{"header":{"message":"Arith: Implement rational numbers\n","description":null,"timestamp":"2020-06-10T04:07:28Z","authors":[{"email":"schnetter@gmail.com","name":"Erik Schnetter"}]},"hash":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC","authors":[],"deps":{"hashes":[["SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC","Arith: Implement rational numbers\n"],["AA",null],["HORXVU5QMFSZAMX6HO4O42J73IFN7SH6IWU5PGYE347QIX3TBALQC","Arith: New classes vec, mat; new function sum\n"],["O4KDCA5IHMJJEJZIYAMD3TDFQ2U6Z6VXE7JWSFFTOCBZ6S2IVALAC","Arith: Rename thorn Dual to Arith\n"],["DBMXGY4DEQNQQ2G3B66DMPIVNUOLHAJ2QJ6BBNPASUUTTHXLPV2AC","Dual: New thorn implementing dual numbers\n"]],"deps":["HORXVU5QMFSZAMX6HO4O42J73IFN7SH6IWU5PGYE347QIX3TBALQC"],"known":["DBMXGY4DEQNQQ2G3B66DMPIVNUOLHAJ2QJ6BBNPASUUTTHXLPV2AC","O4KDCA5IHMJJEJZIYAMD3TDFQ2U6Z6VXE7JWSFFTOCBZ6S2IVALAC"]},"hunks":[{"Replacement":{"inode":{"change":3,"pos":6031},"path":"Arith/src/make.code.defn","line":4,"ins":{"up_context":[{"change":3,"pos":6108}],"down_context":[{"change":3,"pos":6124}],"flag":"BLOCK","start":0,"end":53,"inode":{"change":3,"pos":6031}},"del":{"edges":[{"previous":"BLOCK","flag":"BLOCK | DELETED","from":{"change":3,"pos":6108},"to":{"change":2,"start":109,"end":149},"introduced_by":2}],"inode":{"change":3,"pos":6031}},"ins_contents":[{"Add":{"text":"SRCS = dual.cxx mat.cxx rational.cxx sum.cxx vec.cxx","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:52"}}],"del_contents":[{"Del":{"text":"SRCS = dual.cxx mat.cxx sum.cxx vec.cxx","pos":"HORXVU5QMFSZAMX6HO4O42J73IFN7SH6IWU5PGYE347QIX3TBALQC:148"}}]}},{"FileAdd":{"meta":{"basename":"rational.cxx","metadata":420},"path":"Arith/src/rational.cxx","context":[{"change":3,"pos":425}],"contents":[{"Add":{"text":"#include \"rational.hxx\"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:93"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:94"}},{"Add":{"text":"#include ","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:113"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:114"}},{"Add":{"text":"namespace Arith {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:132"}},{"Add":{"text":"using namespace std;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:153"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:154"}},{"Add":{"text":"template constexpr bool isgood(const rational &x) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:222"}},{"Add":{"text":" return x.den >= 0 && gcd(x.num, x.den) == 1;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:269"}},{"Add":{"text":"}","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:271"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:272"}},{"Add":{"text":"// This function is compiled, but not executed. The tests are \"run\" at","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:343"}},{"Add":{"text":"// compile time. If this function compiles, the tests pass.","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:403"}},{"Add":{"text":"void TestRational() {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:425"}},{"Add":{"text":" static_assert(rational().num == 0);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:463"}},{"Add":{"text":" static_assert(rational(1).num == 1);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:502"}},{"Add":{"text":" static_assert(rational(1, 2).num == 1);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:544"}},{"Add":{"text":" static_assert(rational(2, 4).num == 1);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:586"}},{"Add":{"text":" static_assert(rational().den == 1);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:624"}},{"Add":{"text":" static_assert(rational(1).den == 1);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:663"}},{"Add":{"text":" static_assert(rational(1, 2).den == 2);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:705"}},{"Add":{"text":" static_assert(rational(2, 4).den == 2);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:747"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:748"}},{"Add":{"text":" constexpr auto n = rational();","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:781"}},{"Add":{"text":" constexpr auto e = rational(1);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:815"}},{"Add":{"text":" constexpr auto x = rational(1, 2);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:852"}},{"Add":{"text":" constexpr auto y = rational(2, 3);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:889"}},{"Add":{"text":" constexpr auto z = rational(3, 4);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:926"}},{"Add":{"text":" constexpr auto a = 4;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:950"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:951"}},{"Add":{"text":" +x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:957"}},{"Add":{"text":" -x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:963"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:964"}},{"Add":{"text":" x + y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:973"}},{"Add":{"text":" x - y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:982"}},{"Add":{"text":" x *y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:990"}},{"Add":{"text":" x / y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:999"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1000"}},{"Add":{"text":" a + y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1009"}},{"Add":{"text":" a - y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1018"}},{"Add":{"text":" a *y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1026"}},{"Add":{"text":" a / y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1035"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1036"}},{"Add":{"text":" x + a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1045"}},{"Add":{"text":" x - a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1054"}},{"Add":{"text":" x *a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1062"}},{"Add":{"text":" x / a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1071"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1072"}},{"Add":{"text":" auto r = x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1086"}},{"Add":{"text":" r = x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1095"}},{"Add":{"text":" r += y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1105"}},{"Add":{"text":" r = x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1114"}},{"Add":{"text":" r -= y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1124"}},{"Add":{"text":" r = x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1133"}},{"Add":{"text":" r *= y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1143"}},{"Add":{"text":" r = x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1152"}},{"Add":{"text":" r /= y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1162"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1163"}},{"Add":{"text":" r = x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1172"}},{"Add":{"text":" r += a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1182"}},{"Add":{"text":" r = x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1191"}},{"Add":{"text":" r -= a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1201"}},{"Add":{"text":" r = x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1210"}},{"Add":{"text":" r *= a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1220"}},{"Add":{"text":" r = x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1229"}},{"Add":{"text":" r /= a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1239"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1240"}},{"Add":{"text":" x == y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1250"}},{"Add":{"text":" x != y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1260"}},{"Add":{"text":" x < y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1269"}},{"Add":{"text":" x > y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1278"}},{"Add":{"text":" x <= y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1288"}},{"Add":{"text":" x >= y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1298"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1299"}},{"Add":{"text":" a == y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1309"}},{"Add":{"text":" a != y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1319"}},{"Add":{"text":" a < y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1328"}},{"Add":{"text":" a > y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1337"}},{"Add":{"text":" a <= y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1347"}},{"Add":{"text":" a >= y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1357"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1358"}},{"Add":{"text":" x == a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1368"}},{"Add":{"text":" x != a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1378"}},{"Add":{"text":" x < a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1387"}},{"Add":{"text":" x > a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1396"}},{"Add":{"text":" x <= a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1406"}},{"Add":{"text":" x >= a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1416"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1417"}},{"Add":{"text":" static_assert(isgood(abs(x)));","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1450"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1451"}},{"Add":{"text":" static_assert(isgood(max(x, y)));","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1487"}},{"Add":{"text":" static_assert(isgood(min(x, y)));","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1523"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1524"}},{"Add":{"text":" static_assert(isgood(pow(x, a)));","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1560"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1561"}},{"Add":{"text":" static_assert(+x == n + x);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1591"}},{"Add":{"text":" static_assert(x + n == x);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1620"}},{"Add":{"text":" static_assert(n + x == x);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1649"}},{"Add":{"text":" static_assert(x + (y + z) == (x + y) + z);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1694"}},{"Add":{"text":" static_assert(x + y == y + x);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1727"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1728"}},{"Add":{"text":" static_assert(-x == n - x);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1758"}},{"Add":{"text":" static_assert(-(-x) == x);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1787"}},{"Add":{"text":" static_assert(x + (-y) == x - y);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1823"}},{"Add":{"text":" static_assert(x - x == n);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1852"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1853"}},{"Add":{"text":" static_assert(x * e == x);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1882"}},{"Add":{"text":" static_assert(e * x == x);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1911"}},{"Add":{"text":" static_assert(x * (y * z) == (x * y) * z);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1956"}},{"Add":{"text":" static_assert(x * y == y * x);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:1989"}},{"Add":{"text":" static_assert(n * x == n);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2018"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2019"}},{"Add":{"text":" static_assert(1 / (1 / x) == x);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2054"}},{"Add":{"text":" static_assert(x / x == e);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2083"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2084"}},{"Add":{"text":" static_assert(x * (y + z) == x * y + x * z);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2131"}},{"Add":{"text":"}","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2133"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2134"}},{"Add":{"text":"} // namespace Arith","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2155"}}]}},{"FileAdd":{"meta":{"basename":"rational.hxx","metadata":420},"path":"Arith/src/rational.hxx","context":[{"change":3,"pos":425}],"contents":[{"Add":{"text":"#ifndef RATIONAL_HXX","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2193"}},{"Add":{"text":"#define RATIONAL_HXX","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2214"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2215"}},{"Add":{"text":"#include ","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2236"}},{"Add":{"text":"#include ","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2255"}},{"Add":{"text":"#include ","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2272"}},{"Add":{"text":"#include ","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2291"}},{"Add":{"text":"#include ","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2310"}},{"Add":{"text":"#include ","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2330"}},{"Add":{"text":"#include ","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2349"}},{"Add":{"text":"#include ","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2372"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2373"}},{"Add":{"text":"namespace Arith {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2391"}},{"Add":{"text":"using namespace std;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2412"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2413"}},{"Add":{"text":"template struct rational {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2463"}},{"Add":{"text":" I