X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Futils.cpp;h=5ac9a60f9bb75056923a253cae2e2679089defa4;hp=6b86740284946c815e3c3dbe6ee56aa613bd9929;hb=41e8c15b635c78bfbc677e7f1c00ce5f3ca97f1d;hpb=da64e515abf7243bc4c84ca3631470931c4e6691

diff --git a/ginac/utils.cpp b/ginac/utils.cpp
index 6b867402..5ac9a60f 100644
--- a/ginac/utils.cpp
+++ b/ginac/utils.cpp
@@ -4,7 +4,7 @@
  *  but not of any interest to the user of the library. */
 
 /*
- *  GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2020 Johannes Gutenberg University Mainz, Germany
  *
  *  This program is free software; you can redistribute it and/or modify
  *  it under the terms of the GNU General Public License as published by
@@ -53,6 +53,19 @@ unsigned log2(unsigned n)
 	return k;
 }
 
+/** Compute the multinomial coefficient n!/(p1!*p2!*...*pk!) where
+ *  n = p1+p2+...+pk, i.e. p is a partition of n.
+ */
+const numeric
+multinomial_coefficient(const std::vector<unsigned> & p)
+{
+	numeric n = 0, d = 1;
+	for (auto & it : p) {
+		n = n.add(numeric(it));
+		d = d.mul(factorial(numeric(it)));
+	}
+	return factorial(n).div(d);
+}
 
 //////////
 // flyweight chest of numbers is initialized here:
@@ -64,305 +77,306 @@ int library_init::count = 0;
 
 // static numeric -120
 const numeric *_num_120_p;
-const numeric &_num_120 = *_num_120_p;
-const ex _ex_120 = _num_120;
+const ex _ex_120 = _ex_120;
 
 // static numeric -60
 const numeric *_num_60_p;
-const numeric &_num_60 = *_num_60_p;
-const ex _ex_60 = _num_60;
+const ex _ex_60 = _ex_60;
 
 // static numeric -48
 const numeric *_num_48_p;
-const numeric &_num_48 = *_num_48_p;
-const ex _ex_48 = _num_48;
+const ex _ex_48 = _ex_48;
 
 // static numeric -30
 const numeric *_num_30_p;
-const numeric &_num_30 = *_num_30_p;
-const ex _ex_30 = _num_30;
+const ex _ex_30 = _ex_30;
 
 // static numeric -25
 const numeric *_num_25_p;
-const numeric &_num_25 = *_num_25_p;
-const ex _ex_25 = _num_25;
+const ex _ex_25 = _ex_25;
 
 // static numeric -24
 const numeric *_num_24_p;
-const numeric &_num_24 = *_num_24_p;
-const ex _ex_24 = _num_24;
+const ex _ex_24 = _ex_24;
 
 // static numeric -20
 const numeric *_num_20_p;
-const numeric &_num_20 = *_num_20_p;
-const ex _ex_20 = _num_20;
+const ex _ex_20 = _ex_20;
 
 // static numeric -18
 const numeric *_num_18_p;
-const numeric &_num_18 = *_num_18_p;
-const ex _ex_18 = _num_18;
+const ex _ex_18 = _ex_18;
 
 // static numeric -15
 const numeric *_num_15_p;
-const numeric &_num_15 = *_num_15_p;
-const ex _ex_15 = _num_15;
+const ex _ex_15 = _ex_15;
 
 // static numeric -12
 const numeric *_num_12_p;
-const numeric &_num_12 = *_num_12_p;
-const ex _ex_12 = _num_12;
+const ex _ex_12 = _ex_12;
 
 // static numeric -11
 const numeric *_num_11_p;
-const numeric &_num_11 = *_num_11_p;
-const ex _ex_11 = _num_11;
+const ex _ex_11 = _ex_11;
 
 // static numeric -10
 const numeric *_num_10_p;
-const numeric &_num_10 = *_num_10_p;
-const ex _ex_10 = _num_10;
+const ex _ex_10 = _ex_10;
 
 // static numeric -9
 const numeric *_num_9_p;
-const numeric &_num_9 = *_num_9_p;
-const ex _ex_9 = _num_9;
+const ex _ex_9 = _ex_9;
 
