INSTRUCTION MANUAL

INTRODUCTION

With the program SC-103PU you get a powerful and freely available scientific calculator for the Palm platform. Apart from scientific functions it also offers a full set of logical operations and conversions between different numeric systems. Additionally the calculator offers a units mode for easy conversions between different units including currencies, as well as calculations with mixed units. The program is designed in a way, that it simulates the visual and operational aspects of a true calculator, such that the user will be immediately familiar with its interface.

CONTENTS

• INTRODUCTION
• 1. BACKGROUND
  • Installing the SC-103PU on the Palm Device
  • Preferences
• 2. OPERATING MODES
• 3. SCIENTIFIC MODE
  • Calculations
  • Basic Usage
  • Scientific Calculations
  • Usage of the Parenthesis Keys
  • Decimal Digits
  • Priority Levels of Operations
• 4. LOGIC MODE
  • Conversion Between Different Numeric Systems
  • Selecting the Bit Width, Number Display and Sign Mode
  • Basic Arithmetic Calculations
  • Boolean Algebra
  • Bit Shift Operations
  • Swapping Bytes and Nibbles
  • Parenthesis and Priority Levels of Operations
• 5. UNITS MODE
  • Predefined Units
  • Different View Modes of the Units Mode
  • One Line View Mode
  • Two Lines View Mode
  • Calculations with Mixed Units
  • Parenthesis and Priority Levels of Operations
  • Usage of the Memories
  • Combining of Units and Scientific Mode
  • Defining Units
  • Defining Unit Sets
• 6. INPUTS
  • Direct Manipulation of the Memories
  • Entering using Graffiti®
  • Data Exchange with the Clipboard
• 7. ERRORS
  • Error Conditions
  • Calculation Range

The calculator program SC-103PU can be executed on all devices equipped with the Palm Operating System version 2.0 or higher. In addition, it requires the freely available MathLib which is shipped as part of the calculator for your convenience.

The calculator program automatically adapts to single and multi color devices. Starting with version 1.26 of the SC-103PU, high resolution displays of SONY Clié devices and devices equipped with Palm Operating System version 5 or higher are also automatically detected and supported. There is no need for different versions of the program.

The calculator SC-103PU is shipped in three different languages: English, german and esperanto. Only menu items and dialog boxes have been translated; key and display labeling is identical in all versions. To select the desired language, you have to install the proper program module. Since the name of the program module is the same for all languages, you can only have one language version installed at the same time.

Installation of the SC-103PU on the Palm Device

The calculator program SC-103PU as well as the MathLib have to be installed on your Palm device. The SC-103PU uses the MathLib for some of its calculations. If you don't know, how to install additional applications on your Palm device, please refer to the instruction manual which is shipped with your Palm device.

Installation Procedure:

1. First, install the file MathLib.prc on your Palm device, if it isn't already installed.
   NOTE: Due to the fact that the MathLib is required by many Palm applications, it is probably already installed on your Palm device and you don't have to install it again. (The MathLib is not visible as an application. If you are not sure if the MathLib is already on your Palm device, then simply install it to be safe.)
2. Select one of the available language versions of the SC-103PU. You find the various language versions in the subdirectories english, deutsch and esperanto. Install file SC-103PU.prc from the selected subdirectory on your Palm device as usual.
3. Now you should find an application called SC-103PU in the category "unfiled". If you select the corresponding symbol, the SC-103PU will be displayed.

Preferences

To display the preferences window, select the menu item "Preferences...", which is located in the "Options" menu.

Format of Number Display

You can specify how the calculator should display the numbers. If you select "Localized number format", then seperator characters for numbers are used according to the global system preferences. Otherwise, commas are always displayed as dots and spaces are used to separate groups of three digits. Separator characters for groups of three digits will, however, only be used if you select "grouped" number display mode. In "compact" mode digits are displayed with equal spacing. Number settings only have effect in SCIENTIFIC and UNITS mode, the appearance of numbers in LOGIC mode can not be changed.

NOTE: All examples shown in these operating instructions assume that the "Localized number format" is not active and that the compact number display is selected. If you use other settings, then numbers displayed on your device may appear in a different format.

Flickering of the Display

The flickering of the display serves as a visual feedback to show you that the calculator has accepted your input. In addition, the pressed key will be highlighted but this effect is often not noticable during fast input because of the delay time of the usually used liquid crystal displays.

The flickering effect of the display can be made stronger or softer. If a greater hide time is selected, the display will be hidden for a longer time and the flickering effect will be stronger. Select a value according to your personal taste.
Note: If the flickering effect is enabled, then the display will be dark as long as you press a key. If you release the key before the selected hide time is reached, then the display will stay dark at least until the selected hide time is over. Not all keys, e.g. number keys, result in a flickering effect of the display because some result in a visual display change anyway and also to simply prevent a too nervous display.

The calculator SC-103PU offers three general operating modes for different tasks. To select the desired operating mode there are the three vertically arranged fields at the right border of the display which are labeled SCIENTIFIC, LOGIC and UNITS. To select the desired operating mode, tip on the corresponding field with the stylus. The field indicating the currently selected mode is shown in a dark background color.

		On color devices		On B/W devices
SCIENTIFIC mode
LOGIC mode
UNITS mode

In SCIENTIFIC mode, the SC-103PU acts like a scientific calculator with 14 digits. In LOGIC mode, conversions between four different numeric systems are possible and basic arithmetic calculations and boolean operations can be performed. In UNITS mode, conversions between different units including currencies and mixed unit calculations can be performed.

The Palm handheld can be used like a calculator with 14 digits. For that purpose the program SC-103PU has to be switched into SCIENTIFIC mode. You can activate the SCIENTIFIC mode by tapping on the corresponding field at the right border.

This is how the calculator in SCIENTIFIC mode looks like:

On color devices		On B/W devices

Calculations

Now we will perform some simple calculations. Press the following keys and look at the display:

	Input			Display
		123			123.
					123.
		654			654.
					777.

Did you get the right result? If not, press the key and try the same calculation again.
Next, the value of pi () should be recalled. The symbol "" is located above the key . Press the symbol.

	Input			Display
					3.1415926535898

The Display now shows the value of .
Now 10⁴ should be calculated. For this operation the function 10^x will be used.

	Input			Display
		4			10000.

Following the most important keys will be outlined:

*  (Clear) (red rsp. dark key)

If this key is pressed immediately after input of numerical data or after a recall of the memory contents, this data will be cleared. In any other case, pressing the key clears the operator and/or the numerical data which have been entered. The content of the memory will not be cleared by pressing the key.

