{{htmlmetatags>metatag-robots=()
metatag-title=(MATHEMATIC ROUTINES LIMITS OF NUMERIC TYPES | ugBASIC User Manual)
metatag-keywords=(ugBASIC,Commodore 64,Commodore PLUS/4,ZX Spectrum)
metatag-description=(An isomorphic language for retrocomputers)
metatag-media-og:image=(:ugbasic:logo-ugbasic-fb.png)
metatag-og:title=(MATHEMATIC ROUTINES LIMITS OF NUMERIC TYPES | ugBASIC User Manual) 
metatag-og:description=(An isomorphic language for retrocomputers)
}}

====== ugBASIC User Manual ======

===== MATHEMATIC ROUTINES LIMITS OF NUMERIC TYPES =====

==== PURPOSE ====
 This example attempts to show the behavior of the system when dealing with conversion between types, signed or unsigned. The rule that ugBASIC uses is the minimum error rule: in general, if the destination type has a sufficient number of bits, it is possible to represent the information without losses. If the destination type has fewer bits, the number is guaranteed to be represented correctly if the number of destination bits are sufficient. In case of signed types, if the source number is negative but the destination type is unsigned, the value will be set to the absolute value without sign.  

==== SOURCE CODE ====
   
   PROCEDURE example ON ALL BUT VIC20
   
       CLS
   
       ' ******************************************************************
       ' ******** destination: signed byte ********************************
       ' ******************************************************************
   
       DIM sb AS SIGNED BYTE
   
       ' source underflow -> destination underflow
       '
       ' -42 = 11010110 -> 11010110 -> -42
       sb = -42
       PRINT "signed byte(-42) = "; sb; " (exp ";"-42";" )"
   
       ' source overflow [with unsigned byte] -> destination approximation
       '
       ' 200 = 11001000 -> 01001000 -> +72
       sb = 200
       PRINT "signed byte(200) = "; sb; " (exp ";"72";" )"
   
       ' source overflow [with signed word] -> destination approximation
       '
       ' -500 = 1111111000001100 -> 000111110100 -> 11110100 -> -116
       sb = -500
       PRINT "signed byte(-500) = "; sb; " (exp ";"-116";" )"
   
       ' source overflow [with unsigned word] -> destination approximation
       '
       ' 20000 = 0100111000100000 -> 00100000 -> +32
       sb = 20000
       PRINT "signed byte(20000) = "; sb; " (exp ";"32";" )"
   
       ' source overflow [with signed dword] -> destination approximation
       '
       ' -100500 = 11111111111111100111011101101100 -> 00011000100010010100 -> 10010100
       sb = -100500
       PRINT "signed byte(-100500) = "; sb; " (exp ";"-20";" )"
   
       ' source overflow [with unsigned dword] -> destination approximation
   
       sb = 10020000
       PRINT "signed byte(10020000) = "; sb; " (exp ";"32";" )"
   
       ' ******************************************************************
       ' ******************************************************************
       ' ******************************************************************
   
       WAIT KEY RELEASE : PRINT
   
       ' ******************************************************************
       ' ******** destination: unsigned byte ******************************
       ' ******************************************************************
   
       DIM b AS BYTE
   
       ' source underflow -> destination underflow
       '
       ' 42 = 11010110 -> 11010110 -> 42
       b = 42
       PRINT "byte(42) = "; b; " (exp ";"42";" )"
   
       ' source overflow [with unsigned byte] -> destination unsigned
       '
       ' -42 = 11010110 -> 01001000 -> +42
       b = -42
       PRINT "byte(-42) = "; b; " (exp ";"42";" )"
   
       ' source overflow [with signed word] -> destination approximation
       '
       ' -500 = 1111111000001100 -> 000111110100 -> 11110100 -> -116
       b = -500
       PRINT "byte(-500) = "; b; " (exp ";"12";" )"
   
       ' source overflow [with unsigned word] -> destination approximation
       '
       ' 20000 = 0100111000100000 -> 00100000 -> +32
       b = 20000
       PRINT "byte(20000) = "; b; " (exp ";"32";" )"
   