 // static numeric -8
 const numeric *_num_8_p;
-const numeric &_num_8 = *_num_8_p;
-const ex _ex_8 = _num_8;
+const ex _ex_8 = _ex_8;
 
 // static numeric -7
 const numeric *_num_7_p;
-const numeric &_num_7 = *_num_7_p;
-const ex _ex_7 = _num_7;
+const ex _ex_7 = _ex_7;
 
 // static numeric -6
 const numeric *_num_6_p;
-const numeric &_num_6 = *_num_6_p;
-const ex _ex_6 = _num_6;
+const ex _ex_6 = _ex_6;
 
 // static numeric -5
 const numeric *_num_5_p;
-const numeric &_num_5 = *_num_5_p;
-const ex _ex_5 = _num_5;
+const ex _ex_5 = _ex_5;
 
 // static numeric -4
 const numeric *_num_4_p;
-const numeric &_num_4 = *_num_4_p;
-const ex _ex_4 = _num_4;
+const ex _ex_4 = _ex_4;
 
 // static numeric -3
 const numeric *_num_3_p;
-const numeric &_num_3 = *_num_3_p;
-const ex _ex_3 = _num_3;
+const ex _ex_3 = _ex_3;
 
 // static numeric -2
 const numeric *_num_2_p;
-const numeric &_num_2 = *_num_2_p;
-const ex _ex_2 = _num_2;
+const ex _ex_2 = _ex_2;
 
 // static numeric -1
 const numeric *_num_1_p;
-const numeric &_num_1 = *_num_1_p;
-const ex _ex_1 = _num_1;
+const ex _ex_1 = _ex_1;
 
 // static numeric -1/2
 const numeric *_num_1_2_p;
-const numeric &_num_1_2= *_num_1_2_p;
-const ex _ex_1_2= _num_1_2;
+const ex _ex_1_2= _ex_1_2;
 
 // static numeric -1/3
 const numeric *_num_1_3_p;
-const numeric &_num_1_3= *_num_1_3_p;
-const ex _ex_1_3= _num_1_3;
+const ex _ex_1_3= _ex_1_3;
 
 // static numeric -1/4
 const numeric *_num_1_4_p;
-const numeric &_num_1_4= *_num_1_4_p;
-const ex _ex_1_4= _num_1_4;
+const ex _ex_1_4= _ex_1_4;
 
 // static numeric 0
 const numeric *_num0_p;
 const basic *_num0_bp;
-const numeric &_num0 = *_num0_p;
-const ex _ex0 = _num0;
+const ex _ex0 = _ex0;
 
 // static numeric 1/4
 const numeric *_num1_4_p;
-const numeric &_num1_4 = *_num1_4_p;
-const ex _ex1_4 = _num1_4;
+const ex _ex1_4 = _ex1_4;
 
 // static numeric 1/3
 const numeric *_num1_3_p;
-const numeric &_num1_3 = *_num1_3_p;
-const ex _ex1_3 = _num1_3;
+const ex _ex1_3 = _ex1_3;
 
 // static numeric 1/2
 const numeric *_num1_2_p;
-const numeric &_num1_2 = *_num1_2_p;
-const ex _ex1_2 = _num1_2;
+const ex _ex1_2 = _ex1_2;
 
 // static numeric 1
 const numeric *_num1_p;
-const numeric &_num1 = *_num1_p;
-const ex _ex1 = _num1;
+const ex _ex1 = _ex1;
 
 // static numeric 2
 const numeric *_num2_p;
-const numeric &_num2 = *_num2_p;
-const ex _ex2 = _num2;
+const ex _ex2 = _ex2;
 
 // static numeric 3
 const numeric *_num3_p;
-const numeric &_num3 = *_num3_p;
-const ex _ex3 = _num3;
+const ex _ex3 = _ex3;
 
 // static numeric 4
 const numeric *_num4_p;
-const numeric &_num4 = *_num4_p;
-const ex _ex4 = _num4;
+const ex _ex4 = _ex4;
 
 // static numeric 5
 const numeric *_num5_p;
-const numeric &_num5 = *_num5_p;
-const ex _ex5 = _num5;
+const ex _ex5 = _ex5;
 
