//----------------------------------------------------------------------------- // // Examples: // // 012345678 // -2 ......... // -1 ......... // 0 ..hello.. x=2, y=0, h=1, w=5 // 1 ......... // 2 ......... // // 012345678 // -2 ......... // -1 ..355.... // 0 ..---.... x=2, y=-1, h=3, w=3 // 1 ..113.... // 2 ......... // //----------------------------------------------------------------------------- #include "stdafx.h" #include "defs.h" #define YMAX 10000 struct glyph { int c, x, y; } chartab[YMAX]; extern U *minus_one_half; static void emit_expr(U *); static void emit_term(U *); static void emit_multiply(U *, int); static void emit_factor(U *); static void emit_power(U *); static void emit_denominator(U *, int); static void emit_subexpr(U *); static void fixup_power(int, int); static void move(int, int, int, int); static void get_size(int, int, int *, int *, int *); static void emit_function(U *); static void emit_symbol(U *); static void emit_string(U *); static void fixup_fraction(int, int, int); static void emit_number(U *, int); static void __emit_char(int); static void __emit_str(char *); static void print_it(); static int count_denominators(U *); static int __is_negative(U *); static void emit_fraction(U *, int); static void emit_numerical_fraction(U *); static void emit_tensor(U *); static int isdenominator(U *p); static void emit_flat_tensor(U *); static void emit_tensor_inner(U *, int, int *); static void emit_top_expr(U *); static void emit_index_function(U *); static void emit_factorial_function(U *); static void emit_numerators(U *); static void emit_denominators(U *); static int yindex, level, emit_x; static int expr_level; int display_flag; void display(U *p) { int h, w, y; save(); yindex = 0; level = 0; emit_x = 0; emit_top_expr(p); // if too wide then print flat get_size(0, yindex, &h, &w, &y); if (w > 100) { printline(p); restore(); return; } print_it(); restore(); } static void emit_top_expr(U *p) { if (car(p) == symbol(SETQ)) { emit_expr(cadr(p)); __emit_str(" = "); emit_expr(caddr(p)); return; } if (p->k == TENSOR) emit_tensor(p); else emit_expr(p); } static int will_be_displayed_as_fraction(U *p) { if (level > 0) return 0; if (isfraction(p)) return 1; if (car(p) != symbol(MULTIPLY)) return 0; if (isfraction(cadr(p))) return 1; while (iscons(p)) { if (isdenominator(car(p))) return 1; p = cdr(p); } return 0; } static void emit_expr(U *p) { // if (level > 0) { // printexpr(p); // return; // } expr_level++; if (car(p) == symbol(ADD)) { p = cdr(p); if (__is_negative(car(p))) { __emit_char('-'); if (will_be_displayed_as_fraction(car(p))) __emit_char(' '); } emit_term(car(p)); p = cdr(p); while (iscons(p)) { if (__is_negative(car(p))) { //if (expr_level == 1) __emit_char(' '); __emit_char('-'); //if (expr_level == 1) __emit_char(' '); } else { //if (expr_level == 1) __emit_char(' '); __emit_char('+'); //if (expr_level == 1) __emit_char(' '); } emit_term(car(p)); p = cdr(p); } } else { if (__is_negative(p)) { __emit_char('-'); if (will_be_displayed_as_fraction(p)) __emit_char(' '); } emit_term(p); } expr_level--; } static void emit_unsigned_expr(U *p) { if (car(p) == symbol(ADD)) { p = cdr(p); // if (__is_negative(car(p))) // __emit_char('-'); emit_term(car(p)); p = cdr(p); while (iscons(p)) { if (__is_negative(car(p))) { __emit_char(' '); __emit_char('-'); __emit_char(' '); } else { __emit_char(' '); __emit_char('+'); __emit_char(' '); } emit_term(car(p)); p = cdr(p); } } else { // if (__is_negative(p)) // __emit_char('-'); emit_term(p); } } static