(math-besJ0,math-besJ1,math-besY0,math-besY1,math-bernoulli-b-cache):

Use math-read-number to insert bignums.
author: Jay Belanger 2007-06-22 05:45:52 +0000
committer: Jay Belanger 2007-06-22 05:45:52 +0000
commit: a8775b6dcf9bcf193fe040b2eb9c7825e9c370c1 (patch)
tree: c8dc77c0f0f9598e232ee4950f071bf835ffca7c
parent: 3b6d80bc94a396997cdeab4706fa3373a6cc9fb5 (diff)
download: emacs-a8775b6dcf9bcf193fe040b2eb9c7825e9c370c1.tar.gz
emacs-a8775b6dcf9bcf193fe040b2eb9c7825e9c370c1.zip
1 files changed, 143 insertions, 87 deletions
diff --git a/lisp/calc/calc-funcs.el b/lisp/calc/calc-funcs.el
index 479116b0c76..00cadf69920 100644
--- a/lisp/calc/calc-funcs.el
+++ b/lisp/calc/calc-funcs.el
@@ -567,42 +567,54 @@
        ((Math-lessp '(float 8 0) (math-abs-approx x))
         (let* ((z (math-div '(float 8 0) x))
                (y (math-sqr z))
-                (xx (math-add x '(float (bigneg 164 398 785) -9)))
+                (xx (math-add x 
+                              (eval-when-compile
+                                (math-read-number-simple "-0.785398164"))))
                (a1 (math-poly-eval y
-                                    '((float (bigpos 211 887 093 2) -16)
+                        (eval-when-compile
-                                      (float (bigneg 639 370 073 2) -15)
+                          (list
-                                      (float (bigpos 407 510 734 2) -14)
+                           (math-read-number-simple "0.0000002093887211")
-                                      (float (bigneg 627 628 098 1) -12)
+                           (math-read-number-simple "-0.000002073370639")
-                                      (float 1 0))))
+                           (math-read-number-simple "0.00002734510407")
+                           (math-read-number-simple "-0.001098628627")
+                           '(float 1 0)))))
                (a2 (math-poly-eval y
-                                    '((float (bigneg 152 935 934) -16)
+                         (eval-when-compile
-                                      (float (bigpos 161 095 621 7) -16)
+                           (list
-                                      (float (bigneg 651 147 911 6) -15)
+                            (math-read-number-simple "-0.0000000934935152")
-                                      (float (bigpos 765 488 430 1) -13)
+                            (math-read-number-simple "0.0000007621095161")
-                                      (float (bigneg 995 499 562 1) -11))))
+                            (math-read-number-simple "-0.000006911147651")
+                            (math-read-number-simple "0.0001430488765")
+                            (math-read-number-simple "-0.01562499995")))))
                (sc (math-sin-cos-raw xx)))
               (if yflag
                   (setq sc (cons (math-neg (cdr sc)) (car sc))))
               (math-mul (math-sqrt
-                          (math-div '(float (bigpos 722 619 636) -9) x))
+                          (math-div (eval-when-compile
+                                      (math-read-number-simple "0.636619722"))
+ x))
                         (math-sub (math-mul (cdr sc) a1)
                                   (math-mul (car sc) (math-mul z a2))))))
         (t
          (let ((y (math-sqr x)))
            (math-div (math-poly-eval y
-                                      '((float (bigneg 456 052 849 1) -7)
+                            (eval-when-compile
-                                        (float (bigpos 017 233 739 7) -5)
+                              (list
-                                        (float (bigneg 418 442 121 1) -2)
+                               (math-read-number "-184.9052456")
-                                        (float (bigpos 407 196 516 6) -1)
+                               (math-read-number "77392.33017")
-                                        (float (bigneg 354 590 362 13) 0)
+                               (math-read-number "-11214424.18")
-                                        (float (bigpos 574 490 568 57) 0)))
