wip: integer division approximation

Signed-off-by: Aleksey Gurtovoy <aleks@wildbitscomputing.com>

Author: agurtovoy

source/common/aa.system/04data.inc

@@ -1,27 +1,12 @@
-; ************************************************************************************************
-; ************************************************************************************************
-;
-;		Name:		04data.inc
-;		Purpose:	Main Data
-;		Created:	18th September 2022
-;		Reviewed: 	23rd November 2022
-;		Author:		Paul Robson (paul@robsons.org.uk)
-;
-; ************************************************************************************************
-; ************************************************************************************************
 
-; ************************************************************************************************
-;
-;									Mandatory Zero page code
-;
-; ************************************************************************************************
+;		Mandatory zero-page data
 
 		.section zeropage
 
 codePtr:	 								; address of current line (allow for 32 bit)
 		.fill 	4
 basicStack: 								; BASIC stack address
-		.fill 	2		
+		.fill 	2
 zTemp0: 									; temporary words used in the interpreter.
 		.fill 	2
 zTemp1:
@@ -32,61 +17,68 @@ zsTemp:	 									; allocated string temporary.
 		.fill 	2
 zaTemp: 									; allocated array temporary
 		.fill 	2
-		
+
 safePtr = codePtr 							; minimise direct tinkering
-			
-		.send zeropage
 
-; ************************************************************************************************
-;
-;								   Preferable Zero page code
-;
-; ************************************************************************************************
+		.send zeropage
 
-NSBIsNegative = $80 						; bit 7 : sign of mantissa (where numeric)
-NSBIsReference = $20 						; bit 5 : is a reference
-NSBIsString = $10 							; bit 4 : set if string (procedures don't go on the stack)
-NSBTypeMask = $18 							; bits 4,3 : 00 int 01 float 10 string 11 procedure
-NSBRefMask = $03 							; bits 0,1 : Bytes of reference, 00 = 4,01 = 1,10=2
-NSBIsArray = $04
 
-NSTInteger = $00 							; base types for bits 3..4
-NSTFloat = $08
-NSTString = $10
-NSTProcedure = $18
+; 		Preferably zero-page data
 
 		.section zeropref
 
-; ************************************************************************************************
-;
-;							The number stack (works up from zero)
-;
-; ************************************************************************************************
+; Number stack status masks
 
+NSBIsNegative 	= $80 						; bit 7: sign of mantissa (where numeric)
+NSBIsReference 	= $20 						; bit 5: is a reference
+NSBIsString 	= $10 						; bit 4: set if string (procedures don't go on the stack)
+NSBTypeMask 	= $18 						; bits 4,3: 00 int 01 float 10 string 11 procedure
+NSBRefMask	 	= $03 						; bits 0,1: Bytes of reference, 00 = 4,01 = 1,10=2
+NSBIsArray 		= $04
+
+NSTInteger 		= $00 						; base types for bits 3..4
+NSTFloat 		= $08
+NSTString 		= $10
+NSTProcedure 	= $18
+
+;;
+; The number stack (works up from zero)
+;;
 NSStatus: 									; Status bits of stack.
 		.fill 	MathStackSize
-NSMantissa0: 								; Mantissa on stack (address in 0,1 for string/reference)
-		.fill 	MathStackSize 				; (this is my integer mantissa system)
-NSMantissa1: 								; the order of the mantissa elements is required.
+
+; 4 mantissa bytes (little-endian, 31 bits + sign)
+;
+; Stores an integer magnitude. Normalized non-zero mantissa always has bit 30 set.
+;
+; Note that on the number stack, the sign is kept in `NSStatus` (`NSBIsNegative` mask), so the
+; mantissa itself only carries magnitude; when a float is written out to a variable, the sign
+; bit gets packed into the top bit of the highest mantissa byte.
+NSMantissa0:
+		.fill 	MathStackSize
+NSMantissa1:
 		.fill 	MathStackSize
 NSMantissa2:
 		.fill 	MathStackSize
 NSMantissa3:
 		.fill 	MathStackSize
-NSExponent: 								; Exponent , 0 = Mantissa is integer
+
+
+; a signed 8-bit base-2 exponent stored in two's complement format; 0 if mantissa is integer
+;
+; floating-point value = mantissa x 2^decoded exponent, where
+; decoded exponent = exponent if exponent < 128 else exponent - 256
+NSExponent:
 		.fill 	MathStackSize
 