	Input			Display
		123  456			456.
					0.
		786			912.	(123 + 789 = 912)
		6  2			12.
					0.
		6  2			12.
		5			8.

The key can also be used to clear an error condition.

	Input		Display
	5  0

*  (Display mode switch)

With this key you can switch the display mode for the result of a calculation from floating point system (normal mode) to fixed point system (FIX), scientific notation (SCI), engineering notation (ENG) or vice versa.

	Input		Dispay
	23  1000

*  (specifies the number of decimal digits)

In comibation with a number key, this key can be used to specify the number of decimal digits (digits after the decimal point). Press the clear key so that "0." is displayed. Press the key , then "0.000" (FIX mode) appeares on the display.

1. Specification of 2 decimal digits.

	Input		Display
	2
	5 8

2. Specification of 5 decimal digits.

	Input		Display
	5

*  (specifies the angular mode)

This key is used to specify the angular mode for numerical data for trigonometric functions, inverse trigonometrc functions and coordinate transformations.

	Input		Display
				(Degree)
				(Radian)
				(Grad)
				(Degree)

*  (transforms between angular modes)

This key is used for transformations between angular modes and simultaneously specifies the angular mode for numerical data for trigonometric functions, inverse trigonometrc functions and coordinate transformations.

	Input		Dispay
	180			(Degree)
				(Radian)
				(Grad)
				(Degree)

*  to , , and

: Used to enter numbers in exponential notation (an "E" following the entered number appears on the display).

	Input			Display
		4 3			4.E 003	(4 × 103)
					4000.
					-4000.

: Used to enter negative numbers (or to inverse the sign from negative to positive).

	Input			Display
		1.23			-1.23
		5			-1.23E-005	(-1.23 × 10-5)
					-0.0000123
					0.0000123

*  (Backspace)

With this key the last entered digit can be deleted.

	Input			Display
		125			125.
					12.
		3			123.
		478			478.
					47.
					4.
		56			456.
					579.	(123 + 456 = 579)
		1.456  19			1.456E 019
					1.456E 001.
		2			1.456E 012.
		1000			1456000000.	(1.456 × 1012 / 1000 = 1456000000)

Basic Usage

1. Addition and Subtraction

Input: 12 45.6 32.1 789 741 213
	Result: 286.5

2. Multiplication and Division

a.	Input: 841 586 12
	Result: 41068.833333333
b.	Input: 427 54 32 7 39 2
	Result: 595.85714285714

Note that multiplication and division have priority over addition and subtraction. Internally, the calculator first calculates the multiplication and division.

Input: 3 5		Result: 15
Input: 10		Result: 30

Division with a constant:
The value entered after the division sign acts as a constant.

Input: 15 3		Result: 5
Input: 30		Result: 10

Note:
Depending on the priority, the calculator puts some calculations in pending state. In case of chain calculations, the last calculation instruction, taking into account the priority rules, and the relevant numeric value are retained and can be used for further calculations or as constants, respectively.

3. Memory Calculations

The independently accessible memory can be maintained with the three keys , and . Before starting a calculation clear the memory by pressing and .
If a value other than zero is stored in memory "" is displayed.

Input: 12 5
	Result: 17
For subtraction enter: 2 5
	Result of this equation: -7
Enter to recall memory contents: 10 will be displayed.
Input: 12 2
	Result: 24 (replaces 10 in memory)
Input: 6 2
	Result: 4 : 28

To subtract a value from memory contents, the keys and can be pressed.

In addition to the memory which can be modified with the key, there are 10 memory slots available which can be modified with to .
To read the contents of these memories you have to press the keys to just like for the independently accessible memory.

Scientific Calculations

To calculate trigonometric and inverse trigonometric equations and for coordinate transformations the angular mode has to be assigned. The assignment of the angular mode DEG, RAD or GRAD happens by pressing the key.

1. Trigonometric Functions

Exercise: sin 30° + cos 40°
Angular mode to DEG
Input: 30  + 40		Result: 1.266044443119
Exercise: cos 0,25
Angular mode to RAD
Input: 0.25		Result: 0.7071067811865

2. Inverse Trigonometric Functions

Exercise: sin-1 0,5
Angular mode to DEG
Input: 0.5		Result: 30
Exercise: cos-1 -1
Angular mode to RAD
Input: 1		To input a negative number, press the key after entering the number.
Result: 3.1415926535898 (Value of )

The results of inverse trigonometric functions are only valid between the following ranges:

= sin-1 x,  = tan-1 x		= cos-1 x
DEG: -90 <=  <= 90 [°]		DEG: 0 <=  <= 180 [°]
RAD: -/2 <=  <= /2 [rad]		RAD: 0 <=  <=  [rad]
GRAD: -100 <= <= 100 [g]		GRAD: 0 <= <= 200 [g]

3. Hyperbolic- and Inverse Hyperbolic Functions

Exercise: sinh 4
Input: 4		Result: 27.289917197128
Exercise: sinh-1 9
Input: 9		Result: 2.8934439858859

4. Power Functions

Exercise: 202
Input: 20		Result: 400
Exercise: 33 and 34
Input: 3 3		Result: 27
Input: 3 4		Result: 81

5. Roots

Exercise: Square root of 25
Input: 25		Result: 5
Exercise: Cube root of 27
Input: 27		Result: 3
Exercise: Fourth root of 81
Input: 81 4		Result: 3

6. Logarithmic Functions

Exercise: ln 21, log 173
Natural Logarithms
Input: 21		Result: 3.0445224377234
Common Logarithms
Input: 173		Result: 2.2380461031288

7. Exponential Functions

Exercise: e3,0445
Input: 3.0445		Result: 20.999528813094 (see ln 21)
Exercise: 102,238
Input: 2.238		Result: 172.98163592151 (see log 173)

8. Reciprocals

Exercise: 1/6 + 1/7
Input: 6 7		Result: 0.3095238095238

9. Factorial

Exercise: 170!
Input: 170
	Result: 7.257415615308E 306 (= 7,257415615308 × 10306)

On calculating the factorial it is easily possible to overflow the calculation limits of the SC-103PU which results in the error indication "E". The section Calculation Range discusses the calculation limits of the calculator.

