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Compact Scientific Calculator 27 for Windows 98, Windows 2000, Windows Server (2000, 2003, 2008, 2012), Windows XP and Vista
Type 1+2 into Edit Formula window and left-click on button Calculate. In the Result window +3 appears. Right-click on the 1+2 in the Edit Formula windows and choose Select All. Right-click again and choose Cut. Type, using either keyboard or clicking on buttons, 32!. That is thirty two factorial. Click Calculate. The result is +263130836933693530167218012160000000. Such a huge number it is hard to read. Left click the check-box Grouping and click Calculate again. The result becomes +263130,8369336935,3016721801,2160000000. Groups of ten digits are separated by comma. Now we see that the result has 36 digits. This is an exact number. Now try 33!. The result is +8.683,317,618,811,886,495,518,194,40E36. The mantissa has only 27 digits but the exponent E36 shows that the exact result has 36 digits after the first digit (before decimal point) digits. It might be zeroes, might be nonzero digits. So, we don’t know the last ten digits. Thus we calculated the result with precision (accuracy) 27 digits. The precision 27 is guaranteed for all arithmetic operations. Although sometimes we get greater accuracy. This calculator follows classical approach when uncertainty of f(x) calculation is estimated by formula max|(derivative(f))|*|x*uncertainty(x)|, where maximum of function derivative is considered on interval [x-uncertainty(x),|x+uncertainty(x)], and uncertainty(x)=|x|*10^(-precision). Thus sin(2π)=0+-1E-27 and sin(2*1E20*π)=0+-1E-7. As we see, the result’s accuracy degrades with grows of argument, but such approach allows to preserve all trigonometry facts like sin(even number*π+x)=sin(x). Calculators with multi-precision allows to calculate sin of big argument, like 1E40, with any precision, but cannot calculate sin(1E40*π) since they don’t have π. The π becomes for them a “floating” number with arbitrary precision. It seems strange, because 2π corresponds to one rotation and counting rotations is much easier then measuring 1E40 radians. Let’s continue. You can type into Edit Formula window a mathematical expression of any length and complexity. For example, type (1+sin(2+cos(3))+tan(4))/(ln(5)-tan(6)+atan(7)). Typing of such expression takes time. If you want to repeat such formula (after other calculations), go to Tab History. In the History rich-text-box find the formula and select it (pressing left button on mouse and dragging mouse). Right-click mouse and choose from context-menu Copy. Return to Tab Formula. Right-click into Edit windows and from context-menu choose Paste. All text-boxes in the calculator have similar right-click menus. Open tab Variables. There are ten variables available. Type into text-boxes any numbers you want to use often in your formulas. Press Parse. Return into tab Formula and type formulas with variables. For example x0+cos(x1)+sin(x2)+tan(x3).
Let’s continue. You can type into Edit Formula window a mathematical expression of any length and complexity. For example, type (1+sin(2+cos(3))+tan(4))/(ln(5)-tan(6)+atan(7)). Typing such expression takes time. If you want to repeat such formula (after other calculations), go to Tab History. In the History rich-text-box find the formula and select it (pressing left button on mouse and dragging mouse). Right-click mouse and choose from context-menu Copy. Return to Tab Formula. Right-click into Edit windows and from context-menu choose Paste. All text-boxes in the calculator have similar right-click menus. Open tab Variables. There are ten variables available. Type into text-boxes any numbers you want to use often in your formulas. Press Parse. Return into tab Formula and type formulas with variables. For example x0+cos(x1)+sin(x2)+tan(x3).
The easiest way to edit formula is left-clicking buttons. It allows to keep brackets balanced, functions names correct and so on. Clicking the button "calculate" triggers calculation of entered formula. The result of calculation appears in the window (text-box) named Result.
The second way is to use keyboard (and keypad). All controls usual for editing are available. Pressing the key Enter triggers calculation. Before using keyboard don't forget to click inside text-box to get focus (blinking cursor).
After calculation the entered formula is not deleted from the Edit window allowing to modify formula. If you want to delete formula select it by mouse and delete. For selecting text you can use right-click menu "Select All" or left-click mouse dragging along the text. For deleting selected text use right-click menu "Cut" or "Delete".
Using right-click menu you can copy and paste text between Edit window and all other text-box windows.
For copying text from saved History file open saved History file (usually in WordPad, Notepad, or MS Word ), drag mouse along the text for selection and then choose Copy from right-click menu. Then go to Formula tab, right-click onto Edit window, select command Paste.
Apply the same procedure for copying text from History window or saved History file into variables windows in Variables tab.
Functions and operations have to be entered exactly as they appears by pressing buttons. Alternative names are not supported.
Numbers can be entered in wide variety of formats. But for exponent always use E, since "e" is reserved for "number e". Long numbers will be rounded for 54 digits. For example, 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 will become 1.23456789012345678901234567890123456789012345678901235E99. Note the last digits 1235. The last 5 appears as result of rounding 12345... . In default Mixed mode (until Scientific mode check-box is checked) integer numbers appears "as is" up to 63 digits. If Scientific check-box is checked then all numbers in variable-boxes and result-box are given in scientific format 1.23456789012345678901234567890123456789012345678901234En, where n has maximum 9 digits, from E-999999999 to E999999999. Numbers with greater exponents will be given status Infinity. Exponents E+9...9 and E9...9 are the same.
In general, the calculator works with real numbers. However, some real numbers, which are infinite sequences of digits, are replaced by finite sequences. Thus the calculator does not distinguish number π, which is infinite sequence of digits, and finite sequence +3.14159265358979323846264338327950288419716939937510582E0.
The greatest exponent available is E999999999 (nine nines). Numbers with greater exponents are given status Infinity (what is a big simplification, of course). Numbers with negative exponent less than E-999999999 are given status Zero. Number Infinity is extended number with special properties. Number Zero is a usual real number and a special numbers as well. Other special numbers are Uncertainty and NaN. We get Uncertainty dividing Zero by Zero, for example. We get NaN by taking square root of -1, for example. Direct entry of special numbers into edit text-box is not allowed, but you can experiment with special numbers, using 1/0, 0/0, (-1)^0.5, log(-1), and so on.
Arithmetic of special numbers:
f(NaN)=NaN, NaN+any=NaN, NaN-any=NaN, NaN*any=NaN, NaN/any=NaN, any/NaN=NaN;
0/0=Uncertainty, Infinity/Infinity=Uncertainty, Infinity+Infinity=Uncertainty, Infinity-Infinity=Uncertainty, 0*Infinity=Uncertainty, f(Uncertainty)=Uncertainty, Uncertainty+any=Uncertainty, Uncertainty-any=Uncertainty, Uncertainty*any=Uncertainty, Uncertainty/any=Uncertainty, any/Uncertainty=Uncertainty.
1/0=Infinity, 1/Infinity=0, Infinity*0=Uncertainty, Infinity*Infinity=Unfinity, periodic function f(Infinity)=Uncertainty,2^Infinity=Infinity, 1^Infinity=1, (-1)^Infinity=NaN, log(Infinity)=Infinity, log(0)=Infinty.
{Infinity)!=Uncertainty, because (x)! has different behavior for positive and negative x.
2^Infinity=Uncertainty, because 2^x has different behavior for positive and negative x.
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