eigenmath/defs.h

// Symbolic expressions are built by connecting U structs.
//
// For example, (a b + c) is built like this:
//
//           _______      _______                                _______
//          |CONS   |--->|CONS   |----------------------------->|CONS   |
//          |       |    |       |                              |       |
//          |_______|    |_______|                              |_______|
//              |            |                                      |
//           ___v___      ___v___      _______      _______      ___v___
//          |ADD    |    |CONS   |--->|CONS   |--->|CONS   |    |SYM c  |
//          |       |    |       |    |       |    |       |    |       |
//          |_______|    |_______|    |_______|    |_______|    |_______|
//                           |            |            |
//                        ___v___      ___v___      ___v___
//                       |MUL    |    |SYM a  |    |SYM b  |
//                       |       |    |       |    |       |
//                       |_______|    |_______|    |_______|

typedef struct U {
	union {
		struct {
			struct U *car;		// pointing down
			struct U *cdr;		// pointing right
		} cons;
		struct {
			struct U *binding;	// symbol's value binding
			struct U *binding2;	// symbol's function binding
		} sym;
		char *str;
		struct tensor *tensor;
		struct {
			unsigned int *a, *b;	// rational number a over b
		} q;
		double d;
	} u;
	unsigned char k, tag;
} U;

// the following enum is for struct U, member k

enum {
	CONS,
	NUM,
	DOUBLE,
	STR,
	TENSOR,
	SYM,
};

// the following enum is for indexing the symbol table

enum {

	// standard functions first, then nil, then everything else

	ABS,
	ADD,
	ADJ,
	AND,
	ARCCOS,
	ARCCOSH,
	ARCSIN,
	ARCSINH,
	ARCTAN,
	ARCTANH,
	ARG,
	ATOMIZE,
	BESSELJ,
	BESSELY,
	BINDING2,
	BINOMIAL,
	BREAK,
	CARAC,
	CEILING,
	CHECK,
	CIRCEXP,
	CLEAR,
	CLS,
	COEFF,
	COFACTOR,
	CONDENSE,
	CONJ,
	CONTRACT,
	CONVOLUTION,
	COS,
	COSH,
	DECOMP,
	DEGREE,
	DENOMINATOR,
	DERIVATIVE,
	DET,
	DIM,
	DIRAC,
	DISPLAY,
	DIVISORS,
	DO,
	DOT,
	DRAW,
	DSOLVE,
	EIGEN,
	EIGENVAL,
	EIGENVEC,
	ERF,
	ERFC,
	EVAL,
	EXP,
	EXPAND,
	EXPCOS,
	EXPSIN,
	FACTOR,
	FACTORIAL,
	FACTORPOLY,
	FILTER,
	FLOATF,
	FLOOR,
	FOR,
	FOURIER,
	GAMMA,
	GCD,
	HEAVISIDE,
	HERMITE,
	HILBERT,
	IMAG,
	INDEX,
	INNER,
	INTEGRAL,
	INV,
	INVFOURIER,
	INVG,
	ISINTEGER,
	ISPRIME,
	LAGUERRE,
	LCM,
	LEGENDRE,
	LOG,
	MAG,
	MOD,
	MULTIPLY,
	NOT,
	NUMBER,
	NUMERATOR,
	OPERATOR,
	OR,
	OUTER,
	POLAR,
	POWER,
	PRIME,
	PRINT,
	PRODUCT,
	PROG,
	QUOTE,
	QUOTIENT,
	RANK,
	RATIONALIZE,
	REAL,
	YYRECT,
	RETURN,
	ROOTS,
	SETQ,
	SGN,
	SIMFAC,
	SIMPLIFY,
	SIN,
	SINH,
	SQRT,
	STOP,
	SUBST,
	SUM,
	SUMMARIZE,
	TAB,
	TAN,
	TANH,
	TAYLOR,
	TCHEBYCHEVT,
	TCHEBYCHEVU,
	TEST,
	TESTEQ,
	TESTGE,
	TESTGT,
	TESTLE,
	TESTLT,
	TRACE,
	TRANSPOSE,
	UNIT,
	ZERO,

	NIL,	// nil goes here, after standard functions

	AUTOEXPAND,
	BAKE,
	LAST,
	TTY,
	YYE,
	YYLAST,
	SECRETX,
	METAA,
	METAB,
	METAX,

	// symbols appearing above are printed in roman type

	// the following symbols are printed in italic type

	PI,
	SYMBOL_A,
	SYMBOL_B,
	SYMBOL_C,
	SYMBOL_D,
	SYMBOL_N,
	SYMBOL_R,
	SYMBOL_T,
	SYMBOL_X,
	SYMBOL_Y,
	SYMBOL_Z,

	C1,
	C2,
	C3,
	C4,
	C5,
	C6,

	USR_SYMBOLS,	// this must be last
};