+                               (math-read-number "651619640.7")
+                               (math-read-number "-13362590354.0")
+                               (math-read-number "57568490574.0"))))
                      (math-poly-eval y
-                                      '((float 1 0)
+                             (eval-when-compile
-                                        (float (bigpos 712 532 678 2) -7)
+                               (list
-                                        (float (bigpos 853 264 927 5) -5)
+                                '(float 1 0)
-                                        (float (bigpos 718 680 494 9) -3)
+                                (math-read-number "267.8532712")
-                                        (float (bigpos 985 532 029 1) 0)
+                                (math-read-number "59272.64853")
-                                        (float (bigpos 411 490 568 57) 0))))))))
+                                (math-read-number "9494680.718")
+                                (math-read-number "1029532985.0")
+                                (math-read-number "57568490411.0")))))))))
 (defun math-besJ1 (x &optional yflag)
  (cond ((and (math-negp (calcFunc-re x)) (not yflag))
@@ -610,25 +622,33 @@
        ((Math-lessp '(float 8 0) (math-abs-approx x))
         (let* ((z (math-div '(float 8 0) x))
                (y (math-sqr z))
-                (xx (math-add x '(float (bigneg 491 194 356 2) -9)))
+                (xx (math-add x (eval-when-compile 
+                                  (math-read-number "-2.356194491"))))
                (a1 (math-poly-eval y
-                                    '((float (bigneg 019 337 240) -15)
+                            (eval-when-compile
-                                      (float (bigpos 174 520 457 2) -15)
+                              (list
-                                      (float (bigneg 496 396 516 3) -14)
+                               (math-read-number "-0.000000240337019")
-                                      (float 183105 -8)
+                               (math-read-number "0.000002457520174")
-                                      (float 1 0))))
+                               (math-read-number "-0.00003516396496")
+                               '(float 183105 -8)
+                               '(float 1 0)))))
                (a2 (math-poly-eval y
-                                    '((float (bigpos 412 787 105) -15)
+                             (eval-when-compile
-                                      (float (bigneg 987 228 88) -14)
+                               (list
-                                      (float (bigpos 096 199 449 8) -15)
+                                (math-read-number "0.000000105787412")
-                                      (float (bigneg 873 690 002 2) -13)
+                                (math-read-number "-0.00000088228987")
-                                      (float (bigpos 995 499 687 4) -11))))
+                                (math-read-number "0.000008449199096")
+                                (math-read-number "-0.0002002690873")
+                                (math-read-number "0.04687499995")))))
                (sc (math-sin-cos-raw xx)))
           (if yflag
               (setq sc (cons (math-neg (cdr sc)) (car sc)))
             (if (math-negp x)
                 (setq sc (cons (math-neg (car sc)) (math-neg (cdr sc))))))
-           (math-mul (math-sqrt (math-div '(float (bigpos 722 619 636) -9) x))
+           (math-mul (math-sqrt (math-div 
+                                 (eval-when-compile
+                                   (math-read-number "0.636619722"))
+                                 x))
                     (math-sub (math-mul (cdr sc) a1)
                               (math-mul (car sc) (math-mul z a2))))))
        (t
@@ -636,20 +656,23 @@
           (math-mul
            x
            (math-div (math-poly-eval y
-                                      '((float (bigneg 606 036 016 3) -8)