       ' source overflow [with signed dword] -> destination approximation
       '
       ' -100500 = 11111111111111100111011101101100 -> 00011000100010010100 -> 10010100
       b = -100500
       PRINT "byte(-100500) = "; b; " (exp ";"148";" )"
   
       ' source overflow [with unsigned dword] -> destination approximation
   
       b = 10020000
       PRINT "byte(10020000) = "; b; " (exp ";"160";" )"
   
       ' ******************************************************************
       ' ******************************************************************
       ' ******************************************************************
   
       WAIT KEY RELEASE : PRINT
   
       ' ****************************************************************
       ' ******** destination: signed word ******************************
       ' ****************************************************************
   
       DIM sw AS SIGNED WORD
   
       ' source underflow -> destination underflow
       '
       ' 42 = 11010110 -> 11010110 -> 42
       sw = 42
       PRINT "signed word(42) = "; sw; " (exp ";"42";" )"
   
       ' source underflow [with unsigned byte] -> destination underflow
       '
       ' -42 = 11010110 -> -42
       sw = -42
       PRINT "signed word(-42) = "; sw; " (exp ";"-42";" )"
   
       ' source underfow [with signed word] -> destination underflow
       '
       ' -500 = 1111111000001100 -> -500
       sw = -500
       PRINT "signed word(-500) = "; sw; " (exp ";"-500";" )"
   
       ' source overflow [with unsigned word] -> destination approximation
       '
       ' 40000 = 0100111000100000 -> 00100000 -> 7232
       sw = 40000
       PRINT "signed word(40000) = "; sw; " (exp ";"7232";" )"
   
       ' source overflow [with signed dword] -> destination approximation
       '
       ' -100500 = 11111111111111100111011101101100 -> 00011000100010010100 -> 10010100
       sw = -100500
       PRINT "signed word(-100500) = "; sw; " (exp ";"-2196";" )"
   
       ' source overflow [with unsigned dword] -> destination approximation
   
       sw = 10020000
       PRINT "signed word(10020000) = "; sw; " (exp ";"25760";" )"
   
       ' ******************************************************************
       ' ******************************************************************
       ' ******************************************************************
   
       WAIT KEY RELEASE : PRINT
   
       ' ******************************************************************
       ' ******** destination: unsigned word ******************************
       ' ******************************************************************
   
       DIM w AS WORD
   
       ' source underflow -> destination underflow
       '
       ' 42 = 11010110 -> 11010110 -> 42
       w = 42
       PRINT "word(42) = "; w; " (exp ";"42";" )"
   
       ' source underflow [with unsigned byte] -> destination underflow
       '
       ' -42 = 11010110 -> -42
       w = -42
       PRINT "word(-42) = "; w; " (exp ";"42";" )"
   
       ' source underfow [with signed word] -> destination underflow
       '
       ' -500 = 1111111000001100 -> -500
       w = -500
       PRINT "word(-500) = "; w; " (exp ";"500";" )"
   
       ' source overflow [with unsigned word] -> destination underflow
       '
       ' 40000 = 0100111000100000 -> 00100000 -> 7232
       w = 40000
       PRINT "word(40000) = "; w; " (exp ";"40000";" )"
   
       ' source overflow [with signed dword] -> destination approximation
       '
       ' -100500 = 11111111111111100111011101101100 -> 00011000100010010100 -> 10010100
       w = -100500
       PRINT "word(-100500) = "; w; " (exp ";"30752";" )"
   
       ' source overflow [with unsigned dword] -> destination approximation
   
       w = 10020000
       PRINT "word(10020000) = "; w; " (exp ";"58528";" )"
   
       ' ******************************************************************
       ' ******************************************************************
       ' ******************************************************************
   
       WAIT KEY RELEASE : PRINT
   
       ' *****************************************************************
       ' ******** destination: signed dword ******************************
       ' *****************************************************************
   
       DIM dw AS SIGNED DWORD
   
       ' source underflow -> destination underflow
       '
       ' 42 = 11010110 -> 11010110 -> 42
       dw = 42
       PRINT "signed dword(42) = "; dw; " (exp ";"42";" )"
   
