUP_DECL(group); @@ -83,18 +84,22 @@ mpfr_log (mpfr_ptr r, mpfr_srcptr a, mpfr_rnd_t rnd_mode) MPFR_ASSERTD (MPFR_IS_ZERO (a)); MPFR_SET_INF (r); MPFR_SET_NEG (r); - mpfr_set_divby0 (); + MPFR_SET_DIVBY0 (); MPFR_RET (0); /* log(0) is an exact -infinity */ } } + /* If a is negative, the result is NaN */ - else if (MPFR_UNLIKELY (MPFR_IS_NEG (a))) + if (MPFR_UNLIKELY (MPFR_IS_NEG (a))) { MPFR_SET_NAN (r); MPFR_RET_NAN; } - /* If a is 1, the result is 0 */ - else if (MPFR_UNLIKELY (MPFR_GET_EXP (a) == 1 && mpfr_cmp_ui (a, 1) == 0)) + + exp_a = MPFR_GET_EXP (a); + + /* If a is 1, the result is +0 */ + if (MPFR_UNLIKELY (exp_a == 1 && mpfr_cmp_ui (a, 1) == 0)) { MPFR_SET_ZERO (r); MPFR_SET_POS (r); @@ -103,8 +108,8 @@ mpfr_log (mpfr_ptr r, mpfr_srcptr a, mpfr_rnd_t rnd_mode) q = MPFR_PREC (r); - /* use initial precision about q+lg(q)+5 */ - p = q + 5 + 2 * MPFR_INT_CEIL_LOG2 (q); + /* use initial precision about q+2*lg(q)+cte */ + p = q + 2 * MPFR_INT_CEIL_LOG2 (q) + 10; /* % ~(mpfr_prec_t)GMP_NUMB_BITS ; m=q; while (m) { p++; m >>= 1; } */ /* if (MPFR_LIKELY(p % GMP_NUMB_BITS != 0)) @@ -116,13 +121,28 @@ mpfr_log (mpfr_ptr r, mpfr_srcptr a, mpfr_rnd_t rnd_mode) MPFR_ZIV_INIT (loop, p); for (;;) { - long m; + mpfr_exp_t m; mpfr_exp_t cancel; - /* Calculus of m (depends on p) */ - m = (p + 1) / 2 - MPFR_GET_EXP (a) + 1; + /* Calculus of m (depends on p) + If mpfr_exp_t has N bits, then both (p + 3) / 2 and |exp_a| fit + on N-2 bits, so that there cannot be an overflow. */ + m = (p + 3) / 2 - exp_a; + + /* In standard configuration (_MPFR_EXP_FORMAT <= 3), one has + mpfr_exp_t <= long, so that the following assertion is always + true. */ + MPFR_ASSERTN (m >= LONG_MIN && m <= LONG_MAX); + /* FIXME: Why 1 ulp and not 1/2 ulp? Ditto with some other ones + below. The error concerning the AGM should be explained since + 4/s is inexact (one needs a bound on its derivative). */ mpfr_mul_2si (tmp2, a, m, MPFR_RNDN); /* s=a*2^m, err<=1 ulp */ + MPFR_ASSERTD (MPFR_EXP (tmp2) >= (p + 3) / 2); + /* [FIXME] and one can have the equality, even if p is even. + This means that if a is a power of 2 and p is even, then + s = (1/2) * 2^((p+2)/2) = 2^(p/2), so that the condition + s > 2^(p/2) from algorithms.tex is not satisfied. */ mpfr_div (tmp1, __gmpfr_four, tmp2, MPFR_RNDN);/* 4/s, err<=2 ulps */ mpfr_agm (tmp2, __gmpfr_one, tmp1, MPFR_RNDN); /* AG(1,4/s),err<=3 ulps */ mpfr_mul_2ui (tmp2, tmp2, 1, MPFR_RNDN); /* 2*AG(1,4/s), err<=3 ulps */ @@ -143,19 +163,19 @@ mpfr_log (mpfr_ptr r, mpfr_srcptr a, mpfr_rnd_t rnd_mode) /* we have 7 ulps of error from the above roundings, 4 ulps from the 4/s^2 second order term, plus the canceled bits */ - if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp1, p-cancel-4, q, rnd_mode))) + if (MPFR_LIKELY (MPFR_CAN_ROUND (tmp1, p - cancel - 4, q, rnd_mode))) break; /* VL: I think it is better to have an increment that it isn't too low; in particular, the increment must be positive even if cancel = 0 (can this occur?). */ - p += cancel >= 8 ? cancel : 8; + p += cancel + MPFR_INT_CEIL_LOG2 (p); } else { /* TODO: find why this case can occur and what is best to do with it. */ - p += 32; + p += MPFR_INT_CEIL_LOG2 (p); } MPFR_ZIV_NEXT (loop, p); |