added: 'constgen' directory -- there is a program there to generate some constants used in ttmathbig.h
changed: the size of built-in variables (constants) in ttmathbig.h
now they consist of 256 32bit words
macro TTMATH_BUILTIN_VARIABLES_SIZE is equal: 256u on a 32bit platform and 128ul on a 64bit platform
added: macro CONSTANTSGENERATOR which is useful for generating constants
(it's used by 'gen' program in 'constgen' directory)
after declaring this macro the methods: ExpSurrounding0() and LnSurrounding1() will be public visible
and the inner loop can do more iterations than TTMATH_ARITHMETIC_MAX_LOOP
changed: in methods: ExpSurrounding0() and LnSurrounding1() - the way of comparising with the last word
(now we're comparing not with the last state but with a state from a few words back)
git-svn-id: svn://ttmath.org/publicrep/ttmath/trunk@105 e52654a7-88a9-db11-a3e9-0013d4bc506e
This commit is contained in:
parent
978815f12d
commit
460608859c
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@ -0,0 +1,27 @@
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o = main.o
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CC = g++
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CFLAGS = -s -O2 -DCONSTANTSGENERATOR
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name = gen
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.SUFFIXES: .cpp .o
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.cpp.o:
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$(CC) -c $(CFLAGS) $<
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all: $(name)
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$(name): $(o)
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$(CC) -o $(name) $(CFLAGS) $(o)
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main.o: main.cpp
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clean:
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rm -f *.o
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rm -f *.s
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rm -f $(name)
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rm -f $(name).exe
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@ -0,0 +1,126 @@
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/*
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* This file is a part of TTMath Bignum Library
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* and is distributed under the (new) BSD licence.
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* Author: Tomasz Sowa <t.sowa@slimaczek.pl>
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*/
|
||||
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||||
/*
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||||
* Copyright (c) 2006-2009, Tomasz Sowa
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||||
* All rights reserved.
|
||||
*
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||||
* Redistribution and use in source and binary forms, with or without
|
||||
* modification, are permitted provided that the following conditions are met:
|
||||
*
|
||||
* * Redistributions of source code must retain the above copyright notice,
|
||||
* this list of conditions and the following disclaimer.
|
||||
*
|
||||
* * Redistributions in binary form must reproduce the above copyright
|
||||
* notice, this list of conditions and the following disclaimer in the
|
||||
* documentation and/or other materials provided with the distribution.
|
||||
*
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||||
* * Neither the name Tomasz Sowa nor the names of contributors to this
|
||||
* project may be used to endorse or promote products derived
|
||||
* from this software without specific prior written permission.
|
||||
*
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||||
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
||||
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
|
||||
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
||||
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
||||
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||||
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
||||
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
||||
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
|
||||
* THE POSSIBILITY OF SUCH DAMAGE.
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*/
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/*
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this simple program is used to make constants which then are put into ttmathbig.h
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*/
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#include "../ttmath/ttmath.h"
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#include <iostream>
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void CalcPi()
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{
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ttmath::Big<1,400> pi;
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// 3100 digits after commna, taken from: http://zenwerx.com/pi.php
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pi = "3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679"
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"8214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196"
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"4428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273"
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"7245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094"
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"3305727036575959195309218611738193261179310511854807446237996274956735188575272489122793818301194912"
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"9833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132"
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"0005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235"
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"4201995611212902196086403441815981362977477130996051870721134999999837297804995105973173281609631859"
|
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"5024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303"
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"5982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989"
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"3809525720106548586327886593615338182796823030195203530185296899577362259941389124972177528347913151"
|
||||
"5574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012"
|
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"8583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912"
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"9331367702898915210475216205696602405803815019351125338243003558764024749647326391419927260426992279"
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"6782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955"
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"3211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000"
|
||||
"8164706001614524919217321721477235014144197356854816136115735255213347574184946843852332390739414333"
|
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"4547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383"
|
||||
"8279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863"
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"0674427862203919494504712371378696095636437191728746776465757396241389086583264599581339047802759009"
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"9465764078951269468398352595709825822620522489407726719478268482601476990902640136394437455305068203"
|
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"4962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382"
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"6868386894277415599185592524595395943104997252468084598727364469584865383673622262609912460805124388"
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"4390451244136549762780797715691435997700129616089441694868555848406353422072225828488648158456028506"
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"0168427394522674676788952521385225499546667278239864565961163548862305774564980355936345681743241125"
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"1507606947945109659609402522887971089314566913686722874894056010150330861792868092087476091782493858"
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"9009714909675985261365549781893129784821682998948722658804857564014270477555132379641451523746234364"
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"5428584447952658678210511413547357395231134271661021359695362314429524849371871101457654035902799344"
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"0374200731057853906219838744780847848968332144571386875194350643021845319104848100537061468067491927"
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"8191197939952061419663428754440643745123718192179998391015919561814675142691239748940907186494231961"
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"5679452080951465502252316038819301420937621378559566389377870830390697920773467221825625996615014215";
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std::cout << "---------------- PI ----------------" << std::endl;
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pi.mantissa.PrintTable(std::cout);
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}
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void CalcE()
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{
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ttmath::Big<1,400> e;
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ttmath::uint steps;
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// macro CONSTANTSGENERATOR has to be defined
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e.ExpSurrounding0(1, &steps);
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std::cout << "---------------- e ----------------" << std::endl;
