mirror of https://gitlab.com/camelot/kickc.git
753 lines
15 KiB
NASM
753 lines
15 KiB
NASM
// Generates a 16-bit signed sine
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/// @file
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/// Sine Generator functions using only multiplication, addition and bit shifting
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///
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/// Uses a single division for converting the wavelength to a reciprocal.
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/// Generates sine using the series sin(x) = x - x^/3! + x^-5! - x^7/7! ...
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/// Uses the approximation sin(x) = x - x^/6 + x^/128
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/// Optimization possibility: Use symmetries when generating sine tables. wavelength%2==0 -> mirror symmetry over PI, wavelength%4==0 -> mirror symmetry over PI/2.
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// Commodore 64 PRG executable file
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.file [name="sinusgen16.prg", type="prg", segments="Program"]
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.segmentdef Program [segments="Basic, Code, Data"]
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.segmentdef Basic [start=$0801]
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.segmentdef Code [start=$80d]
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.segmentdef Data [startAfter="Code"]
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.segment Basic
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:BasicUpstart(main)
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// PI*2 in u[4.28] format
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.const PI2_u4f28 = $6487ed51
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// PI in u[4.28] format
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.const PI_u4f28 = $3243f6a9
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// PI/2 in u[4.28] format
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.const PI_HALF_u4f28 = $1921fb54
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.const SIZEOF_INT = 2
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.label print_screen = $400
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.label print_char_cursor = $c
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// Remainder after unsigned 16-bit division
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.label rem16u = $e
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.segment Code
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main: {
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.label wavelength = $78
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.label sw = $1a
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.label st1 = $24
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// sin16s_gen(sintab1, wavelength)
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jsr sin16s_gen
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// print_cls()
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jsr print_cls
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lda #<print_screen
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sta.z print_char_cursor
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lda #>print_screen
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sta.z print_char_cursor+1
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lda #<sintab1
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sta.z st1
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lda #>sintab1
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sta.z st1+1
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__b1:
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// for(signed word* st1 = sintab1; st1<sintab1+wavelength; st1++ )
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lda.z st1+1
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cmp #>sintab1+wavelength*SIZEOF_INT
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bcc __b2
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bne !+
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lda.z st1
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cmp #<sintab1+wavelength*SIZEOF_INT
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bcc __b2
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!:
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// }
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rts
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__b2:
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// signed word sw = *st1
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ldy #0
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lda (st1),y
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sta.z sw
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iny
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lda (st1),y
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sta.z sw+1
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// if(sw>=0)
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bmi __b3
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// print_str(" ")
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lda #<str1
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sta.z print_str.str
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lda #>str1
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sta.z print_str.str+1
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jsr print_str
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__b3:
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// print_sint(sw)
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jsr print_sint
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// print_str(" ")
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lda #<str
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sta.z print_str.str
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lda #>str
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sta.z print_str.str+1
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jsr print_str
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// for(signed word* st1 = sintab1; st1<sintab1+wavelength; st1++ )
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lda #SIZEOF_INT
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clc
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adc.z st1
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sta.z st1
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bcc !+
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inc.z st1+1
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!:
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jmp __b1
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.segment Data
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sintab1: .fill 2*$78, 0
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str: .text " "
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.byte 0
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str1: .text " "
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.byte 0
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}
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.segment Code
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// Generate signed (large) unsigned int sine table - on the full -$7fff - $7fff range
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// sintab - the table to generate into
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// wavelength - the number of sine points in a total sine wavelength (the size of the table)
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// void sin16s_gen(__zp($1a) int *sintab, unsigned int wavelength)
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sin16s_gen: {
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.label __2 = $18
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.label step = $20
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.label sintab = $1a
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// u[4.28]
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// Iterate over the table
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.label x = $1c
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.label i = $12
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// unsigned long step = div32u16u(PI2_u4f28, wavelength)
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// u[4.28] step = PI*2/wavelength
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jsr div32u16u
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// unsigned long step = div32u16u(PI2_u4f28, wavelength)
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lda #<main.sintab1
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sta.z sintab