+                             (eval-when-compile
-                                        (float (bigpos 826 044 157) -4)
+                               (list
-                                        (float (bigneg 439 611 972 2) -3)
+                                (math-read-number "-30.16036606")
-                                        (float (bigpos 531 968 423 2) -1)
+                                (math-read-number "15704.4826")
-                                        (float (bigneg 235 059 895 7) 0)
+                                (math-read-number "-2972611.439")
-                                        (float (bigpos 232 614 362 72) 0)))
+                                (math-read-number "242396853.1")
+                                (math-read-number "-7895059235.0")
+                                (math-read-number "72362614232.0"))))
                      (math-poly-eval y
-                                      '((float 1 0)
+                              (eval-when-compile
-                                        (float (bigpos 397 991 769 3) -7)
+                                (list
-                                        (float (bigpos 394 743 944 9) -5)
+                                 '(float 1 0)
-                                        (float (bigpos 474 330 858 1) -2)
+                                 (math-read-number "376.9991397")
-                                        (float (bigpos 178 535 300 2) 0)
+                                 (math-read-number "99447.43394")
-                                        (float (bigpos 442 228 725 144)
+                                 (math-read-number "18583304.74")
-                                               0)))))))))
+                                 (math-read-number "2300535178.0")
+                                 (math-read-number "144725228442.0"))))))))))
 (defun calcFunc-besY (v x)
  (math-inexact-result)
@@ -690,20 +713,25 @@
         (let ((y (math-sqr x)))
           (math-add
            (math-div (math-poly-eval y
-                                      '((float (bigpos 733 622 284 2) -7)
+                            (eval-when-compile
-                                        (float (bigneg 757 792 632 8) -5)
+                              (list
-                                        (float (bigpos 129 988 087 1) -2)
+                               (math-read-number "228.4622733")
-                                        (float (bigneg 036 598 123 5) -1)
+                               (math-read-number "-86327.92757")
-                                        (float (bigpos 065 834 062 7) 0)
+                               (math-read-number "10879881.29")
-                                        (float (bigneg 389 821 957 2) 0)))
+                               (math-read-number "-512359803.6")
+                               (math-read-number "7062834065.0")
+                               (math-read-number "-2957821389.0"))))
                      (math-poly-eval y
-                                      '((float 1 0)
+                            (eval-when-compile
-                                        (float (bigpos 244 030 261 2) -7)
+                              (list
-                                        (float (bigpos 647 472 474) -4)
+                               '(float 1 0)
-                                        (float (bigpos 438 466 189 7) -3)
+                               (math-read-number "226.1030244")
-                                        (float (bigpos 648 499 452 7) -1)
+                               (math-read-number "47447.2647")
-                                        (float (bigpos 269 544 076 40) 0))))
+                               (math-read-number "7189466.438")
-            (math-mul '(float (bigpos 772 619 636) -9)
+                               (math-read-number "745249964.8")
+                               (math-read-number "40076544269.0")))))
+            (math-mul (eval-when-compile
+                        (math-read-number "0.636619772"))