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e.mantissa.PrintTable(std::cout);
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std::cout << "ExpSurrounding0(1): " << steps << " iterations" << std::endl;
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}
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void CalcLn(int x)
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{
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ttmath::Big<1,400> ln;
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ttmath::uint steps;
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// macro CONSTANTSGENERATOR has to be defined
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ln.LnSurrounding1(x, &steps);
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std::cout << "---------------- ln(" << x << ") ----------------" << std::endl;
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ln.mantissa.PrintTable(std::cout);
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std::cout << "LnSurrounding1(" << x << "): " << steps << " iterations" << std::endl;
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}
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int main()
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{
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CalcPi();
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CalcE();
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CalcLn(2);
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CalcLn(10);
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return 0;
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}
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@ -32,20 +32,21 @@ MyBig atemp;
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if( !atemp.Add(b) )
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std::cout << "a + b = " << atemp << std::endl;
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else
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std::cout << "a + b = (carry) " << atemp << std::endl;
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std::cout << "a + b = (carry)" << std::endl;
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// it have no sense to print 'atemp' (it's undefined)
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atemp = a;
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if( !atemp.Sub(b) )
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std::cout << "a - b = " << atemp << std::endl;
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else
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std::cout << "a - b = (carry) " << atemp << std::endl;
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std::cout << "a - b = (carry)" << std::endl;
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atemp = a;
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if( !atemp.Mul(b) )
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std::cout << "a * b = " << atemp << std::endl;
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else
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std::cout << "a * b = (carry: the result is too big) " << std::endl;
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// it have no sense to print 'atemp' (it's undefined)
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std::cout << "a * b = (carry)" << std::endl;
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atemp = a;
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if( !atemp.Div(b) )
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@ -68,9 +69,8 @@ MyBig a,b;
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// 'a' will have the max value which can be held in this type
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a.SetMax();
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// at the moment conversions from double (or float etc.) are not supported
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// you cannot do that: b = 456.32f
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b = "456.32";
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// conversion from double
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b = 456.32;
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// Look at the value 'a' and the product from a+b and a-b
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// Don't worry this is the nature of floating point numbers
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@ -89,9 +89,9 @@ a * b = 12193540837712.2708
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a / b = 0.0012499665458095765
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Calculating with a carry
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a = 1.624801256070839555e+646457012
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b = 456.32
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b = 456.31999999999999
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a + b = 1.624801256070839555e+646457012
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a - b = 1.624801256070839555e+646457012
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a * b = (carry: the result is too big)
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a / b = 3.56066193914542329e+646457009
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a * b = (carry)
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a / b = 3.56066193914542334e+646457009
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*/
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|
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@ -1,5 +1,5 @@
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/*
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* This file is a part of TTMath Mathematical Library
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* This file is a part of TTMath Bignum Library
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||||
* and is distributed under the (new) BSD licence.
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* Author: Tomasz Sowa <t.sowa@slimaczek.pl>
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*/
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@ -61,51 +61,6 @@ int main()
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using namespace ttmath;
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/*
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Int<300> uu, oo;
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uu = -2;
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oo = 5;
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uint ccc = uu.Pow(oo);
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if( ccc )
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std::cout << "carry: " << ccc << std::endl;
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else
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std::cout << uu << std::endl;
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return 0;
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*/
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/*
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UInt<2> w = 100;
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w.GetBit(64);
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std::cout << w << std::endl;
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return 0;
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*/
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/*
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uint q = 100;
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uint last = UInt<3>::SetBitInWord(q, 3);
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std::cout << "nowa wartosc: " << q << ", wczesniejszy bit: " << last << std::endl;
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return 0;
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*/
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/*
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Big<1, 3> a = -26;
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Int<3> b = -8;
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uint c = a.Pow(b);
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||||
if ( c )
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std::cout << "carry: " << c << std::endl;
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||||
else
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||||
std::cout << a << std::endl;
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||||
return 0;
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||||
*/
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test_uint();
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||||
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||||
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||||
|
|
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|||
|
|
@ -1,5 +1,5 @@
|
|||
/*
|
||||
* This file is a part of TTMath Mathematical Library
|
||||
* This file is a part of TTMath Bignum Library
|
||||
* and is distributed under the (new) BSD licence.
|
||||
* Author: Tomasz Sowa <t.sowa@slimaczek.pl>
|
||||
*/
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
/*
|
||||
* This file is a part of TTMath Mathematical Library
|
||||
* This file is a part of TTMath Bignum Library
|
||||
* and is distributed under the (new) BSD licence.
|
||||
* Author: Tomasz Sowa <t.sowa@slimaczek.pl>
|
||||
*/
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
/*
|
||||
* This file is a part of TTMath Mathematical Library
|
||||
* This file is a part of TTMath Bignum Library
|
||||
* and is distributed under the (new) BSD licence.
|
||||
* Author: Tomasz Sowa <t.sowa@slimaczek.pl>
|
||||
*/
|
||||
|
||||
/*
|
||||
* Copyright (c) 2006-2008, Tomasz Sowa
|
||||
* Copyright (c) 2006-2009, Tomasz Sowa
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
/*
|
||||
* This file is a part of TTMath Mathematical Library
|
||||
* This file is a part of TTMath Bignum Library
|
||||
* and is distributed under the (new) BSD licence.
