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In article <1993Mar5.105326.22133@metapro.DIALix.oz.au> bernie@metapro.DIALix.oz.au (Bernd Felsche) writes:
>In <39610@cbmvax.cbm.commodore.com>
>
>If at all possible, don't use trig functions at all.
>
>Most graphics applications are accurate enough with the first 2
>or 3 terms of an equivalent Taylor series. Error is usually of
>the order of 1:1000.
>
The following code is what I use. It's accurate enough for
computing texture map coordinates in my ray-tracer:
acos::
; input d0=cos output d0=acos(d0) 1 -> 0 0 > .25 -1 > .5
; trashes d1/d2,a0
tst.w d0
bmi.s negacos
posacos: move d0,d2
and.w #$001f,d2
lsr #5,d0
add d0,d0
lea acos_tbl(pc),a0
move 2(a0,d0.w),d1
move 0(a0,d0.w),d0
sub d0,d1
muls d2,d1
asr.w #5,d1
add d1,d0
rts
negacos: neg.w d0
bsr.s posacos
neg.w d0
add.w #$7ffe,d0 ; acos(-x) = .5-acos(x)
rts
and here's the boring part:
acos_tbl:
dc.w $3fff
dc.w $3ff5
dc.w $3feb
dc.w $3fe1
dc.w $3fd7
dc.w $3fcd
dc.w $3fc2
dc.w $3fb8
dc.w $3fae
dc.w $3fa4
dc.w $3f9a
dc.w $3f8f
dc.w $3f85
dc.w $3f7b
dc.w $3f71
dc.w $3f67
dc.w $3f5d
dc.w $3f52
dc.w $3f48
dc.w $3f3e
dc.w $3f34
dc.w $3f2a
dc.w $3f1f
dc.w $3f15
dc.w $3f0b
dc.w $3f01
dc.w $3ef7
dc.w $3eec
dc.w $3ee2
dc.w $3ed8
dc.w $3ece
dc.w $3ec4
dc.w $3eb9
dc.w $3eaf
dc.w $3ea5
dc.w $3e9b
dc.w $3e91
dc.w $3e87
dc.w $3e7c
dc.w $3e72
dc.w $3e68
dc.w $3e5e
dc.w $3e54
dc.w $3e49
dc.w $3e3f
dc.w $3e35
dc.w $3e2b
dc.w $3e21
dc.w $3e16
dc.w $3e0c
dc.w $3e02
dc.w $3df8
dc.w $3dee
dc.w $3de3
dc.w $3dd9
dc.w $3dcf
dc.w $3dc5
dc.w $3dbb
dc.w $3db0
dc.w $3da6
dc.w $3d9c
dc.w $3d92
dc.w $3d88
dc.w $3d7d
dc.w $3d73
dc.w $3d69
dc.w $3d5f
dc.w $3d55
dc.w $3d4a
dc.w $3d40
dc.w $3d36
dc.w $3d2c
dc.w $3d22
dc.w $3d17
dc.w $3d0d
dc.w $3d03
dc.w $3cf9
dc.w $3cee
dc.w $3ce4
dc.w $3cda
dc.w $3cd0
dc.w $3cc6
dc.w $3cbb
dc.w $3cb1
dc.w $3ca7
dc.w $3c9d
dc.w $3c92
dc.w $3c88
dc.w $3c7e
dc.w $3c74
dc.w $3c6a
dc.w $3c5f
dc.w $3c55
dc.w $3c4b
dc.w $3c41
dc.w $3c36
dc.w $3c2c
dc.w $3c22
dc.w $3c18
dc.w $3c0e
dc.w $3c03
dc.w $3bf9
dc.w $3bef
dc.w $3be5
dc.w $3bda
dc.w $3bd0
dc.w $3bc6
dc.w $3bbc
dc.w $3bb1
dc.w $3ba7
dc.w $3b9d
dc.w $3b93
dc.w $3b88
dc.w $3b7e
dc.w $3b74
dc.w $3b6a
dc.w $3b5f
dc.w $3b55
dc.w $3b4b
dc.w $3b41
dc.w $3b36
dc.w $3b2c
dc.w $3b22
dc.w $3b18
dc.w $3b0d
dc.w $3b03
dc.w $3af9
dc.w $3aef