Exercise: 8P3 = 8!/(8-3)!
Input: 8 8 3
	Result: 336

10. Percent calculations

Exercise: 45% of 2780 (2.780 × 45/100)
Input: 2780 45		Result: 1251
Exercise: 200 - 200 × 30/100
Input: 200 30		Result: 140

11. Angle/Time conversions

To convert an angle or time (°, ', ", rsp. hours, minutes, seconds) to its decimal equivalent the degrees have to be given as integer portion and the minutes and seconds as decimal digits.

Exercise: Transformation of 12°47'52" to its decimal equivalent

Input: 12.4752

Result: 12.797777777778

When converting decimal degrees to the equivalent degrees/minutes/seconds, the answer is broken down:
integer portion = degrees; 1st and 2nd decimal digits = minutes; 3rd and 4th digits = seconds; and 5th through end decimal digits are decimal seconds.

Exercise: Conversion of the decimal angle 24.7256 to its degree/minute/second equivalent

Input: 24.7256

Result: 24.433216 or 24°43'32"

A horse has leap times of 2 minutes 25 seconds, 2 minutes 38 seconds and 2 minutes 22 seconds. What is the average running time? Result 2: 0.0412037037037

Input: 0.0225 0.0238 0.0222
	Result 1: 0.1236111111111
Input: 3
Input:
	Result 3: 0.0228333333333 or the average time is 2 minutes 28 seconds.

12. Coordinate Conversion

Converting rectangular coordinates to polar (x, y  r, ).

DEG: RAD: GRAD:

0 <= | | <= 180 0 <= | | <= 0 <= | | <= 200

Convert rectangular coordinates x = 6 and y = 4 to polar coordinates.
Angular mode: DEG

Input: 6 4		Result: 7.211102550928 (r)
Input:		Result: 33.69006752598 ()

Calculate the magnitude and direction (phase) in a vector i = 12 + j9

Input: 12 9		Result: 15 (r)
Input:		Result: 36.869897645844 ()

Converting polar coordinates to rectangular (r,   x, y).
Solve for P(14, /3), r = 14, 0 /3
Angular mode: RAD

Input: 3 14
	Result: 7 (x)
Input:
	Result: 12.124355652982 (y)

Hint:
In the above example  = /3 is entered first and is replaced by r = 14 by pushing the key after entering r.

Usage of the Parenthesis Keys

Usage of the parenthesis keys and is required if series of calculations are combined together and the priority of operations has to be changed.
After pressing the key, "( )" is displayed in the top of the display.
Calculations between parenthesis have priority over all other calculations. The parentheses can be nested more than once. First the calculations between the innermost parenthesis will be made.

Exercise: 12 + 42 ÷ (8 - 6)
Input: 12  42   8
	Result: 33

Exercise: 126 ÷ {(3 + 4) × (3 - 1)}
Input: 126    3  4    3  1
	Result: 9

Hint:
It is not neccessary to close the parenthesis immediately before the key (or key).

Decimal Digits

The number of decimal digits in a calculation result can be specified; to do this use the key in combination with the keys to . In this case, the display has to be switched to fixed point (FIX), scientific notation (SCI) or engineering notation (ENG).

			No decimal digits. (The number will be roundet to the next integer number.)
			One decimal digit. (The number will be roundet to the first decimal digit.)
			Nine decimal digits. (The number will be roundet to the 9th decimal digit.)

To clear the TAB setting (definition of places after decimal digit) leave the calculator application and restart it again. Then the normal display will be shown again.

Example:

9
0.5 9			0.055555556 (FIX mode) (The number is roundet to the 9th place after decimal digit.)
			5.555555556E-002 (SCI mode) (The mantissa is roundet to the 9th place after decimal digit.)
			5.556E-002 (SCI mode) (The mantissa is roundet to the third place after decimal digit.)
			55.556E-003 (ENG mode)
			0.0555555555556

Priority Levels of Operations

The program is provided with a function that judges the priority level of individual calculations; thus, you can enter your calculations in the same order as in a given mathematical formula. The following table shows the priority level of individual calculations.

Priority Levels of Operations

Example:
Key operation and sequence of calculation in 5 + 2 × sin 30 + 24 × 5³ =

The numbers - show the sequence of the calculations.
When calculations with higher priority are executed, those with lower priority must be saved in the meantime. The program is equipped with additional memories for such pending operations.
As these memories are also used for calculations with parentheses, calculations can be performed according to a given mathematical formula unless parentheses and pending operations exceed 30 levels in total.

• Functions with only one variable (x², 1/x, n!, DEG, D.MS, etc.) are calculated immediately after key operation without being retained.

Calculations without Parentheses

Example:

	Pending of 1 level
	Pending of 2 levels
	Pending of 3 levels
	By pressing the key, 3 pending levels are reached. After pressing the key the calculations "yx" will be performed with highest priority and "×" with the same priority. Thus, after pressing the key, two pending levels remain.

Calculations with Parenthesis

Example:

i)		4 numbers and operations stay pending.
ii)		After pressing the key first the calculation between parentheses 3 - 4 ÷ 5 will be performed; 2 calculations stay pending.

Computer engineers and programmers are in need of simple conversions between various numeric systems as well as for calculations with boolean logic. With the calculator SC-103PU this problem is solved by providing the LOGIC mode. The LOGIC mode can be selected by tapping on the corresponding field at the right border.

Note:
You should first read the sections "Calculations" and "Basic Usage" in the chapter "3. SCIENTIFIC MODE", to get familiar with the operation of the calculator and its basic functions before you use the LOGIC mode.

This is how the calculator looks in LOGIC mode (hexadecimal notation selected):

On color devices		On B/W devices

The calculator can operate with integer values up to a bit width of 32 bits in four different numeric systems.

Conversion Between Different Numeric Systems

	To convert a number to its hexadecimal equivalent; at the same time the calculator will be switched to hexadecimal notation HEX. ( is shown in the displayed.)
	To convert a number to its decimal equivalent; at the same time the calculator will be switched to decimal notation DEC. ( is shown in the display.)
	To convert a number to its octal equivalent; at the same time the calculator will be switched to octal notation OCT. ( is shown in the display.)
	To convert a nubmer to its binary equivalent; at the same time the calculator will be switched to binary notation BIN. ( is shown in the display.)

Exercise:
Conversion from decimal 30 to hexadecimal notation:
Press key if calculator is not currently in decimal notation ( is displayed).