 // static numeric 6
 const numeric *_num6_p;
-const numeric &_num6 = *_num6_p;
-const ex _ex6 = _num6;
+const ex _ex6 = _ex6;
 
 // static numeric 7
 const numeric *_num7_p;
-const numeric &_num7 = *_num7_p;
-const ex _ex7 = _num7;
+const ex _ex7 = _ex7;
 
 // static numeric 8
 const numeric *_num8_p;
-const numeric &_num8 = *_num8_p;
-const ex _ex8 = _num8;
+const ex _ex8 = _ex8;
 
 // static numeric 9
 const numeric *_num9_p;
-const numeric &_num9 = *_num9_p;
-const ex _ex9 = _num9;
+const ex _ex9 = _ex9;
 
 // static numeric 10
 const numeric *_num10_p;
-const numeric &_num10 = *_num10_p;
-const ex _ex10 = _num10;
+const ex _ex10 = _ex10;
 
 // static numeric 11
 const numeric *_num11_p;
-const numeric &_num11 = *_num11_p;
-const ex _ex11 = _num11;
+const ex _ex11 = _ex11;
 
 // static numeric 12
 const numeric *_num12_p;
-const numeric &_num12 = *_num12_p;
-const ex _ex12 = _num12;
+const ex _ex12 = _ex12;
 
 // static numeric 15
 const numeric *_num15_p;
-const numeric &_num15 = *_num15_p;
-const ex _ex15 = _num15;
+const ex _ex15 = _ex15;
 
 // static numeric 18
 const numeric *_num18_p;
-const numeric &_num18 = *_num18_p;
-const ex _ex18 = _num18;
+const ex _ex18 = _ex18;
 
 // static numeric 20
 const numeric *_num20_p;
-const numeric &_num20 = *_num20_p;
-const ex _ex20 = _num20;
+const ex _ex20 = _ex20;
 
 // static numeric 24
 const numeric *_num24_p;
-const numeric &_num24 = *_num24_p;
-const ex _ex24 = _num24;
+const ex _ex24 = _ex24;
 
 // static numeric 25
 const numeric *_num25_p;
-const numeric &_num25 = *_num25_p;
-const ex _ex25 = _num25;
+const ex _ex25 = _ex25;
 
 // static numeric 30
 const numeric *_num30_p;
-const numeric &_num30 = *_num30_p;
-const ex _ex30 = _num30;
+const ex _ex30 = _ex30;
 
 // static numeric 48
 const numeric *_num48_p;
-const numeric &_num48 = *_num48_p;
-const ex _ex48 = _num48;
+const ex _ex48 = _ex48;
 
 // static numeric 60
 const numeric *_num60_p;
-const numeric &_num60 = *_num60_p;
-const ex _ex60 = _num60;
+const ex _ex60 = _ex60;
 
 // static numeric 120
 const numeric *_num120_p;
-const numeric &_num120 = *_num120_p;
-const ex _ex120 = _num120;
+const ex _ex120 = _ex120;
 
