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# Larger numbers

Hector 4 years ago updated by Pavel Holoborodko 4 years ago

Pavel, there are larger numbers than 1e + 308 and less than 1e-318 ? Completed

Of course, toolbox supports large/small numbers:

```>> mp.Digits(34);

>> besselk(0,1000)  % double
ans =
0

>> besselk(0,mp(1000)) % multiprecision
ans =
2.0115e-436

>> besselk(0,mp(10000))
ans =
1.4231e-4345
```

Do you have a simple example demonstrating your issue?

We have User's Manual with many details on how to use the toolbox: http://www.advanpix.com/documentation/users-manual/ function Num=Random1(Max,Min)

r=mp(rand(1,1));

Num=Min+(Max-Min)*r;

---------------------------------

main program

mp.Digits(1000000)

GMin=mp(0);

GMax=mp(1e+5000)

Number=abs(Random1(GMin,GMax))

---------------------------------

OUT

GMax=inf

Number = NaN The code mp(1e+500) is incorrect. The 1e+500 is converted to double precision first (truncated to 1e+308).

mp.Digits(1000000) is too high. The usual mp.Digits(34) is enough to handle such small number as 1e+500 :).

Also please check the following chapter in our User Guide, it has examples on the issue: function Num=Random1(Max,Min)

r=mp(rand(1,1));

Num=abs(Min+(Max-Min)*r);

---------------------------------------------------

% main program

clear all

clc

% Estimator order parameters

% I need to estimate the order of the parameters, because it was out range

mp.Digits(34)

GMinR=mp('0');

GMaxR=mp('1e+10000');

GMinRtc=mp('0');

GMaxRtc=mp('1e+10000');

GMinc=mp('0');

GMaxc=mp('1');

fre= mp('0.13');

DRe= mp('8241.3');
DIm= mp('-14145');

for j=1:30

j

for k=1:1000

R=Random1(GMinR,GMaxR);

Rtc=Random1(GMinRtc,GMaxRtc);

c=Random1(GMinc,GMaxc);

Fun=mp(funcion(fre,R,Rtc,c,DRe,DIm));

L(k,:)=[R Rtc c Fun];

end

L=sortrows(L,4);

GMaxR=L(1,1);

GMaxRtc=L(1,2);

GMaxc=L(1,3);

end

GMaxR

GMaxRtc

GMaxc

Fun=L(1,4)
----------------------------------------
OUT
GMaxR = NaN
GMaxRtc = NaN
GMaxc = 0.7807950309700372182319938474392984

Fun = NaN IEEE 2008-754 quadruple 34-digits precision is not enough to hold the 1e+10000 numbers. Please use higher precision.

You can always check the max/min number for current precision using functions: mp.realmax, mp.realmin:

```>> mp.Digits(34);
>> mp.realmax, mp.realmin
ans =
1.1897e+4932
ans =
3.3621e-4932

>> mp.Digits(100);
>> mp.realmax, mp.realmin
ans =
5.2464e+323228495
ans =
9.5303e-323228497``` mp.Digits(N);

ExpMax=fix(log(mp.realmax)/log(10))

ExpMin=fix(log(mp.realmin)/log(10))

___________________________________

N=100

ExpMax = 323228495.0000

ExpMin =-323228496.0000

N=1000

ExpMax = 323228495.0000

ExpMin =-323228496.0000 Yes, max/min numbers are the same for all precisions except IEEE quadruple.

Range of numbers depends on floating point exponent.

It is small for IEEE quadruple. For all other precisions we use the same large exponent. Using the code that I shared with you, was a way to find the orders of magnitude of R and Rtc could create length mantissa and exponent precision real, arbitrary?

would political project create real length and precision, arbitrary ? Toolbox allows working with floating-point numbers from 9.5303e-323228497 to 5.2464e+323228495 with arbitrary precision (arbitrary length of mantissa):

```>> format longG
>> mp.Digits(34);
>> mp('pi')
ans =
3.141592653589793238462643383279503

>> mp.Digits(100);
>> mp('pi')
ans =
3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862
8034825342117068

>> mp.Digits(1000);
>> mp('pi')
ans =
3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862
80348253421170679821480865132823066470938446095505822317253594081284811174502841027019385
21105559644622948954930381964428810975665933446128475648233786783165271201909145648566923
46034861045432664821339360726024914127372458700660631558817488152092096282925409171536436
78925903600113305305488204665213841469519415116094330572703657595919530921861173819326117
93105118548074462379962749567351885752724891227938183011949129833673362440656643086021394
94639522473719070217986094370277053921717629317675238467481846766940513200056812714526356
08277857713427577896091736371787214684409012249534301465495853710507922796892589235420199
56112129021960864034418159813629774771309960518707211349999998372978049951059731732816096
31859502445945534690830264252230825334468503526193118817101000313783875288658753320838142
06171776691473035982534904287554687311595628638823537875937519577818577805321712268066130
01927876611195909216420199
```

The range 9.5303e-323228497 to 5.2464e+323228495 is fixed but mantissa(precision) can be of any length.

The range covers pretty much all atoms in universe.

Could you show example where you need wider exponent range?