	Input			Display
		30			1E

Exercise:
Further conversion of hexadecimal 1E to binary format:

	Input			Display
					11110

The Hexadecimal Notation

The hexadecimal notation system is mainly used in computer programming. The base for a hexadecimal number is 16; hexadecimal numbers consist of the digits 0 to 9 and the major letters A to F, which stand for the numbers 10 to 15 in the decimal system. Keys for the letters A to F will be shown as soon as the calculator is in hexadecimal notation. The symbol means, that numerical values on the display are shown in hexadecimal notation and that basic integer arithmetic and boolean operations can be performed.

The Decimal Notation

In LOGIC mode even in decimal notation only integer values with a bit width of a maximum of 32 bits can be handled. In decimal notation only the keys for the digits 0 to 9 are shown. The symbol means, that numerical values on the display are shown in decimal notation and that basic integer arithmetic and boolean operations can be performed.

The Octal Notation

The base for a octal number is 8; octal numbers consist of the digits 0 to 7. In octal notation only the keys for the digits 0 to 7 are shown. The symbol means, that numerical values on the display are shown in octal notation and that basic integer arithmetic and boolean operations can be performed.

The Binary Notation

The binary notation system is mainly used in computer programming. The base for a binary number is 2; binary numbers consist of the digits 0 and 1. In binary notation only the keys for the digits 0 and 1 are shown. A smaller font is used so all of the 32 positions can be displayed in one row. Additionally, a ruler is shown above the digits to support the identification of nibbles, bytes and words. The symbol means that numerical values on the display are shown in binary notation and that basic integer arithmetic and boolean operations can be performed.

Direct Bit Manipulation

In the binary notation system a digit can be swapped from 0 to 1 and vice versa by tapping on the digit position below the ruler. If an empty area is tapped then the digit 1 will be set there. With this functionality it is possible to directly modify the bits of a value.

Selecting the Bit Width, Number Display and Sign Mode

The calculator can be switched to bit widths of 8, 16 and 32 bits which are commonly used in the computer industry. With the key the next higher and with the key the next lower bit width is selected. The currently selected bit width is shown in the display.

With the key you can switch leading zeros on and off. Press the key once to show numbers with leading zeros filled to the selcted bit width ( will be shown in the display). Press the key once more to switch back to normal number display. If is activated then leading zeros can be entered during input.

Example:
Settings: , notation,

	Input			Display
		1AB			1AB
					01AB
					0000 01AB
	Input			Display
		000AB8			00 0AB8
					0000 0AB8
		456			002E 79D0
					2E 79D0

With the key, the calculator can be switched between signed and unsigned mode. In the display the symbol appears if the signed mode is active.

Signs are only shown in HEX, DEC and OCT notations. In the BIN notation only the bits are shown, always without a sign.

With the key the sign of a number can be changed. If the sign of a positive number is changed, the 2's complement of the number is calculated. In signed mode the number will then be shown as negative number in unsigned mode as 2's complement.

Example:
Settings: , notation,

	Input			Display
		180			-180
					FE80
					1111111010000000

Number Range

The selected bit width in combination with the sign mode has influence on the number range which can be handled. In contrast to the SCIENTIFIC mode, too big or too small numbers do not lead to an error condition in LOGIC mode but to an overflow.

Exercise:
Solve of 250 + 15 with unsigned 8 bit arithmetic (overflow calculation):

Press the key to select decimal notation ( is shown in the display).
Press the until is shown in display.
With the key select unsigned mode (symbol cleared in display).

	Input			Display
		250  15			9

Exercise:
Display the result of the last calculation in binary notation:

	Input			Display
					1001

Basic Arithmetic Calculations

The arithmetic operations addition, subtraction, multiplication and division can be used like in SCIENTIFIC mode. But only integer values can be handled.

Calculating with Numbers in LOGIC Mode

Exercise:
Addition of two hexadecimal numbers
A4 + BA =

	Input			Display
					0
		A4 BA			15E

Exercise:
4 × 4 =

	Input			Display
					0
		4			10

Exercise:
32 bit multiplication of the octal number 73 with the binary number 110 and display of the result as a decimal number
73 oct × 110 bin =
Press until is shown in display

	Input			Display
					0
		73			111011
		110			101100010
					354

Exercise:
(12 + D) × B =

	Input			Display
					0
		12 D B			155

Exercise:

	43A	-	3CB	=
+)	A38	-	2FB	=
---------------
			total

	Input			Display
					0.
		43A 3CB			6F
		A38 2FB			73D
					7AC

The following hints have to be noted:

• Calculations in LOGIC mode do not take into account fractions.
• The result of a division will always be shown as an integer value. If a fraction results during a calculation the fractional part is cut and only the integer part will be displayed.

Examples:

Input: E 3		Result: 4
Input: B 3 2		Result: 6

With the modulo operation the remainder of a division can be computed.

Input: E 3

Result: 2

By pressing the key it is possible to calculate the complement of a number in a simple way.
Settings: Unsigned mode (symbol is not shown, notation,

Input: AB

Result: FFFF FF55

Boolean Algebra

The operators of the boolean algebra AND, OR, XOR (exclusive or) and NOT can be used. In a logical operation two numbers will be transformed to binary representation (2's complement) and the logical relation will then be evaluated for every bit pair.

The following section will shown the results of the logical operators for these bit evaluations:

After every bit pair has been assigned the corresponding result (a 1 or a 0) according to the above table, the resulting binary number will be converted back to the selected numeric system. This number is the result of the logical operation.

	41 AND 27  gives 9
Input: 41  27			Result: 9
	41 OR 27  gives 59
Input: 41  27			Result: 59
	41 XOR 27  gives 50
Input: 41  27			Result: 50
	NOT 3 gives -4 (2's complement)
Input:3			Result: -4

NOT x can generaly be computed with the equation NOT x = -(x + 1).

Bit Shift Operations

Bit Shift Right

During the bit shift right operation the single bits of a value will be shiftet to the right by the given amount of positions. This is equivalent to a division by the power of 2.

	Input:			Display:
		80 3			10

In signed mode () an arithmetical shift right will be performed whereas in unsigned mode a logical shift right is executed. Arithmetical shift means that the sign of a number is retained; logical shift right always results in a cleared sign bit, treating all bits equal.

	Input:			Result:
					0
		120			-120
					10001000
		1			11000100
					-60

	Input:			Result:
					196
		2			49
					110001

Bit Shift Left

During the bit shift left operation the single bits of a value will be shiftet the given amount of positions to the left. This is equivalent to a multiplication with the power of 2.

