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List:       gmp-discuss
Subject:    About memory-usage of mpz_mul
From:       Paul.Zimmermann () inria ! fr (paul zimmermann)
Date:       2016-06-22 9:07:44
Message-ID: mwvb114mn3.fsf () tomate ! loria ! fr
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       Dear Akira,

for large inputs, mpz_mul uses FFT (see section "FFT Multiplication"
in the GMP manual). Fast multiplication algorithms like FFT imply a
larger memory usage. Very roughly for a n x n product, you need two
buffers of size about 4n, thus the extra memory usage is 8n (in
addition to the space needed for the inputs and outputs).

In your case 8 * 2.9 GB = 23.2 GB, which is very near from your 23.7 GB of
swap-area.

Paul Zimmermann

> From: Akira Wada <a-wada at mars.dti.ne.jp>
> Date: Wed, 22 Jun 2016 17:17:48 +0900
> 
> Dear Sir.
> 
> I tried to compute 1,000,000,000 digits of PI with S.Lyster's 2terms arctan_formula \
> i.e. 
> PI/4 = 22 * arctan (1/28) + arctan \
> (1744507482180328366854565127/98646395734210062276153190241239) 
> using my program to compute PI using ARCTAN formuae. It taked time about 2 hours 53 \
> minuts, but 
> for 100,000,000 digits only 15 minuts. At last stage of the binary-splitting, \
> mpz_mul (a, b, c) is called 
> i.e.  a = b * c  here length of a : 2.9 GB, b : 1.6 GB , c : 1.3 GB and my PC has \
> 7.8 GB RAM available, 
> and the other large DATA is written out to FILEs. Looking by the system-moniteor, \
> for over 2 hours, 
> " max 23.7 GB of swap-area is in work, and all CPU-usage is holded under 5 % "   \
> WHY ??? 
> 
> Thanks advance.
> 
> Regard,   A.Wada
> 
> PS. Using GMP version is 6.1.0
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