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Re: cosl test failure
From: |
Paolo Bonzini |
Subject: |
Re: cosl test failure |
Date: |
Mon, 15 Mar 2010 07:53:20 +0100 |
On Sun, Mar 14, 2010 at 23:18, Bruno Haible <address@hidden> wrote:
> Hi Paolo,
>
> On 2010-01-18, in
> <http://lists.gnu.org/archive/html/bug-gnulib/2010-01/msg00256.html>,
> I observed that gnulib's cosl replacement function does not have the
> necessary accuracy. This was due to a wrong formula: The term
> sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1
> was being subtracted, when it should have been added.
I totally cannot recall, sorry. Thanks for fixing it, it was on my
todo list but you beat me.
Paolo
> Also, in this formula and the other one for sinl(), you omitted one of
> the five summands; I cannot see a reason why.
>
> This fixes it.
>
>
> 2010-03-14 Bruno Haible <address@hidden>
>
> Fix values returned by sinl, cosl.
> * lib/trigl.h: Add specification comments.
> * lib/sincosl.c (kernel_sinl, kernel_cosl): Fix comments and formula
> that combines the values from the precomputed table with the values of
> the Chebyshev polynomials.
>
> *** lib/trigl.h.orig Sun Mar 14 23:11:58 2010
> --- lib/trigl.h Sun Mar 14 22:14:54 2010
> ***************
> *** 18,24 ****
> You should have received a copy of the GNU General Public License
> along with this program. If not, see <http://www.gnu.org/licenses/>. */
>
> extern int ieee754_rem_pio2l (long double x, long double *y);
> extern long double kernel_sinl (long double x, long double y, int iy);
> - extern long double kernel_cosl (long double x, long double y);
>
> --- 18,35 ----
> You should have received a copy of the GNU General Public License
> along with this program. If not, see <http://www.gnu.org/licenses/>. */
>
> + /* Decompose x into x = k * π/2 + r
> + where k is an integer and abs(r) <= π/4.
> + Store r in y[0] and y[1] (main part in y[0], small additional part in
> + y[1], r = y[0] + y[1]).
> + Return k. */
> extern int ieee754_rem_pio2l (long double x, long double *y);
> +
> + /* Compute and return sinl (x + y), where x is the main part and y is the
> + small additional part of a floating-point number.
> + iy is 0 when y is known to be 0.0, otherwise iy is 1. */
> extern long double kernel_sinl (long double x, long double y, int iy);
>
> + /* Compute and return cosl (x + y), where x is the main part and y is the
> + small additional part of a floating-point number. */
> + extern long double kernel_cosl (long double x, long double y);
> *** lib/sincosl.c.orig Sun Mar 14 23:11:58 2010
> --- lib/sincosl.c Sun Mar 14 23:04:53 2010
> ***************
> *** 136,146 ****
> else
> {
> /* So that we don't have to use too large polynomial, we find
> ! l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
> ! possible values for h. We look up cosl(h) and sinl(h) in
> pre-computed tables, compute cosl(l) and sinl(l) using a
> Chebyshev polynomial of degree 10(11) and compute
> ! sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */
> x -= 0.1484375L;
> index = (int) (x * 128L + 0.5L);
> h = index / 128.0L;
> --- 136,147 ----
> else
> {
> /* So that we don't have to use too large polynomial, we find
> ! k and l such that x = k + l, where fabsl(l) <= 1.0/256 with 83
> ! possible values for k. We look up cosl(k) and sinl(k) in
> pre-computed tables, compute cosl(l) and sinl(l) using a
> Chebyshev polynomial of degree 10(11) and compute
> ! sinl(k+l) = sinl(k)cosl(l) + cosl(k)sinl(l).
> ! Furthermore write k = 0.1484375 + h. */
> x -= 0.1484375L;
> index = (int) (x * 128L + 0.5L);
> h = index / 128.0L;
> ***************
> *** 158,168 ****
> z * (SCOS1 + z * (SCOS2 + z * (SCOS3 + z * (SCOS4 + z * SCOS5))));
>
> index *= 4;
> z =
> ! sincosl_table[index + SINCOSL_SIN_HI] +
> ! (sincosl_table[index + SINCOSL_SIN_LO] +
> ! (sincosl_table[index + SINCOSL_SIN_HI] * cos_l_m1) +
> ! (sincosl_table[index + SINCOSL_COS_HI] * sin_l));
> return z * sign;
> }
> }
> --- 159,172 ----
> z * (SCOS1 + z * (SCOS2 + z * (SCOS3 + z * (SCOS4 + z * SCOS5))));
>
> index *= 4;
> + /* We rely on this expression not being "contracted" by the compiler
> + (cf. ISO C 99 section 6.5 paragraph 8). */
> z =
> ! sincosl_table[index + SINCOSL_SIN_HI]
> ! + (sincosl_table[index + SINCOSL_COS_HI] * sin_l
> ! + (sincosl_table[index + SINCOSL_SIN_HI] * cos_l_m1
> ! + (sincosl_table[index + SINCOSL_SIN_LO] * (1 + cos_l_m1)
> ! + sincosl_table[index + SINCOSL_COS_LO] * sin_l)));
> return z * sign;
> }
> }
> ***************
> *** 195,205 ****
> else
> {
> /* So that we don't have to use too large polynomial, we find
> ! l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
> ! possible values for h. We look up cosl(h) and sinl(h) in
> pre-computed tables, compute cosl(l) and sinl(l) using a
> Chebyshev polynomial of degree 10(11) and compute
> ! sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l). */
> x -= 0.1484375L;
> index = (int) (x * 128L + 0.5L);
> h = index / 128.0L;
> --- 199,210 ----
> else
> {
> /* So that we don't have to use too large polynomial, we find
> ! k and l such that x = k + l, where fabsl(l) <= 1.0/256 with 83
> ! possible values for k. We look up cosl(k) and sinl(k) in
> pre-computed tables, compute cosl(l) and sinl(l) using a
> Chebyshev polynomial of degree 10(11) and compute
> ! cosl(k+l) = cosl(k)cosl(l) - sinl(k)sinl(l).
> ! Furthermore write k = 0.1484375 + h. */
> x -= 0.1484375L;
> index = (int) (x * 128L + 0.5L);
> h = index / 128.0L;
> ***************
> *** 213,222 ****
> z * (SCOS1 + z * (SCOS2 + z * (SCOS3 + z * (SCOS4 + z * SCOS5))));
>
> index *= 4;
> ! z = sincosl_table [index + SINCOSL_COS_HI]
> ! + (sincosl_table [index + SINCOSL_COS_LO]
> ! - (sincosl_table [index + SINCOSL_SIN_HI] * sin_l)
> ! - (sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
> return z;
> }
> }
> --- 218,231 ----
> z * (SCOS1 + z * (SCOS2 + z * (SCOS3 + z * (SCOS4 + z * SCOS5))));
>
> index *= 4;
> ! /* We rely on this expression not being "contracted" by the compiler
> ! (cf. ISO C 99 section 6.5 paragraph 8). */
> ! z =
> ! sincosl_table [index + SINCOSL_COS_HI]
> ! - (sincosl_table [index + SINCOSL_SIN_HI] * sin_l
> ! - (sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1
> ! + (sincosl_table [index + SINCOSL_COS_LO] * (1 + cos_l_m1)
> ! - sincosl_table [index + SINCOSL_SIN_LO] * sin_l)));
> return z;
> }
> }
>
>