#define E YYE

#define TOS 1000000
#define BUF 10000

#define MAX_PROGRAM_SIZE 100001
#define MAXPRIMETAB 10000

#define _USE_MATH_DEFINES // for MS C++

#include <stdio.h>
#include <stdlib.h>
#include <ctype.h>
#include <fcntl.h>
#include <string.h>
#include <setjmp.h>
#include <math.h>
#include <errno.h>

#define MAXDIM 24

typedef struct tensor {
	int ndim;
	int dim[MAXDIM];
	int nelem;
	U *elem[1];
} T;

struct display {
	int h, w, n;
	struct {
		int c, x, y;
	} a[1]; // a for array
};

struct text_metric {
	int ascent, descent, width;
};

#define bind(x,y) symbol(x)->u.sym.binding = y
#define push_binding(p) push((p)->u.sym.binding)
#define pop_binding(p) (p)->u.sym.binding = pop()
#define symbol(x) (symtab + (x))
#define iscons(p) ((p)->k == CONS)
#define isrational(p) ((p)->k == NUM)
#define isdouble(p) ((p)->k == DOUBLE)
#define isnum(p) (isrational(p) || isdouble(p))
#define isstr(p) ((p)->k == STR)
#define istensor(p) ((p)->k == TENSOR)
#define issymbol(p) ((p)->k == SYM)
#define iskeyword(p) (issymbol(p) && symbol_index(p) < NIL)

#define car(p) (iscons(p) ? (p)->u.cons.car : symbol(NIL))
#define cdr(p) (iscons(p) ? (p)->u.cons.cdr : symbol(NIL))
#define caar(p) car(car(p))
#define cadr(p) car(cdr(p))
#define cdar(p) cdr(car(p))
#define cddr(p) cdr(cdr(p))
#define caadr(p) car(car(cdr(p)))
#define caddr(p) car(cdr(cdr(p)))
#define cadar(p) car(cdr(car(p)))
#define cdadr(p) cdr(car(cdr(p)))
#define cddar(p) cdr(cdr(car(p)))
#define cdddr(p) cdr(cdr(cdr(p)))
#define caaddr(p) car(car(cdr(cdr(p))))
#define cadadr(p) car(cdr(car(cdr(p))))
#define caddar(p) car(cdr(cdr(car(p))))
#define cdaddr(p) cdr(car(cdr(cdr(p))))
#define cadddr(p) car(cdr(cdr(cdr(p))))
#define cddddr(p) cdr(cdr(cdr(cdr(p))))
#define caddddr(p) car(cdr(cdr(cdr(cdr(p)))))
#define cadaddr(p) car(cdr(car(cdr(cdr(p)))))
#define cddaddr(p) cdr(cdr(car(cdr(cdr(p)))))
#define caddadr(p) car(cdr(cdr(car(cdr(p)))))
#define cdddaddr(p) cdr(cdr(cdr(car(cdr(cdr(p))))))
#define caddaddr(p) car(cdr(cdr(car(cdr(cdr(p))))))

#define isadd(p) (car(p) == symbol(ADD))
#define ispower(p) (car(p) == symbol(POWER))
#define isfactorial(p) (car(p) == symbol(FACTORIAL))

#define MSIGN(p) (((int *) (p))[-2])
#define MLENGTH(p) (((int *) (p))[-1])

#define MZERO(p) (MLENGTH(p) == 1 && (p)[0] == 0)
#define MEQUAL(p, n) (MLENGTH(p) == 1 && (long long) MSIGN(p) * (p)[0] == (n))

extern int tos;
extern int expanding;
extern int exp_flag;
extern int conjugating;
extern int fmt_x;
extern int fmt_index;
extern int fmt_level;
extern int verbosing;
extern int floating;
extern int primetab[MAXPRIMETAB];
extern int esc_flag;
extern int mtotal;
extern int little_endian;
extern int nsym;
extern int trigmode;
extern char logbuf[];
extern char program_buf[];
extern U symtab[];
extern U *stack[];
extern U **frame;
extern U *p1, *p2, *p3, *p4, *p5, *p6, *p7, *p8;
extern U *formal_arg[6];
extern U *zero, *one, *imaginaryunit;
extern U *table_of_fourier;
extern U *meta_a;
extern U *meta_b;
extern U *meta_c;
extern U *meta_n;
extern U *meta_x;
extern U *varlist;
extern U symtab[];

#include "prototypes.h"