	Input:			Display:
		3 2			12

Swapping Bytes and Nibbles

Example:
Settings: Unsigned mode (symbol is not shown), notation,

	Input			Display
		1234ABCD			1234 ABCD
					CDAB 3412
					3412
					1234

In 8 bit notation the nibbles will be swapped:

Example:
Settings: Unsigned mode (symbol is not shown), notation,

	Input			Display
		AB			AB
					BA

Parenthesis and Priority Levels of Operations

During the processing of complex expressions the calculator follows a set of predefined priorities which determine the sequence in which the operators have to be applied. In LOGIC mode, the same rules for priority of operators and parenthesis are valid as described in SCIENTIFIC mode in section "Priority Levels of Operations" but the additional boolean operators have to be taken into account:

Priority Levels of Operations

1. Functions like not or x²
2. ×, ÷, mod
3. +, -
4. «, »
5. and
6. xor
7. or
8. =, M+
(Calculations which are on the same priority level are executed in sequence.)

The UNITS mode offers easy conversions between different units and calculations with mixed units. The conversion factors and unit symbols can be freely defined by the user. The calculator is shipped with 84 physical units, 16 SI prefixes, the 12 Euro related national currencies and the Euro predefined. Each unit rsp. currency is assigned to a key. The UNITS mode can be selected by tapping on the corresponding field at the right border.

Note:
You should first read the sections "Calculations" and "Basic Usage" in the chapter "3. SCIENTIFIC MODE", to get familiar with the operation of the calculator and its basic functions before you use the UNITS mode.

This is how the calculator looks like in UNITS mode:

On color devices		On B/W devices

Predefined Units

The UNITS Mode offers 10 unit sets each with 17 unit keys. Nine of the unit sets are predefined by default. The first unit set is predefined with currency units and the remaining with physical units.
The following table shows all predefined unit sets and their units:

Unit Set	Unit	Unit Symbol	Category	Factor	Offset
CURRENCY	Euro	€*	Currency	1	0
	Austrian Schilling	ATS		13.7603
	Belgian Franc	BEF		40.3399
	German Mark	DEM		1.95583
	Spanish Peseta	ESP		166.386
	Finnish Markka	FIM		5.94573
	French Franc	FRF		6.55957
	Greek Drachma	GRD		340.75
	Irish Punt	IEP		0.787564
	Italian Lira	ITL		1936.27
	Luxembourg Franc	LUF		40.3399
	Dutch Guilder	NLG		2.20371
	Portuguese Escudo	PTE		200.482
LENGTH	micrometre	µm	Length	1×106	0
	millimetre	mm		1000
	centimetre	cm		100
	decimetre	dm		10
	metre	m		1
	kilometre	km		1×10-3
	mil	mil		1/2.54×10-5
	inch	in		1/2.54×10-2
	foot	ft		1/3.048×10-1
	yard	yd		1/9.144×10-1
	mile (international)	mi		1/1609.344
	mile (nautical)	nmi		1/1852.0
	astronomical unit	au		6.684587153547039139×10-12
AREA	square millimetre	mm²	Area	1×106	0
	square centimetre	cm²		1×104
	square metre	m²		1
	are	a		1×10-2
	hectare	ha		1×10-4
	square kilometre	km²		1×10-6
	square inch	in²		1/6.4516×10-4
	square foot (international)	ft²		1/9.290304×10-2
	square yard	yd²		1/8.3612736×10-1
	Joch (Austria)	Joch		1.0/5754.642
	acre (Morgen)	acre		1/4046.85644642784
	square mile (international)	mi²		1/1609.3442
VOLUME	cubic centimetre	cm³	Volume	1×103	0
	litre	l		1
	cubic metre	m³		1×10-3
	teaspoon (US)	tsp		0.264172052358148×768
	tablespoon (US)	tbsp		0.264172052358148×256
	cubic inch	in³		0.264172052358148×231
	fluid ounce (US)	oz		0.264172052358148×128
	cup	cu		0.264172052358148×16
	pint, liquid (US)	pt		0.264172052358148×8
	quart, liquid (US)	qt		0.264172052358148×4
	gallon, liquid (US)	gal		0.264172052358148
	cubic foot	ft³		0.0353146667214886
MASS (Masse und Temperatur)	milligram	mg	Mass	1×106	0
	carat	ct		5×103
	gram	g		1×103
	kilogram	kg		1
	metric ton	t		1×10-33
	grain	gr		7000×(35.2739616/16)
	ounce (avoirdupois)	oz		35.2739616
	ounce (troy)	ozt		32.15074625
	pound (troy)	lbt		32.15074625/12
	pound (avoirdupois)	lb		35.2739616/16
	short ton (US, 2000lb)	tn		35.2739616/(16×2000)
	long ton (UK, 2240lb)	l.tn		35.2739616/(16×2240)
PWR/ENERGY (Power and Energy)	watt	W	Power	1	0
	kilowatt	kW		1×10-3
	Pferdestärken	PS		1.359619307×10-3
	horsepower	HP		1.341021859×10-3
	joule	J	Energy	1	0
	kilojoule	J		1×10-3
	calorie	cal		1/4.1868
	kilocalorie	kcal		1/4186.8
	watt hour	Wh		1/3600
	kilowatt hour	kWh		1/3600000
	electron volt	ev		1/1.60217733×10-19
	foot pound weight	ftlb		1/1.355818
	british thermal unit	BTU		1/1.05505585262e+03
TEMP/PRESS (Temperatur und Druck)	kelvin	K	Temperature	1	273.15
	degree Fahrenheit	°F		1.8	32
	degree Celsius	°C		1	0
	degree Réamur	°r		0.8	0
	pascal	PA	Pressure	1×105	0
	bar	bar		1
	atmosphere standard	atm		1/1.01325
	atmosphere technical	at		1.0197162
	millimetre of mercury (Torr)	mmHg		750.06158
	pound per square inch	psi		14.50377439
	inch of mercury	inHg		29.529983
	foot of water	ftW		33.4560927
SPEED/TIME	metre per second	m/s	Velocity	1	0
	kilometre per hour	km/h		3.6
	knot	knot		1.9438445
	mile per hour	mi/h		1/0.44704
	foot per second	ft/s		1/0.3048
	second	s	Time	86400	0
	minute	min		1440
	hour	h		24
	day	day		1
	year (365 days)	year		1/365
SI PREFIX	atto	a	SI Prefix	1×1018	0
	femto	f		1×1015
	pico	p		1×1012
	nano	n		1×109
	micro	µ		1×106
	milli	m		1×103
	zenti	c		1×102
	deci	d		1×101
	Basis	base		1
	deka	da		1×10-1
	hekto	h		1×10-2
	kilo	k		1×10-3
	mega	M		1×10-6
	giga	G		1×10-9
	tera	T		1×10-12
	peta	P		1×10-15
	exa	E		1×1018

* On devices which are not equipped with a Euro symbol (€), that is, devices with a PalmOS version less than 3.3, EUR will be displayed instead of the Euro symbol.