 /** Ctor of static initialization helpers.  The fist call to this is going
  *  to initialize the library, the others do nothing. */
 library_init::library_init()
 {
 	if (count++==0) {
-		(_num_120_p = new numeric(-120))->setflag(status_flags::dynallocated);
-		(_num_60_p = new numeric(-60))->setflag(status_flags::dynallocated);
-		(_num_48_p = new numeric(-48))->setflag(status_flags::dynallocated);
-		(_num_30_p = new numeric(-30))->setflag(status_flags::dynallocated);
-		(_num_25_p = new numeric(-25))->setflag(status_flags::dynallocated);
-		(_num_24_p = new numeric(-24))->setflag(status_flags::dynallocated);
-		(_num_20_p = new numeric(-20))->setflag(status_flags::dynallocated);
-		(_num_18_p = new numeric(-18))->setflag(status_flags::dynallocated);
-		(_num_15_p = new numeric(-15))->setflag(status_flags::dynallocated);
-		(_num_12_p = new numeric(-12))->setflag(status_flags::dynallocated);
-		(_num_11_p = new numeric(-11))->setflag(status_flags::dynallocated);
-		(_num_10_p = new numeric(-10))->setflag(status_flags::dynallocated);
-		(_num_9_p = new numeric(-9))->setflag(status_flags::dynallocated);
-		(_num_8_p = new numeric(-8))->setflag(status_flags::dynallocated);
-		(_num_7_p = new numeric(-7))->setflag(status_flags::dynallocated);
-		(_num_6_p = new numeric(-6))->setflag(status_flags::dynallocated);
-		(_num_5_p = new numeric(-5))->setflag(status_flags::dynallocated);
-		(_num_4_p = new numeric(-4))->setflag(status_flags::dynallocated);
-		(_num_3_p = new numeric(-3))->setflag(status_flags::dynallocated);
-		(_num_2_p = new numeric(-2))->setflag(status_flags::dynallocated);
-		(_num_1_p = new numeric(-1))->setflag(status_flags::dynallocated);
-		(_num_1_2_p = new numeric(-1,2))->setflag(status_flags::dynallocated);
-		(_num_1_3_p = new numeric(-1,3))->setflag(status_flags::dynallocated);
-		(_num_1_4_p = new numeric(-1,4))->setflag(status_flags::dynallocated);
-		(_num0_p = new numeric(0))->setflag(status_flags::dynallocated);
+		_num_120_p = (const numeric *)&dynallocate<numeric>(-120);
+		_num_60_p = (const numeric *)&dynallocate<numeric>(-60);
+		_num_48_p = (const numeric *)&dynallocate<numeric>(-48);
+		_num_30_p = (const numeric *)&dynallocate<numeric>(-30);
+		_num_25_p = (const numeric *)&dynallocate<numeric>(-25);
+		_num_24_p = (const numeric *)&dynallocate<numeric>(-24);
+		_num_20_p = (const numeric *)&dynallocate<numeric>(-20);
+		_num_18_p = (const numeric *)&dynallocate<numeric>(-18);
+		_num_15_p = (const numeric *)&dynallocate<numeric>(-15);
+		_num_12_p = (const numeric *)&dynallocate<numeric>(-12);
+		_num_11_p = (const numeric *)&dynallocate<numeric>(-11);
+		_num_10_p = (const numeric *)&dynallocate<numeric>(-10);
+		_num_9_p = (const numeric *)&dynallocate<numeric>(-9);
+		_num_8_p = (const numeric *)&dynallocate<numeric>(-8);
+		_num_7_p = (const numeric *)&dynallocate<numeric>(-7);
+		_num_6_p = (const numeric *)&dynallocate<numeric>(-6);
+		_num_5_p = (const numeric *)&dynallocate<numeric>(-5);
+		_num_4_p = (const numeric *)&dynallocate<numeric>(-4);
+		_num_3_p = (const numeric *)&dynallocate<numeric>(-3);
+		_num_2_p = (const numeric *)&dynallocate<numeric>(-2);
+		_num_1_p = (const numeric *)&dynallocate<numeric>(-1);
+		_num_1_2_p = (const numeric *)&dynallocate<numeric>(-1,2);
+		_num_1_3_p = (const numeric *)&dynallocate<numeric>(-1,3);
+		_num_1_4_p = (const numeric *)&dynallocate<numeric>(-1,4);
+		_num0_p = (const numeric *)&dynallocate<numeric>(0);
 		_num0_bp  = _num0_p;  // Cf. class ex default ctor.
-		(_num1_4_p = new numeric(1,4))->setflag(status_flags::dynallocated);
-		(_num1_3_p = new numeric(1,3))->setflag(status_flags::dynallocated);
-		(_num1_2_p = new numeric(1,2))->setflag(status_flags::dynallocated);
-		(_num1_p = new numeric(1))->setflag(status_flags::dynallocated);
-		(_num2_p = new numeric(2))->setflag(status_flags::dynallocated);
-		(_num3_p = new numeric(3))->setflag(status_flags::dynallocated);
-		(_num4_p = new numeric(4))->setflag(status_flags::dynallocated);
-		(_num5_p = new numeric(5))->setflag(status_flags::dynallocated);
-		(_num6_p = new numeric(6))->setflag(status_flags::dynallocated);
-		(_num7_p = new numeric(7))->setflag(status_flags::dynallocated);