|
||||
* Author: Tomasz Sowa <t.sowa@slimaczek.pl>
|
||||
*/
|
||||
|
|
@ -212,20 +212,35 @@ private:
|
|||
0x99c32718, 0x6af4e23c, 0x1a946834, 0xb6150bda, 0x2583e9ca, 0x2ad44ce8, 0xdbbbc2db, 0x04de8ef9,
|
||||
0x2e8efc14, 0x1fbecaa6, 0x287c5947, 0x4e6bc05d, 0x99b2964f, 0xa090c3a2, 0x233ba186, 0x515be7ed,
|
||||
0x1f612970, 0xcee2d7af, 0xb81bdd76, 0x2170481c, 0xd0069127, 0xd5b05aa9, 0x93b4ea98, 0x8d8fddc1,
|
||||
0x86ffb7dc, 0x90a6c08f, 0x4df435c9, 0x34028492, 0x36c3fab4, 0xd27c7026, 0xc1d4dcb2, 0x602646df // (last one was: 0x602646de)
|
||||
// 0xc9751e76, ...
|
||||
// (the last word was rounded up because the next one is 0xc9751e76 -- first bit is one 0xc..)
|
||||
// 128 32bit words for the mantissa -- about 1232 valid digits (decimal)
|
||||
0x86ffb7dc, 0x90a6c08f, 0x4df435c9, 0x34028492, 0x36c3fab4, 0xd27c7026, 0xc1d4dcb2, 0x602646de,
|
||||
0xc9751e76, 0x3dba37bd, 0xf8ff9406, 0xad9e530e, 0xe5db382f, 0x413001ae, 0xb06a53ed, 0x9027d831,
|
||||
0x179727b0, 0x865a8918, 0xda3edbeb, 0xcf9b14ed, 0x44ce6cba, 0xced4bb1b, 0xdb7f1447, 0xe6cc254b,
|
||||
0x33205151, 0x2bd7af42, 0x6fb8f401, 0x378cd2bf, 0x5983ca01, 0xc64b92ec, 0xf032ea15, 0xd1721d03,
|
||||
0xf482d7ce, 0x6e74fef6, 0xd55e702f, 0x46980c82, 0xb5a84031, 0x900b1c9e, 0x59e7c97f, 0xbec7e8f3,
|
||||
0x23a97a7e, 0x36cc88be, 0x0f1d45b7, 0xff585ac5, 0x4bd407b2, 0x2b4154aa, 0xcc8f6d7e, 0xbf48e1d8,
|
||||
0x14cc5ed2, 0x0f8037e0, 0xa79715ee, 0xf29be328, 0x06a1d58b, 0xb7c5da76, 0xf550aa3d, 0x8a1fbff0,
|
||||
0xeb19ccb1, 0xa313d55c, 0xda56c9ec, 0x2ef29632, 0x387fe8d7, 0x6e3c0468, 0x043e8f66, 0x3f4860ee,
|
||||
0x12bf2d5b, 0x0b7474d6, 0xe694f91e, 0x6dbe1159, 0x74a3926f, 0x12fee5e4, 0x38777cb6, 0xa932df8c,
|
||||
0xd8bec4d0, 0x73b931ba, 0x3bc832b6, 0x8d9dd300, 0x741fa7bf, 0x8afc47ed, 0x2576f693, 0x6ba42466,
|
||||
0x3aab639c, 0x5ae4f568, 0x3423b474, 0x2bf1c978, 0x238f16cb, 0xe39d652d, 0xe3fdb8be, 0xfc848ad9,
|
||||
0x22222e04, 0xa4037c07, 0x13eb57a8, 0x1a23f0c7, 0x3473fc64, 0x6cea306b, 0x4bcbc886, 0x2f8385dd,
|
||||
0xfa9d4b7f, 0xa2c087e8, 0x79683303, 0xed5bdd3a, 0x062b3cf5, 0xb3a278a6, 0x6d2a13f8, 0x3f44f82d,
|
||||
0xdf310ee0, 0x74ab6a36, 0x4597e899, 0xa0255dc1, 0x64f31cc5, 0x0846851d, 0xf9ab4819, 0x5ded7ea1,
|
||||
0xb1d510bd, 0x7ee74d73, 0xfaf36bc3, 0x1ecfa268, 0x359046f4, 0xeb879f92, 0x4009438b, 0x481c6cd7,
|
||||
0x889a002e, 0xd5ee382b, 0xc9190da6, 0xfc026e47, 0x9558e447, 0x5677e9aa, 0x9e3050e2, 0x765694df,
|
||||
0xc81f56e8, 0x80b96e71, 0x60c980dd, 0x98a573ea, 0x4472065a, 0x139cd290, 0x6cd1cb72, 0x9ec52a53 // last one was: 0x9ec52a52
|
||||
//0x86d44014, ...
|
||||
// (the last word 0x9ec52a52 was rounded up because the next one is 0x86d44014 -- first bit is one 0x8..)
