example.Numbers Maven / Gradle / Ivy
/*
* Zorbage: an algebraic data hierarchy for use in numeric processing.
*
* Copyright (c) 2016-2021 Barry DeZonia All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification,
* are permitted provided that the following conditions are met:
*
* Redistributions of source code must retain the above copyright notice, this list
* of conditions and the following disclaimer.
*
* Redistributions in binary form must reproduce the above copyright notice, this
* list of conditions and the following disclaimer in the documentation and/or other
* materials provided with the distribution.
*
* Neither the name of the nor the names of its contributors may
* be used to endorse or promote products derived from this software without specific
* prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
* IN NO EVENT SHALL BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
* BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
* DAMAGE.
*/
package example;
/**
* @author Barry DeZonia
*/
class Numbers {
/*
* Zorbage has support for many numeric types (well beyond what other libraries
* provide). In Zorbage you use Algebras (covered elsewhere in this directory)
* to create and manipulate the numeric types. These types have the following
* properties:
*
* SignedInt1Member
* Min: -1
* Max: 0
* Memory size: 1 byte
*
* SignedInt2Member
* Min: -2
* Max: 1
* Memory size: 1 byte
*
* SignedInt3Member
* Min: -4
* Max: 3
* Memory size: 1 byte
*
* SignedInt4Member
* Min: -8
* Max: 7
* Memory size: 1 byte
*
* SignedInt5Member
* Min: -16
* Max: 15
* Memory size: 1 byte
*
* SignedInt6Member
* Min: -32
* Max: 31
* Memory size: 1 byte
*
* SignedInt7Member
* Min: -64
* Max: 63
* Memory size: 1 byte
*
* SignedInt8Member
* Min: -128
* Max: 127
* Memory size: 1 byte
*
* SignedInt9Member
* Min: -256
* Max: 255
* Memory size: 2 bytes
*
* SignedInt10Member
* Min: -512
* Max: 511
* Memory size: 2 bytes
*
* SignedInt11Member
* Min: -1024
* Max: 1023
* Memory size: 2 bytes
*
* SignedInt12Member
* Min: -2048
* Max: 2047
* Memory size: 2 bytes
*
* SignedInt13Member
* Min: -4096
* Max: 4095
* Memory size: 2 bytes
*
* SignedInt14Member
* Min: -8192
* Max: 8191
* Memory size: 2 bytes
*
* SignedInt15Member
* Min: -16384
* Max: 16383
* Memory size: 2 bytes
*
* SignedInt16Member
* Min: -32768
* Max: 32767
* Memory size: 2 bytes
*
* SignedInt32Member
* Min: -2147483648
* Max: 2147483647
* Memory size: 4 bytes
*
* SignedInt64Member
* Min: -9223372036854775808
* Max: 9223372036854775807
* Memory size: 8 bytes
*
* SignedInt128Member
* Min: -170141183460469231731687303715884105728
* Max: 170141183460469231731687303715884105727
* Memory size: 16 bytes
*
* UnsignedInt1Member
* Min: 0
* Max: 1
* Memory size: 1 byte
*
* UnsignedInt2Member
* Min: 0
* Max: 3
* Memory size: 1 byte
*
* UnsignedInt3Member
* Min: 0
* Max: 7
* Memory size: 1 byte
*
* UnsignedInt4Member
* Min: 0
* Max: 15
* Memory size: 1 byte
*
* UnsignedInt5Member
* Min: 0
* Max: 31
* Memory size: 1 byte
*
* UnsignedInt6Member
* Min: 0
* Max: 63
* Memory size: 1 byte
*
* UnsignedInt7Member
* Min: 0
* Max: 127
* Memory size: 1 byte
*
* UnsignedInt8Member
* Min: 0
* Max: 255
* Memory size: 1 byte
*
* UnsignedInt9Member
* Min: 0
* Max: 511
* Memory size: 2 bytes
*
* UnsignedInt10Member
* Min: 0
* Max: 1023
* Memory size: 2 bytes
*
* UnsignedInt11Member
* Min: 0
* Max: 2047
* Memory size: 2 bytes
*
* UnsignedInt12Member
* Min: 0
* Max: 4095
* Memory size: 2 bytes
*
* UnsignedInt13Member
* Min: 0
* Max: 8191
* Memory size: 2 bytes
*
* UnsignedInt14Member
* Min: 0
* Max: 16383
* Memory size: 2 bytes
*
* UnsignedInt15Member
* Min: 0
* Max: 32767
* Memory size: 2 bytes
*
* UnsignedInt16Member
* Min: 0
* Max: 65535
* Memory size: 2 bytes
*
* UnsignedInt32Member
* Min: 0
* Max: 4294967295
* Memory size: 4 bytes
*
* UnsignedInt64Member
* Min: 0
* Max: 18446744073709551615
* Memory size: 8 bytes
*
* UnsignedInt128Member
* Min: 0
* Max: 340282366920938463463374607431768211455
* Memory size: 16 bytes
*