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lda #>main.sintab1
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sta.z sintab+1
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lda #<0
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sta.z x
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sta.z x+1
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lda #<0>>$10
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sta.z x+2
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lda #>0>>$10
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sta.z x+3
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lda #<0
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sta.z i
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sta.z i+1
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// u[4.28]
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__b1:
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// for( unsigned int i=0; i<wavelength; i++)
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lda.z i+1
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cmp #>main.wavelength
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bcc __b2
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bne !+
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lda.z i
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cmp #<main.wavelength
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bcc __b2
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!:
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// }
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rts
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__b2:
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// sin16s(x)
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lda.z x
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sta.z sin16s.x
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lda.z x+1
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sta.z sin16s.x+1
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lda.z x+2
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sta.z sin16s.x+2
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lda.z x+3
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sta.z sin16s.x+3
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jsr sin16s
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// *sintab++ = sin16s(x)
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ldy #0
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lda.z __2
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sta (sintab),y
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iny
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lda.z __2+1
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sta (sintab),y
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// *sintab++ = sin16s(x);
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lda #SIZEOF_INT
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clc
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adc.z sintab
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sta.z sintab
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bcc !+
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inc.z sintab+1
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!:
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// x = x + step
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clc
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lda.z x
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adc.z step
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sta.z x
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lda.z x+1
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adc.z step+1
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sta.z x+1
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lda.z x+2
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adc.z step+2
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sta.z x+2
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lda.z x+3
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adc.z step+3
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sta.z x+3
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// for( unsigned int i=0; i<wavelength; i++)
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inc.z i
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bne !+
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inc.z i+1
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!:
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jmp __b1
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}
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// Clear the screen. Also resets current line/char cursor.
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print_cls: {
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// memset(print_screen, ' ', 1000)
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jsr memset
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// }
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rts
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}
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// Print a zero-terminated string
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// void print_str(__zp($12) char *str)
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print_str: {
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.label str = $12
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__b1:
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// while(*str)
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ldy #0
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lda (str),y
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cmp #0
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bne __b2
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// }
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rts
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__b2:
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// print_char(*(str++))
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ldy #0
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lda (str),y
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jsr print_char
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// print_char(*(str++));
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inc.z str
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bne !+
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inc.z str+1
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!:
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jmp __b1
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}
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// Print a signed int as HEX
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// void print_sint(__zp($1a) int w)
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print_sint: {
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.label w = $1a
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// if(w<0)
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lda.z w+1
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bmi __b1
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// print_char(' ')
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lda #' '
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jsr print_char
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__b2:
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// print_uint((unsigned int)w)
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jsr print_uint
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// }
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rts
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__b1:
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// print_char('-')
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lda #'-'
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jsr print_char
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// w = -w
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lda #0
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sec
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sbc.z w
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sta.z w
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lda #0
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sbc.z w+1
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sta.z w+1
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jmp __b2
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}
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// Divide unsigned 32-bit unsigned long dividend with a 16-bit unsigned int divisor
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// The 16-bit unsigned int remainder can be found in rem16u after the division