|
||||
// 256 32bit words for the mantissa -- about 2464 valid decimal digits
|
||||
};
|
||||
|
||||
// the value of PI is comming from the website "Paul's 8192 Digits of Pi"
|
||||
// http://www.escape.com/~paulg53/math/pi/8192.html
|
||||
// 2999 digits were taken from this website
|
||||
// (later they were compared with http://zenwerx.com/pi.php)
|
||||
// and they were set into Big<1,300> type (using operator=(const char*) on 32bit platform)
|
||||
// and then the first 128 words were taken into this table
|
||||
// (TTMATH_BUILTIN_VARIABLES_SIZE on 32bit platform should have the value 128,
|
||||
// and on 64bit platform value 64 (128/2=64))
|
||||
// the value of PI is comming from the website http://zenwerx.com/pi.php
|
||||
// 3101 digits were taken from this website
|
||||
// (later the digits were compared with:
|
||||
// http://www.eveandersson.com/pi/digits/1000000 and http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html )
|
||||
// and they were set into Big<1,400> type (using operator=(const char*) on a 32bit platform)
|
||||
// and then the first 256 words were taken into this table
|
||||
// (TTMATH_BUILTIN_VARIABLES_SIZE on 32bit platform should have the value 256,
|
||||
// and on 64bit platform value 128 (256/2=128))
|
||||
|
||||
mantissa.SetFromTable(temp_table, sizeof(temp_table) / sizeof(int));
|
||||
}
|
||||
|
|
@ -288,17 +303,34 @@ public:
|
|||
0xac7d5f42, 0xd69f6d18, 0x7763cf1d, 0x55034004, 0x87f55ba5, 0x7e31cc7a, 0x7135c886, 0xefb4318a,
|
||||
0xed6a1e01, 0x2d9e6832, 0xa907600a, 0x918130c4, 0x6dc778f9, 0x71ad0038, 0x092999a3, 0x33cb8b7a,
|
||||
0x1a1db93d, 0x7140003c, 0x2a4ecea9, 0xf98d0acc, 0x0a8291cd, 0xcec97dcf, 0x8ec9b55a, 0x7f88a46b,
|
||||
0x4db5a851, 0xf44182e1, 0xc68a007e, 0x5e0dd902, 0x0bfd64b6, 0x45036c7a, 0x4e677d2c, 0x38532a3a
|
||||
//0x23ba4442,...
|
||||
// 128 32bit words for the mantissa -- about 1232 valid digits (decimal)
|
||||
0x4db5a851, 0xf44182e1, 0xc68a007e, 0x5e0dd902, 0x0bfd64b6, 0x45036c7a, 0x4e677d2c, 0x38532a3a,
|
||||
0x23ba4442, 0xcaf53ea6, 0x3bb45432, 0x9b7624c8, 0x917bdd64, 0xb1c0fd4c, 0xb38e8c33, 0x4c701c3a,
|
||||
0xcdad0657, 0xfccfec71, 0x9b1f5c3e, 0x4e46041f, 0x388147fb, 0x4cfdb477, 0xa52471f7, 0xa9a96910,
|
||||
0xb855322e, 0xdb6340d8, 0xa00ef092, 0x350511e3, 0x0abec1ff, 0xf9e3a26e, 0x7fb29f8c, 0x183023c3,
|
||||
0x587e38da, 0x0077d9b4, 0x763e4e4b, 0x94b2bbc1, 0x94c6651e, 0x77caf992, 0xeeaac023, 0x2a281bf6,
|
||||
0xb3a739c1, 0x22611682, 0x0ae8db58, 0x47a67cbe, 0xf9c9091b, 0x462d538c, 0xd72b0374, 0x6ae77f5e,
|
||||
0x62292c31, 0x1562a846, 0x505dc82d, 0xb854338a, 0xe49f5235, 0xc95b9117, 0x8ccf2dd5, 0xcacef403,
|
||||
0xec9d1810, 0xc6272b04, 0x5b3b71f9, 0xdc6b80d6, 0x3fdd4a8e, 0x9adb1e69, 0x62a69526, 0xd43161c1,
|
||||
0xa41d570d, 0x7938dad4, 0xa40e329c, 0xcff46aaa, 0x36ad004c, 0xf600c838, 0x1e425a31, 0xd951ae64,
|
||||
0xfdb23fce, 0xc9509d43, 0x687feb69, 0xedd1cc5e, 0x0b8cc3bd, 0xf64b10ef, 0x86b63142, 0xa3ab8829,
|
||||
0x555b2f74, 0x7c932665, 0xcb2c0f1c, 0xc01bd702, 0x29388839, 0xd2af05e4, 0x54504ac7, 0x8b758282,
|
||||
0x2846c0ba, 0x35c35f5c, 0x59160cc0, 0x46fd8251, 0x541fc68c, 0x9c86b022, 0xbb709987, 0x6a460e74,
|
||||
0x51a8a931, 0x09703fee, 0x1c217e6c, 0x3826e52c, 0x51aa691e, 0x0e423cfc, 0x99e9e316, 0x50c1217b,
|
||||
0x624816cd, 0xad9a95f9, 0xd5b80194, 0x88d9c0a0, 0xa1fe3075, 0xa577e231, 0x83f81d4a, 0x3f2fa457,
|
||||
0x1efc8ce0, 0xba8a4fe8, 0xb6855dfe, 0x72b0a66e, 0xded2fbab, 0xfbe58a30, 0xfafabe1c, 0x5d71a87e,
|
||||
0x2f741ef8, 0xc1fe86fe, 0xa6bbfde5, 0x30677f0d, 0x97d11d49, 0xf7a8443d, 0x0822e506, 0xa9f4614e,
|
||||
0x011e2a94, 0x838ff88c, 0xd68c8bb7, 0xc51eef6d, 0x49ea8ab4, 0xf2c3df5b, 0xb4e0735a, 0xb0d68749
|
||||
// 0x2fe26dd4, ...
