Z80:Advanced Math - Revision history

Xeda112358: /* Exponentiation */

2016-04-24T00:36:13Z

Exponentiation

← Older revision		Revision as of 00:36, 24 April 2016
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	Here, exponentiation refers to <math>2^{x}</math>.		Here, exponentiation refers to <math>2^{x}</math>.
	Observe that <math>2^{39/16}=2^{2+7/16} = 2^{2+0/2+1/4+1/8+1/16}=2^{2}2^{0/2}2^{1/4}2^{1/8}2^{1/16}</math>		Observe that <math>2^{39/16}=2^{2+7/16} = 2^{2+0/2+1/4+1/8+1/16}=2^{2}2^{0/2}2^{1/4}2^{1/8}2^{1/16}</math>
	The observant reader will see that taking away the trivial integer part of the power, the fractional part can be represented as a sequence of square roots with 2s wherever there are 1s in the binary expansion. So to compute 2^^x^^ where x is on [0,1), in pseudo code we have:		The observant reader will see that taking away the trivial integer part of the power, the fractional part can be represented as a sequence of square roots with 2s wherever there are 1s in the binary expansion. So to compute <math>2^{x}</math> where x is on [0,1), in pseudo code we have:

Xeda112358: /* Exponentiation */ formatting issues

2016-04-24T00:35:37Z

Exponentiation: formatting issues

← Older revision		Revision as of 00:35, 24 April 2016
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	== Exponentiation and Logarithms ==		== Exponentiation and Logarithms ==
	=== Exponentiation ===		=== Exponentiation ===
	Here, exponentiation refers to 2^^x^^.		Here, exponentiation refers to <math>2^{x}</math>.
	Observe that 2^^39/16^^ = 2^^2+7/16^^ = 2^^2/1+0/2+1/4+1/8+1/16^^=2^^2^^2^^0/2^^2^^1/4^^2^^1/8^^2^^1/16~~^^ = 2^^2^^sqrt(sqrt(2))sqrt(sqrt(sqrt(2)))sqrt(sqrt(sqrt(sqrt(2)))) = 2^^2^^sqrt(sqrt(2sqrt(2sqrt(2))))~~		Observe that <math>2^{39/16}=2^{2+7/16} = 2^{2+0/2+1/4+1/8+1/16}=2^{2}2^{0/2}2^{1/4}2^{1/8}2^{1/16}</math>

	The observant reader will see that taking away the trivial integer part of the power, the fractional part can be represented as a sequence of square roots with 2s wherever there are 1s in the binary expansion. So to compute 2^^x^^ where x is on [0,1), in pseudo code we have:		The observant reader will see that taking away the trivial integer part of the power, the fractional part can be represented as a sequence of square roots with 2s wherever there are 1s in the binary expansion. So to compute 2^^x^^ where x is on [0,1), in pseudo code we have:


	If X == 0		If x==0
	~~Return~~ 1		return 1.0
	~~Else~~		repeat until carry is set
	~~While (~~carry is ~~not~~ set)		x>>=1 ;shift X right
	X>> ;shift X right		y=sqrt(2)
	~~End~~		while x>0
	y=sqrt(2)		x>>=1
	~~While X~~>0		if (carry is set)
	X>>		y*=2
	If (carry is set)		y=sqrt(y)
	y=y*2
	y=sqrt(y)
	~~End~~

	Converting that to assembly:		Converting that to assembly:

Xeda112358: /* Addition and Subtraction */ formatting issues and bugs

2016-04-24T00:22:26Z

Addition and Subtraction: formatting issues and bugs

Show changes

Xeda112358: /* Multiplication */

2016-04-24T00:04:31Z

Multiplication

← Older revision		Revision as of 00:04, 24 April 2016
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	ret		ret

	And you might realise that multiplying an 8-bit number by a 16-bit number can yield up to a 24-bit number, so to take care of that overflow by turning rlca into adc a,a which is the same size and speed. Note that adc a,a can be replaced with rla for the same effect.		And you might realise that multiplying an 8-bit number by a 16-bit number can yield up to a 24-bit number, so to take care of that overflow by turning rlca into adc a,a which is the same size and speed. Note that adc a,a can be replaced with rla for the same effect. Some overflow may occur from ''add hl,de'', so we take care of that, too

	.module DE_Times_A		.module DE_Times_A
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	ld hl,0 ; Use HL to store the product		ld hl,0 ; Use HL to store the product
	ld b,8 ; Eight bits to check		ld b,8 ; Eight bits to check
			ld c,h
	_loop:		_loop:
	add hl,hl		add hl,hl
	adc a,a ; Check most-significant bit of accumulator		adc a,a ; Check most-significant bit of accumulator
	jr nc,_skip ; If zero, skip addition		jr nc,_skip ; If zero, skip addition
	add hl,de		add hl,de
			adc a,c ;add in overflow as needed.
	_skip:		_skip:
	djnz _loop		djnz _loop
	ret		ret


	== Division ==		== Division ==

Xeda112358: /* replacing an old entry of mine with a significantly better one */

2016-04-23T23:58:33Z

replacing an old entry of mine with a significantly better one

Show changes

KermMartian at 05:37, 5 February 2016

2016-02-05T05:37:47Z

Show changes

KermMartian: Adjusted lowercase z80

2016-02-03T21:04:10Z

Adjusted lowercase z80

← Older revision		Revision as of 21:04, 3 February 2016
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	= Decimal Math =		= Decimal Math =