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// __zp($20) unsigned long div32u16u(unsigned long dividend, unsigned int divisor)
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div32u16u: {
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.label return = $20
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.label quotient_hi = $a
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.label quotient_lo = $10
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// unsigned int quotient_hi = divr16u(WORD1(dividend), divisor, 0)
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lda #<PI2_u4f28>>$10
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sta.z divr16u.dividend
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lda #>PI2_u4f28>>$10
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sta.z divr16u.dividend+1
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lda #<0
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sta.z divr16u.rem
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sta.z divr16u.rem+1
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jsr divr16u
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// unsigned int quotient_hi = divr16u(WORD1(dividend), divisor, 0)
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lda.z divr16u.return
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sta.z quotient_hi
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lda.z divr16u.return+1
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sta.z quotient_hi+1
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// unsigned int quotient_lo = divr16u(WORD0(dividend), divisor, rem16u)
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lda #<PI2_u4f28&$ffff
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sta.z divr16u.dividend
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lda #>PI2_u4f28&$ffff
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sta.z divr16u.dividend+1
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jsr divr16u
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// unsigned int quotient_lo = divr16u(WORD0(dividend), divisor, rem16u)
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// unsigned long quotient = MAKELONG( quotient_hi, quotient_lo )
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lda.z quotient_hi
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sta.z return+2
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lda.z quotient_hi+1
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sta.z return+3
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lda.z quotient_lo
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sta.z return
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lda.z quotient_lo+1
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sta.z return+1
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// }
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rts
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}
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// Calculate signed int sine sin(x)
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// x: unsigned long input u[4.28] in the interval $00000000 - PI2_u4f28
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// result: signed int sin(x) s[0.15] - using the full range -$7fff - $7fff
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// __zp($18) int sin16s(__zp($14) unsigned long x)
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sin16s: {
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.label __4 = 2
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.label x = $14
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.label return = $18
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.label x1 = $c
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.label x2 = $e
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.label x3 = $e
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.label x3_6 = $a
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.label usinx = $18
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.label x4 = $e
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.label x5 = $a
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.label x5_128 = $a
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.label sinx = $18
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// if(x >= PI_u4f28 )
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lda.z x+3
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cmp #>PI_u4f28>>$10
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bcc __b4
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bne !+
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lda.z x+2
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cmp #<PI_u4f28>>$10
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bcc __b4
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bne !+
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lda.z x+1
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cmp #>PI_u4f28
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bcc __b4
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bne !+
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lda.z x
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cmp #<PI_u4f28
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bcc __b4
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!:
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// x = x - PI_u4f28
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lda.z x
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sec
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sbc #<PI_u4f28
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sta.z x
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lda.z x+1
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sbc #>PI_u4f28
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sta.z x+1
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lda.z x+2
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sbc #<PI_u4f28>>$10
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sta.z x+2
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lda.z x+3
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sbc #>PI_u4f28>>$10
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sta.z x+3
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ldy #1
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jmp __b1
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__b4:
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ldy #0
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__b1:
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// if(x >= PI_HALF_u4f28 )
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lda.z x+3
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cmp #>PI_HALF_u4f28>>$10
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bcc __b2
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bne !+
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lda.z x+2
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cmp #<PI_HALF_u4f28>>$10
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bcc __b2
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bne !+
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lda.z x+1
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cmp #>PI_HALF_u4f28
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bcc __b2
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bne !+
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lda.z x
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cmp #<PI_HALF_u4f28
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bcc __b2
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!:
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// x = PI_u4f28 - x
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lda #<PI_u4f28
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sec
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sbc.z x
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sta.z x
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lda #>PI_u4f28
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sbc.z x+1
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sta.z x+1
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lda #<PI_u4f28>>$10
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sbc.z x+2
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sta.z x+2
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lda #>PI_u4f28>>$10
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sbc.z x+3
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sta.z x+3
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__b2:
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// x<<3
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lda.z x
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asl
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sta.z __4