|
||||
// 256 32bit words for the mantissa -- about 2464 valid decimal digits
|
||||
};
|
||||
|
||||
// above value was calculated using Big<1,300> on 32bit platform
|
||||
// and then the first 128 words were taken,
|
||||
// above value was calculated using Big<1,400> type on a 32bit platform
|
||||
// and then the first 256 words were taken,
|
||||
// the calculating was made by using ExpSurrounding0(1) method
|
||||
// which took 1110 iterations
|
||||
// (TTMATH_BUILTIN_VARIABLES_SIZE on 32bit platform should have the value 128,
|
||||
// and on 64bit platform value 64 (128/2=64))
|
||||
// which took 1420 iterations
|
||||
// (the result was compared with e taken from http://antwrp.gsfc.nasa.gov/htmltest/gifcity/e.2mil)
|
||||
// (TTMATH_BUILTIN_VARIABLES_SIZE on 32bit platform should have the value 256,
|
||||
// and on 64bit platform value 128 (256/2=128))
|
||||
|
||||
mantissa.SetFromTable(temp_table, sizeof(temp_table) / sizeof(int));
|
||||
exponent = -sint(man)*sint(TTMATH_BITS_PER_UINT) + 2;
|
||||
|
|
@ -328,18 +360,35 @@ public:
|
|||
0x57339ba2, 0xbeba7d05, 0x2ac5b61c, 0xc4e9207c, 0xef2f0ce2, 0xd7373958, 0xd7622658, 0x901e646a,
|
||||
0x95184460, 0xdc4e7487, 0x156e0c29, 0x2413d5e3, 0x61c1696d, 0xd24aaebd, 0x473826fd, 0xa0c238b9,
|
||||
0x0ab111bb, 0xbd67c724, 0x972cd18b, 0xfbbd9d42, 0x6c472096, 0xe76115c0, 0x5f6f7ceb, 0xac9f45ae,
|
||||
0xcecb72f1, 0x9c38339d, 0x8f682625, 0x0dea891e, 0xf07afff3, 0xa892374e, 0x175eb4af, 0xc8daadd9 // (last one was: 0xc8daadd8)
|
||||
// 0x85db6ab0, ...
|
||||
// (the last word was rounded up because the next one is 0x85db6ab0 -- first bit is one 0x8..)
|
||||
// 128 32bit words for the mantissa -- about 1232 valid digits (decimal)
|
||||
0xcecb72f1, 0x9c38339d, 0x8f682625, 0x0dea891e, 0xf07afff3, 0xa892374e, 0x175eb4af, 0xc8daadd8,
|
||||
0x85db6ab0, 0x3a49bd0d, 0xc0b1b31d, 0x8a0e23fa, 0xc5e5767d, 0xf95884e0, 0x6425a415, 0x26fac51c,
|
||||
0x3ea8449f, 0xe8f70edd, 0x062b1a63, 0xa6c4c60c, 0x52ab3316, 0x1e238438, 0x897a39ce, 0x78b63c9f,
|
||||
0x364f5b8a, 0xef22ec2f, 0xee6e0850, 0xeca42d06, 0xfb0c75df, 0x5497e00c, 0x554b03d7, 0xd2874a00,
|
||||
0x0ca8f58d, 0x94f0341c, 0xbe2ec921, 0x56c9f949, 0xdb4a9316, 0xf281501e, 0x53daec3f, 0x64f1b783,
|
||||
0x154c6032, 0x0e2ff793, 0x33ce3573, 0xfacc5fdc, 0xf1178590, 0x3155bbd9, 0x0f023b22, 0x0224fcd8,
|
||||
0x471bf4f4, 0x45f0a88a, 0x14f0cd97, 0x6ea354bb, 0x20cdb5cc, 0xb3db2392, 0x88d58655, 0x4e2a0e8a,
|
||||
0x6fe51a8c, 0xfaa72ef2, 0xad8a43dc, 0x4212b210, 0xb779dfe4, 0x9d7307cc, 0x846532e4, 0xb9694eda,
|
||||
0xd162af05, 0x3b1751f3, 0xa3d091f6, 0x56658154, 0x12b5e8c2, 0x02461069, 0xac14b958, 0x784934b8,
|
||||
0xd6cce1da, 0xa5053701, 0x1aa4fb42, 0xb9a3def4, 0x1bda1f85, 0xef6fdbf2, 0xf2d89d2a, 0x4b183527,
|
||||
0x8fd94057, 0x89f45681, 0x2b552879, 0xa6168695, 0xc12963b0, 0xff01eaab, 0x73e5b5c1, 0x585318e7,
|
||||
0x624f14a5, 0x1a4a026b, 0x68082920, 0x57fd99b6, 0x6dc085a9, 0x8ac8d8ca, 0xf9eeeea9, 0x8a2400ca,
|
||||
0xc95f260f, 0xd10036f9, 0xf91096ac, 0x3195220a, 0x1a356b2a, 0x73b7eaad, 0xaf6d6058, 0x71ef7afb,
|
||||
0x80bc4234, 0x33562e94, 0xb12dfab4, 0x14451579, 0xdf59eae0, 0x51707062, 0x4012a829, 0x62c59cab,
|
||||
0x347f8304, 0xd889659e, 0x5a9139db, 0x14efcc30, 0x852be3e8, 0xfc99f14d, 0x1d822dd6, 0xe2f76797,
|
||||
0xe30219c8, 0xaa9ce884, 0x8a886eb3, 0xc87b7295, 0x988012e8, 0x314186ed, 0xbaf86856, 0xccd3c3b6,
|
||||
0xee94e62f, 0x110a6783, 0xd2aae89c, 0xcc3b76fc, 0x435a0ce1, 0x34c2838f, 0xd571ec6c, 0x1366a993 // last one was: 0x1366a992
|
||||
//0xcbb9ac40, ...