Notes:

• Only units of the same category can be converted into each other. On color devices each category is assigned a color for easy recognition.
• A unit is converted into another unit, using the factors and offsets. For each category there is a unit with the factor 1 (shown in boldface). This unit is called the base unit of the category, and all other units of the same category are related to it.
• The calculator uses the following equation to convert a value from one unit to another unit:
  value₂ = (value₁ - offset₁) / factor₁ × factor₂ + offset₂

Selecting the Unit Set

If the units mode is selected from scientific or logic mode by pressing the field labeled UNITS on the right border, then the recently used unit set will be selected.

In units mode the field labeled UNITS is provided with two arrows, one pointing up an one pointing down. By pressing this arrows the next or previous unit set can be selected.

If in units mode the UNITS label itself is pressed, a selection list with all available unit sets is displayed and the desired unit set can be directly selected.

Different View Modes of the Units Mode

In unit mode for each unit set a "one line" or "two lines" view mode can be selected independently. By default the "two lines" view mode is selected for the first unit set which holds the currency units. All other unit sets use the "one line" view mode by default.

The same unit set shown in the two possible view modes:

One line view mode		Two lines view mode

Switching Between The Two View Modes

With the menu item "One/Two Lines Display" in the "Options" menu the calculator can be toggled between "one line" and "two lines" view mode.

Alternate ways to change the view mode:

• To switch from "two lines" into "one line" view mode: Press  . This clears the unit of the second line.
• To switch from "one line" view mode to "two lines" view mode: Press the key  followed by a units key. This specifies the unit for the second line.

One Line View Mode

The "one line" view mode of the UNITS mode can be seen as extension to the SCIENTIFIC mode where unit conversions can be performed. The actual value will be simply convertet without permanently assigning it to a unit. For this reason, opposite to the "two line" view mode there are no restrictions in the calculations which can be performed.

Following the most important keys will be outlined:

* Unit keys , , etc.

With the unit keys a displayed number can be convertet from one unit to another. The key area with the unit keys is surrounded by a thin line. For conversion two unit keys have to be pressed in sequence. The shown number will be converted from the first into the second unit. A conversion can only be performed between units of the same category.

Example:
Conversion from 12.5 inch to millimetre.

• Select the unit set LENGTH after pressing the UNITS filed in the right border.

	Input			Display
		12.5			12.5
					12.5	in
					317.5

Result: 12.5 inch are 317.5 mm

How many feet an inch are 1.75 m?

	Input			Display
		1.75			1.75	m
					5.741469816273		Result 1: 5 feet
		5			0.741469816273	ft
					8.897637795276		Result 2: 8.9 inch

Result: 1.75 m are 5 feet and 8.9 inch.

*  (switching into "two lines" view mode)

With the key and a following unit key the calculator can be switched from "one line" view mode to "two lines" view mode. For the second display line the pressed unit will be selected. For the first display line a unit compatible to the unit of the second line will be used. If in "one line" view mode a unit ist currently specified then this unit will also be used for the first display line in "two lines" view mode if it is compatible with the one selected for the second line.

Example:
Conversion of 3.8, 14.6 und 26.6 square metres to the corresponding square yards by using the "two lines" view mode and thereafter switching back to "one line" view mode.

• Select the unit set AREA after pressing the field UNITS at the right border.

	Input			Display
					0.
		3.8			3.8
					3.8	m²
					3.8 4.544762175944	m² yd²
					0. 0.	m² yd²
		14.6			14.6 17.461454676	m² yd²
					0. 0.	m² yd²
		26.6			26.6 31.81333523161	m² yd²
					26.6

Two Lines View Mode

The "two lines" view mode is especially usefull for fast and easy conversion between two units. In the display two lines will be shown. User inputs are displayed in the first line. In the second line the entered or calculated value can instantly be viewed in a different unit. The numbers displayed in the two lines always represent the same value but in different units.

Following the most important keys will be outlined:

* Unit keys , etc.

With the unit keys the unit of the number in the first display line can be selected. The key area with the unit keys is surrounded by a thin line. By pressing the key for example the currency DEM will be assigned as unit to the value oft the first line in the display. During input of a number the unit can be assigned at any time without effecting the numerical value.

*  (specify second line)

With the key you specify the second display line. The consecutively pressed key will the be related to the second display line instead of the first display line. So by pressing of the currency unit ATS will be assigned to the second line. If the unit of the second line will be changed then the numerical value of the second line will also be changed because the value of the first line will be converted to the new unit of the second line.

Example:
How many Euro (€), are 123.5 Austrian Schilling (ATS).

• Select the currency ATS for the first line by pressing the key.
• Select the currency Euro for the second line by pressing  .

Showing the 123.5 ATS of the last example in BEF:

	Input			Display
					23.5 362.05	ATS BEF

To start a new conversion, press the key first to clear the display and start a new input.

	Input			Display
					0. 0.00	ATS BEF
		527.9			527.9 1547.60	ATS BEF
					527.9 38.36	ATS €

*  (exchange units)

With this key the units of the first line and the second line can be exchanged. Only the units will be new assigned. The values will not be exchanged.

Example:
Conversions between various currencies.

	Input			Display
					0. 0.00	DEM ATS
		12.6			12.6 88.65	DEM ATS
					12.6 0.92	ATS DEM
					0. 0.00	ATS DEM
		100			100. 14.21	ATS DEM

*  (clear unit assignement)

If the key is pressed, the unit assignement for the first display line will be removed. So the number in the first display line has no unit. Simultaneously the second display line will be hidden ("---" will be shown) because a value without a unit can not be converted to a number with a unit.

By pressing of  , the calculator will be switched into "one line" view mode.

*  (specifies the number of decimal digits)

In combination with a number key, this key can be used to specify the number of decimal digits (digits after the decimal point). In combination with the key, the number of decimal digits for the second display line can be specified.