                      (math-mul (math-besJ0 x) (math-ln-raw x))))))
        ((math-negp (calcFunc-re x))
         (math-add (math-besJ0 (math-neg x) t)
@@ -719,22 +747,26 @@
            (math-mul
             x
             (math-div (math-poly-eval y
-                                       '((float (bigpos 935 937 511 8) -6)
+                             (eval-when-compile
-                                         (float (bigneg 726 922 237 4) -3)
+                               (list
-                                         (float (bigpos 551 264 349 7) -1)
+                                (math-read-number "8511.937935")
-                                         (float (bigneg 139 438 153 5) 1)
+                                (math-read-number "-4237922.726")
-                                         (float (bigpos 439 527 127) 4)
+                                (math-read-number "734926455.1")
-                                         (float (bigneg 943 604 900 4) 3)))
+                                (math-read-number "-51534381390.0")
+                                (math-read-number "1275274390000.0")
+                                (math-read-number "-4900604943000.0"))))
                       (math-poly-eval y
-                                       '((float 1 0)
+                             (eval-when-compile
-                                         (float (bigpos 885 632 549 3) -7)
+                               (list
-                                         (float (bigpos 605 042 102) -3)
+                                '(float 1 0)
-                                         (float (bigpos 002 904 245 2) -2)
+                                (math-read-number "354.9632885")
-                                         (float (bigpos 367 650 733 3) 0)
+                                (math-read-number "102042.605")
-                                         (float (bigpos 664 419 244 4) 2)
+                                (math-read-number "22459040.02")
-                                         (float (bigpos 057 958 249) 5)))))
+                                (math-read-number "3733650367.0")
-            (math-mul '(float (bigpos 772 619 636) -9)
+                                (math-read-number "424441966400.0")
-                      (math-sub (math-mul (math-besJ1 x) (math-ln-raw x))
+                                (math-read-number "24995805700000.0"))))))
+            (math-mul (eval-when-compile (math-read-number "0.636619772"))
+                      (math-sub (math-mul (math-besJ1 x) (math-ln-raw x))
                                (math-div 1 x))))))
        ((math-negp (calcFunc-re x))
         (math-neg
@@ -799,16 +831,40 @@
                    (calcFunc-euler n '(float 5 -1)))
                (calcFunc-euler n '(frac 1 2))))))
-(defvar math-bernoulli-b-cache '((frac -174611
+(defvar math-bernoulli-b-cache 
-                                       (bigpos 0 200 291 698 662 857 802))
+  (eval-when-compile
-                                 (frac 43867 (bigpos 0 944 170 217 94 109 5))
+    (list
-                                 (frac -3617 (bigpos 0 880 842 622 670 10))
+     (list 'frac 
-                                 (frac 1 (bigpos 600 249 724 74))
+           -174611
-                                 (frac -691 (bigpos 0 368 674 307 1))
+           (math-read-number "802857662698291200000"))
-                                 (frac 1 (bigpos 160 900 47))
+     (list 'frac 
-                                 (frac -1 (bigpos 600 209 1))
+           43867 
-                                 (frac 1 30240) (frac -1 720)
+           (math-read-number "5109094217170944000"))
-                                 (frac 1 12) 1 ))
+     (list 'frac 
+           -3617 
+           (math-read-number "10670622842880000"))
+     (list 'frac 
+           1 
+           (math-read-number "74724249600"))
+     (list 'frac 
+           -691 
+           (math-read-number "1307674368000"))
+     (list 'frac 
+           1 