|
||||
// (the last word 0x1366a992 was rounded up because the next one is 0xcbb9ac40 -- first bit is one 0xc..)
|
||||
// 256 32bit words for the mantissa -- about 2464 valid decimal digits
|
||||
};
|
||||
|
||||
// above value was calculated using Big<1,300> on 32bit platform
|
||||
// and then the first 128 words were taken,
|
||||
// above value was calculated using Big<1,400> type on a 32bit platform
|
||||
// and then the first 256 words were taken,
|
||||
// the calculating was made by using LnSurrounding1(2) method
|
||||
// which took 3030 iterations
|
||||
// (TTMATH_BUILTIN_VARIABLES_SIZE on 32bit platform should have the value 128,
|
||||
// and on 64bit platform value 64 (128/2=64))
|
||||
// which took 4035 iterations
|
||||
// (the result was compared with ln(2) taken from http://ja0hxv.calico.jp/pai/estart.html)
|
||||
// (TTMATH_BUILTIN_VARIABLES_SIZE on 32bit platform should have the value 256,
|
||||
// and on 64bit platform value 128 (256/2=128))
|
||||
|
||||
mantissa.SetFromTable(temp_table, sizeof(temp_table) / sizeof(int));
|
||||
exponent = -sint(man)*sint(TTMATH_BITS_PER_UINT);
|
||||
|
|
@ -379,21 +428,38 @@ public:
|
|||
0xed69b13d, 0xc1a03730, 0xb6524dc1, 0x8c167e86, 0x99d6d20e, 0xa2defd2b, 0xd006f8b4, 0xbe145a2a,
|
||||
0xdf3ccbb3, 0x189da49d, 0xbc1261c8, 0xb3e4daad, 0x6a36cecc, 0xb2d5ae5b, 0x89bf752f, 0xb5dfb353,
|
||||
0xff3065c4, 0x0cfceec8, 0x1be5a9a9, 0x67fddc57, 0xc4b83301, 0x006bf062, 0x4b40ed7a, 0x56c6cdcd,
|
||||
0xa2d6fe91, 0x388e9e3e, 0x48a93f5f, 0x5e3b6eb4, 0xb81c4a5b, 0x53d49ea6, 0x8e668aea, 0xba83c7f9 // (last one was: 0xba83c7f8)
|
||||
///0xfb5f06c3, ...
|
||||
//(the last word was rounded up because the next one is 0xfb5f06c3 -- first bit is one 0xf..)
|
||||
// 128 32bit words for the mantissa -- about 1232 valid digits (decimal)
|
||||
0xa2d6fe91, 0x388e9e3e, 0x48a93f5f, 0x5e3b6eb4, 0xb81c4a5b, 0x53d49ea6, 0x8e668aea, 0xba83c7f8,
|
||||
0xfb5f06c3, 0x58ac8f70, 0xfa9d8c59, 0x8c574502, 0xbaf54c96, 0xc84911f0, 0x0482d095, 0x1a0af022,
|
||||
0xabbab080, 0xec97efd3, 0x671e4e0e, 0x52f166b6, 0xcd5cd226, 0x0dc67795, 0x2e1e34a3, 0xf799677f,
|
||||
0x2c1d48f1, 0x2944b6c5, 0x2ba1307e, 0x704d67f9, 0x1c1035e4, 0x4e927c63, 0x03cf12bf, 0xe2cd2e31,
|
||||
0xf8ee4843, 0x344d51b0, 0xf37da42b, 0x9f0b0fd9, 0x134fb2d9, 0xf815e490, 0xd966283f, 0x23962766,
|
||||
0xeceab1e4, 0xf3b5fc86, 0x468127e2, 0xb606d10d, 0x3a45f4b6, 0xb776102d, 0x2fdbb420, 0x80c8fa84,
|
||||
0xd0ff9f45, 0xc58aef38, 0xdb2410fd, 0x1f1cebad, 0x733b2281, 0x52ca5f36, 0xddf29daa, 0x544334b8,
|
||||
0xdeeaf659, 0x4e462713, 0x1ed485b4, 0x6a0822e1, 0x28db471c, 0xa53938a8, 0x44c3bef7, 0xf35215c8,
|
||||
0xb382bc4e, 0x3e4c6f15, 0x6285f54c, 0x17ab408e, 0xccbf7f5e, 0xd16ab3f6, 0xced2846d, 0xf457e14f,
|
||||
0xbb45d9c5, 0x646ad497, 0xac697494, 0x145de32e, 0x93907128, 0xd263d521, 0x79efb424, 0xd64651d6,
|
||||
0xebc0c9f0, 0xbb583a44, 0xc6412c84, 0x85bb29a6, 0x4d31a2cd, 0x92954469, 0xa32b1abd, 0xf7f5202c,
|
||||
0xa4aa6c93, 0x2e9b53cf, 0x385ab136, 0x2741f356, 0x5de9c065, 0x6009901c, 0x88abbdd8, 0x74efcf73,
|
||||
0x3f761ad4, 0x35f3c083, 0xfd6b8ee0, 0x0bef11c7, 0xc552a89d, 0x58ce4a21, 0xd71e54f2, 0x4157f6c7,
|
||||
0xd4622316, 0xe98956d7, 0x450027de, 0xcbd398d8, 0x4b98b36a, 0x0724c25c, 0xdb237760, 0xe9324b68,
|
||||
0x7523e506, 0x8edad933, 0x92197f00, 0xb853a326, 0xb330c444, 0x65129296, 0x34bc0670, 0xe177806d,
|
||||
0xe338dac4, 0x5537492a, 0xe19add83, 0xcf45000f, 0x5b423bce, 0x6497d209, 0xe30e18a1, 0x3cbf0687,
|
||||
0x67973103, 0xd9485366, 0x81506bba, 0x2e93a9a4, 0x7dd59d3f, 0xf17cd746, 0x8c2075be, 0x552a4348 // last one was: 0x552a4347
|
||||
// 0xb4a638ef, ...