int __is_negative(U *p) { if (isnegativenumber(p)) return 1; if (car(p) == symbol(MULTIPLY) && isnegativenumber(cadr(p))) return 1; return 0; } static void emit_term(U *p) { int n; if (car(p) == symbol(MULTIPLY)) { n = count_denominators(p); if (n && level == 0) emit_fraction(p, n); else emit_multiply(p, n); } else emit_factor(p); } static int isdenominator(U *p) { if (car(p) == symbol(POWER) && cadr(p) != symbol(E) && __is_negative(caddr(p))) return 1; else return 0; } static int count_denominators(U *p) { int count = 0; U *q; p = cdr(p); // if (isfraction(car(p))) { // count++; // p = cdr(p); // } while (iscons(p)) { q = car(p); if (isdenominator(q)) count++; p = cdr(p); } return count; } // n is the number of denominators, not counting a fraction like 1/2 static void emit_multiply(U *p, int n) { if (n == 0) { p = cdr(p); if (isplusone(car(p)) || isminusone(car(p))) p = cdr(p); emit_factor(car(p)); p = cdr(p); while (iscons(p)) { __emit_char(' '); emit_factor(car(p)); p = cdr(p); } } else { emit_numerators(p); __emit_char('/'); // need grouping if more than one denominator if (n > 1 || isfraction(cadr(p))) { __emit_char('('); emit_denominators(p); __emit_char(')'); } else emit_denominators(p); } } #define A p3 #define B p4 // sign of term has already been emitted static void emit_fraction(U *p, int d) { int count, k1, k2, n, x; save(); A = _one; B = _one; // handle numerical coefficient if (cadr(p)->k == NUM) { push(cadr(p)); numerator(); absval(); A = pop(); push(cadr(p)); denominator(); B = pop(); } if (cadr(p)->k == DOUBLE) { push(cadr(p)); absval(); A = pop(); } // count numerators if (isplusone(A)) n = 0; else n = 1; p1 = cdr(p); if (isnum(car(p1))) p1 = cdr(p1); while (iscons(p1)) { p2 = car(p1); if (isdenominator(p2)) ; else n++; p1 = cdr(p1); } // emit numerators x = emit_x; k1 = yindex; count = 0; // emit numerical coefficient if (!isplusone(A)) { emit_number(A, 0); count++; } // skip over "multiply" p1 = cdr(p); // skip over numerical coefficient, already handled if (isnum(car(p1))) p1 = cdr(p1); while (iscons(p1)) { p2 = car(p1); if (isdenominator(p2)) ; else { if (count > 0) __emit_char(' '); if (n == 1) emit_expr(p2); else emit_factor(p2); count++; } p1 = cdr(p1); } if (count == 0) __emit_char('1'); // emit denominators k2 = yindex; count = 0; if (!isplusone(B)) { emit_number(B, 0); count++; d++; } p1 = cdr(p); if (car(p1)->k == NUM) p1 = cdr(p1); while (iscons(p1)) { p2 = car(p1); if (isdenominator(p2)) { if (count > 0) __emit_char(' '); emit_denominator(p2, d); count++; } p1 = cdr(p1); } fixup_fraction(x, k1, k2); restore(); } // p points to a multiply static void emit_numerators(U *p) { int n; save(); p1 = _one; p = cdr(p); if (car(p)->k == NUM) { push(car(p)); numerator(); absval(); p1 = pop(); p = cdr(p); } else if (car(p)->k == DOUBLE) { push(car(p)); absval(); p1 = pop(); p = cdr(p); } n = 0; if (!isplusone(p1)) { emit_number(p1, 0); n++; } while (iscons(p)) { if (isdenominator(car(p))) ; else { if (n > 0) __emit_char(' '); emit_factor(car(p)); n++; } p = cdr(p); } if (n == 0) __emit_char('1'); restore(); } // p points to a multiply static void emit_denominators(U *p) { int n; save(); n = 0; p = cdr(p); if (isfraction(car(p))) { push(car(p)); denominator(); p1 = pop(); emit_number(p1, 0); n++; p = cdr(p); } while (iscons(p)) { if (isdenominator(car(p))) { if (n > 0) __emit_char(' '); emit_denominator(car(p), 0); n++; } p = cdr(p); } restore(); } static void emit_factor(U *p) { if (p->k == TENSOR) { if (level == 0) //emit_tensor(p); emit_flat_tensor(p); else