6.84 LargePositiveInteger

Defined in namespace Smalltalk

Category: Language-Data types

Just like my brother LargeNegativeInteger, I provide a few methods that allow LargeInteger to determine the sign of a large integer in a fast way during its calculations. For example, I know that I am larger than any LargeNegativeInteger. In addition I implement the guts of arbitrary precision arithmetic.

6.84.1 LargePositiveInteger: arithmetic		(instance)
6.84.2 LargePositiveInteger: converting		(instance)
6.84.3 LargePositiveInteger: helper byte-level methods		(instance)
6.84.4 LargePositiveInteger: numeric testing		(instance)
6.84.5 LargePositiveInteger: primitive operations		(instance)

6.84.1 LargePositiveInteger: arithmetic

+ aNumber

Sum the receiver and aNumber, answer the result

- aNumber

Subtract aNumber from the receiver, answer the result

gcd: anInteger

Calculate the GCD between the receiver and anInteger

highBit

Answer the receiver's highest bit's index

6.84.2 LargePositiveInteger: converting

asFloat

Answer the receiver converted to a Float

reverseStringBase: radix on: str

Return in a string the base radix representation of the receiver in reverse order

6.84.3 LargePositiveInteger: helper byte-level methods

bytes: byteArray1 from: j compare: byteArray2

Private - Answer the sign of byteArray2 - byteArray1; the j-th byte of byteArray1 is compared with the first of byteArray2, the j+1-th with the second, and so on.

bytes: byteArray1 from: j subtract: byteArray2

Private - Sutract the bytes in byteArray2 from those in byteArray1

bytes: bytes multiply: anInteger

Private - Multiply the bytes in bytes by anInteger, which must be < 255. Put the result back in bytes.

bytesLeftShift: aByteArray

Private - Left shift by 1 place the bytes in aByteArray

bytesLeftShift: aByteArray big: totalShift

Private - Left shift the bytes in aByteArray by totalShift places

bytesLeftShift: aByteArray n: shift

Private - Left shift by shift places the bytes in aByteArray (shift <= 7)

bytesRightShift: aByteArray big: totalShift

Private - Right shift the bytes in aByteArray by totalShift places

bytesRightShift: bytes n: aNumber

Private - Right shift the bytes in `bytes' by 'aNumber' places (shift <= 7)

bytesTrailingZeros: bytes

Private - Answer the number of trailing zero bits in the receiver

primDivide: rhs

Private - Implements Knuth's divide and correct algorithm from `Seminumerical Algorithms' 3rd Edition, section 4.3.1 (which is basically an enhanced version of the divide `algorithm' for two-digit divisors which is taught in primary school!!!)

6.84.4 LargePositiveInteger: numeric testing

abs

Answer the receiver's absolute value

negative

Answer whether the receiver is < 0

positive

Answer whether the receiver is >= 0

sign

Answer the receiver's sign

strictlyPositive

Answer whether the receiver is > 0

6.84.5 LargePositiveInteger: primitive operations

divide: aNumber using: aBlock

Private - Divide the receiver by aNumber (unsigned division). Evaluate aBlock passing the result ByteArray, the remainder ByteArray, and whether the division had a remainder

isSmall

Private - Answer whether the receiver is small enough to employ simple scalar algorithms for division and multiplication

multiply: aNumber

Private - Multiply the receiver by aNumber (unsigned multiply)