+           (math-read-number "47900160"))
+     (list 'frac 
+           -1 
+           (math-read-number "1209600"))
+     (list 'frac 
+           1 
+           30240) 
+     (list 'frac 
+           -1 
+           720)
+     (list 'frac 
+           1 
+           12) 
+     1 )))
 (defvar math-bernoulli-B-cache '((frac -174611 330) (frac 43867 798)
                                 (frac -3617 510) (frac 7 6) (frac -691 2730)
author	Jay Belanger	2007-06-22 05:45:52 +0000
committer	Jay Belanger	2007-06-22 05:45:52 +0000
commit	a8775b6dcf9bcf193fe040b2eb9c7825e9c370c1 (patch)
tree	c8dc77c0f0f9598e232ee4950f071bf835ffca7c
parent	3b6d80bc94a396997cdeab4706fa3373a6cc9fb5 (diff)
download	emacs-a8775b6dcf9bcf193fe040b2eb9c7825e9c370c1.tar.gz emacs-a8775b6dcf9bcf193fe040b2eb9c7825e9c370c1.zip

diff --git a/lisp/calc/calc-funcs.el b/lisp/calc/calc-funcs.el index 479116b0c76..00cadf69920 100644 --- a/lisp/calc/calc-funcs.el +++ b/lisp/calc/calc-funcs.el
@@ -567,42 +567,54 @@
567	((Math-lessp '(float 8 0) (math-abs-approx x))	567	((Math-lessp '(float 8 0) (math-abs-approx x))
568	(let* ((z (math-div '(float 8 0) x))	568	(let* ((z (math-div '(float 8 0) x))
569	(y (math-sqr z))	569	(y (math-sqr z))
570	(xx (math-add x '(float (bigneg 164 398 785) -9)))	570	(xx (math-add x
		571	(eval-when-compile
		572	(math-read-number-simple "-0.785398164"))))
571	(a1 (math-poly-eval y	573	(a1 (math-poly-eval y
572	'((float (bigpos 211 887 093 2) -16)	574	(eval-when-compile
573	(float (bigneg 639 370 073 2) -15)	575	(list
574	(float (bigpos 407 510 734 2) -14)	576	(math-read-number-simple "0.0000002093887211")
575	(float (bigneg 627 628 098 1) -12)	577	(math-read-number-simple "-0.000002073370639")
576	(float 1 0))))	578	(math-read-number-simple "0.00002734510407")
		579	(math-read-number-simple "-0.001098628627")
		580	'(float 1 0)))))
577	(a2 (math-poly-eval y	581	(a2 (math-poly-eval y
578	'((float (bigneg 152 935 934) -16)	582	(eval-when-compile
579	(float (bigpos 161 095 621 7) -16)	583	(list
580	(float (bigneg 651 147 911 6) -15)	584	(math-read-number-simple "-0.0000000934935152")
581	(float (bigpos 765 488 430 1) -13)	585	(math-read-number-simple "0.0000007621095161")
582	(float (bigneg 995 499 562 1) -11))))	586	(math-read-number-simple "-0.000006911147651")
		587	(math-read-number-simple "0.0001430488765")
		588	(math-read-number-simple "-0.01562499995")))))
583	(sc (math-sin-cos-raw xx)))	589	(sc (math-sin-cos-raw xx)))
584	(if yflag	590	(if yflag
585	(setq sc (cons (math-neg (cdr sc)) (car sc))))	591	(setq sc (cons (math-neg (cdr sc)) (car sc))))
586	(math-mul (math-sqrt	592	(math-mul (math-sqrt
587	(math-div '(float (bigpos 722 619 636) -9) x))	593	(math-div (eval-when-compile
		594	(math-read-number-simple "0.636619722"))
		595	x))
588	(math-sub (math-mul (cdr sc) a1)	596	(math-sub (math-mul (cdr sc) a1)
589	(math-mul (car sc) (math-mul z a2))))))	597	(math-mul (car sc) (math-mul z a2))))))
590	(t	598	(t
591	(let ((y (math-sqr x)))	599	(let ((y (math-sqr x)))
592	(math-div (math-poly-eval y	600	(math-div (math-poly-eval y
593	'((float (bigneg 456 052 849 1) -7)	601	(eval-when-compile
594	(float (bigpos 017 233 739 7) -5)	602	(list
595	(float (bigneg 418 442 121 1) -2)	603	(math-read-number "-184.9052456")
596	(float (bigpos 407 196 516 6) -1)	604	(math-read-number "77392.33017")
597	(float (bigneg 354 590 362 13) 0)	605	(math-read-number "-11214424.18")
598	(float (bigpos 574 490 568 57) 0)))	606	(math-read-number "651619640.7")
		607	(math-read-number "-13362590354.0")
		608	(math-read-number "57568490574.0"))))
599	(math-poly-eval y	609	(math-poly-eval y
600	'((float 1 0)	610	(eval-when-compile
601	(float (bigpos 712 532 678 2) -7)	611	(list
602	(float (bigpos 853 264 927 5) -5)	612	'(float 1 0)
603	(float (bigpos 718 680 494 9) -3)	613	(math-read-number "267.8532712")
604	(float (bigpos 985 532 029 1) 0)	614	(math-read-number "59272.64853")
605	(float (bigpos 411 490 568 57) 0))))))))	615	(math-read-number "9494680.718")
		616	(math-read-number "1029532985.0")
		617	(math-read-number "57568490411.0")))))))))
