Summation on HP 42S

[Albert Chan]

(09-26-2018 10:10 AM)Frido Bohn Wrote:  The result is (real HP42S) 4.02387322958 10^2567 for both codes. That is precise to the 5th decimal place.
By using the natural logarithm (LN) instead of the decadic (LOG) the precision is increased by 1 decimal place.

To increase precision (speed too!), do 1000! in "shells", 4 numbers at a time
So, only 250 log10() calls instead of full 1000

I use my own fsum.lua code, to collect errors.

Lua> p = require "fsum" () -- goal is log10(1000!)
Lua> shell = function(x) return x * (x+1) * (1000-x) * (1001-x) end
Lua> log10 = math.log10
Lua> for x = 1,500,2 do p:add(log10(shell(x))) end
Lua> = p:total()
2567.6046442221327
Lua> p:add(-2567)
Lua> = 10 ^ p:total()
4.023872600770903

BTW, straight sum of log10 of shells produce mantissa of 4.023872600761316