Welcome to the

MathU™ 1.0 for iPhone

RPN Scientific Calculator

Documentation

Contents

• What is MathU?
• What is new in Version 1.0?
• System Requirements
• Installation
• Free Trial
• Registration
• Two Keypads
• Basic Operations and walkthrough
• Menus
• Preferences
• Basic Functions
• Stack and Register Functions
• Scientific Functions
• Trigonometric Functions
• Time Functions
• Polar Coordinates
• Number Base Functions
• Modular Functions
• Financial Functions
• Statistical Functions
• Legal Stuff
• Contacting Creative Creek, LLC

What is MathU?

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Thank you for evaluating MathU. MathU is a Reverse Polish Notation (RPN) scientific and financial calculator for the iPhone. It runs within the Safari Browser on the iPhone. The calculator supports double precision accuracy and has 80 functions including 5 financial functions, 4 number bases and 8 statistical functions. There are 20 memory registers (two banks of 10 each).

Technical specifications

• Written entirely in Javascript so that you do not need to be connected to the web to run it (Safari must be running however)
• Remembers your stack and register contents between runs
• Double precision accuracy.
• 16 element stack
• 80 built-in functions (including 5 financial functions and 8 statistical functions)
• Hex, oct, and bin conversions
• 20 memory registers

What is new in Version 1.0?

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MathU 1.0 for iPhone is the first release for the iPhone. It has similar features to MathU 3.0 for Palm OS.

System Requirements

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MathU runs within the Safari web browser on the iPhone or iPod touch. It will work with iPhone OS version 1.1 or higher. Support for the home screen icon requires iPhone OS version 1.1.3 or higher.

Installation

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Since MathU is hosted on the web, you run it by going to http://www.creativecreek.com/app/mathu.php in the Safari browser. The first time you do this you will be presented with a login screen. Simply enter your registration code and you will automatically be taken to MathU. If you have not purchased a registration code yet, then tap the "free trial" link to get a temporary code e-mailed to you that lasts for 15 days.

Do this directly from the iPhone and you can start using MathU right away.

Free Trial

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MathU features a free 15 day trial. All the features of MathU are available during the trial. The only difference between the trial and a registered version is that a notice displays on startup. After the 15 day trial, the five key (5) becomes disabled. If you decide that you like MathU, purchase a registration code to unlock it.

Registration

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A registration code can be obtained by purchasing MathU from [IPMATHU_BUYIT].

A registration code will be e-mailed to you. To register your software, tap the "Enter registration code link" in the notice or click on the link provided in the e-mail.

If for any reason you have trouble registering your software please contact us via contact page.

Two Keypads

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MathU for iPhone supports both a portrait and landscape keypad

Simply rotate the iphone to switch between landscape and portrait keypads.

Add icon to home screen

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To add a MathU icon to the home screen, tap the + button as shown in the picture while running MathU (Requires iPhone OS 1.1.3 or higher).

Basic Operations

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MathU is based on Reverse Polish Notation (RPN). RPN differs from standard mathematical notation in that the numbers to be operated on are pushed onto a stack and then executed upon by a function. MathU has a 16 element stack. The first four elements of this stack are referred to by the names x,y,z, and t.

The value of the x register is what is displayed.

RPN is just like the way you were probably taught to add numbers.  First you wrote the two numbers above each other like this:

5
7
--

Then you added the operator and wrote down the answer (I'm skipping the calculation part in your head)

 5
+7
--
12

In RPN you place the two numbers on the stack. To set up the same problem as above the keystrokes are  5 ENTER 7.  This produces the stack picture:

just like what you put on the paper.  The ENTER key pushes the current value up on the stack and allows you to put a new number in its place (The empty boxes will contain the values from previous calculations).

When you hit + the two values are added together.  The + key always adds the x and y registers together and then places the result into x:

All the functions in MathU work like this using values on the stack. Some like + work with x and y while others like SIN just use the value in the x register and replace it with the result.   In this documentation, the former are called binary functions while the latter are called unary functions.