emit_flat_tensor(p); return; } if (p->k == DOUBLE) { emit_number(p, 0); return; } if (car(p) == symbol(ADD) || car(p) == symbol(MULTIPLY)) { emit_subexpr(p); return; } if (car(p) == symbol(POWER)) { emit_power(p); return; } if (iscons(p)) { //if (car(p) == symbol(FORMAL) && cadr(p)->k == SYM) // emit_symbol(cadr(p)); //else emit_function(p); return; } if (isnum(p)) { if (level == 0) emit_numerical_fraction(p); else emit_number(p, 0); return; } if (issym(p)) { emit_symbol(p); return; } if (p->k == STR) { emit_string(p); return; } } static void emit_numerical_fraction(U *p) { int k1, k2, x; save(); push(p); numerator(); absval(); A = pop(); push(p); denominator(); B = pop(); if (isplusone(B)) { emit_number(A, 0); restore(); return; } x = emit_x; k1 = yindex; emit_number(A, 0); k2 = yindex; emit_number(B, 0); fixup_fraction(x, k1, k2); restore(); } // if it's a factor then it doesn't need parens around it, i.e. 1/sin(theta)^2 static int isfactor(U *p) { // sqrt ? // if (car(p) == symbol(POWER) && equal(caddr(p), plus_one_half)) // return 1; if (iscons(p) && car(p) != symbol(ADD) && car(p) != symbol(MULTIPLY) && car(p) != symbol(POWER)) return 1; if (issymbol(p)) return 1; if (isfraction(p)) return 0; if (isnegativenumber(p)) return 0; if (isnum(p)) return 1; return 0; } static void emit_power(U *p) { int k1, k2, x; U *q; if (cadr(p) == symbol(E)) { __emit_str("exp("); emit_expr(caddr(p)); __emit_char(')'); return; } // if (equal(caddr(p), plus_one_half)) { // __emit_str("sqrt("); // emit_expr(cadr(p)); // __emit_char(')'); // return; // } if (equal(p, unit_imaginary)) { q = symbol(IM)->u.sym.binding; if (issymbol(q)) __emit_str(get_printname(q)); else __emit_str("i"); return; } if (level > 0) { if (isminusone(caddr(p))) { __emit_char('1'); __emit_char('/'); if (isfactor(cadr(p))) emit_factor(cadr(p)); else emit_subexpr(cadr(p)); } else { if (isfactor(cadr(p))) emit_factor(cadr(p)); else emit_subexpr(cadr(p)); __emit_char('^'); if (isfactor(caddr(p))) emit_factor(caddr(p)); else emit_subexpr(caddr(p)); } return; } // special case: 1 over something if (__is_negative(caddr(p))) { x = emit_x; k1 = yindex; __emit_char('1'); k2 = yindex; //level++; emit_denominator(p, 1); //level--; fixup_fraction(x, k1, k2); return; } k1 = yindex; if (isfactor(cadr(p))) emit_factor(cadr(p)); else emit_subexpr(cadr(p)); k2 = yindex; level++; emit_expr(caddr(p)); level--; fixup_power(k1, k2); } // if n == 1 then emit as expr (no parens) // p is a power static void emit_denominator(U *p, int n) { int k1, k2; // special case: 1 over something if (isminusone(caddr(p))) { if (n == 1) emit_expr(cadr(p)); else emit_factor(cadr(p)); return; } // special case: 1 over sqrt // if (equal(caddr(p), minus_one_half)) { // __emit_str("sqrt("); // emit_expr(cadr(p)); // __emit_char(')'); // return; // } k1 = yindex; // emit base if (isfactor(cadr(p))) emit_factor(cadr(p)); else emit_subexpr(cadr(p)); k2 = yindex; // emit exponent, don't emit minus sign level++; emit_unsigned_expr(caddr(p)); level--; fixup_power(k1, k2); } static void emit_function(U *p) { if (car(p) == symbol(INDEX) && cadr(p)->k == SYM) { emit_index_function(p); return; } if (car(p) == symbol(FACTORIAL)) { emit_factorial_function(p); return; } if (car(p) == symbol(DERIVATIVE)) __emit_char('d'); else emit_symbol(car(p)); __emit_char('('); p = cdr(p); if (iscons(p)) { emit_expr(car(p)); p = cdr(p); while (iscons(p)) { __emit_char(','); //__emit_char(' '); emit_expr(car(p)); p = cdr(p); } } __emit_char(')'); } static void