Meanderings

A ant walks exploring each lattice point in the first quadrant of the plane with the following pattern:

37	→	38	→	39	→	40	→	41	→	42	→	43
↑												↓
36	←	35	←	34	←	33	←	32	←	31		44
										↑		↓
17	→	18	→	19	→	20	→	21		30		45
↑								↓		↑		↓
16	←	15	←	14	←	13		22		29		46
						↑		↓		↑		↓
5	→	6	→	7		12		23		28		47
↑				↓		↑		↓		↑		↓
4	←	3		8		11		24		27		48
		↑		↓		↑		↓		↑		↓
1	→	2		9	→	10		25	→	26		49

The 1st point visited (index = 1) is (0,0)
The 10th point is (3,0)
The 100000th point is (143,316)

What is the 10^17-th point?
What is the index of the point (718281828,141592653)?

Answer format: x,y/index

Example: 143,316/51594074 // For 10^5 and (7182,1415)
[My timing: < 100 ms]