Hence the operation

12.5 + 7

is keyed as

1 2 . 5 ENTER 7 +

The ENTER key is used to separate the two values. Most buttons on MathU can access three functions. The function or number on the top of each button is accessed without shifts. The function just above the button is accessed by pressing the f-shift key f before pressing the button. The f-shift indicator will light in the display when the f-shift is active. Similarly to access the functions on the front of the buttons use the g-shift key g. The g-shift indicator will light in the display when the g-shift is active.

Most functions remember the last x register value used during a computation. This value can be accessed via the LASTX button.

Preferences

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The preference screen is displayed when you execute the PREFS function or when you tap the degree indicator on the screen.

• Format: MathU can display results in either fixed, scientific, or engineering format.
  • Fixed format displays results with a fixed number of decimal digits but will over- or underflow to scientific notation showing all digits if the value is too big or too small.
  • Scientific format displays all results in scientific notation with a fixed number of decimal digits. Numbers in scientific notation are displayed as
    
    which is interpreted as the number 1.234567890 x 10⁹⁹.
  • Engineering format is just like scientific format except that the exponent is always a multiple of three.
• Digits: Number of digits or All if you want all the significant digits to displayed. The number of digits displayed depends on the format. In scientific and fixed format, it is the number of digits after the decimal. In engineering format one more than the number chosen decimal digits are displayed.
• Angles: Angle domain for trigonometric functions. The state of this preference is also indicated in the display.
• Payments due: Financial annuity mode. Payments can be due at the beginning of the pay period (annuity due) or at the end of the period (ordinary annuity). The state of this preference is also indicated in the display.
• Wordsize: Number of bits to use for integer base functions like Hex, Oct, and Bin. Values larger than this number of bits will continue to be displayed. Execute an integer base function to truncate such integers to bring them into range. Values between 1 and 48 are supported.

Tap each setting line to go to screen that displays the choices. Tap the desired new setting to select it and return to the settings screen.

Basic Functions

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7 8 9 4 5 6 1 2 3 0 .	Numerals
A B C D E F	Hexadecimal	Hexadecimal digits. Active only when in HEX mode.
CHS	Change sign of mantissa or exponent.
EEX	Start entering exponent
	Undo last character (or clear x register)
−	Minus.
+	Plus
Χ	Times
÷	Divide
ENTER	Separate values and prepare x register to be overwritten

Stack and Register Functions

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MathU has 20 registers -- 10 primary registers and 10 secondary registers. The secondary registers are used to store values for the financial and statistical functions. The secondary registers can be used to store your own values but you must be careful not to use any financial or statistical functions if you do so.

The 10 primary registers are accessed by pressing STO or RCL and then the register number 0 through 9. To access the secondary registers (registers 10 through 19) press STO . and then the register number 0 through 9. Another way to access the secondary registers is to swap the primary and secondary registers with P^<>S and then use STO or RCL (without the .).

Key	Function	Description	Stack effect
STO n	sto	Store into register n. Specify . n to access the secondary register (register 10+n)
STO fn	sto	Store into financial register. fn can be N, i,PMT,PV, or FV.
STO + n	sto	Add contents of x register to register n
STO − n	sto	Subtract contents of x register from register n
STO Χ n	sto	Multiply register n with contents of x register
STO ÷ n	sto	Divide register n by contents of x register
RCL n	rcl	Recall from register n. Specify . n to access the secondary register (register 10+n)
RCL fn	rcl	Recall financial register. fn can be N, i,PMT,PV, or FV.
RCL Σ+	rcl	Recall statistics sums.
P<>S	p<>s	Swap primary and secondary banks of registers
CLREG	clreg	Clear all registers
x<>y	x<>y	Exchange x and y registers
LST Χ	lastx	Recall last x value
CLX	clx	Clear x register
CLSTK	clstk	Clear stack
R↑/td>	rollup	Rotate stack contents up
R↓	rolldown	Rotate stack contents down
ENTER	enter	Push current value onto stack.
	undo	When entering a number undo the last character, otherwise clear the x register the same as clx.