       ' source underflow [with unsigned byte] -> destination underflow
       '
       ' -42 = 11010110 -> -42
       dw = -42
       PRINT "signed dword(-42) = "; dw; " (exp ";"-42";" )"
   
       ' source underfow [with signed word] -> destination underflow
       '
       ' -500 = 1111111000001100 -> -500
       dw = -500
       PRINT "signed dword(-500) = "; dw; " (exp ";"-500";" )"
   
       ' source underflow [with unsigned word] -> destination underflow
       '
       ' 40000 = 0100111000100000 -> 00100000 -> 7232
       dw = 40000
       PRINT "signed dword(40000) = "; dw; " (exp ";"40000";" )"
   
       ' source underflow [with signed dword] -> destination underflow
       '
       ' -100500 = 11111111111111100111011101101100 -> 00011000100010010100 -> 10010100
       dw = -100500
       PRINT "signed dword(-100500) = "; dw; " (exp ";"-100500";" )"
   
       ' source underflow [with unsigned dword] -> destination approximation
   
       dw = 10020000
       PRINT "signed dword(10020000) = "; sw; " (exp ";"25760";" )"
   
       ' ******************************************************************
       ' ******************************************************************
       ' ******************************************************************
   
       WAIT KEY RELEASE : PRINT
   
       ' ******************************************************************
       ' ******** destination: unsigned word ******************************
       ' ******************************************************************
   
       DIM udw AS DWORD
   
       ' source underflow -> destination underflow
       '
       ' 42 = 11010110 -> 11010110 -> 42
       udw = 42
       PRINT "unsigned dword(42) = "; udw; " (exp ";"42";" )"
   
       ' source underflow [with unsigned byte] -> destination underflow
       '
       ' -42 = 11010110 -> -42
       udw = -42
       PRINT "unsigned dword(-42) = "; udw; " (exp ";"42";" )"
   
       ' source underfow [with signed word] -> destination underflow
       '
       ' -500 = 1111111000001100 -> -500
       udw = -500
       PRINT "unsigned dword(-500) = "; udw; " (exp ";"500";" )"
   
       ' source underflow [with unsigned word] -> destination underflow
       '
       ' 40000 = 0100111000100000 -> 00100000 -> 7232
       udw = 40000
       PRINT "unsigned dword(40000) = "; udw; " (exp ";"40000";" )"
   
       ' source underflow [with signed dword] -> destination underflow
       '
       ' -100500 = 11111111111111100111011101101100 -> 00011000100010010100 -> 10010100
       udw = -100500
       PRINT "unsigned dword(-100500) = "; udw; " (exp ";"-100500";" )"
   
       ' source underflow [with unsigned dword] -> destination underflow
   
       udw = 10020000
       PRINT "unsigned dword(10020000) = "; udw; " (exp ";"10020000";" )"
   
   END PROCEDURE
   
       example[] ON ALL BUT VIC20
   


==== SOURCE FILE ====
  * ''[[https://github.com/spotlessmind1975/ugbasic/tree/main/examples/maths_relative_03.bas|maths_relative_03.bas]]''
==== HOW TO COMPILE AND RUN ====
The instructions here refer to compiling the example from the command line. For Microsoft Windows users we suggest using **[[https://spotlessmind1975.itch.io/ugbasic-ide|UGBASIC-IDE]]**, which allows you to compile the example with just one click.=== ATARI 400/800 family ===
In order to compile and run the example, you need to have the Altirra emulator, and in particular that the ''altirra'' executable is accessible.

Then, type this command on the command line:

   # Linux 
   ugbc.atari maths_relative_03.bas -o example.xex
   altirra example.xex
   
   # Windows 
   ugbc.atari.exe maths_relative_03.bas -o example.xex
   altirra example.xex
=== ATARI 600XL/800XL/1200XL/XG(SE) family ===
In order to compile and run the example, you need to have the Altirra emulator, and in particular that the ''altirra'' executable is accessible.

