Option menu Numbers and Precision
This option designates the number manipulation on the program unit where no OPTION ARITHMETIC is written.
- Decimal 15 digits
A numeric value that a numeric variable holds is a decimal 15 digits floating point number.
The result of a numeric operation is as follows.
The result of the four operation is rounded to decimal of precision of the digits between 19 and 27 .
The result of an irrational function or a power operation is rounded to decimal of precision of 17 digits, while the 17-th digit is even.
The computational result of a numeric expression is rounded to 15 digits when it is assigned to a variable.
Computational results are displayed rounded to 15 digits.
When More Places Displayed option is selected, computational results are displayed without modification.
- Decimal Thousand Digits
Decimal fractions of 1000 significant digits are accurate.
The computational result is rounded to decimal of precision of digits between 1000 and 1008.
The rounding method is truncating.
Any transcendental functions such as trigonometric, exponential or logarithmic functions are not available.
The exponent of a power is limited to an integer between -9223372036854775807 and 9223372036854775807( -263 ～ 263-1).
When a exponent is not an integer, an exception shall be caused.
When Use Transcendental Functions option is selected, transcendental functions and non-integral exponents are allowed while their computational results have precision of 17 digits.
- Binary approximately 16 digits
The smallest positive number is about 5.0E-324, and the largest positive number is about 1.7E308.
Calculation is fast, though decimal fractions can not be represented correctly.
Integers between -9007199254740992 and 9007199254740992 (253) can be represented correctly.
Integers of type 10n is accurate if n is a positive integer of not greater than 1E36.
On the other hand, decimal fractions as 0.1 and 0.01 are generally can not be represented correctly.
When a number can not be represented correctly, it is approximated by a representable number.
For example, 0.1 is approximated by a number that is slightly larger than the accurate value.
The computational results are displayed rounded to decimal of 15 digits.
When More Places Displayed option is selected, the precision increases up to 19 digits.
Complex numbers are represented internally by a couple of binary double precision numbers.
PRINT statements displays an imaginary number by putting the two numbers in parentheses.
When the base is a positive number, exponents can be imaginary numbers on a power operation.
When the base is an imaginary number, only exponents of integers between -2147483647 and 2147483647 are allowed.
The domain of the functions ABS(x), SQR(x), EXP(x) and LOG(x) are extended to the complex numbers.
The functions COMPLEX(x,y)，RE(x)，IM(x)，CONJ(x)，ARG(x) are provided exclusively on the complex operation mode.
Transform functions SCALE and SHIFT are extended to the complex numbers.
If an imaginary number is used anywhere else, an exception may be caused.
- Rational (multi-precision)
Multi-precision rational operation shall be performed.
The computational results are displayed in the form of an improper fraction.
However improper fraction form can not be used on the input or in DATA statements.
The exponents of power operations are limited to integers between -2147483647 and 2147483647.
Any irrational function including PI can not be used.
When Use Transcendental Functions option is selected, irrational functions and non-integral power operations can be used while their computational results have precision of 17 digits, but PI have precision of about 1000 digits.