Scientific Functions

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The unary functions operate on the value in the x register and replace it with the function result (f(x))

while the binary functions use the values in both the x and y registers and place the result in the x register.

Key	Function	Description	Type
f		f shift. Use to access functions above each button.
g		g shift. Use to access the functions at bottom of each button.
MOD	mod	Modulo (y - x * floor(y/x))	binary
π	pi	Value of pi	unary
LN	ln	Natural logarithm (base e)	unary
LOG	log	Base 10 logarithm	unary
ex	exp	Exponential function	unary
10x	pow10	Ten to the x power	unary
yx	ytox	y to the power of x	binary
x2	sq	Square	unary
√x	sqrt	Square root	unary
1/x	inv	Reciprocal	unary
FRAC	frac	Fractional part	unary
INT	int	Integer part	unary
N!	fact	Factorial	unary
%	%	Percent (y * x) / 100	binary
%CH	% ch	Percent change 100 * (x - y) / y	binary

 

The INT and FRAC functions round to 9 decimal digits before determining the integer and fractional parts. Under this definition FRAC is computed using the formula

frac(x) = x - int(x)

Most of the time this produces the desired results but does treat the input as if it only had 10 digits of accuracy. One of the ramifications of this is that the fractional part doesn't always have the same sign as x. Take for example the number 1.99999999964 (i.e. 2 - 36e-11). When displayed in MathU this number looks like it is 2.0. Because of the rounding int(x) is 2 (as expected) while frac(x) is -36e-10.

Trigonometric Functions

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The trigonometric functions are sensitive to the angle mode: degrees, radians, or grads (deg, rad, or grd in the display where 360 degrees = 2 pi radians = 400 grads).

• When in degree mode, inputs to SIN, COS, and TAN are assumed to be in degrees and the results from SIN⁻¹, COS⁻¹, and TAN⁻¹ are in degrees.
• When in radian mode, the inputs and outputs are assumed to be in radians.
• When in grads mode, the inputs and outputs are assumed to be in grads.

Set the angle mode using the Settings screen. These functions operate on the value in the x register and replace it with the function result (f(x)).

Key	Function	Description	Type
SIN	sin	Sine	unary
COS	cos	Cosine	unary
TAN	tan	Tangent	unary
COS−1	acos	Arccosine	unary
SIN−1	asin	Arcsine	unary
TAN−1	atan	Arctangent	unary
π	pi	Pushes the value of pi (3.14159...) onto the stack.
→DEG	deg	Radians to degrees conversion	unary
→RAD	rad	Degrees to radians conversion	unary

Time Functions

MathU has two time functions

• H.MS Converts x stack value from fractional hours to H.MS format. In H.MS format, the integer part of the value is the number of hours while the fractional part is broken into two fields: M, the minutes, and S, the seconds. Each field comprises two digits of the fraction. For example, the number 2.03165 is interpreted as 2 hours, 3 minutes, 16.5 seconds or 2°3'16.5" using standard degrees, minutes, seconds notation. Thus, the H.MS interpretation is also valid for D.MS as well. When using the H.MS and hours functions is usually helpful to set the number of digits displayed to be 4 or greater.
• HOUR Converts x stack value from H.MS format to fractional hours. Digits after the fourth fractional digit are interpreted as fractions of a second.

