; Date: Wed, 15 May 1996 22:27:55 -0400 (EDT) ; From: Jingyang Xu [br00416@bingsuns.cc.binghamton.edu] ; Subject: LZ: Trig Routines: SIN/COS/TAN ; Someone asked me about these and here are the bug-free version of my ; sin/cos/tan routines: ; Note that sin and cos uses the same table and tan uses its own table. ; The arguments to sinx and cosx are: a=multiplier bc=angle ; and the return is now in bc: b=integer part c=fractional part. ; So bc is a 16 bit signed number, the key here is signed - if the high bit ; of b is set, that means bc is the twos complement of the positive value ; of bc. ; For the tangent routine. de is the multiplier (this is a 16 bit ; multiplier) and hl is the angle. I think it returns the result in hl, in ; the same format as that for bc. AdjustAngleinBC: xor a cp b jr z,Alldone ld h,b ld l,c ld bc,360 and a sbc hl,bc jr nc,AAHalfDone add hl,bc AAHalfDone: ld b,h ld c,l jr Alldone Alldone: ret sinx: push af ;save argument ld d,1 ;d=1, use for later ld hl,180 and a ;clear carry sbc hl,bc jr nc,LessE180 ;is angle greater than 180 degrees? Great180: ld h,b ; ld l,c ;load bc into hl ld bc,180 ; and a ; bc=bc-180 sbc hl,bc ; ld b,h ; ld c,l ;load hl into bc inc d ; d=2, remember negated LessE180: ;0<=bc<=180 -> 0 is in b and 0<=c<=180 ld a,d ;save d ld de,(PROGRAM_ADDR) ld hl,Trig_Look_Up ;hl=addr of table add hl,de ld d,a ;restore d ld a,c ;load angle into accumulator cp 90 ;is it 90 degrees? jr nz,not90 ld a,128 ;if 90 degrees, sin90=1 jr sinloaded not90: sub 90 jr nc,Greater90 ;is angle less than or greater than 90 Less90: add hl,bc ;if less than, go directly to table ld a,(hl) jr sinloaded Greater90: ld a,180 ;if greater, sin(x)=sin(180-x) sub c ;subtract from 180 ld c,a add hl,bc ;read from table ld a,(hl) sinloaded: ;x/128 is in a, d will determine sign ld b,a ;save result pop af ;get multiplicand back bit 7,a ;test to see if a is negative jr z,apositive neg ;if negative, negate inc d ;store negative memory in d apositive: ;now we want a*b/128 ld e,a ;save a ld a,b ; cp 0 ;see if e=0 jr z,multiplyby0 ; ld c,0 xor a sinmultiplyloop: add a,e jr nc,nocarry ;multipy a by b inc c ;16bit result in ca nocarry: djnz sinmultiplyloop rl a ;shift ca to the left rl c ;ca/128 now in c ld b,c ld c,a dec d jr z,sinxend and a ld hl,0 sbc hl,bc ld b,h ld c,l dec d jr z,sinxend and a ld hl,0 sbc hl,bc ld b,h ld c,l dec d jr z,sinxend multiplyby0: ld bc,0 sinxend: ret cosx: ld hl,90 add hl,bc ld b,h ld c,l ld d,a CALL_(AdjustAngleinBC) ld a,d CALL_(sinx) ret Trig_Look_Up: .db 0,2,4,6,8,11,13,15,17,20 .db 22,24,26,28,30,33,35,37,39,41 .db 43,45,47,50,52,54,56,58,60,62 .db 64,65,67,69,71,73,75,77,78,80 .db 82,83,85,87,88,90,92,93,95,96 .db 98,99,100,102,103,104,106,107,108,109 .db 110,111,113,114,115,116,116,117,118,119 .db 120,121,121,122,123,123,124,124,125,125 .db 126,126,126,127,127,127,127,127,127,127 tanx: ;multiplier in de, angle in hl push de push de ;save multiplier ld b,h ;make another copy of angle in bc ld c,l ; ld de,180 ;subtract 180 from and a ;angle to see if it is sbc hl,de ;greater than 180 jr c,tanLess180 ;if not, goto tanless180 ld b,h ;if greater than 180, load angle ld c,l ;minus 180 into bc tanLess180: ;bc has the semi-reference inc d ;load 1 into d ld hl,90 ;subtract angle from 90 and a ;to see if it is less than sbc hl,bc ;90 jr nc,tanLess90 ;if so, jump to tanless90 ld hl,180 ;if greater, load 180 into hl and a ;subtract angle from it sbc hl,bc ; inc d ;load 2 into d ld b,h ;save final reference in bc ld c,l ; tanLess90: ;already has reference angle sla c ;multiply bc by 2 rl b ; ld a,d ;preserves d ld de,(PROGRAM_ADDR) ;reference the table ld hl,Tan_Table ; add hl,de ; add hl,bc ; ld d,(hl) ; inc hl ;load result into de ld e,(hl) ; ld h,a ;whatever we had in d before dec h ;see if h=1 or 2 jr z,tanNotNegative ;if 1, positive set 7,d ;if result negative, then tell it so tanNotNegative: ;guess what pop hl ;get multiplier CALL_(MulDEbyHL) ;multiply the result by the multiplier push af ld h,c ld l,d bit 7,e jr z,TanRoundDown inc hl TanRoundDown: pop af jr z,ResPositive ex de,hl ld hl,0 and a sbc hl,de pop de ret ResPositive: pop de ret MulDEbyHL: ld ix,TempLine bit 7,d jr z,DEPositive res 7,d bit 7,h jr z,HLPositive res 7,h jr DEPositive HLPositive: set 7,h DEPositive: ld (ix+0),h ld (ix+1),l ld b,8 xor a ld c,a ld hl,0 MulLoop1: rrc (ix+1) jr nc,NoAdd1 add hl,de adc a,c NoAdd1: sla e rl d rl c djnz MulLoop1 ld b,7 ld e,d ld d,c ld c,0 rl c ld (ix+5),l ld l,h ld h,a xor a MulLoop2: rrc (ix+0) jr nc,NoAdd2 add hl,de adc a,c NoAdd2: sla e rl d rl c djnz MulLoop2 ld b,a ld c,h ld d,l ld e,(ix+5) bit 0,(ix+0) ret Tan_Table: .db 0,0,0,4,0,9,0,13,0,18,0,22,0,27,0,31,0,36,0,41 .db 0,45,0,50,0,54,0,59,0,64,0,69,0,73,0,78,0,83,0,88 .db 0,93,0,98,0,103,0,109,0,114,0,119,0,125,0,130,0,136,0,142 .db 0,148,0,154,0,160,0,166,0,173,0,179,0,186,0,193,0,200,0,207 .db 0,215,0,223,0,231,0,239,0,247,1,0,1,9,1,19,1,28,1,38 .db 1,49,1,60,1,72,1,84,1,96,1,110,1,124,1,138,1,154,1,170 .db 1,187,1,206,1,225,1,246,2,13,2,37,2,63,2,91,2,122,2,155 .db 2,191,2,231,3,20,3,69,3,125,3,187,4,3,4,85,4,180,5,37 .db 5,172,6,80,7,30,8,37,9,132,11,110,14,77,19,21,28,163,57,74