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[Maxima-commits] [git] Maxima CAS branch master updated. branch-5_48-base-224-geb00d1358
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From: willisbl <wil...@us...> - 2025-10-13 19:18:52
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- Log -----------------------------------------------------------------
commit eb00d13582520edbf58aed89d2d4d7aeb9217236
Author: Barton Willis <wi...@un...>
Date: Mon Oct 13 14:18:39 2025 -0500
Fix #4614: correct atan2 reflection rule
- Fixed reflection rule conditional for atan2 in comm2.lisp
- Added new function atan2-to-atan in tlimit.lisp to convert atan2 expressions to atan expressions
- Incorporated tests from the bug report into rtest_atan2.mac
- Added additional bug report tests to rtest_limit_extra.mac
- Updated and corrected tests in rtest_trig.mac and rtest_abs_integrate.mac
Tested with SBCL 2.4.7 and Clozure CL 1.13; no unexpected failures in core or share test suites.
diff --git a/share/contrib/integration/rtest_abs_integrate.mac b/share/contrib/integration/rtest_abs_integrate.mac
index 9f79fcd7e..520d3dee4 100644
--- a/share/contrib/integration/rtest_abs_integrate.mac
+++ b/share/contrib/integration/rtest_abs_integrate.mac
@@ -551,9 +551,12 @@ radcan(subst(x=5,i) - subst(x=0,i) - integrate(sqrt(5),x,0,5));
/* abs_integrate causes stack overflow - ID: 3533723 */
integrate(log(sin(x)),x);
-x*log(sin(x)) -(x*log(sin(x)^2+cos(x)^2+2*cos(x)+1)+x*log(sin(x)^2+cos(x)^2
- -2*cos(x)+1)+2*%i*x*atan2(sin(x),cos(x)+1) -2*%i*x*atan2(sin(x),1 -cos(x))
- -2*%i*li[2](%e^(%i*x)) -2*%i*li[2]( -%e^(%i*x)) -%i*x^2)/(2)$
+x*log(sin(x))-(x*log(sin(x)^2+cos(x)^2+2*cos(x)+1)
+ +x*log(sin(x)^2+cos(x)^2-2*cos(x)+1)
+ +2*%i*x*atan2(sin(x),cos(x)+1)
+ +2*%i*x*atan2(-sin(x),1-cos(x))-%i*x^2
+ -2*%i*li[2](%e^(%i*x))-2*%i*li[2](-%e^(%i*x)))
+ /2$
/* SF bug #2557: "abs_integrate leaks assumptions into enclosing context" */
@@ -596,8 +599,12 @@ expand(integrate(x*ceiling(x)*floor(x),x));
/* see SF bug 2853*/
integrate(log(abs(sin(x))),x);
- x*log(abs(sin(x)))-(x*log(sin(x)^2+cos(x)^2+2*cos(x)+1) +x*log(sin(x)^2+cos(x)^2-2*cos(x)+1)
- +2*%i*x*atan2(sin(x),cos(x)+1) -2*%i*x*atan2(sin(x),1-cos(x))-2*%i*li[2](%e^(%i*x))-2*%i*li[2](-%e^(%i*x))-%i*x^2)/2$
+x*log(abs(sin(x)))-(x*log(sin(x)^2+cos(x)^2+2*cos(x)+1)
+ +x*log(sin(x)^2+cos(x)^2-2*cos(x)+1)
+ +2*%i*x*atan2(sin(x),cos(x)+1)
+ +2*%i*x*atan2(-sin(x),1-cos(x))-%i*x^2
+ -2*%i*li[2](%e^(%i*x))-2*%i*li[2](-%e^(%i*x)))
+ /2$
block([ans : integrate(log(abs(sin(x))),x,0,%pi/2)], [ans, expand(ans)]);
[-((6*%pi*log(2)-%i*%pi^2)/12)-(%i*%pi^2)/12,-((%pi*log(2))/2)]$
diff --git a/src/comm2.lisp b/src/comm2.lisp
index 2af9828f3..88550c7de 100644
--- a/src/comm2.lisp
+++ b/src/comm2.lisp
@@ -681,12 +681,10 @@ the hashtable.")