606		618
607	(defun math-besJ1 (x &optional yflag)	619	(defun math-besJ1 (x &optional yflag)
608	(cond ((and (math-negp (calcFunc-re x)) (not yflag))	620	(cond ((and (math-negp (calcFunc-re x)) (not yflag))
@@ -610,25 +622,33 @@
610	((Math-lessp '(float 8 0) (math-abs-approx x))	622	((Math-lessp '(float 8 0) (math-abs-approx x))
611	(let* ((z (math-div '(float 8 0) x))	623	(let* ((z (math-div '(float 8 0) x))
612	(y (math-sqr z))	624	(y (math-sqr z))
613	(xx (math-add x '(float (bigneg 491 194 356 2) -9)))	625	(xx (math-add x (eval-when-compile
		626	(math-read-number "-2.356194491"))))
614	(a1 (math-poly-eval y	627	(a1 (math-poly-eval y
615	'((float (bigneg 019 337 240) -15)	628	(eval-when-compile
616	(float (bigpos 174 520 457 2) -15)	629	(list
617	(float (bigneg 496 396 516 3) -14)	630	(math-read-number "-0.000000240337019")
618	(float 183105 -8)	631	(math-read-number "0.000002457520174")
619	(float 1 0))))	632	(math-read-number "-0.00003516396496")
		633	'(float 183105 -8)
		634	'(float 1 0)))))
620	(a2 (math-poly-eval y	635	(a2 (math-poly-eval y
621	'((float (bigpos 412 787 105) -15)	636	(eval-when-compile
622	(float (bigneg 987 228 88) -14)	637	(list
623	(float (bigpos 096 199 449 8) -15)	638	(math-read-number "0.000000105787412")
624	(float (bigneg 873 690 002 2) -13)	639	(math-read-number "-0.00000088228987")
625	(float (bigpos 995 499 687 4) -11))))	640	(math-read-number "0.000008449199096")
		641	(math-read-number "-0.0002002690873")
		642	(math-read-number "0.04687499995")))))
626	(sc (math-sin-cos-raw xx)))	643	(sc (math-sin-cos-raw xx)))
627	(if yflag	644	(if yflag
628	(setq sc (cons (math-neg (cdr sc)) (car sc)))	645	(setq sc (cons (math-neg (cdr sc)) (car sc)))
629	(if (math-negp x)	646	(if (math-negp x)
630	(setq sc (cons (math-neg (car sc)) (math-neg (cdr sc))))))	647	(setq sc (cons (math-neg (car sc)) (math-neg (cdr sc))))))
631	(math-mul (math-sqrt (math-div '(float (bigpos 722 619 636) -9) x))	648	(math-mul (math-sqrt (math-div
		649	(eval-when-compile
		650	(math-read-number "0.636619722"))
		651	x))
632	(math-sub (math-mul (cdr sc) a1)	652	(math-sub (math-mul (cdr sc) a1)
633	(math-mul (car sc) (math-mul z a2))))))	653	(math-mul (car sc) (math-mul z a2))))))
634	(t	654	(t
@@ -636,20 +656,23 @@
636	(math-mul	656	(math-mul
637	x	657	x
638	(math-div (math-poly-eval y	658	(math-div (math-poly-eval y
639	'((float (bigneg 606 036 016 3) -8)	659	(eval-when-compile
640	(float (bigpos 826 044 157) -4)	660	(list
641	(float (bigneg 439 611 972 2) -3)	661	(math-read-number "-30.16036606")
642	(float (bigpos 531 968 423 2) -1)	662	(math-read-number "15704.4826")
643	(float (bigneg 235 059 895 7) 0)	663	(math-read-number "-2972611.439")
644	(float (bigpos 232 614 362 72) 0)))	664	(math-read-number "242396853.1")
		665	(math-read-number "-7895059235.0")
		666	(math-read-number "72362614232.0"))))
645	(math-poly-eval y	667	(math-poly-eval y
646	'((float 1 0)	668	(eval-when-compile
647	(float (bigpos 397 991 769 3) -7)	669	(list
648	(float (bigpos 394 743 944 9) -5)	670	'(float 1 0)
649	(float (bigpos 474 330 858 1) -2)	671	(math-read-number "376.9991397")
650	(float (bigpos 178 535 300 2) 0)	672	(math-read-number "99447.43394")
651	(float (bigpos 442 228 725 144)	673	(math-read-number "18583304.74")
652	0)))))))))	674	(math-read-number "2300535178.0")
		675	(math-read-number "144725228442.0"))))))))))
653		676
654	(defun calcFunc-besY (v x)	677	(defun calcFunc-besY (v x)
655	(math-inexact-result)	678	(math-inexact-result)
@@ -690,20 +713,25 @@
690	(let ((y (math-sqr x)))	713	(let ((y (math-sqr x)))
691	(math-add	714	(math-add
692	(math-div (math-poly-eval y	715	(math-div (math-poly-eval y
693	'((float (bigpos 733 622 284 2) -7)	716	(eval-when-compile
694	(float (bigneg 757 792 632 8) -5)	717	(list
695	(float (bigpos 129 988 087 1) -2)	718	(math-read-number "228.4622733")
696	(float (bigneg 036 598 123 5) -1)	719	(math-read-number "-86327.92757")
697	(float (bigpos 065 834 062 7) 0)	720	(math-read-number "10879881.29")
698	(float (bigneg 389 821 957 2) 0)))	721	(math-read-number "-512359803.6")