-fnStackLevel:								; saved stack level for function evaluation
+; saved stack level for function evaluation
+fnStackLevel:
 		.fill 	1
 
 		.send zeropref
 
 
-; ************************************************************************************************
-;
-;										Non Zero Page Data
-;
-; ************************************************************************************************
+; 		Non-zero page data
 
 		.section storage
 
@@ -95,7 +87,7 @@ identStart: 								; start of identifier in line buffer
 identTypeStart: 							; start of type information (#$ and ( in the line buffer)
 		.fill 	1
 identTypeEnd: 								; character after end of type information in the line buffer
-		.fill 	1		
+		.fill 	1
 identHash: 									; hash of identifier (including the type characters)
 		.fill 	1
 identTypeByte: 								; type descriptor in format used in identifier record
@@ -113,63 +105,63 @@ lowMemPtr: 									; memory allocation after program.
 arrayMemPtr: 								; array/alloc storage pointer (slots 2-3, $4000-$7FFF)
 		.fill 	2
 stringMemory: 								; allocate concrete strings from here
-		.fill 	2			
-stringInitialised: 							; string 
-		.fill 	1		
+		.fill 	2
+stringInitialised: 							; string
+		.fill 	1
 stringTempPointer:							; temporary string
-		.fill 	2		
+		.fill 	2
 
 breakCheck:									; break check counter/shift
 		.fill 	1
-		
+
 decimalPlaces: 								; no of decimals.
 		.fill 	1
 dbOffset:									; offset into decimal buffer.
-		.fill 	1		
+		.fill 	1
 
 lastParameter: 								; final stack offset when all parameters handled.
 		.fill 	1
-		
+
 dataPointer:								; operates like code pointer for DATA statements
 		.fill 	5
 inDataStatement:							; non zero when in data statement, e.g. pointing to data
-		.fill 	1				
+		.fill 	1
 
 tbOffset:									; offset into token buffer
-		.fill 	1		
+		.fill 	1
 
 AssemblerAddress:							; address being assembled at
 		.fill 	2
 AssemblerControl:							; assembler control byte - bit 0 (errors ok), bit 1 (listing on)
-		.fill 	1			
+		.fill 	1
 ParamStart: 								; offset of parameter.
-		.fill 	2	
+		.fill 	2
 IsGroup1:		 							; flag set if group.1
-		.fill 	1		
+		.fill 	1
 BaseOpcode: 								; base opcode
-		.fill 	1		
+		.fill 	1
 ModeMask: 									; modes allowed
-		.fill 	1		
+		.fill 	1
 listIndent:	 								; list indent level.
 		.fill 	1
 listElseFound:								; flag set when ELSE found on line (for indent fix)
 		.fill 	1
 listEndToken:								; closing token for LIST proc/fn
 		.fill 	1
 lcLastCharacter: 							; last character output.
-		.fill 	1	
+		.fill 	1
 isPrintFlag:	 							; zero if input, non-zero if print, bit 6 zero = character print
-		.fill 	1			
+		.fill 	1
 currentListColour: 							; current set colour when listing.
 		.fill 	1
 ;
 ;		New tokenised line - these three *must* be contiguous as they are used as a single entity
-;		
+;
 tokenOffset: 								; used for tokenising - tokenised result goes here
-		.fill 	1		
+		.fill 	1
 tokenLineNumber:
-		.fill 	2		
-tokenBuffer: 	
+		.fill 	2
+tokenBuffer:
 		.fill 	253
 
 lineBuffer: 								; used for input - ASCII line goes here
@@ -193,19 +185,3 @@ decimalBuffer: 								; buffer for number -> string conversion.
 		.fill 	24
 
 		.send 	storage
-
-; ************************************************************************************************
-;
-;									Changes and Updates
-;
-; ************************************************************************************************
-;
-;		Date			Notes
-;		==== 			=====
-;		1/12/2022 		Changed the recorded values used in the reference byte size which were
-;						incorrect, no code change.
-;		2/12/2022 		Made line buffer long again, as long lines can be entered via cross 
-;						development which would crash the interpreter.
-;
-; ************************************************************************************************
-

source/common/expressions/float/integer.asm

@@ -1,60 +1,46 @@
-; ************************************************************************************************
-; ************************************************************************************************
-;
-;		Name:		integer.asm
-;		Purpose:	Make FPA Denormalised integer
-;		Created:	29th September 2022
-;		Reviewed: 	28th November 2022
-;		Author : 	Paul Robson (paul@robsons.org.uk)
-;
-; ************************************************************************************************
-; ************************************************************************************************
 