To remove the fixed number of digits after the decimal point and switch back to floating point mode press .

Note: The number of decimal digits can not be set during input of a number only after a calculation or after pressing the key.

1. Specification of 3 decimal digits for the first line.

	Input			Display
					0. 0.00	ATS DEM
		3			0.000 0.00	ATS DEM
		5  8			0.625 0.09	ATS DEM

2. Specification of 5 decimal digits for the second line.

	Input			Display
		5			0.625 0.08883	ATS DEM

3. Floating point display for the second line.

	Input			Display
					0.625 0.088834818282	ATS DEM

Calculations with Mixed Units

In "two lines" view mode of the UNITS mode the basic operations plus percent calculations can be performed as shown in SCIENTIFIC mode. However, units will be taken into account. So it is possible to perform calculations with mixed units.

Example:
Calculate 120 ATS + 20.5 DEM and show the result in DEM and Euro.

	Input			Display
					0. 0.00	ATS €
		120			120. 8.72	ATS €
					120. 8.72	ATS €
		20.5			20.5 1.49	ATS €
					20.5 10.48	DEM €
					37.55628511006 19.20	DEM €

The result of calculations with units is displayed in the unit of the second operand, if one has been assigned. Otherwise, the unit of the first operand will be used for the result. Not all unit combinations are valid in calculations. The following table shows combinations of operations and their result units:

By trying to apply a illegal calculation, the calculator will be set into an error condition and the symbol "E" will be displayed. The error condition can be cleared by pressing the key.

On multiplications and divisions the calculator selects no unit for the second operand by default. But a unit can be assigned to the second operand explicitely.

Example:

	Input			Display
					0. 0.00	ATS €
		1000			1000. 72.67	ATS €
					1000. 72.67	ATS €
		2			2.
					500. 36.34	ATS €
	Input			Display
					0. 0.00	ATS €
		1000			1000. 72.67	ATS €
					1000. 72.67	ATS €
		20			20.
					20. 10.23	DEM €
					7.106785462526

After pressing an operator key (, etc.) or the keys rsp. the unit assigned to the value in the first line of the display will be shown in bold face. This indicates, that the unit is dedicated to the value. Pressing a unit key in this situation yields to a conversion of the value to the new unit and not the simple assignement of a new unit to the value.

Parenthesis and Priority Levels of Operations

During the processing of complex expressions the calculator follows a set of predefined priorities which determine the sequence in which the operators have to be applied. In UNITS mode, the same rules for priority of operators and parenthesis are valid as described in SCIENTIFIC mode in section "Priority Levels of Operations".

Usage of the Memories

The usage of the memories in UNITS mode is basically the same as in SCIENTIFIC mode. With a value will be stored in the independently accessible memory and with a value can be added to the current memory contents. Note that units are ignored when values are added to memory. No unit conversion is performed. The memory contents can be retrieved with the key like usual.

In addition to the independently accessible memory, 10 memory slots are available as in SCIENTIFIC mode which can be accessed with rsp. followed by a digit key.

In "two lines" view mode normally the value in the first display line will be stored in the memory. However, by using the key the value of the second display line can be stored. Press one of the following key sequences:  ,   for independently accessible memory or   followed by a digit key to store the value of the second line in one of the 10 memory slots.

Combining UNITS and SCIENTIFIC mode

During input of a calculation the calculator can be switched between UNITS and SCIENTIFIC mode at any time without loosing the pending operations an entered digits. Especially the "one line" view mode can be used in combination with the SCIENTIFIC mode.

Example:
How much feet and inch is the diagonal c of a rectangle with the side length of a = 30 feet, 5 inch and b = 13 feet, 8 inch.
Formula: c = sqrt(a² + b² )

• Select unit set LENGTH after pressing the field UNITS at the right border.

	Input			Display
					0.
		30			30.
		5			5.	in
					0.416666666667
					30.41666666667
					925.1736111111
					925.1736111111
					0.
		13			13.
		8			8.	in
					0.666666666667
					13.66666666667
					938.8402777778
	Switch into SCIENTIFIC mode.
					30.640500612388		Result: 30 feet
		30
					0.6405006123885
	Switch into UNITS mode (LENGTH).
					7.686007348662		Result: 7.686 inch

Result: 30 feet, 7.686 inch

Defining Units

It is always possible to add new units to the already predefined units. Further it is possible to change or delete the predefined units.

The calculator uses the following forumula to convert from unit₁ to unit₂:

value₂ = (value₁ - offset₁) / factor₁ × factor₂ + offset₂

If a unit should be defined factor and offset relating to the other units of the same category have to be specified. In most cases for each category a base unit with a factor of 1 is defined. The offset is needed, if the units have different base points which is the case for example with the temerature units °C, °F and K:

	Faktor	Offset
°C	1.	0
°F	1.8	32
K	1.	273.15

Unit Definition Form

With the unit definition form a new unit can be defined, an existing unit can be modified or deleted. With the menu item "Define Unit Key..." in the "Options" menu you switch into the unit definition mode.

Here, the unit key to be defined can be selected by pressing the key. All unit keys are located in the bordered region. An undefined and therefore unlabeled unit key can also be selected to define its unit.

After selecting the unit key, the unit definition form appears. There the parameters of the unit can be changed and entered. With the key "Delete.." in the form, a unit definition can be erased.

To define a unit, a unit symbol consisting of up to four charachters must be entered, which will be used as label for the unit key. The unit has to be assigned to one of the 15 categories. Only units of the same category can be converted into each other. Also, the conversion factor and offset related to the base unit has to be specified. The base unit is displayed if one exists. The calculator recognizes the base unit of a categoy by its conversion factor of 1.

Note: An alternative way to open the unit definition form for a unit key is to press the unit key for a period of at least 2 seconds and then releasing the key.

Example:
The currency US dollar should be added to the already defined currencies. The unit key above the key should be used. The conversion factor should be 1.20.

In the menu "Options" select the menu item "Define Unit Key..." and then press the unit key you want to define.

The unit definition form appears where the currency symbol US$ can be entered under "New unit symbol". Optionally a descriptive text can be entered under "Description". It has no further function. As "Conversion factor" 1.20 should be entered. Currency units do not need any offset so we leave this field with value 0. For the "Category", "Currency" has to be selected, so that the new currency unit can be convertet to the already defined currencies. By pressing "OK" the unit definition form will be closed and the unit is defined.