-		(_num8_p = new numeric(8))->setflag(status_flags::dynallocated);
-		(_num9_p = new numeric(9))->setflag(status_flags::dynallocated);
-		(_num10_p = new numeric(10))->setflag(status_flags::dynallocated);
-		(_num11_p = new numeric(11))->setflag(status_flags::dynallocated);
-		(_num12_p = new numeric(12))->setflag(status_flags::dynallocated);
-		(_num15_p = new numeric(15))->setflag(status_flags::dynallocated);
-		(_num18_p = new numeric(18))->setflag(status_flags::dynallocated);
-		(_num20_p = new numeric(20))->setflag(status_flags::dynallocated);
-		(_num24_p = new numeric(24))->setflag(status_flags::dynallocated);
-		(_num25_p = new numeric(25))->setflag(status_flags::dynallocated);
-		(_num30_p = new numeric(30))->setflag(status_flags::dynallocated);
-		(_num48_p = new numeric(48))->setflag(status_flags::dynallocated);
-		(_num60_p = new numeric(60))->setflag(status_flags::dynallocated);
-		(_num120_p = new numeric(120))->setflag(status_flags::dynallocated);
+		_num1_4_p = (const numeric *)&dynallocate<numeric>(1,4);
+		_num1_3_p = (const numeric *)&dynallocate<numeric>(1,3);
+		_num1_2_p = (const numeric *)&dynallocate<numeric>(1,2);
+		_num1_p = (const numeric *)&dynallocate<numeric>(1);
+		_num2_p = (const numeric *)&dynallocate<numeric>(2);
+		_num3_p = (const numeric *)&dynallocate<numeric>(3);
+		_num4_p = (const numeric *)&dynallocate<numeric>(4);
+		_num5_p = (const numeric *)&dynallocate<numeric>(5);
+		_num6_p = (const numeric *)&dynallocate<numeric>(6);
+		_num7_p = (const numeric *)&dynallocate<numeric>(7);
+		_num8_p = (const numeric *)&dynallocate<numeric>(8);
+		_num9_p = (const numeric *)&dynallocate<numeric>(9);
+		_num10_p = (const numeric *)&dynallocate<numeric>(10);
+		_num11_p = (const numeric *)&dynallocate<numeric>(11);
+		_num12_p = (const numeric *)&dynallocate<numeric>(12);
+		_num15_p = (const numeric *)&dynallocate<numeric>(15);
+		_num18_p = (const numeric *)&dynallocate<numeric>(18);
+		_num20_p = (const numeric *)&dynallocate<numeric>(20);
+		_num24_p = (const numeric *)&dynallocate<numeric>(24);
+		_num25_p = (const numeric *)&dynallocate<numeric>(25);
+		_num30_p = (const numeric *)&dynallocate<numeric>(30);
+		_num48_p = (const numeric *)&dynallocate<numeric>(48);
+		_num60_p = (const numeric *)&dynallocate<numeric>(60);
+		_num120_p = (const numeric *)&dynallocate<numeric>(120);
+
+		new((void*)&_ex_120) ex(*_num_120_p);
+		new((void*)&_ex_60) ex(*_num_60_p);
+		new((void*)&_ex_48) ex(*_num_48_p);
+		new((void*)&_ex_30) ex(*_num_30_p);
+		new((void*)&_ex_25) ex(*_num_25_p);
+		new((void*)&_ex_24) ex(*_num_24_p);
+		new((void*)&_ex_20) ex(*_num_20_p);
+		new((void*)&_ex_18) ex(*_num_18_p);
+		new((void*)&_ex_15) ex(*_num_15_p);
+		new((void*)&_ex_12) ex(*_num_12_p);
+		new((void*)&_ex_11) ex(*_num_11_p);
+		new((void*)&_ex_10) ex(*_num_10_p);
+		new((void*)&_ex_9) ex(*_num_9_p);
+		new((void*)&_ex_8) ex(*_num_8_p);
+		new((void*)&_ex_7) ex(*_num_7_p);
+		new((void*)&_ex_6) ex(*_num_6_p);
+		new((void*)&_ex_5) ex(*_num_5_p);
+		new((void*)&_ex_4) ex(*_num_4_p);
+		new((void*)&_ex_3) ex(*_num_3_p);
+		new((void*)&_ex_2) ex(*_num_2_p);
+		new((void*)&_ex_1) ex(*_num_1_p);
+		new((void*)&_ex_1_2) ex(*_num_1_2_p);
+		new((void*)&_ex_1_3) ex(*_num_1_3_p);
+		new((void*)&_ex_1_4) ex(*_num_1_4_p);
+		new((void*)&_ex0) ex(*_num0_p);
+		new((void*)&_ex1_4) ex(*_num1_4_p);
+		new((void*)&_ex1_3) ex(*_num1_3_p);
+		new((void*)&_ex1_2) ex(*_num1_2_p);
+		new((void*)&_ex1) ex(*_num1_p);
+		new((void*)&_ex2) ex(*_num2_p);
+		new((void*)&_ex3) ex(*_num3_p);
+		new((void*)&_ex4) ex(*_num4_p);
+		new((void*)&_ex5) ex(*_num5_p);
+		new((void*)&_ex6) ex(*_num6_p);
+		new((void*)&_ex7) ex(*_num7_p);
+		new((void*)&_ex8) ex(*_num8_p);
+		new((void*)&_ex9) ex(*_num9_p);
+		new((void*)&_ex10) ex(*_num10_p);
+		new((void*)&_ex11) ex(*_num11_p);
+		new((void*)&_ex12) ex(*_num12_p);
+		new((void*)&_ex15) ex(*_num15_p);
+		new((void*)&_ex18) ex(*_num18_p);
+		new((void*)&_ex20) ex(*_num20_p);
+		new((void*)&_ex24) ex(*_num24_p);
+		new((void*)&_ex25) ex(*_num25_p);
+		new((void*)&_ex30) ex(*_num30_p);
+		new((void*)&_ex48) ex(*_num48_p);
+		new((void*)&_ex60) ex(*_num60_p);
+		new((void*)&_ex120) ex(*_num120_p);
 
