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The radix 2^51 trick (2017)

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Resurfaced independently across 3 calendar years, with breakout response in 2 of them.

submissions
5
submitters
5
observed span
2020–2025
peak thread · 83 comments
518 pts
latest 20+ return · 2025-05-30
431 pts

Submission timeline

2007–2026

One slot for every year since HN launched. Height is that year's peak points; orange marks a 100+ point or 50+ comment breakout. Select a bar to open its strongest thread.

First comments on top threads

HN comment order

In hardware this would be called a carry save adder [1]. One interesting fact about carry save adders is that the carry part of the register can be extended in order to avoid any carrying between words for very long periods of time. Instead of using 53 bits to represent 52 bits, use 60 bits, and now you can perform 256 sequential additions with no carrying between words before the carry part saturates and needs to be handled. Somewhat surprisingly…

> Aside: Why 13 bits instead of 12? For our purposes, we’re going to ignore the carries in the most significant limb, allowing numbers to wrap when they overflow past 2256 - 1 (just like how unsigned addition works in C with normal size integer types). As a result, we can assign 52 bits to the most significant limb and ignore the fact that it will run out of room for carries before the other limbs do. Why not give…

addaon·431-point thread·

I believe the general name of this trick is "carry save addition". https://en.wikipedia.org/wiki/Carry-save_adder

The first top-level comment from each of the four biggest threads, in HN’s own order. Excerpts are shortened; open a comment for full context.

Breakout years
2

100+ points or 50+ comments

Total points
1004

reference only — not used in Hall rules or ranking

Total comments
171

reference only — not used in Hall rules or ranking

Every submission

DateTitle as submittedByPointsComments
2020-05-29The radix 2^51 trick (2017)First breakout · Best threadmooreds51883
2022-05-30The radix 2^51 trick (2017)ddtaylor20
2022-11-22The radix 2^51 trickshkhuz516
2022-11-22The radix 2^51 trickot20
2025-05-30The radix 2^51 trick (2017)Hall induction · Latest 20+ point returnblobcode43182