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	{{lowercase}}		{{lowercase}}
	[[Category:~~z80~~ Assembly]]		[[Category:Z80 Assembly]]
	[[Category:~~z80~~ Heaven]]		[[Category:Z80 Heaven]]

KermMartian: /* Conclusion */

2016-02-03T17:13:55Z

Conclusion

← Older revision		Revision as of 17:13, 3 February 2016
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	= Conclusion =		= Conclusion =
	For more info, see the TI-83 Asm in 28 ~~days~~, ~~week 3, day 1~~.		For more info, see the TI-83 Asm in 28 Days, Day 15 (link below).

	For ways to perform more accurate math (Floating Point), there are many prebuilt functions that operate on the OP operators. They can be found [http://wikiti.brandonw.net/index.php?title=Category:83Plus:BCALLs:By_Name:FP_Math here].		For ways to perform more accurate math (Floating Point), there are many prebuilt functions that operate on the OP operators. They can be found [http://wikiti.brandonw.net/index.php?title=Category:83Plus:BCALLs:By_Name:FP_Math here].

	Sources:		Sources:
	[http://media.taricorp.net/83pa28d/lesson/day02.html TI-83 Plus ASM in 28 Days, Day 15]		* [http://media.taricorp.net/83pa28d/lesson/day02.html TI-83 Plus ASM in 28 Days, Day 15]
	[http://wikiti.brandonw.net/index.php?title=Category:83Plus:BCALLs:By_Name:FP_Math FP Math on WikiTI]		* [http://wikiti.brandonw.net/index.php?title=Category:83Plus:BCALLs:By_Name:FP_Math FP Math on WikiTI]

	{{lowercase}}		{{lowercase}}
	[[Category:z80 Assembly]]		[[Category:z80 Assembly]]
	[[Category:z80 Heaven]]		[[Category:z80 Heaven]]

KermMartian: Created page with " = Decimal Math = == Addition/Subtraction == To do addition or subtraction on an integer of arbitrary size, we use ADC. LD HL, (word1) ; Get least-significa..."

2016-02-03T17:13:18Z

Created page with " = Decimal Math = == Addition/Subtraction == To do addition or subtraction on an integer of arbitrary size, we use ADC. LD HL, (word1) ; Get least-significa..."

New page

= Decimal Math =

== Addition/Subtraction ==
To do addition or subtraction on an integer of arbitrary size, we use ADC.

LD HL, (word1) ; Get least-significant word of word1
LD DE, (word2) ; Get least-significant word of word2
ADD HL, DE ; Add them
LD (result), HL ; Store least-significant result

LD HL, (dword1 + 2) ; Get most-significant word of word1
LD DE, (dword2 + 2) ; Get most-significant word of word2
ADC HL, DE ; Add them with the carry from the previous addition
LD (result + 2), HL ; Store most-significant result
RET

word1: .DB $B3, $90, $12, $32 ; Each word is stored with the least-significant
word2: .DB $F1, $15, $06, $B8 ; bytes first. You could just as easily have stored
result: .DB $00, $00, $00, $00 ; them in big-endian, but because of how registers are
; loaded from RAM, it wouldn't work.

== Multiplication ==
For multiplication, we could just add them in a DJNZ loop. But that is slow for multiplying big numbers. So we just do it like in base 10, where we multiply each digit separately.

.module DE_Times_A
DE_Times_A: ; HL = DE ร— A
LD HL, 0 ; Use HL to store the product
LD B, 8 ; Eight bits to check
_loop:
RRCA ; Check least-significant bit of accumulator
JR NC, _skip ; If zero, skip addition
ADD HL, DE
_skip:
SLA E ; Shift DE one bit left
RL D
DJNZ _loop
RET

== Division ==
Division is also just like base-10 division as well.
.module Div_HL_D
Div_HL_D: ; HL = HL รท D, A = remainder
XOR A ; Clear upper eight bits of AHL
LD B, 16 ; Sixteen bits in dividend
_loop:
ADD HL, HL ; Do a SLA HL
RLA ; This moves the upper bits of the dividend into A
JR C, _overflow
CP D ; Check if we can subtract the divisor
JR C, _skip ; Carry means D > A
_overflow:
SUB D ; Do subtraction for real this time
INC L ; Set bit 0 of quotient
_skip:
DJNZ _loop
RET

= Exponentiation and Logarithms =

= Conclusion =
For more info, see the TI-83 Asm in 28 days, week 3, day 1.

For ways to perform more accurate math (Floating Point), there are many prebuilt functions that operate on the OP operators. They can be found [http://wikiti.brandonw.net/index.php?title=Category:83Plus:BCALLs:By_Name:FP_Math here].

Sources:
[http://media.taricorp.net/83pa28d/lesson/day02.html TI-83 Plus ASM in 28 Days, Day 15]
[http://wikiti.brandonw.net/index.php?title=Category:83Plus:BCALLs:By_Name:FP_Math FP Math on WikiTI]

{{lowercase}}
[[Category:z80 Assembly]]
[[Category:z80 Heaven]]