/* * Copyright (c) 1993 David I. Bell * Permission is granted to use, distribute, or modify this source, * provided that this copyright notice remains intact. * * Routines to handle numbers modulo a specified number. * a (mod N) */ obj mod {a}; /* definition of the object */ global mod_value; /* modulus value (value of N) */ define mod(a) { local x; obj mod x; if (!isreal(a) || !isint(a)) quit "Bad argument for mod function"; x.a = a % mod_value; return x; } define mod_print(a) { if (digits(mod_value) <= 20) print a.a, "(mod", mod_value : ")" :; else print a.a, "(mod N)" :; } define mod_one() { return mod(1); } define mod_cmp(a, b) { if (isnum(a)) return (a % mod_value) != b.a; if (isnum(b)) return (b % mod_value) != a.a; return a.a != b.a; } define mod_rel(a, b) { if (isnum(a)) a = mod(a); if (isnum(b)) b = mod(b); if (a.a < b.a) return -1; return a.a != b.a; } define mod_add(a, b) { local x; obj mod x; if (isnum(b)) { if (!isint(b)) quit "Adding non-integer"; x.a = (a.a + b) % mod_value; return x; } if (isnum(a)) { if (!isint(a)) quit "Adding non-integer"; x.a = (a + b.a) % mod_value; return x; } x.a = (a.a + b.a) % mod_value; return x; } define mod_sub(a, b) { return a + (-b); } define mod_neg(a) { local x; obj mod x; x.a = mod_value - a.a; return x; } define mod_mul(a, b) { local x; obj mod x; if (isnum(b)) { if (!isint(b)) quit "Multiplying by non-integer"; x.a = (a.a * b) % mod_value; return x; } if (isnum(a)) { if (!isint(a)) quit "Multiplying by non-integer"; x.a = (a * b.a) % mod_value; return x; } x.a = (a.a * b.a) % mod_value; return x; } define mod_square(a) { local x; obj mod x; x.a = a.a^2 % mod_value; return x; } define mod_inc(a) { local x; x = a; if (++x.a == mod_value) x.a = 0; return x; } define mod_dec(a) { local x; x = a; if (--x.a < 0) x.a = mod_value - 1; return x; } define mod_inv(a) { local x; obj mod x; x.a = minv(a.a, mod_value); return x; } define mod_div(a, b) { local c, x, y; obj mod x, y; if (isnum(a)) a = mod(a); if (isnum(b)) b = mod(b); c = gcd(a.a, b.a); x.a = a.a / c; y.a = b.a / c; return x * inverse(y); } define mod_pow(a, b) { local x, y, z; obj mod x; y = a; z = b; if (b < 0) { y = inverse(a); z = -b; } x.a = pmod(y.a, z, mod_value); return x; } mod_value = 100; /* default */ global lib_debug; if (!isnum(lib_debug) || lib_debug>0) print "obj mod {a} defined" if (!isnum(lib_debug) || lib_debug>0) print "mod(a) defined" if (!isnum(lib_debug) || lib_debug>0) print "mod_print(a) defined" if (!isnum(lib_debug) || lib_debug>0) print "mod_one(a) defined" if (!isnum(lib_debug) || lib_debug>0) print "mod_cmp(a, b) defined" if (!isnum(lib_debug) || lib_debug>0) print "mod_rel(a, b) defined" if (!isnum(lib_debug) || lib_debug>0) print "mod_add(a, b) defined" if (!isnum(lib_debug) || lib_debug>0) print "mod_sub(a, b) defined" if (!isnum(lib_debug) || lib_debug>0) print "mod_mod(a, b) defined" if (!isnum(lib_debug) || lib_debug>0) print "mod_square(a) defined" if (!isnum(lib_debug) || lib_debug>0) print "mod_inc(a) defined" if (!isnum(lib_debug) || lib_debug>0) print "mod_dec(a) defined" if (!isnum(lib_debug) || lib_debug>0) print "mod_inv(a) defined" if (!isnum(lib_debug) || lib_debug>0) print "mod_div(a, b) defined" if (!isnum(lib_debug) || lib_debug>0) print "mod_pow(a, b) defined" if (!isnum(lib_debug) || lib_debug>0) print "mod_value defined" if (!isnum(lib_debug) || lib_debug>0) print "set mod_value as needed"