8f34c2760d
project:cfg:BoardConfig_IPC: Added fastboot BoardConfig file and firmware post-scripts, distinguishing between the BoardConfigs for Luckfox Pico Pro and Luckfox Pico Max. project:app: Added fastboot_client and rk_smart_door for quick boot applications; updated rkipc app to adapt to the latest media library. media:samples: Added more usage examples. media:rockit: Fixed bugs; removed support for retrieving data frames from VPSS. media:isp: Updated rkaiq library and related tools to support connection to RKISP_Tuner. sysdrv:Makefile: Added support for compiling drv_ko on Luckfox Pico Ultra W using Ubuntu; added support for custom root filesystem. sysdrv:tools:board: Updated Buildroot optional mirror sources, updated some software versions, and stored device tree files and configuration files that undergo multiple modifications for U-Boot and kernel separately. sysdrv:source:mcu: Used RISC-V MCU SDK with RT-Thread system, mainly for initializing camera AE during quick boot. sysdrv:source:uboot: Added support for fastboot; added high baud rate DDR bin for serial firmware upgrades. sysdrv:source:kernel: Upgraded to version 5.10.160; increased NPU frequency for RV1106G3; added support for fastboot. Signed-off-by: luckfox-eng29 <eng29@luckfox.com>
97 lines
2.9 KiB
Plaintext
Executable File
97 lines
2.9 KiB
Plaintext
Executable File
PI(= 3.1415926535897932384626...) Calculation Program
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ver. LG1.1.2-MP1.5.2a Nov. 1999
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Files:
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fftsg_h.c : FFT Package - split-radix - use no work areas
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pi_fftcs.c : PI Calculation Program - memory save version
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-- use rdft() in "fft*g_h.c"
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readme.txt : this file
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Makefile : - for gcc modify for your own compiler.
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To Compile:
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Check macros in "pi_fftcs.c" and modify if necessary.
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DBL_ERROR_MARGIN is very impotant parameter.
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If DBL_ERROR_MARGIN is very small then efficiency will be bad.
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If DBL_ERROR_MARGIN >= 0.5 then it may calculate a wrong result.
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Example Compilation:
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GNU:
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gcc -O -funroll-loops -fomit-frame-pointer pi_fftcs.c fftsg_h.c -lm -o pi_css5
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SUN:
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cc -fast pi_fftcs.c fftsg_h.c -lm -o pi_css5
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HP:
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aCC -fast pi_fftcs.c fftsg_h.c -lm -o pi_css5
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Microsoft:
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cl -O2 pi_fftcs.c fftsg_h.c -o pi_css5
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Relationship between Number of Digits and FFT Length:
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ndigit = nfft*log_10(R), R >= 10000 or 1000
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R is a radix of multiple-precision format.
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R depends on DBL_ERROR_MARGIN and
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FFT+machine+compiler's tolerance.
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Number of Floating Point Operations:
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pi_fftcs.c + fftsg_h.c:
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42*nfft*(log_2(nfft))^2 [Operations]
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Memory Use:
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pi_fftcs.c:
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nfft*(6*sizeof(short int)+3*sizeof(double)) [Bytes]
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AGM Algorithm:
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---- a formula based on the AGM (Arithmetic-Geometric Mean) ----
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c = sqrt(0.125);
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a = 1 + 3 * c;
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b = sqrt(a);
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e = b - 0.625;
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b = 2 * b;
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c = e - c;
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a = a + e;
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npow = 4;
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do {
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npow = 2 * npow;
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e = (a + b) / 2;
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b = sqrt(a * b);
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e = e - b;
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b = 2 * b;
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c = c - e;
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a = e + b;
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} while (e > SQRT_SQRT_EPSILON);
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e = e * e / 4;
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a = a + b;
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pi = (a * a - e - e / 2) / (a * c - e) / npow;
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---- modification ----
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This is a modified version of Gauss-Legendre formula
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(by T.Ooura). It is faster than original version.
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Reference:
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1. E.Salamin,
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Computation of PI Using Arithmetic-Geometric Mean,
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Mathematics of Computation, Vol.30 1976.
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2. R.P.Brent,
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Fast Multiple-Precision Evaluation of Elementary Functions,
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J. ACM 23 1976.
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3. D.Takahasi, Y.Kanada,
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Calculation of PI to 51.5 Billion Decimal Digits on
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Distributed Memoriy Parallel Processors,
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Transactions of Information Processing Society of Japan,
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Vol.39 No.7 1998.
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4. T.Ooura,
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Improvement of the PI Calculation Algorithm and
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Implementation of Fast Multiple-Precision Computation,
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Information Processing Society of Japan SIG Notes,
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98-HPC-74, 1998.
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Copyright
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source files:
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Copyright(C) 1999 Takuya OOURA
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Email: ooura@mmm.t.u-tokyo.ac.jp
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URL: http://momonga.t.u-tokyo.ac.jp/~ooura/fft.html
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You may use, copy, modify this code for any purpose and
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without fee. You may distribute this ORIGINAL package.
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