Technical Considerations, How computers handle maths

Technical Considerations

There are various technical considerations that should be borne in mind when using a computer to perform mathematical calculations. Most of the following has been gleaned from AppleÕs Inside Macintosh series of books, available via AppleÕs web site or in print form from Addison-Wesley.

Apple Macintosh computers that use the PowerPC chip (601, 603, 603e, 604, 604e and 750 [G3] microprocessors) use PowerPC Numerics as a floating point environment for mathematical computation. Earlier Apple computers that use a 68k chip (68000, 68020, 68030, 68040 and LC68040 microprocessors) use the earlier SANE (Standard Apple Numerics Environment) for mathematical computation. There are differences between the two numerics systems.

Any computer will also have certain numerical limitations when it comes to mathematical computation, which is a result of the way computers use binary to represent and handle numbers and computations.

Technical Considerations

How computers handle maths

PowerPC Numerics is a floating-point environment that complies with IEEE Standard 754. There are two IEEE standards for floating-point arithmetic: IEEE Standard 754 for binary floating- point arithmetic and IEEE Standard 854 for radix-independent floating-point arithmetic.

The IEEE standards ensure that computers represent real numbers as accurately as possible and that computers perform arithmetic on real numbers as accurately as possible. Although there are infinitely many real numbers, a computer can represent only a finite number of them. Computers represent real numbers

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