|
||||
//(the last word 0x552a4347 was rounded up because the next one is 0xb4a638ef -- first bit is one 0xb..)
|
||||
// 256 32bit words for the mantissa -- about 2464 valid digits (decimal)
|
||||
};
|
||||
|
||||
// above value was calculated using Big<1,300> on 32bit platform
|
||||
// and then the first 128 32bit words were taken,
|
||||
// above value was calculated using Big<1,400> type on a 32bit platform
|
||||
// and then the first 256 32bit words were taken,
|
||||
// the calculating was made by using LnSurrounding1(10) method
|
||||
// which took 16555 iterations
|
||||
// which took 22080 iterations
|
||||
// (the result was compared with ln(10) taken from http://ja0hxv.calico.jp/pai/estart.html)
|
||||
// (the formula used in LnSurrounding1(x) converges badly when
|
||||
// the x is greater than one but in fact we can use it, only the
|
||||
// number of iterations will be greater)
|
||||
// (TTMATH_BUILTIN_VARIABLES_SIZE on 32bit platform should have the value 128,
|
||||
// and on 64bit platform value 64 (128/2=64))
|
||||
// (TTMATH_BUILTIN_VARIABLES_SIZE on 32bit platform should have the value 256,
|
||||
// and on 64bit platform value 128 (256/2=128))
|
||||
|
||||
mantissa.SetFromTable(temp_table, sizeof(temp_table) / sizeof(int));
|
||||
exponent = -sint(man)*sint(TTMATH_BITS_PER_UINT) + 2;
|
||||
|
|
@ -1203,12 +1269,16 @@ public:
|
|||
|
||||
private:
|
||||
|
||||
#ifdef CONSTANTSGENERATOR
|
||||
public:
|
||||
#endif
|
||||
|
||||
/*!
|
||||
Exponent this = exp(x) = e^x where x is in (-1,1)
|
||||
|
||||
we're using the formula exp(x) = 1 + (x)/(1!) + (x^2)/(2!) + (x^3)/(3!) + ...
|
||||
*/
|
||||
void ExpSurrounding0(const Big<exp,man> & x)
|
||||
void ExpSurrounding0(const Big<exp,man> & x, uint * steps = 0)
|
||||
{
|
||||
TTMATH_REFERENCE_ASSERT( x )
|
||||
|
||||
|
|
@ -1221,22 +1291,20 @@ private:
|
|||
denominator.SetOne();
|
||||
denominator_i.SetOne();
|
||||
|
||||
// this is only to avoid getting a warning about an uninitialized object
|
||||
// gcc 4.1.2 reports: 'old_value.info' may be used uninitialized in this function
|
||||
// (in fact we will initialize it later when the condition 'testing' is fulfilled)
|
||||
old_value.info = 0;
|
||||
|
||||
// every 'step_test' times we make a test
|
||||
const uint step_test = 5;
|
||||
uint i;
|
||||
old_value = *this;
|
||||
|
||||
// we begin from 1 in order to not testing at the start
|
||||
for(uint i=1 ; i<=TTMATH_ARITHMETIC_MAX_LOOP ; ++i)
|
||||
// we begin from 1 in order to not testing at the beginning
|
||||
#ifdef CONSTANTSGENERATOR
|
||||
for(i=1 ; true ; ++i)
|
||||
#else
|
||||
for(i=1 ; i<=TTMATH_ARITHMETIC_MAX_LOOP ; ++i)
|
||||
#endif
|
||||
{
|
||||
bool testing = ((i % step_test) == 0);
|
||||
|
||||
if( testing )
|
||||
old_value = *this;
|
||||
|
||||
next_part = numerator;
|
||||
|
||||
if( next_part.Div( denominator ) )
|
||||
|
|
@ -1249,9 +1317,12 @@ private:
|
|||
Add( next_part );
|
||||
|
||||
if( testing && old_value==*this )
|
||||
// we've added a next part of the formula but the result
|
||||
// we've added next few parts of the formula but the result
|
||||
// is still the same then we break the loop
|
||||
break;
|
||||
else
|
||||
old_value = *this;
|
||||
|
||||
|
||||
// we set the denominator and the numerator for a next part of the formula
|
||||
if( denominator_i.Add(one) )
|
||||
|
|
@ -1264,10 +1335,11 @@ private:
|
|||
if( numerator.Mul(x) )
|
||||
break;
|
||||
}
|
||||
|
||||
if( steps )
|
||||
*steps = i;
|
||||
}
|
||||
|
||||
|
||||
|
||||
public:
|
||||
|
||||
|
||||
|
|
@ -1346,13 +1418,17 @@ public:
|
|||
|
||||
private:
|
||||
|
||||
#ifdef CONSTANTSGENERATOR
|
||||
public:
|
||||
#endif
|
||||
|
||||
/*!
