* lib/expl.c: Fix an ambiguous comment.
* lib/expm1.c: Likewise.
* lib/expm1l.c: Likewise.
* lib/exp2.c: Likewise.
* lib/exp2l.c: Likewise.
+2012-03-10 Bruno Haible <bruno@clisp.org>
+
+ Fix some comments.
+ * lib/expl.c: Fix an ambiguous comment.
+ * lib/expm1.c: Likewise.
+ * lib/expm1l.c: Likewise.
+ * lib/exp2.c: Likewise.
+ * lib/exp2l.c: Likewise.
+
2012-03-10 Paul Eggert <eggert@cs.ucla.edu>
regex: allow inclusion of <regex.h> before <limits.h>
+ 21844/6081075 * z^13
- 929569/638512875 * z^15
+ ...
- Since |z| <= log(2)/1024 < 0.0007, the relative error of the z^7 term
- is < 0.0007^6 < 2^-60 <= 2^-DBL_MANT_DIG, therefore we can truncate
- the series after the z^5 term. */
+ Since |z| <= log(2)/1024 < 0.0007, the relative contribution of the
+ z^7 term is < 0.0007^6 < 2^-60 <= 2^-DBL_MANT_DIG, therefore we can
+ truncate the series after the z^5 term. */
{
double nm = round (x * 256.0); /* = 256 * n + m */
+ 21844/6081075 * z^13
- 929569/638512875 * z^15
+ ...
- Since |z| <= log(2)/1024 < 0.0007, the relative error of the z^13 term
- is < 0.0007^12 < 2^-120 <= 2^-LDBL_MANT_DIG, therefore we can truncate
- the series after the z^11 term. */
+ Since |z| <= log(2)/1024 < 0.0007, the relative contribution of the
+ z^13 term is < 0.0007^12 < 2^-120 <= 2^-LDBL_MANT_DIG, therefore we
+ can truncate the series after the z^11 term. */
{
long double nm = roundl (x * 256.0L); /* = 256 * n + m */
+ 21844/6081075 * z^13
- 929569/638512875 * z^15
+ ...
- Since |z| <= log(2)/1024 < 0.0007, the relative error of the z^13 term
- is < 0.0007^12 < 2^-120 <= 2^-LDBL_MANT_DIG, therefore we can truncate
- the series after the z^11 term.
+ Since |z| <= log(2)/1024 < 0.0007, the relative contribution of the
+ z^13 term is < 0.0007^12 < 2^-120 <= 2^-LDBL_MANT_DIG, therefore we
+ can truncate the series after the z^11 term.
Given the usual bounds LDBL_MAX_EXP <= 16384, LDBL_MIN_EXP >= -16381,
LDBL_MANT_DIG <= 120, we can estimate x: -11440 <= x <= 11357.
+ 21844/6081075 * z^13
- 929569/638512875 * z^15
+ ...
- Since |z| <= log(2)/1024 < 0.0007, the relative error of the z^7 term
- is < 0.0007^6 < 2^-60 <= 2^-DBL_MANT_DIG, therefore we can truncate
- the series after the z^5 term.
+ Since |z| <= log(2)/1024 < 0.0007, the relative contribution of the
+ z^7 term is < 0.0007^6 < 2^-60 <= 2^-DBL_MANT_DIG, therefore we can
+ truncate the series after the z^5 term.
Given the usual bounds DBL_MAX_EXP <= 16384, DBL_MANT_DIG <= 120, we
can estimate x: -84 <= x <= 11357.
+ 21844/6081075 * z^13
- 929569/638512875 * z^15
+ ...
- Since |z| <= log(2)/1024 < 0.0007, the relative error of the z^13 term
- is < 0.0007^12 < 2^-120 <= 2^-LDBL_MANT_DIG, therefore we can truncate
- the series after the z^11 term.
+ Since |z| <= log(2)/1024 < 0.0007, the relative contribution of the
+ z^13 term is < 0.0007^12 < 2^-120 <= 2^-LDBL_MANT_DIG, therefore we
+ can truncate the series after the z^11 term.
Given the usual bounds LDBL_MAX_EXP <= 16384, LDBL_MANT_DIG <= 120, we
can estimate x: -84 <= x <= 11357.