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lda.z x+1
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rol
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sta.z __4+1
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lda.z x+2
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rol
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sta.z __4+2
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lda.z x+3
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rol
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sta.z __4+3
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asl.z __4
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rol.z __4+1
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rol.z __4+2
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rol.z __4+3
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asl.z __4
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rol.z __4+1
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rol.z __4+2
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rol.z __4+3
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// unsigned int x1 = WORD1(x<<3)
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// sinx = x - x^3/6 + x5/128;
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lda.z __4+2
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sta.z x1
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lda.z __4+3
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sta.z x1+1
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// unsigned int x2 = mulu16_sel(x1, x1, 0)
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lda.z x1
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sta.z mulu16_sel.v1
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lda.z x1+1
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sta.z mulu16_sel.v1+1
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lda.z x1
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sta.z mulu16_sel.v2
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lda.z x1+1
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sta.z mulu16_sel.v2+1
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// u[1.15]
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ldx #0
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jsr mulu16_sel
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// unsigned int x2 = mulu16_sel(x1, x1, 0)
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lda.z mulu16_sel.return
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sta.z x2
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lda.z mulu16_sel.return+1
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sta.z x2+1
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// unsigned int x3 = mulu16_sel(x2, x1, 1)
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lda.z x1
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sta.z mulu16_sel.v2
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lda.z x1+1
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sta.z mulu16_sel.v2+1
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// u[2.14] x^2
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ldx #1
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jsr mulu16_sel
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// unsigned int x3 = mulu16_sel(x2, x1, 1)
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lda.z mulu16_sel.return
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sta.z mulu16_sel.return_1
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lda.z mulu16_sel.return+1
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sta.z mulu16_sel.return_1+1
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// unsigned int x3_6 = mulu16_sel(x3, 0x10000/6, 1)
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// u[2.14] x^3
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ldx #1
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lda #<$10000/6
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sta.z mulu16_sel.v2
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lda #>$10000/6
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sta.z mulu16_sel.v2+1
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jsr mulu16_sel
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// unsigned int x3_6 = mulu16_sel(x3, 0x10000/6, 1)
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// unsigned int usinx = x1 - x3_6
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// u[1.15] x^3/6;
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lda.z x1
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sec
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sbc.z x3_6
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sta.z usinx
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lda.z x1+1
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sbc.z x3_6+1
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sta.z usinx+1
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// unsigned int x4 = mulu16_sel(x3, x1, 0)
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lda.z x1
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sta.z mulu16_sel.v2
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lda.z x1+1
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sta.z mulu16_sel.v2+1
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// u[1.15] x - x^3/6
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ldx #0
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jsr mulu16_sel
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// unsigned int x4 = mulu16_sel(x3, x1, 0)
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lda.z mulu16_sel.return
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sta.z mulu16_sel.return_1
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lda.z mulu16_sel.return+1
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sta.z mulu16_sel.return_1+1
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// unsigned int x5 = mulu16_sel(x4, x1, 0)
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lda.z x1
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sta.z mulu16_sel.v2
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lda.z x1+1
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sta.z mulu16_sel.v2+1
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// u[3.13] x^4
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ldx #0
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jsr mulu16_sel
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// unsigned int x5 = mulu16_sel(x4, x1, 0)
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// unsigned int x5_128 = x5>>4
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// u[4.12] x^5
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lsr.z x5_128+1
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ror.z x5_128
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lsr.z x5_128+1
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ror.z x5_128
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lsr.z x5_128+1
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ror.z x5_128
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lsr.z x5_128+1
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ror.z x5_128
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// usinx = usinx + x5_128
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clc
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lda.z usinx
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adc.z x5_128
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sta.z usinx
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lda.z usinx+1
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adc.z x5_128+1
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sta.z usinx+1
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// if(isUpper!=0)
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cpy #0
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beq __b3
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// sinx = -(signed int)usinx
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lda #0
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sec
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sbc.z sinx
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sta.z sinx
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lda #0
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sbc.z sinx+1
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sta.z sinx+1
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__b3:
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// }
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rts
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}
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// Copies the character c (an unsigned char) to the first num characters of the object pointed to by the argument str.