|
||||
Natural logarithm this = ln(x) where x in range <1,2)
|
||||
|
||||
we're using the formula:
|
||||
ln x = 2 * [ (x-1)/(x+1) + (1/3)((x-1)/(x+1))^3 + (1/5)((x-1)/(x+1))^5 + ... ]
|
||||
*/
|
||||
void LnSurrounding1(const Big<exp,man> & x)
|
||||
void LnSurrounding1(const Big<exp,man> & x, uint * steps = 0)
|
||||
{
|
||||
Big<exp,man> old_value, next_part, denominator, one, two, x1(x), x2(x);
|
||||
|
||||
|
|
@ -1377,16 +1453,19 @@ private:
|
|||
denominator.SetOne();
|
||||
SetZero();
|
||||
|
||||
// this is only to avoid getting a warning about an uninitialized object
|
||||
// gcc 4.1.2 reports: 'old_value.info' may be used uninitialized in this function
|
||||
// (in fact we will initialize it later when the condition 'testing' is fulfilled)
|
||||
old_value.info = 0;
|
||||
old_value = *this;
|
||||
|
||||
// every 'step_test' times we make a test
|
||||
const uint step_test = 5;
|
||||
uint i;
|
||||
|
||||
|
||||
#ifdef CONSTANTSGENERATOR
|
||||
for(i=1 ; true ; ++i)
|
||||
#else
|
||||
// we begin from 1 in order to not testing at the beginning
|
||||
for(uint i=1 ; i<=TTMATH_ARITHMETIC_MAX_LOOP ; ++i)
|
||||
for(i=1 ; i<=TTMATH_ARITHMETIC_MAX_LOOP ; ++i)
|
||||
#endif
|
||||
{
|
||||
bool testing = ((i % step_test) == 0);
|
||||
|
||||
|
|
@ -1398,9 +1477,6 @@ private:
|
|||
// it means there are too many parts of the formula
|
||||
break;
|
||||
|
||||
if( testing )
|
||||
old_value = *this;
|
||||
|
||||
// there shouldn't be a carry here
|
||||
Add(next_part);
|
||||
|
||||
|
|
@ -1408,6 +1484,8 @@ private:
|
|||
// we've added next (step_test) parts of the formula but the result
|
||||
// is still the same then we break the loop
|
||||
break;
|
||||
else
|
||||
old_value = *this;
|
||||
|
||||
if( x1.Mul(x2) )
|
||||
// if there is a carry here the result we return as good
|
||||
|
|
@ -1420,6 +1498,9 @@ private:
|
|||
// this = this * 2
|
||||
// ( there can't be a carry here because we calculate the logarithm between <1,2) )
|
||||
exponent.AddOne();
|
||||
|
||||
if( steps )
|
||||
*steps = i;
|
||||
}
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
/*
|
||||
* This file is a part of TTMath Mathematical Library
|
||||
* This file is a part of TTMath Bignum Library
|
||||
* and is distributed under the (new) BSD licence.
|
||||
* Author: Tomasz Sowa <t.sowa@slimaczek.pl>
|
||||
*/
|
||||
|
|
|
|||
|
|
@ -1,11 +1,11 @@
|
|||
/*
|
||||
* This file is a part of TTMath Mathematical Library
|
||||
* This file is a part of TTMath Bignum Library
|
||||
* and is distributed under the (new) BSD licence.
|
||||
* Author: Tomasz Sowa <t.sowa@slimaczek.pl>
|
||||
*/
|
||||
|
||||
/*
|
||||
* Copyright (c) 2006-2008, Tomasz Sowa
|
||||
* Copyright (c) 2006-2009, Tomasz Sowa
|
||||
* All rights reserved.
|
||||
*
|
||||
* Redistribution and use in source and binary forms, with or without
|
||||
|
|
@ -141,7 +141,7 @@ namespace ttmath
|
|||
which are kept in built-in variables for a Big<> type
|
||||
(these variables are defined in ttmathbig.h)
|
||||
*/
|
||||
#define TTMATH_BUILTIN_VARIABLES_SIZE 128u
|
||||
#define TTMATH_BUILTIN_VARIABLES_SIZE 256u
|
||||
|
||||
#else
|
||||
|
||||
|
|
@ -172,7 +172,7 @@ namespace ttmath
|
|||
which are kept in built-in variables for a Big<> type
|
||||
(these variables are defined in ttmathbig.h)
|
||||
*/
|
||||
#define TTMATH_BUILTIN_VARIABLES_SIZE 64ul
|
||||
#define TTMATH_BUILTIN_VARIABLES_SIZE 128ul
|
||||
|
||||
#endif
|
||||
}
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
/*
|
||||
* This file is a part of TTMath Mathematical Library
|
||||
* This file is a part of TTMath Bignum Library
|
||||
* and is distributed under the (new) BSD licence.
|
||||
* Author: Tomasz Sowa <t.sowa@slimaczek.pl>
|
||||
*/
|
||||
|
|
@ -114,7 +114,7 @@ public:
|
|||
}
|
||||
}
|
||||
|
||||
output << std::endl;
|
||||
output << std::dec << std::endl;
|
||||
}
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
/*
|
||||
* This file is a part of TTMath Mathematical Library
|
||||
* This file is a part of TTMath Bignum Library
|
||||
* and is distributed under the (new) BSD licence.
|
||||
* Author: Tomasz Sowa <t.sowa@slimaczek.pl>
|
||||
*/
|
||||
|
|
|
|||
Loading…
Reference in New Issue