 		// Initialize print context class info (this is not strictly necessary
 		// but we do it anyway to make print_context_class_info::dump_hierarchy()
@@ -387,12 +401,64 @@ library_init::library_init()
 library_init::~library_init()
 {
 	if (--count==0) {
-		// In theory, we would have to clean up here.  But since we were
-		// only initializing memory in the ctor and that memory is reclaimed
-		// anyways by the OS when the program exits, we skip this.
+		// It's really necessary to clean up, since the program
+		// lifetime might not be the same as libginac.{so,dll} one
+		// (e.g. consider // dlopen/dlsym/dlclose sequence).
+		// Let the ex dtors care for deleting the numerics!
+		_ex120.~ex();
+		_ex_120.~ex();
+		_ex60.~ex();
+		_ex_60.~ex();
+		_ex48.~ex();
+		_ex_48.~ex();
+		_ex30.~ex();
+		_ex_30.~ex();
+		_ex25.~ex();
+		_ex_25.~ex();
+		_ex24.~ex();
+		_ex_24.~ex();
+		_ex20.~ex();
+		_ex_20.~ex();
+		_ex18.~ex();
+		_ex_18.~ex();
+		_ex15.~ex();
+		_ex_15.~ex();
+		_ex12.~ex();
+		_ex_12.~ex();
+		_ex11.~ex();
+		_ex_11.~ex();
+		_ex10.~ex();
+		_ex_10.~ex();
+		_ex9.~ex();
+		_ex_9.~ex();
+		_ex8.~ex();
+		_ex_8.~ex();
+		_ex7.~ex();
+		_ex_7.~ex();
+		_ex6.~ex();
+		_ex_6.~ex();
+		_ex5.~ex();
+		_ex_5.~ex();
+		_ex4.~ex();
+		_ex_4.~ex();
+		_ex3.~ex();
+		_ex_3.~ex();
+		_ex2.~ex();
+		_ex_2.~ex();
+		_ex1.~ex();
+		_ex_1.~ex();
+		_ex1_2.~ex();
+		_ex_1_2.~ex();
+		_ex1_3.~ex();
+		_ex_1_3.~ex();
+		_ex1_4.~ex();
+		_ex_1_4.~ex();
+		_ex0.~ex();
 	}
 }
 
+void library_init::init_unarchivers() { }
+
 // comment skeleton for header files