* RationalMember (a fraction of arbitrary precision integers)
* Min: no limit
* Max: no limit
* Memory size: unlimited
*
* UnboundedMember (an arbitrary precision integer)
* Min: no limit
* Max: no limit
* Memory size: unlimited
*
* Float16Member
* 1 component
* Min: -65504
* Max: +65504
* Precision: 3 digits
* Memory size: 2 bytes
*
* Float32Member
* 1 component
* Min: -3.40282347 * 10^38
* Max: +3.40282347 * 10^38
* Precision: 7 digits
* Memory size: 4 bytes
*
* Float64Member
* 1 component
* Min: -1.7 * 10^308
* Max: +1.7 * 10^308
* Precision: 16 digits
* Memory size: 8 bytes
*
* Float128Member
* 1 component
* Min: -1.1897 * 10^4932
* Max: +1.1897 * 10^4932
* Precision: ~34 digits
* Memory size: 16 bytes
*
* HighPrecisionMember
* 1 component
* Min: unlimited*
* Max: unlimited*
* Precision: 1 to 4000 decimal places
* Memory size: unlimited*
*
* ComplexFloat16Member
* Each (of 2) components
* Min: -65504
* Max: +65504
* Precision: 3 digits
* Memory size: 4 bytes
*
* ComplexFloat32Member
* Each (of 2) components
* Min: -3.40282347 * 10^38
* Max: +3.40282347 * 10^38
* Precision: 7 digits
* Memory size: 8 bytes
*
* ComplexFloat64Member
* Each (of 2) components
* Min: -1.7 * 10^308
* Max: +1.7 * 10^308
* Precision: 16 digits
* Memory size: 16 bytes
*
* ComplexFloat128Member
* Each (of 2) components
* Min: -1.1897 * 10^4932
* Max: +1.1897 * 10^4932
* Precision: ~34 digits
* Memory size: 32 bytes
*
* ComplexHighPrecisionMember
* Each (of 2) components
* Min: unlimited*
* Max: unlimited*
* Precision: 1 to 4000 decimal places
* Memory size: unlimited*
*
* QuaternionFloat16Member
* Each (of 4) components
* Min: -65504
* Max: +65504
* Precision: 3 digits
* Memory size: 8 bytes
*
* QuaternionFloat32Member
* Each (of 4) components
* Min: -3.40282347 * 10^38
* Max: +3.40282347 * 10^38
* Precision: 7 digits
* Memory size: 16 bytes
*
* QuaternionFloat64Member
* Each (of 4) components
* Min: -1.7 * 10^308
* Max: +1.7 * 10^308
* Precision: 16 digits
* Memory size: 32 bytes
*
* QuaternionFloat128Member
* Each (of 4) components
* Min: -1.1897 * 10^4932
* Max: +1.1897 * 10^4932
* Precision: ~34 digits
* Memory size: 64 bytes
*
* QuaternionHighPrecisionMember
* Each (of 4) components
* Min: unlimited*
* Max: unlimited*
* Precision: 1 to 4000 decimal places
* Memory size: unlimited*
*
* OctonionFloat16Member
* Each (of 8) components
* Min: -65504
* Max: +65504
* Precision: 3 digits
* Memory size: 16 bytes
*
* OctonionFloat32Member
* Each (of 8) components
* Min: -3.40282347 * 10^38
* Max: +3.40282347 * 10^38
* Precision: 7 digits
* Memory size: 32 bytes
*
* OctonionFloat64Member
* Each (of 8) components
* Min: -1.7 * 10^308
* Max: +1.7 * 10^308
* Precision: 16 digits
* Memory size: 64 bytes
*
* OctonionFloat128Member
* Each (of 8) components
* Min: -1.1897 * 10^4932
* Max: +1.1897 * 10^4932
* Precision: ~34 digits
* Memory size: 128 bytes
*
* OctonionHighPrecisionMember
* Each (of 8) components
* Min: unlimited*
* Max: unlimited*
* Precision: 1 to 4000 decimal places
* Memory size: unlimited*
*
* GaussianInt8Member
* Each (of 2) components
* Min: -128
* Max: 127
* Memory size: 2 bytes
*
* GaussianInt16Member
* Each (of 2) components
* Min: -32768
* Max: 32767
* Memory size: 4 bytes
*
* GaussianInt32Member
* Each (of 2) components
* Min: -2147483648
* Max: 2147483647
* Memory size: 8 bytes
*
* GaussianInt64Member
* Each (of 2) components
* Min: -9223372036854775808
* Max: 9223372036854775807
* Memory size: 16 bytes
*
* GaussianIntUnboundedMember
* Each (of 2) components
* Min: unlimited*
* Max: unlimited*
* Memory size: unlimited*
*
* * Note that unlimited memory size objects are limited to the available RAM
* within your computer. One consequence, as of the writing of this help file,
* is that unlimited precision types cannot be saved to disk based containers
* because their data is not of a fixed size.
*
* For more information about some of these types see also (in this directory)
*
* IntegerTypes
* FloatingTypes
* Complexes
* Quaternions
* Octonions
*/
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