		722	(math-read-number "7062834065.0")
		723	(math-read-number "-2957821389.0"))))
699	(math-poly-eval y	724	(math-poly-eval y
700	'((float 1 0)	725	(eval-when-compile
701	(float (bigpos 244 030 261 2) -7)	726	(list
702	(float (bigpos 647 472 474) -4)	727	'(float 1 0)
703	(float (bigpos 438 466 189 7) -3)	728	(math-read-number "226.1030244")
704	(float (bigpos 648 499 452 7) -1)	729	(math-read-number "47447.2647")
705	(float (bigpos 269 544 076 40) 0))))	730	(math-read-number "7189466.438")
706	(math-mul '(float (bigpos 772 619 636) -9)	731	(math-read-number "745249964.8")
		732	(math-read-number "40076544269.0")))))
		733	(math-mul (eval-when-compile
		734	(math-read-number "0.636619772"))
707	(math-mul (math-besJ0 x) (math-ln-raw x))))))	735	(math-mul (math-besJ0 x) (math-ln-raw x))))))
708	((math-negp (calcFunc-re x))	736	((math-negp (calcFunc-re x))
709	(math-add (math-besJ0 (math-neg x) t)	737	(math-add (math-besJ0 (math-neg x) t)
@@ -719,22 +747,26 @@
719	(math-mul	747	(math-mul
720	x	748	x
721	(math-div (math-poly-eval y	749	(math-div (math-poly-eval y
722	'((float (bigpos 935 937 511 8) -6)	750	(eval-when-compile
723	(float (bigneg 726 922 237 4) -3)	751	(list
724	(float (bigpos 551 264 349 7) -1)	752	(math-read-number "8511.937935")
725	(float (bigneg 139 438 153 5) 1)	753	(math-read-number "-4237922.726")
726	(float (bigpos 439 527 127) 4)	754	(math-read-number "734926455.1")
727	(float (bigneg 943 604 900 4) 3)))	755	(math-read-number "-51534381390.0")
		756	(math-read-number "1275274390000.0")
		757	(math-read-number "-4900604943000.0"))))
728	(math-poly-eval y	758	(math-poly-eval y
729	'((float 1 0)	759	(eval-when-compile
730	(float (bigpos 885 632 549 3) -7)	760	(list
731	(float (bigpos 605 042 102) -3)	761	'(float 1 0)
732	(float (bigpos 002 904 245 2) -2)	762	(math-read-number "354.9632885")
733	(float (bigpos 367 650 733 3) 0)	763	(math-read-number "102042.605")
734	(float (bigpos 664 419 244 4) 2)	764	(math-read-number "22459040.02")
735	(float (bigpos 057 958 249) 5)))))	765	(math-read-number "3733650367.0")
736	(math-mul '(float (bigpos 772 619 636) -9)	766	(math-read-number "424441966400.0")
737	(math-sub (math-mul (math-besJ1 x) (math-ln-raw x))	767	(math-read-number "24995805700000.0"))))))
		768	(math-mul (eval-when-compile (math-read-number "0.636619772"))
		769	(math-sub (math-mul (math-besJ1 x) (math-ln-raw x))
738	(math-div 1 x))))))	770	(math-div 1 x))))))
739	((math-negp (calcFunc-re x))	771	((math-negp (calcFunc-re x))
740	(math-neg	772	(math-neg
@@ -799,16 +831,40 @@
799	(calcFunc-euler n '(float 5 -1)))	831	(calcFunc-euler n '(float 5 -1)))
800	(calcFunc-euler n '(frac 1 2))))))	832	(calcFunc-euler n '(frac 1 2))))))
801		833
802	(defvar math-bernoulli-b-cache '((frac -174611	834	(defvar math-bernoulli-b-cache
803	(bigpos 0 200 291 698 662 857 802))	835	(eval-when-compile
804	(frac 43867 (bigpos 0 944 170 217 94 109 5))	836	(list
805	(frac -3617 (bigpos 0 880 842 622 670 10))	837	(list 'frac
806	(frac 1 (bigpos 600 249 724 74))	838	-174611
807	(frac -691 (bigpos 0 368 674 307 1))	839	(math-read-number "802857662698291200000"))
808	(frac 1 (bigpos 160 900 47))	840	(list 'frac
809	(frac -1 (bigpos 600 209 1))	841	43867
810	(frac 1 30240) (frac -1 720)	842	(math-read-number "5109094217170944000"))
811	(frac 1 12) 1 ))	843	(list 'frac
		844	-3617
		845	(math-read-number "10670622842880000"))
		846	(list 'frac
		847	1
		848	(math-read-number "74724249600"))
		849	(list 'frac
		850	-691
		851	(math-read-number "1307674368000"))
		852	(list 'frac
		853	1
		854	(math-read-number "47900160"))
		855	(list 'frac
		856	-1
		857	(math-read-number "1209600"))
		858	(list 'frac
		859	1
		860	30240)
		861	(list 'frac
		862	-1
		863	720)
		864	(list 'frac
		865	1
		866	12)
		867	1 )))
812		868
813	(defvar math-bernoulli-B-cache '((frac -174611 330) (frac 43867 798)	869	(defvar math-bernoulli-B-cache '((frac -174611 330) (frac 43867 798)
814	(frac -3617 510) (frac 7 6) (frac -691 2730)	870	(frac -3617 510) (frac 7 6) (frac -691 2730)