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// void * memset(void *str, char c, unsigned int num)
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memset: {
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.const c = ' '
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.const num = $3e8
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.label str = print_screen
|
|
.label end = str+num
|
|
.label dst = $18
|
|
lda #<str
|
|
sta.z dst
|
|
lda #>str
|
|
sta.z dst+1
|
|
__b1:
|
|
// for(char* dst = str; dst!=end; dst++)
|
|
lda.z dst+1
|
|
cmp #>end
|
|
bne __b2
|
|
lda.z dst
|
|
cmp #<end
|
|
bne __b2
|
|
// }
|
|
rts
|
|
__b2:
|
|
// *dst = c
|
|
lda #c
|
|
ldy #0
|
|
sta (dst),y
|
|
// for(char* dst = str; dst!=end; dst++)
|
|
inc.z dst
|
|
bne !+
|
|
inc.z dst+1
|
|
!:
|
|
jmp __b1
|
|
}
|
|
// Print a single char
|
|
// void print_char(__register(A) char ch)
|
|
print_char: {
|
|
// *(print_char_cursor++) = ch
|
|
ldy #0
|
|
sta (print_char_cursor),y
|
|
// *(print_char_cursor++) = ch;
|
|
inc.z print_char_cursor
|
|
bne !+
|
|
inc.z print_char_cursor+1
|
|
!:
|
|
// }
|
|
rts
|
|
}
|
|
// Print a unsigned int as HEX
|
|
// void print_uint(__zp($1a) unsigned int w)
|
|
print_uint: {
|
|
.label w = $1a
|
|
// print_uchar(BYTE1(w))
|
|
ldx.z w+1
|
|
jsr print_uchar
|
|
// print_uchar(BYTE0(w))
|
|
ldx.z w
|
|
jsr print_uchar
|
|
// }
|
|
rts
|
|
}
|
|
// Performs division on two 16 bit unsigned ints and an initial remainder
|
|
// Returns the quotient dividend/divisor.
|
|
// The final remainder will be set into the global variable rem16u
|
|
// Implemented using simple binary division
|
|
// __zp($10) unsigned int divr16u(__zp($c) unsigned int dividend, unsigned int divisor, __zp($e) unsigned int rem)
|
|
divr16u: {
|
|
.label rem = $e
|
|
.label dividend = $c
|
|
.label quotient = $10
|
|
.label return = $10
|
|
ldx #0
|
|
txa
|
|
sta.z quotient
|
|
sta.z quotient+1
|
|
__b1:
|
|
// rem = rem << 1
|
|
asl.z rem
|
|
rol.z rem+1
|
|
// BYTE1(dividend)
|
|
lda.z dividend+1
|
|
// BYTE1(dividend) & 0x80
|
|
and #$80
|
|
// if( (BYTE1(dividend) & 0x80) != 0 )
|
|
cmp #0
|
|
beq __b2
|
|
// rem = rem | 1
|
|
lda #1
|
|
ora.z rem
|
|
sta.z rem
|
|
__b2:
|
|
// dividend = dividend << 1
|
|
asl.z dividend
|
|
rol.z dividend+1
|
|
// quotient = quotient << 1
|
|
asl.z quotient
|
|
rol.z quotient+1
|
|
// if(rem>=divisor)
|
|
lda.z rem+1
|
|
cmp #>main.wavelength
|
|
bcc __b3
|
|
bne !+
|
|
lda.z rem
|
|
cmp #<main.wavelength
|
|
bcc __b3
|
|
!:
|
|
// quotient++;
|
|
inc.z quotient
|
|
bne !+
|
|
inc.z quotient+1
|
|
!:
|
|
// rem = rem - divisor
|
|
lda.z rem
|
|
sec
|
|
sbc #<main.wavelength
|
|
sta.z rem
|
|
lda.z rem+1
|
|
sbc #>main.wavelength
|
|
sta.z rem+1
|
|
__b3:
|
|
// for( char i : 0..15)
|
|
inx
|
|
cpx #$10
|
|
bne __b1
|
|
// rem16u = rem
|
|
// }
|
|
rts
|
|
}
|
|
// Calculate val*val for two unsigned int values - the result is 16 selected bits of the 32-bit result.
