幾種計算圓周率的軟體比較

1. super pi 日本人 Yasumasa Kanada 編寫，圖形介面,最新版 2013年的1.9,網站
2. y-cruncher 美籍華人Alexander J. Yee編寫，命令列,最新版 2016年的0.7.1.9466,網站
3. quick pi 美國人Steve Pagliarulo編寫，命令列，最新版 2008年的4.5,網站
4. PiFast 法國人Xavier Gourdon編寫，命令列，最新版 2003年的4.3 (4.4beta),網站
5. TPI 法國人Fabrice Bellard編寫，命令列，最新版 2010年的0.93,網站
   參考資料：
   https://en.wikipedia.org/wiki/Approximations_of_%CF%80
   http://www.pi314.net/eng/index.php
   http://thestarman.pcministry.com/math/pi/piprogs.html
   https://gmplib.org/pi-with-gmp.html
   測試結果： super pi
   
   y-cruncher

y-cruncher v0.7.1 Build 9466

Detecting Environment...

CPU Vendor:
    AMD         = No
    Intel       = Yes

OS Features:
  * 64-bit      = No
  * OS AVX      = Yes
  * OS AVX512   = No

Hardware Features:
    MMX         = Yes
  * x64         = Yes
  * ABM         = Yes
    RDRAND      = Yes
    RDSEED      = No
    BMI1        = Yes
  * BMI2        = Yes
  * ADX         = No
    MPX         = No
    PREFETCHW   = No
    PREFETCHWT1 = No

SIMD: 128-bit
  * SSE         = Yes
  * SSE2        = Yes
  * SSE3        = Yes
  * SSSE3       = Yes
    SSE4a       = No
  * SSE4.1      = Yes
  * SSE4.2      = Yes
    AES-NI      = Yes
    SHA         = No

SIMD: 256-bit
  * AVX         = Yes
  * XOP         = No
  * FMA3        = Yes
  * FMA4        = No
  * AVX2        = Yes

SIMD: 512-bit
  * AVX512-F    = No
    AVX512-CD   = No
    AVX512-PF   = No
    AVX512-ER   = No
  * AVX512-VL   = No
  * AVX512-BW   = No
  * AVX512-DQ   = No
  * AVX512-IFMA = No
  * AVX512-VBMI = No

Performance Warning:

A 32-bit OS has been detected on an x64 SSE3 capable processor.

To achieve maximum performance, you must run a 64-bit OS.
The 64-bit version of this program can be more than 2x faster.

請按任意鍵繼續. . .



Auto-Selecting: x86 SSE3

D:\y-cruncher v0.7.1.9466\Binaries/x86 SSE3.exe


Launching y-cruncher...
================================================================


Checking processor/OS features...

Required Features:
    SSE, SSE2, SSE3




Unable to acquire the permission, "SeLockMemoryPrivilege".
Large pages and page locking will not be possible.


Constant:   Pi
Algorithm:  Chudnovsky Formula

Decimal Digits:       100,000,000
Hexadecimal Digits:   Disabled

Computation Mode:     Ram Only
Multi-Threading:      Push Pool  ->  4 / ?  (randomization on)

Start Time: Sun Sep 25 12:31:00 2016

Reserving Working Memory...          450 MiB
Constructing Twiddle Tables...      38.0 MiB

Begin Computation:

Summing Series...  7,051,370 terms
Time:    91.377 seconds  ( 1.523 minutes )
Division...
Time:    6.503 seconds  ( 0.108 minutes )
InvSqrt...
Time:    4.025 seconds  ( 0.067 minutes )
Final Multiply...
Time:    2.682 seconds  ( 0.045 minutes )

Pi:  104.592 seconds  ( 1.743 minutes )

Base Converting:
Time:    9.762 seconds  ( 0.163 minutes )

Writing Decimal Digits:   100,000,000  digits written

Verifying Base Conversion...
Time:    3.937 seconds  ( 0.066 minutes )

Start Time: Sun Sep 25 12:31:00 2016
End Time:   Sun Sep 25 12:33:00 2016

Total Computation Time:     114.353 seconds  ( 1.906 minutes )
Start-to-End Wall Time:     120.432 seconds  ( 2.007 minutes )