The new unit is defined. It can be used:

	Input			Display
					0. 0.00	€ US$
		1			1. 1.20	€ US$
					0. 0.00	DEM US$
		64.55			64.55 39.60	DEM US$

Defining Unit Sets

Already existing unit sets can be renamed an new units sets can be defined. Further unit sets can be hidden. For this the unit set definition form has to be opened via the menu item "Name Unit Sets..." in the "Options" menu.

Here the names of the unit sets can be entered. There are 10 unit sets available. By default nine of them are predefined according the following table:

Name of the unit set	Description
CURRENCY	Currency units
LENGTH	Length units
AREA	Area units
VOLUME	Volume units
MASS	Mass (Weight) units
PWR/ENERGY	Power and Energy (Work) units
TEMP/PRESS	Temperature and pressure units
SPEED/TIME	Speed (velocity) and time units
SI PREFIX	SI prefixes

For every unit set it can be selected if it should be visible or not. Invisible unit sets can not be used. Unit sets without a name can not be made visible.

Usually, the digits and operators will be entered by pressing the displayed keys. But all digits and some operators can also be entered using the Graffiti® region of the Palm device or pasted from the clipboard. Values can also be copied to the clipboard. Further it is possible to directly modify the contents of the memories in a special form.

Direct Manipulation of the Memories

A memory manipulation form can be opened via the menu item "Memory..." in the "Edit " menu. In this form the contents of all memories can be seen simultaneously and they can also be modified.

In the first line the actual display value is displayed. In the following line the contents of the independently accessible memory (M) is shown, followed by the 10 memories (1 to 9 and 0) which are assigned to the number keys.
The actual display value can be stored in the independently accessible memory by pressing the key and can be restored using the key .
In addition to the independently accessible memory there are 10 memory slots are available which can be modified with to . To read the contents of these memories you have to press the keys to .
The memory contents can also be changed directly using Graffiti®.

By pressing "OK" the memory form will be closed and all entered values will be written to the memories.

By pressing rsp. followed by a digit key or when selecting "OK", the entered values will be written back to the memories. But first it will be checked if the entered data is a valid value. If no valid value is entered an error requester will be displayed. It can be closed by pressing "OK" to correct the invalid input by hand. But if "Restore from memory" will be pressed, the last memory contents will be restored and the input will be lost.

In the shown example a wrong input is done for memory location 2.

Entering using Graffiti®

Following there is a table containing the keys which have been assigned a symbol which can be entered using Graffiti®

SCIENTIFIC and CURRENCY Mode				LOGIC Mode
Key:		Symbol:		Key:		Symbol:
to		"0" to "9"		to		"0" to "9"
		".", ","		to		"a" to "f", "A" to "F"
		"_"				"_"
		" ", "C"				" "
		Backspace				Backspace
		"/"				"/"
		"*"				"*"
		"-"				"-"
		"+"				"+"
		"=", Enter				"=", Enter
		"(", "[", "{"				"(", "[", "{"
		")", "]", "}"				")", "]", "}"
		"%"				"&"
		"^" (only SCIENTIFIC)				"n", "N", "~"
		"!" (only SCIENTIFIC)				"o", "O", "|"
						"x", "X", "^"
						"m", "M", "%"
						"l", "L", "<">
						"r", "R", ">"

Data Exchange with the Clipboard

With the menu items in the menu "Edit", the value currently shown on the display can be cut or copied to the clipboard or a value in the clipboard can be pasted to the SC-103PU.

While in an error condition the display shows the symbol "E":

An error will be raised from a calculation or command which exceeds the capacity of the program. An error can be cleared by pressing the key.

Error Conditions

1. If the absolute value of a calculation result is greater than 1.7976931348623×10³⁰⁸ (not in LOGIC mode).
2. If a number is divided by 0 (zero) (e.g. 5  0  )
3. If in CURRENCY mode a illegal calculation was entered.
4. If the absolute value of a result of memory calculation is greater than 1.7976931348623×10³⁰⁸ (not in LOGIC mode).
5. If the pending operation inclusive open parentheses exceeds 30 levels.
6. For scientific functions an error occurs if the calculations exceed the following ranges:

Calculation Range

-1.7976931348624×10³⁰⁸ < x<= -2.23×10^-308 for a negative x
2.23×10^-308 <= x < 1.7976931348624×10³⁰⁸ for a positive x

The displayed value for x will be limited by the number of displayable positions.

Functions:

Function	Range of x
sin x cos x tan x	DEG: |x| < 1.7976931348624×10308 RAD: |x| < 1.7976931348624×10308 GRAD: |x| < 1.7976931348624×10308 Further only for tan x: (n = integer) DEG: |x|  90(2n-1) RAD: |x|  (/2)(2n-1) GRAD: |x|  100(2n-1)
sin-1x cos-1x	-1 <= x <= 1
tan-1x	|x| < 1.7976931348624×10308
sinh x cosh x	-710.47586007394 <= x <= 710.47586007394
tanh x	-1.7976931348623×10308 <= x <= 1.7976931348623×10308
sinh-1x	|x| < 1.3407807929943×10154
cosh-1x	1 <= x < 1.3407807929943×10154
tanh-1x	|x| < 1
ln x log x	2.23×10-308 <= x < 1.7976931348624×10308
ex	-1.7976931348624×10308 < x <= 709.78271289338
10x	-1.3407807929943×10154 < x <= 308.25471555991
	|x| < 1.7976931348624×10308
1/x	|x| < 1.7976931348624×10308; x  0
x2	|x| < 1.3407807929943×10154
	0 <= x < 1.7976931348624×10308
n!	0 <= n <= 170 (n = integer)
DMSDEG DEGDMS	|x| < 1.7976931348624×10308
yx (yx=10x log y)	if y > 0, -2.23×10-308 < x log y < 308.25471555992 if y = 0, x > 0 if y < 0, x = integer and 2.23×10-308 < x log |y| < 308.25471555992
(=101/x log y)	if y > 0, -2.23×10-308 < 1/x log y < 308.25471555992; x  0 if y = 0, x > 0 if y < 0, x or 1/x have to be integer and not zero, and 2.23×10-308 < 1/x log |y| < 308.25471555992
x, y  r,	(x2+y2) < 1.7976931348624×10308 y/x < 1.7976931348624×10308  = tan-1(y/x)
r,   x, y	r < 1.7976931348624×10308 x = r cos  |r sin | < 1.7976931348624×10308 y = r sin  |r cos | < 1.7976931348624×10308