num, den;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2477"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2478"}},{"Add":{"text":" struct no_normalize {};","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2504"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2505"}},{"Add":{"text":" constexpr void normalize() {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2536"}},{"Add":{"text":" const I x = gcd(num, den);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2567"}},{"Add":{"text":" num /= x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2581"}},{"Add":{"text":" den /= x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2595"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2599"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2600"}},{"Add":{"text":" constexpr rational() : num(0), den(1) {}","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2643"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2644"}},{"Add":{"text":" constexpr rational(const rational &) = default;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2694"}},{"Add":{"text":" constexpr rational(rational &&) = default;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2739"}},{"Add":{"text":" constexpr rational &operator=(const rational &) = default;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2800"}},{"Add":{"text":" constexpr rational &operator=(rational &&) = default;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2856"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2857"}},{"Add":{"text":" template > * = nullptr>","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2925"}},{"Add":{"text":" constexpr rational(const J &i) : num(i), den(1) {}","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:2978"}},{"Add":{"text":" template > * = nullptr,","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3058"}},{"Add":{"text":" enable_if_t > * = nullptr>","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3114"}},{"Add":{"text":" constexpr rational(const J &num, const K &den, no_normalize)","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3177"}},{"Add":{"text":" : num(num), den(den) {}","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3207"}},{"Add":{"text":" template > * = nullptr,","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3287"}},{"Add":{"text":" enable_if_t > * = nullptr>","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3343"}},{"Add":{"text":" constexpr rational(const J &num, const K &den) : num(num), den(den) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3415"}},{"Add":{"text":" if (this->den < 0) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3440"}},{"Add":{"text":" this->num = -this->num;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3470"}},{"Add":{"text":" this->den = -this->den;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3500"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3506"}},{"Add":{"text":" normalize();","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3523"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3527"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3528"}},{"Add":{"text":" template > * = nullptr>","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3602"}},{"Add":{"text":" constexpr rational(const F &f) : num(0), den(1) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3654"}},{"Add":{"text":" const F f1 = nextafter(f);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3685"}},{"Add":{"text":" const F df = f1 - f;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3710"}},{"Add":{"text":" const F df1 = 1 / df;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3736"}},{"Add":{"text":" assert(df1 == rint(df1));","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3766"}},{"Add":{"text":" den = llrint(df1);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3789"}},{"Add":{"text":" num = llrint(f * df1);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3816"}},{"Add":{"text":" normalize();","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3833"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3837"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3838"}},{"Add":{"text":" template > * = nullptr>","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3912"}},{"Add":{"text":" constexpr operator F() const {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3945"}},{"Add":{"text":" return F(num) / F(den);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3973"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3977"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:3978"}},{"Add":{"text":" friend constexpr rational operator+(const rational &x) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4037"}},{"Add":{"text":" return rational(+x.num, x.den, no_normalize());","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4089"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4093"}},{"Add":{"text":" friend constexpr rational operator-(const rational &x) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4152"}},{"Add":{"text":" return rational(-x.num, x.den, no_normalize());","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4204"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4208"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4209"}},{"Add":{"text":" friend constexpr rational operator+(const rational &x, const rational &y) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4287"}},{"Add":{"text":" return rational(x.num * y.den + x.den * y.num, x.den * y.den);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4354"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4358"}},{"Add":{"text":" friend constexpr rational operator-(const rational &x, const rational &y) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4436"}},{"Add":{"text":" return rational(x.num * y.den - x.den * y.num, x.den * y.den);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4503"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4507"}},{"Add":{"text":" friend constexpr rational operator*(const rational &x, const rational &y) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4585"}},{"Add":{"text":" return rational(x.num * y.num, x.den * y.den);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4636"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4640"}},{"Add":{"text":" friend constexpr rational operator/(const rational &x, const rational &y) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4718"}},{"Add":{"text":" return rational(x.num * y.den, x.den * y.num);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4769"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4773"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4774"}},{"Add":{"text":" constexpr rational &operator+=(const rational &x) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4828"}},{"Add":{"text":" return *this = *this + x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4858"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4862"}},{"Add":{"text":" constexpr