CPU Utilization:          366.64 %  +    0.20 % kernel overhead
Multi-core Efficiency:     91.66 %  +    0.05 % kernel overhead

Last Digits:  Pi
9948682556 3967530560 3352869667 7734610718 4471868529  :  99,999,950
7572203175 2074898161 1683139375 1497058112 0187751592  :  100,000,000

Spot Check: Good through 100,000,000

Version:              0.7.1.9466 (Windows - x86 SSE3)
Processor(s):         Intel(R) Core(TM) i3-4010U CPU @ 1.70GHz
Topology:             4 threads / 2 cores / 1 socket / 1 NUMA node
Physical Memory:      4,294,967,296 (4.00 GiB)
CPU Base Frequency:   1,696,100,096 Hz

Validation File: Pi - 20160925-123301.txt

PiFast (1億位異常退出，改為100萬位)

PiFast, version 4.4 (Copyright 1999-2003 Xavier Gourdon)
http://numbers.computation.free.fr/Constants/PiProgram/pifast.html
Menu :
[0] Compute Pi with Chudnovsky method (Fastest)
[1] Compute Pi with Ramanujan method
[2] Compute E by the exponential series exp(1)
[3] Compute E by the exponential series 1/exp(-1)
[4] Compute Sqrt(2) (useful for testing)
[5] Define your constant with hypergeometric series
[6] Compute a user constant from a .pifast file
[7] Decompress a result file
[8] Check a compress result Pi file
Enter your choice : 0

Choose your computation mode :
[0] standard mode (no disk memory used)
[1] basic disk memory mode (for big computations)
[2] advanced disk memory mode (for huge computations)
Enter your choice : 0

Number of decimal digits : 1000000
Possible FFT modes, with approximate needed memory :

FFT Size= 128 k, Mem=7769 K (Fastest mode)
FFT Size=  64 k, Mem=5077 K (Time: Fastest mode * 1.1)
FFT Size=  32 k, Mem=3797 K (Time: Fastest mode * 1.3)
FFT Size=  16 k, Mem=3155 K (Time: Fastest mode * 1.7)
FFT Size=   8 k, Mem=2835 K (Time: Fastest mode * 2.7)
FFT Size=   4 k, Mem=2674 K (Time: Fastest mode * 4.7)
...

Enter FFT Size in k :128

Compressed output (also useful to specify output format) ? [0=No, 1=Yes] : 0

Total Physical Memory Allocated = 8155 Kbytes
Computing series with index N=70529
Starting step 5
Starting step 4 ...
Starting step 3 ...
Starting step 2 ...
Starting step 1 ...
Starting step 0 ...
Series computing time : 1.47
Division time : 0.22
InvSqrt time : 0.09
Final huge multiplication time : 0.08
---------------------------------------------------------------
Total computation time : 1.87 seconds(~ 0.00 hours)
Writing informations into file pi.txt

The computation seems OK
Appending result to file pi.txt ...

QuickPi

\qpi45 100000000 >1yi.txt

QPI-QuickPi v4.5, (c) 2000-2008 S. Pagliarulo
Freely distributable, email: s_pagliarulo@hotmail.com

o Intel(R) Core(TM) i3-4010U CPU @ 1.70GHz detected
o Processor speed measured at 1.70 GHz
o Single processor with eight cores and 2-way SMT per core
o 1.2 GB of memory available
o Using default training data

Computation of Pi to 100,000,000 digits
Method used : Chudnovsky
Started : Sun Sep 25 13:32:44 2016

Series size : 7051368  (100,000,015 digits)
Series processing time : 232.82
Final value time : 32.28

Total time : 265.09 seconds (4 mins, 25.09 secs)
Total memory used : 973,365,433 (928.27 MB)

Processor utilization : 160.19%

TPI需要64位windows

D:\>tpi
該版本的 D:\tpi.exe 與您執行的 Windows 版本不相容。請檢視計算機的系統資訊，瞭解是否需要 x86 (32 位)或 x64 (64 位)版本的程式，然後聯
系軟體釋出者。