 		.section 	code
 
-; ************************************************************************************************
+;;
+; Convert floating-point entry at position X in the number stack to an
+; integer.
 ;
-;									Make FPA into an integer
-;
-; ************************************************************************************************
-
+; Sets carry if the value was not already an exact integer.
+;;
 FloatIntegerPart:
 		pha
-		;
+		phy
+		ldy		#$0							; store the carry status in Y
+
 		lda 	NSExponent,x 				; is it integer already ?
-		beq 	_FIPExit 					; if so do nothing
+		beq 	_exit 						; if so do nothing
 		jsr 	NSMIsZero 					; is it zero ?
-		beq 	_FIPZero 					; if so return zero.
-		;
+		beq 	_zero 						; if so return zero.
+
 		jsr 	NSNormalise 				; normalise
-		beq 	_FIPZero 					; normalised to zero, exit zero
-		;
-_FIPShift:
+		beq 	_zero 						; normalised to zero, exit zero
+
+	_shift:
 		lda 	NSExponent,x 				; if Exponent >= 0 exit.
-		bpl 	_FIPCheckZero		 		
+		bpl 	_check_zero
 
 		jsr 	NSMShiftRight 				; shift mantissa right
-		inc 	NSExponent,x 				; bump exponent 
-		bra 	_FIPShift
+		bcc 	+
+		ldy 	#$1							; record that we lost a non-zero bit
++   	inc 	NSExponent,x 				; bump exponent
+		bra 	_shift
 
-_FIPCheckZero:
+	_check_zero:
 		jsr 	NSMIsZero 					; avoid -0 problem
-		bne 	_FIPExit 					; set to zero if mantissa zero.		
-_FIPZero:
+		bne 	_exit	 					; set to zero if mantissa zero.
+
+	_zero:
 		jsr 	NSMSetZero
-_FIPExit:
+
+	_exit:
+		cpy		#$1							; sets the carry flag if Y is 1
+		ply
 		pla
-		rts		
+		rts
 
 		.send 	code
-
-; ************************************************************************************************
-;
-;									Changes and Updates
-;
-; ************************************************************************************************
-;
-;		Date			Notes
-;		==== 			=====
-;
-; ************************************************************************************************

source/common/expressions/float/utility.asm

@@ -28,19 +28,20 @@ FloatPrepare:
 _FDType:
 		jmp 	TypeError
 
-; ************************************************************************************************
-;
-;									  Normalise Stack[X]
+
+;;
+; Normalize floating-point entry at position X in the number stack.
 ;
-; ************************************************************************************************
+; \in X         Index of the entry in the number stack.
+;;
 
 NSNormalise:
 		lda 	NSStatus,x 					; make float, keep sign
 		and 	#$80
-		ora 	#NSTFloat  					
+		ora 	#NSTFloat
 		sta 	NSStatus,x
 
-		jsr 	NSMIsZero 					; if zero exit 
+		jsr 	NSMIsZero 					; if zero exit
 		bne 	_NSNormaliseOptimise 		; if so, normalise it.
 		asl 	NSStatus,x 					; clear the sign bit.
 		ror 	NSStatus,x 					; (no -0)
@@ -50,7 +51,7 @@ NSNormalise:
 		;		Normalise by byte if the MSB is zero we can normalise it
 		;		(providing bit 7 of 2nd byte is not set)
 		;
-_NSNormaliseOptimise:						
+_NSNormaliseOptimise:
 		lda 	NSMantissa3,x 				; upper byte zero ?
 		bne 	_NSNormaliseLoop
 		lda 	NSMantissa2,x 				; byte normalise
@@ -71,7 +72,7 @@ _NSNormaliseOptimise:
 		;
 		;		Normalise by bit
 		;
-_NSNormaliseLoop:		
+_NSNormaliseLoop:
 		bit 	NSMantissa3,x 				; bit 30 set ?
 		bvs 	_NSNExit 					; exit if so with Z flag clear
 		jsr 	NSMShiftLeft 				; shift mantissa left
@@ -82,7 +83,7 @@ _NSNExit:
 		rts
 
 		.send 	code
-		
+
 ; ************************************************************************************************
 ;
 ;									Changes and Updates