diff options
Diffstat (limited to 'src/cbrt.c')
| -rw-r--r-- | src/cbrt.c | 19 |
1 files changed, 8 insertions, 11 deletions
diff --git a/src/cbrt.c b/src/cbrt.c index 0536df4fe..c932e2f25 100644 --- a/src/cbrt.c +++ b/src/cbrt.c @@ -26,6 +26,9 @@ https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., /* The computation of y = x^(1/3) is done as follows. Let n = PREC(y), or PREC(y) + 1 if the rounding mode is MPFR_RNDN. + We seek to compute an integer cube root in precision n and the + associated inexact bit (non-zero iff the remainder is non-zero). + Let x = sign * m * 2^(3*e) where m is an integer >= 2^(3n-3), i.e. m has at least 3n-2 bits. @@ -34,23 +37,17 @@ https://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., TODO: Couldn't the size of m be fixed between 3n-2 and 3n? In the case where the initial size of m is > 3n, if a discarded bit was non-zero, - this could be remembered for the sticky bit. Said otherwise, discard + this could be remembered for the inexact bit. Said otherwise, discard 3k bits of the mpz_root argument instead of discarding k bits of its result (integer cube root). The constraint m >= 2^(3n-3) allows one to have sufficient precision for s: s >= 2^(n-1), i.e. s has at least n bits. - FIXME: The description below is incorrect if s has more than n bits - (since n is the target precision). Also, I don't understand the - last case (nearest) since 1 was added to PREC(y) to make it like - the directed rounding modes. - - Then x^(1/3) = s * 2^e if t = 0 - x^(1/3) = (s+1) * 2^e if round up - x^(1/3) = (s-1) * 2^e if round down - x^(1/3) = s * 2^e if nearest and t < 3/2*s^2+3/4*s+1/8 - (s+1) * 2^e otherwise + Let s' be s shifted to the right so that s' has exactly n bits. + Then |x|^(1/3) = s * 2^e or (s+1) * 2^e depending on the rounding mode, + the sign, and whether s' is inexact (t > 0 or some discarded bit in the + shift of s is non-zero). */ int |