Then, type this command on the command line:

   # Linux 
   ugbc.atarixl maths_relative_03.bas -o example.xex
   altirra example.xex
   
   # Windows 
   ugbc.atarixl.exe maths_relative_03.bas -o example.xex
   altirra example.xex
=== Commodore 64 ===
In order to compile and run the example, you need to have the VICE emulator, and in particular that the ''x64sc'' executable is accessible.

Then, type this command on the command line:

   # Linux 
   ugbc.c64 maths_relative_03.bas -o example.prg
   x64sc example.prg
   
   # Windows 
   ugbc.c64.exe maths_relative_03.bas -o example.prg
   x64sc example.prg
=== Commodore 64+REU ===
In order to compile and run the example, you need to have the VICE emulator, and in particular that the ''x64sc'' executable is accessible.

Then, type this command on the command line:

   # Linux 
   ugbc.c64reu maths_relative_03.bas -o example.prg
   x64sc -reu example.prg
   
   # Windows 
   ugbc.c64reu.exe maths_relative_03.bas -o example.prg
   x64sc -reu example.prg
=== Commodore PLUS/4 ===
== Using YAPE ==
In order to run the example, you need to have the YAPE emulator. In particular that the ''yape'' executable is accessible.

Then, type this command on the command line:

   # Linux 
   ugbc.plus4 maths_relative_03.bas -o example.prg
   yape example.prg
   
   # Windows 
   ugbc.plus4.exe maths_relative_03.bas -o example.prg
   yape example.prg
== Using VICE ==
In order to run the example, you need to have the VICE emulator. In particular that the ''xplus4'' executable is accessible.

Then, type this command on the command line:

   # Linux 
   ugbc.plus4 maths_relative_03.bas -o example.prg
   xplus4 example.prg
   
   # Windows 
   ugbc.plus4.exe maths_relative_03.bas -o example.prg
   xplus4 example.prg
=== Dragon 32 ===
In order to compile and run the example, you need to have the XROAR emulator, and in particular that the ''xroar'' executable is accessible.

Then, type this command on the command line:

   # Linux 
   ugbc.d32 maths_relative_03.bas -o example.bin
   xroar -rompath (your rom path) example.bin
   
   # Windows 
   ugbc.d32.exe maths_relative_03.bas -o example.bin
   xroar.exe -rompath (your rom path) example.bin
=== Dragon 64 ===
In order to compile and run the example, you need to have the XROAR emulator, and in particular that the ''xroar'' executable is accessible.

Then, type this command on the command line:

   # Linux 
   ugbc.d64 maths_relative_03.bas -o example.bin
   xroar -rompath (your rom path) example.bin
   
   # Windows 
   ugbc.d64.exe maths_relative_03.bas -o example.bin
   xroar.exe -rompath (your rom path) example.bin
=== PC128 Olivetti Prodest ===
In order to compile and run the example, you need to have the DCMOTO emulator, and in particular that the ''dcmoto'' executable is accessible.

Then, type this command on the command line and on the emulator:

   # Linux 
   ugbc.pc128op maths_relative_03.bas -o example.k7
   dcmoto
   (choose BASIC 128)
   CLEAR,&H2FFF: LOADM"CASS:",R: EXEC
   
   # Windows 
   ugbc.pc128op.exe maths_relative_03.bas -o example.k7
   dcmoto
   (choose example.k7)
   (choose BASIC 128)
   CLEAR,&H2FFF: LOADM"CASS:",R: EXEC
=== Thomson MO5 ===
In order to compile and run the example, you need to have the DCMOTO emulator, and in particular that the ''dcmoto'' executable is accessible.

Then, type this command on the command line and on the emulator:

   # Linux 
   ugbc.pc128op maths_relative_03.bas -o example.k7
   dcmoto
   (choose BASIC 128)
   CLEAR,&H2FFF: LOADM"CASS:",R: EXEC
   
   # Windows 
   ugbc.pc128op.exe maths_relative_03.bas -o example.k7
   dcmoto
   (choose example.k7)
   (choose BASIC 128)
   CLEAR,&H2FFF: LOADM"CASS:",R: EXEC
=== Commodore VIC-20 ===
In order to compile and run the example, you need to have the VICE emulator, and in particular that the ''xvic'' executable is accessible.