Polar Coordinates

MathU provides two functions to convert back and forth between Cartesian (rectangular) coordinates and polar coordinates. The relationship between polar coordinates and Cartesian coordinates is defined by the following picture and formula

x = R cos(theta) y = R sin(theta) R = sqrt(x2 + y2) theta = atan2(y,x)

Key	Function	Description	Effect on stack
R→P	R->P	Convert from Cartesian coordinates to polar coordinates
P→R	P->R	Convert from polar coordinates to Cartesian coordinates

Number Base Functions

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MathU can display and compute with numbers in hexadecimal (base 16), octal (base 8), and binary (base 2) format as well as the default decimal (base 10) format. Non-decimal values are displayed with a subscript following them indicating the number base. The number base functions honor the wordsize set in the preference screen.

The functions hex, oct, bin, and dec convert values between bases and set the number base for further calculations and input.

Key	Function	Description
HEX	hex	Convert x register to hexadecimal number base.
OCT	oct	Convert x register to octal number base.
BIN	bin	Convert x register to binary number base.
DEC	dec	Convert x register to decimal number base.
AND	and	Bitwise AND of x and y
OR	or	Bitwise OR of x and y
XOR	xor	Bitwise exclusive OR of x and y

Values outside the wordsize preference are wrapped (that is, the excess most significant bits are dropped) and are converted to an integer. The display will automatically switch to a smaller font when large numbers are viewed in oct or bin format. Large binary numbers may wrap on the display as well.

Modular Functions

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A few functions behave differently when a non-decimal number base is chosen:

Key	Function	Description
CHS		Two's complement. Replace x register with its two's complement (all bits inverted and 1 added)
+	+	Modular addition. Same as regular addition except that results that exceed the wordsize are wrapped.
−	-	Modular subtraction. Same as regular subtraction except that negative results are returned as two's complement numbers.
Χ	*	Modular multiplication. Same as regular multiplication except that results that exceed the wordsize are wrapped.
÷	/	Modular division. Same as regular division except that results that exceed the wordsize are wrapped and any fractional remainder is discarded.

The other functions on the calculator can be applied to non-decimal numbers. However, if the result is not an integer that is in range, an error is displayed and the number base reverts to decimal. The value in the x register will be the result of the computation. Simply reapply the conversion routine to wrap and truncate the value to be in range.

Financial Functions

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The financial functions are governed by the equation,

This equation is used when the annuity mode (BEGIN/END preference) is set to ordinary annuity (payments due at the end of the period ). When the annuity mode is annuity due (payments due at the beginning of the period ) then PMT in this equation is modified to be PMT * (1 + i).

The financial functions have two modes: input mode and calculation mode. MathU is in input mode if a number has been keyed into the calculator or any non-financial functions have been executed. Executing one of the main financial functions (N, i, PMT, PV, or FV) stores the displayed value in the associated financial register. MathU is in calculation mode after any financial functions have been executed and before any other functions that change the stack are executed. The result of a financial computation is pushed onto the stack:

Most of the time this should behave as you would expect. However, if for some reason MathU stores a value when you intended to compute one, simply execute the financial function again to obtain the desired result.

Cash Flow Convention

Financial problems can be thought of as a series of cash flows. For example a mortgage consists of a large positive cash flow (the loan amount) followed by a series of monthly negative cash flows (the payments) with possibly a final negative cash flow at the end (the balloon payment). The diagram below illustrates this situation.

Positive cash flows (amounts you receive) are shown as upward pointing arrows. Negative cash flows (amounts you pay) are shown as downward pointing arrows. The horizontal axis of the diagram is time, with time increasing to the right. The time between the equally spaced payments is called the period.

For the problem to be solvable with MathU, there must be at least one cash flow in each direction. It is always possible to add a present value or future value cash flow to meet this requirement. Think about your problem to determine which is more appropriate (see example 4 below).

Examples

Example 1: Suppose you are interested in determining the payment for a car loan of $18,500 at 7.25% interest for 5 years. The key strokes to solve this problem using MathU are

1. CLFIN to reset the financial registers (since the values in the registers are maintained between sessions with MathU it is a good idea to reset the financial registers before each use of the financial functions).
2. 5 ENTER 1 2 Χ N to set the number of periods (in months)
3. 7 . 2 5 ENTER 1 2 ÷ i since the interest per month is 7.25/12 %
4. 1 8 5 0 0 PV to set the principal or present value of the loan
5. PMT to compute the payment per period (ans: $-368.51). The value is negative because the payments are made in the opposite cash flow direction from the principle cash flow.