emit_index_function(U *p) { p = cdr(p); if (caar(p) == symbol(ADD) || caar(p) == symbol(MULTIPLY) || caar(p) == symbol(POWER) || caar(p) == symbol(FACTORIAL)) emit_subexpr(car(p)); else emit_expr(car(p)); __emit_char('['); p = cdr(p); if (iscons(p)) { emit_expr(car(p)); p = cdr(p); while(iscons(p)) { __emit_char(','); emit_expr(car(p)); p = cdr(p); } } __emit_char(']'); } static void emit_factorial_function(U *p) { p = cadr(p); if (car(p) == symbol(ADD) || car(p) == symbol(MULTIPLY) || car(p) == symbol(POWER) || car(p) == symbol(FACTORIAL)) emit_subexpr(p); else emit_expr(p); __emit_char('!'); } static void emit_subexpr(U *p) { __emit_char('('); emit_expr(p); __emit_char(')'); } static void emit_symbol(U *p) { char *s; if (p == symbol(E)) { __emit_str("exp(1)"); return; } s = get_printname(p); while (*s) __emit_char(*s++); } static void emit_string(U *p) { char *s; s = p->u.str; while (*s) __emit_char(*s++); } void fixup_fraction(int x, int k1, int k2) { int dx, dy, i, w, y; int h1, w1, y1; int h2, w2, y2; get_size(k1, k2, &h1, &w1, &y1); get_size(k2, yindex, &h2, &w2, &y2); if (w2 > w1) dx = (w2 - w1) / 2; // shift numerator right else dx = 0; dx++; // this is how much is below the baseline y = y1 + h1 - 1; dy = -y - 1; move(k1, k2, dx, dy); if (w2 > w1) dx = -w1; else dx = -w1 + (w1 - w2) / 2; dx++; dy = -y2 + 1; move(k2, yindex, dx, dy); if (w2 > w1) w = w2; else w = w1; w+=2; emit_x = x; for (i = 0; i < w; i++) __emit_char('-'); } static void fixup_power(int k1, int k2) { int dy; int h1, w1, y1; int h2, w2, y2; get_size(k1, k2, &h1, &w1, &y1); get_size(k2, yindex, &h2, &w2, &y2); // move superscript to baseline dy = -y2 - h2 + 1; // now move above base dy += y1 - 1; move(k2, yindex, 0, dy); } static void move(int j, int k, int dx, int dy) { int i; for (i = j; i < k; i++) { chartab[i].x += dx; chartab[i].y += dy; } } // finds the bounding rectangle and vertical position static void get_size(int j, int k, int *h, int *w, int *y) { int i; int min_x, max_x, min_y, max_y; min_x = chartab[j].x; max_x = chartab[j].x; min_y = chartab[j].y; max_y = chartab[j].y; for (i = j + 1; i < k; i++) { if (chartab[i].x < min_x) min_x = chartab[i].x; if (chartab[i].x > max_x) max_x = chartab[i].x; if (chartab[i].y < min_y) min_y = chartab[i].y; if (chartab[i].y > max_y) max_y = chartab[i].y; } *h = max_y - min_y + 1; *w = max_x - min_x + 1; *y = min_y; } void displaychar(int c) { __emit_char(c); } static void __emit_char(int c) { if (yindex == YMAX) return; chartab[yindex].c = c; chartab[yindex].x = emit_x; chartab[yindex].y = 0; yindex++; emit_x++; } static void __emit_str(char *s) { while (*s) __emit_char(*s++); } void emit_number(U *p, int emit_sign) { char *s; static char buf[100]; switch (p->k) { case NUM: s = mstr(p->u.q.a); if (*s == '-' && emit_sign == 0) s++; while (*s) __emit_char(*s++); s = mstr(p->u.q.b); if (strcmp(s, "1") == 0) break; __emit_char('/'); while (*s) __emit_char(*s++); break; case DOUBLE: sprintf(buf, "%g", p->u.d); s = buf; if (*s == '-' && emit_sign == 0) s++; while (*s) __emit_char(*s++); break; default: break; } } static int __cmp(const void *aa, const void *bb) { struct glyph *a, *b; a = (struct glyph *) aa; b = (struct glyph *) bb; if (a->y < b->y) return -1; if (a->y > b->y) return 1; if (a->x < b->x) return -1; if (a->x > b->x) return 1; return 0; } static void print_it(void) { int i, x, y; qsort(chartab, yindex, sizeof (struct glyph), __cmp); x = 0; y = chartab[0].y; for (i = 0; i < yindex; i++) { while (chartab[i].y > y) { printchar('\n'); x = 