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Reference Information

Numerical Ranges

Normal Math Mode

Maximum numerical range: -1E4932 < x < +1E4932.
For trigonometric functions, maximum input range in radians is: -1E18 < x < +1E18
Numerical values smaller in magnitude than 4E-4932 will be equated to zero.

Graphing

Maximum graphing numerical range: -1E100 < x or y < 1E100.

Base-N Modes

Floating Point Base-N Mode:
- Min: -18446744073709551615
- Max: +18446744073709551615
64 Bit Integer:
- Min: -9223372036854775808 (0x8000000000000000)
- Max: +9223372036854775807 (0x7FFFFFFFFFFFFFFF)
32 Bit Integer:
- Min: -2,147483648 (0x80000000)
- Max: +2147483647 (0x7FFFFFFF)

Error Messages

If a calculation cannot be performed, one of the following errors will be shown:

Math Error
The result could not be calculated (i.e. tended toward infinity) or because it was outside the scope supported by the operation.

Range Error
The input value, or the result, was outside the numerical range supported by the calculation.

Divide by Zero
The calculation involved a division by zero.

Syntax Error
The input could not be interpreted, or an attempt was made to perform an illegal or illogical operation.

Timeout Error
Calculation of the result took too long and was terminated. For example, an attempt to find the 15 millionth prime number will generally give you this error.

Internal Precision

DreamCalc has a maximum internal accuracy of 20 decimal digits. In normal math mode, values are displayed to a maximum precision of 18 decimal digits. Unless otherwise stated, results of calculations with real numbers are accurate to ±1 of the last digit. However, as with any calculator, errors may accumulate during repeated operations.

Complex Numbers

Calculations which involve complex numbers often require several intermediate steps. While 18th decimal digit accuracy will often be the case, it cannot be guaranteed.

Financial Calculations

Financial calculations often involve several intermediate steps, and/or require numerical solution techniques. Therefore, 18th decimal digit accuracy cannot be guaranteed.

Algebraic Order of Precedence

DreamCalc uses the following order of precedence rules:

1. Null Operations (i.e. Ran#)
2. Postfix Unary Functions (and percentage %)
3. Binary Functions (except those listed below)
4. Prefix Unary Functions (applicable to prefix algebraic only)
5. Permutation Functions (nPr and nCr)
6. ×, ÷, MOD
7. +, -
8. OR, XOR, XNOR
9. AND

In RPN mode, order of precedence does not apply.

Numeric Screen Layout

Numeric Screen Panel

In Normal Math Mode

1. Shift or Const state.
2. Hyperbolic State. Activated by the [HYP] key. Used with trigonometric functions.
3. Shown when complex numbers are enabled.
4. Calendar Mode. Indicates the day calendar system in use:
- AS - ANSI
- JD - Julian Days
- MJ - Modified Julian Days
- RD - Rata Die
- UX - UNIX Days since 1970
- WN - WINDOWS Days since 1899
5. Statistical Mode:
- SD - Standard Data
- LN - Linear Regression
- LG - Logarithmic Regression
- EX - Exponential Regression
- PW - Power Regression
- IN - Inverse Regression
- QD - Quadratic Regression
- CB - Cubic Regression
- LX - Logistic Regression
6. Input Order:
- MAL - Prefix Algebraic ("Modern")
- CAL - Postfix Algebraic ("Classic")
- RPN - Reverse Polish Notation
7. Angle Mode:
- DEG - Degrees
- RAD - Radians
- GRA - Grads
- CYC - Cycles
8. Precision Mode
- NORM1 - Normal Precision (1)
- NORM2 - Normal Precision (2)
- FIX - Fixed Decimal Digit
- SCI - Fixed Digit Scientific Notation
9. Financial Payment Mode (Pro Edition Only)
- BEGIN - Payments at Beginning of Period
- END - Payment at End of Period
10. Shown when Engineering Mode is active.
11. Shown when Consecutive Memory holds non-zero value.
12. Display Value Exponent.
13. Additional information about the display value.
14. The number of values in the current statistical data list.
15. Number of values in the financial cashflow list (Pro Edition Only)
16. Information hint about recent function. Shows input parameters where applicable.
17. Real-time input expression. In RPN mode, shows lower 3 values of stack.

In Base-N Mode

3. Indicates whether leading digit zero padding is active.
8. Base-N Mode:
- FLOAT - Floating Point Base-N
- INT64 - 64 Bit 2s Complement Integer
- INT32 - 32 Bit 2s Complement Integer
9. Indicates Base-N Mode is active.
12. Shows Current Radix.

Constants Sources

Where applicable, constants values were derived from the following sources.

Physical Constants

Source: 2002 CODATA Recommended Values.

Spacecraft Geodesy

Source: Handbook of Chemistry & Physics 73rd Edition.

Notes: Degree and radian equivalent values are derived from arc-second source values.

Astronomical Constants

Source: Wikipedia (2005).

Notes: Solar irradiances at planetary bodies are calculated using the semi-major axis and the Earth's Solar Constant. Rotation periods are those at the equator.

Periodic Table

Source: Standard Atomic Weights 1989. Includes new values recommended by IUPAC in 1989.

Notes. Melting/Boiling points at 1ATM. Densities given for pure metals at 25 Celsius.