Note: The convenience functions 12x and 12÷ could have been used in steps 2 and 3 to replace the keystrokes 1 2 Χ N and 1 2 ÷ i respectively.

Example 2: What is the payment if you are willing to pay a balloon payment of $2,000 at the end of the loan?

1. 2 0 0 0 CHS FV Set the value $-2,000 as the FV (balloon) for the loan. The value is negative because this is money you will pay out.
2. PMT to compute the new payment per period (ans: $-340.75)

Example 3: How much interest do you end up paying with the balloon payment?

1. N PMT Χ FV FV + PV PV + to compute the total payments minus the loan value
   (ans: $-3,945.17). Note that FV and PV had to be pressed twice since the first time stored the total payments into FV or PV.

Example 4: To compute the effective interest rate in an IRA account that you put $2000 into each year, you will need to enter the current value of the account as a positive future value (FV) even though you haven't sold the assets in the account. To make the example concrete, suppose that you started your IRA in 1985 with a $10,000 rollover and that the value in the account is $80,000 in the year 2001.

1. CLFIN to reset the financial registers
2. 2 0 0 1 ENTER 1 9 8 5 − N to set the number of periods (in years)
3. 1 0 0 0 0 CHS PV to set the starting value of the account. The value is negative since you added this value to the account with the rollover.
4. 2 0 0 0 CHS PMT to set the annual contribution.
5. 8 0 0 0 0 FV to set the current value of the account. The value is positive since this is the money you would receive if you sold all the assets in the account.
6. i to compute the effective annual rate of return in the account (ans: 6.39%)

Statistical Functions

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The statistical functions accumulate sums based on the values in the x and y stack registers. These sums are used to compute the mean and standard deviation σ or can be accessed directly via P^<>S and RCL. Use CL Σ to reset all the statistical registers to zero before accumulating sums. If you make a mistake keying in the x,y values and after pressing Σ+, re-key the errant values and press Σ− to remove them from the sums. The mean and standard deviation are computed as

with similar equations holding for the y component as well.

Key	Function	Description	Effect on stack
Σ+	stats+	Accumulate x,y	n is the number of sums accumulated so far.
Σ−	stats-	Remove x,y	n is the number of sums accumulated so far.
RCL Σ+	rcl	Recall statistics sums.
	mean	Mean
σ	std	Standard deviation
CL Σ	clstats	Clear statistical registers
N!	fact	Factorial
RAND	rand	Random number from 0 to 1.0 (uniformly distributed)
%	%	Percent
%CH	% ch	Percent change

Legal Stuff

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Although care has been taken to insure a bug-free program, Creative Creek, LLC makes no warranty whatsoever, either implied or expressed, as to the correct functioning of this software. When using this software, the user assumes all responsibility for any damages caused, directly or indirectly, by its use.

MathU is copyrighted. Copyright laws apply and the software shall be classified as proprietary material. If you want to tell your friends about MathU just share this link with them: http://www.creativecreek.com/app/mathu.php

When you purchase MathU you are granted a non-exclusive, nontransferable license to use the software and documentation for use in accordance with this License. This License allows use of the software by a single user unless otherwise specified by the description provided at time of purchase.

MathU and Creative Creek are trademarks of Creative Creek, LLC. iPhone and iPod are trademark of Apple, Inc. or its subsidiaries.

Contacting Creative Creek, LLC

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See the Creative Creek web site for up-to-date information about MathU. If you have questions, suggestions, bug reports, or you just want to tell us how you much you like MathU you can contact us on the web at http://www.creativecreek.com/.