Add two new sets of fast quotient and remainder operators

* libguile/numbers.c (scm_euclidean_quo_and_rem, scm_euclidean_quotient,
  scm_euclidean_remainder, scm_centered_quo_and_rem,
  scm_centered_quotient, scm_centered_remainder): New extensible
  procedures `euclidean/', `euclidean-quotient', `euclidean-remainder',
  `centered/', `centered-quotient', `centered-remainder'.

* libguile/numbers.h: Add function prototypes.

* module/rnrs/base.scm: Remove incorrect stub implementations of `div',
  `mod', `div-and-mod', `div0', `mod0', and `div0-and-mod0'.  Instead do
  renaming imports of `euclidean-quotient', `euclidean-remainder',
  `euclidean/', `centered-quotient', `centered-remainder', and
  `centered/', which are equivalent to the R6RS operators.

* module/rnrs/arithmetic/fixnums.scm (fxdiv, fxmod, fxdiv-and-mod,
  fxdiv0, fxmod0, fxdiv0-and-mod0): Remove redundant checks for division
  by zero and unnecessary complexity.
  (fx+/carry): Remove unneeded calls to `inexact->exact'.

* module/rnrs/arithmetic/flonums.scm (fldiv, flmod, fldiv-and-mod,
  fldiv0, flmod0, fldiv0-and-mod0): Remove redundant checks for division
  by zero and unnecessary complexity.  Remove unneeded calls to
  `inexact->exact' and `exact->inexact'

* test-suite/tests/numbers.test: (test-eqv?): New internal predicate for
  comparing numerical outputs with expected values.

  Add extensive test code for `euclidean/', `euclidean-quotient',
  `euclidean-remainder', `centered/', `centered-quotient',
  `centered-remainder'.

* test-suite/tests/r6rs-arithmetic-fixnums.test: Fix some broken test
  cases, and remove `unresolved' test markers for `fxdiv', `fxmod',
  `fxdiv-and-mod', `fxdiv0', `fxmod0', and `fxdiv0-and-mod0'.

* test-suite/tests/r6rs-arithmetic-flonums.test: Remove `unresolved'
  test markers for `fldiv', `flmod', `fldiv-and-mod', `fldiv0',
  `flmod0', and `fldiv0-and-mod0'.

* doc/ref/api-data.texi (Arithmetic): Document `euclidean/',
  `euclidean-quotient', `euclidean-remainder', `centered/',
  `centered-quotient', and `centered-remainder'.

  (Operations on Integer Values): Add cross-references to `euclidean/'
  et al, from `quotient', `remainder', and `modulo'.

* doc/ref/r6rs.texi (rnrs base): Improve documentation for `div', `mod',
  `div-and-mod', `div0', `mod0', and `div0-and-mod0'.  Add
  cross-references to `euclidean/' et al.

* NEWS: Add NEWS entry.

1 files changed, 29 insertions, 0 deletions

diff --git a/NEWS b/NEWS
index f45795ed8..33e49a483 100644
--- a/NEWS
+++ b/NEWS
@@ -12,6 +12,29 @@ Changes in 1.9.15 (since the 1.9.14 prerelease):
 
 ** Changes and bugfixes in numerics code
 
+*** Added two new sets of fast quotient and remainder operators
+
+Added two new sets of fast quotient and remainder operator pairs with
+different semantics than the R5RS operators.  They support not only
+integers, but all reals, including exact rationals and inexact
+floating point numbers.
+
+These procedures accept two real numbers N and D, where the divisor D
+must be non-zero.  `euclidean-quotient' returns the integer Q and
+`euclidean-remainder' returns the real R such that N = Q*D + R and
+0 <= R < |D|.  `euclidean/' returns both Q and R, and is more
+efficient than computing each separately.  Note that when D > 0,
+`euclidean-quotient' returns floor(N/D), and when D < 0 it returns
+ceiling(N/D).
+
+`centered-quotient', `centered-remainder', and `centered/' are similar
+except that the range of remainders is -abs(D/2) <= R < abs(D/2), and
+`centered-quotient' rounds N/D to the nearest integer.
+
+Note that these operators are equivalent to the R6RS integer division
+operators `div', `mod', `div-and-mod', `div0', `mod0', and
+`div0-and-mod0'.
+
 *** `eqv?' and `equal?' now compare numbers equivalently
 
 scm_equal_p `equal?' now behaves equivalently to scm_eqv_p `eqv?' for
@@ -64,6 +87,12 @@ NaNs are neither finite nor infinite.
 
 *** R6RS base library changes
 
+**** `div', `mod', `div-and-mod', `div0', `mod0', `div0-and-mod0'
+
+Efficient versions of these R6RS division operators are now supported.
+See the NEWS entry entitled `Added two new sets of fast quotient and
+remainder operators' for more information.
+
 **** `infinite?' changes
 
 `infinite?' now returns #t for non-real complex infinities, and throws