($logarc
(logarc '%atan2 (list ($logarc y) ($logarc x))))
;; atan2(-y,x) = -atan2(y,x) provided (a) trigsign is true, (b) (great (neg y) y), and
- ;; (c) (x,y) is off the negative real axis. The test for (x,y) off the negative
- ;; real axis should be (or (eq t (mnqp y 0)) (eq t (mgrp x 0))), but that causes
- ;; one testsuite failure, so we'll test using (or (not (eql y 0)) (eq signx '$pos)))
+ ;; (c) (x,y) is off the negative real axis.
((and $trigsign
(eq t (mminusp y))
- (or (not (eql y 0)) (eq signx '$pos)))
+ (or (eq t (mnqp y 0)) (eq t (mgrp x 0))))
(neg (ftake '%atan2 (neg y) x)))
((eq signx '$pos)
;; atan2(y,x) = atan(y/x) when x is positive.
diff --git a/src/tlimit.lisp b/src/tlimit.lisp
index ede8e7627..1c5bf916c 100644
--- a/src/tlimit.lisp
+++ b/src/tlimit.lisp
@@ -61,6 +61,23 @@
(logarc '%atan2 (list (logarc-atan2 (second e)) (logarc-atan2 (third e)))))
(t (recur-apply #'logarc-atan2 e))))
+(defun atan2-to-atan (e)
+ "In the expression `e`, replace all subexpressions of the form atan2(y,x), where y is not explicitly equal to
+ zero, by 2*atan((sqrt(x^2+y^2) - x)/y). The input `e` should be simplified--that way, the general simplifier
+ handles the error case of atan2(0,0) and many other cases as well. "
+ (cond (($mapatom e) e)
+ ((and (consp e) (eq '%atan2 (caar e)))
+ (let ((y (second e)) (x (third e)))
+ (if (zerop1 y)
+ e
+ (mul 2 (ftake '%atan (div (sub (ftake 'mexpt (add (mul x x) (mul y y)) (div 1 2)) x) y))))))
+ (($subvarp (mop e)) ;subscripted function
+ (subfunmake
+ (subfunname e)
+ (subfunsubs e) ;don't map fun onto the operator subscripts
+ (mapcar #'atan2-to-atan (subfunargs e)))) ; map onto the arguments
+ (t (fapply (caar e) (mapcar #'atan2-to-atan (cdr e))))))
+
;; Dispatch Taylor, but recurse on the order until either the recursion
;; depth reaches 15 or the Taylor polynomial is nonzero. If Taylor
;; fails to find a nonzero Taylor polynomial or the recursion depth
@@ -96,12 +113,12 @@
($taylordepth 8)
($radexpand nil)
($taylor_logexpand t)
- ($logexpand t))
+ ($logexpand nil))
(cond
((eq pt '$infinity) nil)
(t
- (setq e (logarc-atan2 e))
+ (setq e (atan2-to-atan e))
(setq ee (catch 'taylor-catch ($totaldisrep ($taylor e x pt n))))
(cond
((and ee (not (eql ee 0))) ee)
diff --git a/tests/rtest_atan2.mac b/tests/rtest_atan2.mac
index d03ed4332..e7a1cb197 100644
--- a/tests/rtest_atan2.mac
+++ b/tests/rtest_atan2.mac
@@ -244,9 +244,20 @@ integrate(sin(t)*atan2(2*sin(t),1-2*cos(t)),t,0,%pi);
integrate(atan2(sin(x), cos(x)), x, 0, 9*%pi);
%pi^2/2$
-(kill(values),0);
+/*\#4614 atan2 reflection rule*/
