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...Algorithm: this is probably the most contentious area. Every computer is made with at least one (some have 2 that can be switched). Some are quite aggressive (will give longish NDL while getting you out of the water fairly quickly) whereas others are more conservative (will give a larger margin of safety). All computers will allow a range of conservatism to allow you to tailor it depending on fitness etc. Read up on the algorithm(s) for the computer you are looking at before you buy it...
Good advice. Below is a relatively complete listing of available computer brands and the decompression algorithms they run. I have categorized each as conservative, moderate, or liberal. Feel free to disagree with my categories, mainly based on 1st dive NDLs and ScubaLab hyperbaric unit repetitive dive simulations. The emphasis here is no stop diving. The availability of hoseless air integration is designated.
Dive computer brands and decompression algorithms
Aqua Lung manufactured by OEM Pelagic Pressure Systems owned by Aqua Lung, runs PZ+ a Buhlmann variant, moderate, HAI
Atomic runs Atomic RGBM, liberal
Cressi runs Cressi RGBM, conservative
Deepblu runs a Buhlmann variant, conservative
Divecomputer.eu/ Deep 6 Buhlmann ZH-L16C with GF, variable from conservative to liberal
Divesoft runs Buhlmann ZH-L16C with custom GFs, variable from conservative to liberal
Garmin runs Buhlmann ZH-L16C with preset and custom GFs, variable from conservative to liberal
Genesis manufactured by PPS, runs DSAT, liberal
Heinrichs Weikamp (not available in US) Buhlmann ZH-L16C with GFs, variable from conservative to liberal, HAI
Mares runs Mares RGBM, conservative, HAI
Oceanic manufactured by PPS, runs both DSAT and PZ+, liberal and moderate, HAI
Ratio runs Buhlmann ZH-L16B with preset and/or custom GFs, variable from conservative to liberal, HAI
Scubapro runs Buhlmann ZH-L8 ADT MB or 16 ADT MB, conservative, HAI
Seac (made by Ratio) runs Buhlmann ZH-L16B with preset GFs, variable from conservative to liberal, HAI
Shearwater runs Buhlmann ZH-L16C with preset or custom GFs, variable from conservative to liberal, HAI (PPS)
Sherwood manufactured by PPS, runs DSAT, liberal, HAI
Suunto runs Suunto RGBM, moderate (HelO2, and D9tx run Technical RGBM. DX, Eon Steel and Core run Fused RGBM (Technical/Full) can be liberal), HAI
Tusa manufactured by PPS, runs PZ+, moderate
Notes:
Buhlmann ZH-L16C: 45/95 would generally be considered liberal, 40/85 moderate, 35/75 conservative
HAI: hoseless air integrated option available
PPS: Pelagic Pressure Systems