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How does storing integers in 32-bit values help the issue of integers being truncated to 53 bits?

53 bits that cannot overflow (it only becomes less accurate) is not enough but 64 bits are, even with the risk of overflow?

Who said anything about 64 bits?

The complaint was that JavaScript doesn't have 64-bit integers but only 53.

Clearly 2^32+2^32 < 2*53, so there is no problem ;-)