rational &operator-=(const rational &x) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4916"}},{"Add":{"text":" return *this = *this - x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4946"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:4950"}},{"Add":{"text":" constexpr rational &operator*=(const rational &x) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5004"}},{"Add":{"text":" return *this = *this * x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5034"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5038"}},{"Add":{"text":" constexpr rational &operator/=(const rational &x) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5092"}},{"Add":{"text":" return *this = *this / x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5122"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5126"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5127"}},{"Add":{"text":" friend constexpr bool operator==(const rational &x, const rational &y) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5202"}},{"Add":{"text":" return x.num * y.den == x.den * y.num;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5245"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5249"}},{"Add":{"text":" friend constexpr bool operator!=(const rational &x, const rational &y) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5324"}},{"Add":{"text":" return !(x == y);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5346"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5350"}},{"Add":{"text":" friend constexpr bool operator<(const rational &x, const rational &y) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5424"}},{"Add":{"text":" return x.num * y.den < x.den * y.num;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5466"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5470"}},{"Add":{"text":" friend constexpr bool operator>(const rational &x, const rational &y) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5544"}},{"Add":{"text":" return y < x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5562"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5566"}},{"Add":{"text":" friend constexpr bool operator<=(const rational &x, const rational &y) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5641"}},{"Add":{"text":" return !(x > y);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5662"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5666"}},{"Add":{"text":" friend constexpr bool operator>=(const rational &x, const rational &y) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5741"}},{"Add":{"text":" return y <= x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5760"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5764"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5765"}},{"Add":{"text":" friend ostream &operator<<(ostream &os, const rational &x) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5828"}},{"Add":{"text":" return os << \"(\" << x.num << \"/\" << x.den << \")\";","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5882"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5886"}},{"Add":{"text":"};","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5889"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5890"}},{"Add":{"text":"template constexpr rational abs(const rational &x) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5962"}},{"Add":{"text":" // std::abs is not constexpr","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:5993"}},{"Add":{"text":" return rational(x.num >= 0 ? x.num : -x.num, x.den);","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6051"}},{"Add":{"text":"}","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6053"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6054"}},{"Add":{"text":"template ","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6076"}},{"Add":{"text":"constexpr rational max(const rational &x, const rational &y) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6148"}},{"Add":{"text":" return x >= y ? x : y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6173"}},{"Add":{"text":"}","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6175"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6176"}},{"Add":{"text":"template ","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6198"}},{"Add":{"text":"constexpr rational min(const rational &x, const rational &y) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6270"}},{"Add":{"text":" return x <= y ? x : y;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6295"}},{"Add":{"text":"}","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6297"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6298"}},{"Add":{"text":"template > * = nullptr>","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6376"}},{"Add":{"text":"constexpr rational pow(rational x, J a) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6424"}},{"Add":{"text":" if (a < 0) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6439"}},{"Add":{"text":" x = 1 / x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6454"}},{"Add":{"text":" a = -a;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6466"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6470"}},{"Add":{"text":" rational r = 1;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6491"}},{"Add":{"text":" while (a > 0) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6509"}},{"Add":{"text":" if (a % 2)","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6524"}},{"Add":{"text":" r *= x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6538"}},{"Add":{"text":" x *= x;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6550"}},{"Add":{"text":" a /= 2;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6562"}},{"Add":{"text":" }","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6566"}},{"Add":{"text":" return r;","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6578"}},{"Add":{"text":"}","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6580"}},{"Add":{"text":"template ","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6602"}},{"Add":{"text":"constexpr double pow(const rational &x, const rational &y) {","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6669"}},{"Add":{"text":" return std::pow(double(x), double(y));","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6710"}},{"Add":{"text":"}","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6712"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6713"}},{"Add":{"text":"} // namespace Arith","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6734"}},{"Add":{"text":"","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6735"}},{"Add":{"text":"#endif // #ifndef RATIONAL_HXX","pos":"SYAEXVWLW45AYAKKAY7OJB5TUUCQWI2GDKRD7UYPSRIH3LPDWAVQC:6766"}}]}}],"owner":"eschnett","repo":"cactusamrex","login":null}

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