|
|
// The select parameter indicates how many of the highest bits of the 32-bit result to skip
|
|
// __zp($a) unsigned int mulu16_sel(__zp($e) unsigned int v1, __zp($10) unsigned int v2, __register(X) char select)
|
|
mulu16_sel: {
|
|
.label __0 = 2
|
|
.label __1 = 2
|
|
.label v1 = $e
|
|
.label v2 = $10
|
|
.label return = $a
|
|
.label return_1 = $e
|
|
// mul16u(v1, v2)
|
|
lda.z v1
|
|
sta.z mul16u.a
|
|
lda.z v1+1
|
|
sta.z mul16u.a+1
|
|
jsr mul16u
|
|
// mul16u(v1, v2)<<select
|
|
cpx #0
|
|
beq !e+
|
|
!:
|
|
asl.z __1
|
|
rol.z __1+1
|
|
rol.z __1+2
|
|
rol.z __1+3
|
|
dex
|
|
bne !-
|
|
!e:
|
|
// WORD1(mul16u(v1, v2)<<select)
|
|
lda.z __1+2
|
|
sta.z return
|
|
lda.z __1+3
|
|
sta.z return+1
|
|
// }
|
|
rts
|
|
}
|
|
// Print a char as HEX
|
|
// void print_uchar(__register(X) char b)
|
|
print_uchar: {
|
|
// b>>4
|
|
txa
|
|
lsr
|
|
lsr
|
|
lsr
|
|
lsr
|
|
// print_char(print_hextab[b>>4])
|
|
tay
|
|
lda print_hextab,y
|
|
// Table of hexadecimal digits
|
|
jsr print_char
|
|
// b&0xf
|
|
lda #$f
|
|
axs #0
|
|
// print_char(print_hextab[b&0xf])
|
|
lda print_hextab,x
|
|
jsr print_char
|
|
// }
|
|
rts
|
|
}
|
|
// Perform binary multiplication of two unsigned 16-bit unsigned ints into a 32-bit unsigned long
|
|
// __zp(2) unsigned long mul16u(__zp($a) unsigned int a, __zp($10) unsigned int b)
|
|
mul16u: {
|
|
.label a = $a
|
|
.label b = $10
|
|
.label return = 2
|
|
.label mb = 6
|
|
.label res = 2
|
|
// unsigned long mb = b
|
|
lda.z b
|
|
sta.z mb
|
|
lda.z b+1
|
|
sta.z mb+1
|
|
lda #0
|
|
sta.z mb+2
|
|
sta.z mb+3
|
|
sta.z res
|
|
sta.z res+1
|
|
lda #<0>>$10
|
|
sta.z res+2
|
|
lda #>0>>$10
|
|
sta.z res+3
|
|
__b1:
|
|
// while(a!=0)
|
|
lda.z a
|
|
ora.z a+1
|
|
bne __b2
|
|
// }
|
|
rts
|
|
__b2:
|
|
// a&1
|
|
lda #1
|
|
and.z a
|
|
// if( (a&1) != 0)
|
|
cmp #0
|
|
beq __b3
|
|
// res = res + mb
|
|
clc
|
|
lda.z res
|
|
adc.z mb
|
|
sta.z res
|
|
lda.z res+1
|
|
adc.z mb+1
|
|
sta.z res+1
|
|
lda.z res+2
|
|
adc.z mb+2
|
|
sta.z res+2
|
|
lda.z res+3
|
|
adc.z mb+3
|
|
sta.z res+3
|
|
__b3:
|
|
// a = a>>1
|
|
lsr.z a+1
|
|
ror.z a
|
|
// mb = mb<<1
|
|
asl.z mb
|
|
rol.z mb+1
|
|
rol.z mb+2
|
|
rol.z mb+3
|
|
jmp __b1
|
|
}
|
|
.segment Data
|
|
print_hextab: .text "0123456789abcdef"
|