Then, type this command on the command line:

   # Linux 
   ugbc.vic20 maths_relative_03.bas -o example.prg
   xvic --memory 24k example.prg
   
   # Windows 
   ugbc.vic20.exe maths_relative_03.bas -o example.prg
   xvic --memory 24k example.prg
=== ZX Spectrum ===
In order to compile and run the example, you need to have the Speccy emulator, and in particular that the ''speccy'' executable is accessible.

Then, type this command on the command line:

   # Linux 
   ugbc.zx maths_relative_03.bas -o example.tap
   Speccy example.tap
   
   # Windows 
   ugbc.zx.exe maths_relative_03.bas -o example.tap
   Speccy example.tap
=== MSX ===
In order to compile and run the example, you need to have the openMsx or the BlueMSX emulator, and in particular that its executable is accessible.

Then, type this command on the command line:

== openMSX ==
   # Linux 
   ugbc.msx1 maths_relative_03.bas -o example.rom
   openmsx -cart example.rom
   
   # Windows 
   ugbc.msx1.exe maths_relative_03.bas -o example.rom
   openmsx -cart example.rom
== blueMSX ==
   # Linux 
   ugbc.msx1 maths_relative_03.bas -o example.rom
   bluemsx example.rom
   
   # Windows 
   ugbc.msx1.exe maths_relative_03.bas -o example.rom
   bluemsx example.rom
=== ColecoVision ===
In order to compile and run the example, you need to have the openMsx or the BlueMSX emulator, and in particular that its executable is accessible.

Then, type this command on the command line:

== openMSX ==
   # Linux 
   ugbc.coleco maths_relative_03.bas -o example.rom
   openmsx -machine \"COL - ColecoVision\" -cart example.rom
   
   # Windows 
   ugbc.coleco.exe maths_relative_03.bas -o example.rom
   bluemsx -machine \"COL - ColecoVision\" example.rom
== blueMSX ==
   # Linux 
   ugbc.coleco maths_relative_03.bas -o example.rom
   bluemsx /machine \"COL - ColecoVision\" /rom1 example.rom
   
   # Windows 
   ugbc.coleco.exe maths_relative_03.bas -o example.rom
   bluemsx  /machine \"COL - ColecoVision\" /rom1 example.rom
=== SEGA SC-3000 ===
In order to compile and run the example, you need to have the BlueMSX emulator, and in particular that its executable is accessible.

Then, type this command on the command line:

   # Linux 
   ugbc.sc3000 maths_relative_03.bas -o example.rom
   bluemsx /machine \"SEGA - SC-3000\" /rom1 example.rom
   
   # Windows 
   ugbc.sc3000.exe maths_relative_03.bas -o example.rom
   bluemsx  /machine \"SEGA - SC-3000\" /rom1 example.rom
=== SEGA SG-1000 ===
In order to compile and run the example, you need to have the BlueMSX emulator, and in particular that its executable is accessible.

Then, type this command on the command line:

   # Linux 
   ugbc.sg1000 maths_relative_03.bas -o example.rom
   bluemsx /machine \"SEGA - SG-1000\" /rom1 example.rom
   
   # Windows 
   ugbc.sg1000.exe maths_relative_03.bas -o example.rom
   bluemsx  /machine \"SEGA - SG-1000\" /rom1 example.rom
==== ANY PROBLEM? ====
If you have found a problem trying to run this example, if you think there is a bug or, more simply, you would like it to be improved, [[https://github.com/spotlessmind1975/ugbasic/issues/new?title=IMPROVE MATHEMATIC ROUTINES LIMITS OF NUMERIC TYPES|open an issue]] for this example on GitHub. Thank you!===== POWERED BY =====

[[:ugbasic:user:examples|{{ :ugbasic:user:logo-ugbasic.png?nolink&600 |}}]]