0; y++; } while (chartab[i].x > x) { printchar_nowrap(' '); x++; } printchar_nowrap(chartab[i].c); x++; } printchar('\n'); } static void fill_buf(void); static char buffer[10000]; char * getdisplaystr(void) { yindex = 0; level = 0; emit_x = 0; emit_expr(pop()); fill_buf(); return buffer; } static void fill_buf(void) { int i, x, y; char *s = buffer; qsort(chartab, yindex, sizeof (struct glyph), __cmp); x = 0; y = chartab[0].y; for (i = 0; i < yindex; i++) { while (chartab[i].y > y) { *s++ = '\n'; x = 0; y++; } while (chartab[i].x > x) { *s++ = ' '; x++; } *s++ = chartab[i].c; x++; } *s++ = '\n'; *s++ = '\0'; } #define N 100 struct elem { int x, y, h, w, index, count; } elem[N]; #define SPACE_BETWEEN_COLUMNS 3 #define SPACE_BETWEEN_ROWS 1 static void emit_tensor(U *p) { int i, n, nrow, ncol; int x, y; int h, w; int dx, dy; int eh, ew; int row, col; if (p->u.tensor->ndim > 2) { emit_flat_tensor(p); return; } nrow = p->u.tensor->dim[0]; if (p->u.tensor->ndim == 2) ncol = p->u.tensor->dim[1]; else ncol = 1; n = nrow * ncol; if (n > N) { emit_flat_tensor(p); return; } // horizontal coordinate of the matrix #if 0 emit_x += 2; // make space for left paren #endif x = emit_x; // emit each element for (i = 0; i < n; i++) { elem[i].index = yindex; elem[i].x = emit_x; emit_expr(p->u.tensor->elem[i]); elem[i].count = yindex - elem[i].index; get_size(elem[i].index, yindex, &elem[i].h, &elem[i].w, &elem[i].y); } // find element height and width eh = 0; ew = 0; for (i = 0; i < n; i++) { if (elem[i].h > eh) eh = elem[i].h; if (elem[i].w > ew) ew = elem[i].w; } // this is the overall height of the matrix h = nrow * eh + (nrow - 1) * SPACE_BETWEEN_ROWS; // this is the overall width of the matrix w = ncol * ew + (ncol - 1) * SPACE_BETWEEN_COLUMNS; // this is the vertical coordinate of the matrix y = -(h / 2); // move elements around for (row = 0; row < nrow; row++) { for (col = 0; col < ncol; col++) { i = row * ncol + col; // first move to upper left corner of matrix dx = x - elem[i].x; dy = y - elem[i].y; move(elem[i].index, elem[i].index + elem[i].count, dx, dy); // now move to official position dx = 0; if (col > 0) dx = col * (ew + SPACE_BETWEEN_COLUMNS); dy = 0; if (row > 0) dy = row * (eh + SPACE_BETWEEN_ROWS); // small correction for horizontal centering dx += (ew - elem[i].w) / 2; // small correction for vertical centering dy += (eh - elem[i].h) / 2; move(elem[i].index, elem[i].index + elem[i].count, dx, dy); } } emit_x = x + w; #if 0 // left brace for (i = 0; i < h; i++) { if (yindex == YMAX) break; chartab[yindex].c = '|'; chartab[yindex].x = x - 2; chartab[yindex].y = y + i; yindex++; } // right brace emit_x++; for (i = 0; i < h; i++) { if (yindex == YMAX) break; chartab[yindex].c = '|'; chartab[yindex].x = emit_x; chartab[yindex].y = y + i; yindex++; } emit_x++; #endif } static void emit_flat_tensor(U *p) { int k = 0; emit_tensor_inner(p, 0, &k); } static void emit_tensor_inner(U *p, int j, int *k) { int i; __emit_char('('); for (i = 0; i < p->u.tensor->dim[j]; i++) { if (j + 1 == p->u.tensor->ndim) { emit_expr(p->u.tensor->elem[*k]); *k = *k + 1; } else emit_tensor_inner(p, j + 1, k); if (i + 1 < p->u.tensor->dim[j]) __emit_char(','); } __emit_char(')'); } static char *s[] = { "format=1", "", "((a,b),(c,d))", "a b\n" "\n" "c d", "1/sqrt(-15)", " i\n" "- -----------\n" " 1/2 1/2\n" " 3 5", "x^(1/a)", " 1/a\n" "x", "x^(a/b)", " a/b\n" "x", "x^(a/2)", " 1/2 a\n" "x", "x^(1/(a+b))", " 1/(a + b)\n" "x", }; void test_display(void) { test(__FILE__, s, sizeof s / sizeof (char *)); }