+block([trigsign : true], subst([x=-1,y=0], atan2(-y,x) + atan2(y,x)));
+2*%pi$
+
+block([trigsign : true,ans],
+ assume(notequal(y,0)),
+ ans : 0,
+ forget(notequal(y,0)),
+ ans);
0$
+(kill(values),0);
+0$
+
facts();
[]$
diff --git a/tests/rtest_limit_extra.mac b/tests/rtest_limit_extra.mac
index ef74f8c33..56c32a3d0 100644
--- a/tests/rtest_limit_extra.mac
+++ b/tests/rtest_limit_extra.mac
@@ -1422,11 +1422,12 @@ log(tan(x)^2+1)+2*%i*li[2](-((%i*((%i+1)*tan(x)+%i-1))/2))+2*%i*li[2](%i*tan(x)+
-2*%i*li[2](-((%i*((%i-1)*tan(x)+%i+1))/2))-4*x*log(tan(x)))/4, 0);
0$
-limit(xxx,x,%pi/4,'minus);
- (4*%i*log(2)*log(sqrt(2)*%i+sqrt(2))-4*%i*log(2)^2+%pi*log(2)+8*%catalan)/8$
+/* see \#4614 atan2 reflection rule*/
+[trigsimp(block([trigsign : false], limit(xxx,x,%pi/4,'minus))), block([trigsign : true], limit(xxx,x,%pi/4,'minus))];
+[%catalan,%catalan]$
-limit(xxx,x,%pi/4,'plus);
--((4*%i*log(2)*log(sqrt(2)*%i-sqrt(2))-4*%i*log(2)^2-%pi*log(2)-2*%i*%pi^2-8*%catalan)/8)$
+[block([trigsign : false], limit(xxx,x,%pi/4,'plus)), block([trigsign : true], limit(xxx,x,%pi/4,'plus))];
+[-((-(4*%pi*log(2))-2*%i*%pi^2-8*%catalan)/8), -((-(4*%pi*log(2))-2*%i*%pi^2-8*%catalan)/8)]$
(remvalue(xxx),0);
0$
diff --git a/tests/rtest_trig.mac b/tests/rtest_trig.mac
index f32ebb373..29ce548f6 100644
--- a/tests/rtest_trig.mac
+++ b/tests/rtest_trig.mac
@@ -615,14 +615,19 @@ done;
acoth (x);
/* SF bug #2620: "atan2(y,x)+atan2(-y,x) doesn't always return 0 " */
+block([ans,trigsign : true],
+ kill(x,y),
+ assume(notequal(y,0)),
+ ans : atan2(y,x)+atan2(-y,x),
+ forget(notequal(y,0)),
+ ans);
+0$
-(kill (x, y), atan2(y,x)+atan2(-y,x));
-0;
-(assume (y > 0), atan2(y,x)+atan2(-y,x));
+(assume (y > 0), block([trigsign : true], atan2(y,x)+atan2(-y,x)));
0;
-(kill (n, p, r), forget (y > 0), assume(n<0,p>0), atan2 (- x, r));
+(kill (n, p, r), forget (y > 0), assume(n<0,p>0, notequal(x,0)), atan2 (- x, r));
- atan2 (x, r);
atan2 (-n, r);
@@ -631,8 +636,8 @@ atan2 (-n, r);
atan2 (-p, r);
- atan2 (p, r);
-forget (n < 0, p > 0);
-[n < 0, p > 0];
+forget (n < 0, p > 0,notequal(x,0));
+[n < 0, p > 0,notequal(x,0)];
/* mailing list 2017-11-27: "trigsimp fails with pderivop" */
-----------------------------------------------------------------------
Summary of changes:
share/contrib/integration/rtest_abs_integrate.mac | 17 ++++++++++++-----
src/comm2.lisp | 6 ++----
src/tlimit.lisp | 21 +++++++++++++++++++--
tests/rtest_atan2.mac | 13 ++++++++++++-
tests/rtest_limit_extra.mac | 9 +++++----
tests/rtest_trig.mac | 17 +++++++++++------
6 files changed, 61 insertions(+), 22 deletions(-)
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