dc.w $3ae4
dc.w $3ada
dc.w $3ad0
dc.w $3ac5
dc.w $3abb
dc.w $3ab1
dc.w $3aa7
dc.w $3a9c
dc.w $3a92
dc.w $3a88
dc.w $3a7e
dc.w $3a73
dc.w $3a69
dc.w $3a5f
dc.w $3a54
dc.w $3a4a
dc.w $3a40
dc.w $3a36
dc.w $3a2b
dc.w $3a21
dc.w $3a17
dc.w $3a0c
dc.w $3a02
dc.w $39f8
dc.w $39ed
dc.w $39e3
dc.w $39d9
dc.w $39cf
dc.w $39c4
dc.w $39ba
dc.w $39b0
dc.w $39a5
dc.w $399b
dc.w $3991
dc.w $3986
dc.w $397c
dc.w $3972
dc.w $3967
dc.w $395d
dc.w $3953
dc.w $3948
dc.w $393e
dc.w $3934
dc.w $392a
dc.w $391f
dc.w $3915
dc.w $390b
dc.w $3900
dc.w $38f6
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dc.w $38a3
dc.w $3899
dc.w $388e
dc.w $3884
dc.w $387a
dc.w $386f
dc.w $3865
dc.w $385b
dc.w $3850
dc.w $3846
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dc.w $3831
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dc.w $15de
dc.w $15ca
dc.w $15b6
dc.w $15a2
dc.w $158e
dc.w $157a
dc.w $1565
dc.w $1551
dc.w $153d
dc.w $1528
dc.w $1513
dc.w $14ff
dc.w $14ea
dc.w $14d5
dc.w $14c1
dc.w $14ac
dc.w $1497
dc.w $1482
dc.w $146c
dc.w $1457
dc.w $1442
dc.w $142c
dc.w $1417
dc.w $1401
dc.w $13ec
dc.w $13d6
dc.w $13c0
dc.w $13aa
dc.w $1394
dc.w $137e
dc.w $1368
dc.w $1352
dc.w $133b
dc.w $1325
dc.w $130e
dc.w $12f8
dc.w $12e1
dc.w $12ca
dc.w $12b3
dc.w $129c
dc.w $1285
dc.w $126e
dc.w $1257
dc.w $123f
dc.w $1227
dc.w $1210
dc.w $11f8
dc.w $11e0
dc.w $11c8
dc.w $11b0
dc.w $1198
dc.w $117f
dc.w $1167
dc.w $114e
dc.w $1135
dc.w $111c
dc.w $1103
dc.w $10ea
dc.w $10d1
dc.w $10b7
dc.w $109e
dc.w $1084
dc.w $106a
dc.w $1050
dc.w $1036
dc.w $101b
dc.w $1001
dc.w $0fe6
dc.w $0fcb
dc.w $0fb0
dc.w $0f95
dc.w $0f7a
dc.w $0f5e
dc.w $0f42
dc.w $0f26
dc.w $0f0a
dc.w $0eee
dc.w $0ed2
dc.w $0eb5
dc.w $0e98
dc.w $0e7b
dc.w $0e5d
dc.w $0e40
dc.w $0e22
dc.w $0e04
dc.w $0de5
dc.w $0dc7
dc.w $0da8
dc.w $0d89
dc.w $0d6a
dc.w $0d4a
dc.w $0d2a
dc.w $0d0a
dc.w $0ce9
dc.w $0cc8
dc.w $0ca7
dc.w $0c86
dc.w $0c64
dc.w $0c42
dc.w $0c1f
dc.w $0bfc
dc.w $0bd9
dc.w $0bb5
dc.w $0b91
dc.w $0b6c
dc.w $0b47
dc.w $0b22
dc.w $0afc
dc.w $0ad5
dc.w $0aae
dc.w $0a87
dc.w $0a5f
dc.w $0a36
dc.w $0a0d
dc.w $09e2
dc.w $09b8
dc.w $098c
dc.w $0960
dc.w $0933
dc.w $0905
dc.w $08d6
dc.w $08a6
dc.w $0875
dc.w $0844
dc.w $0810
dc.w $07dc
dc.w $07a6
dc.w $076f
dc.w $0736
dc.w $06fb
dc.w $06be
dc.w $067f
dc.w $063e
dc.w $05fa
dc.w $05b2
dc.w $0567
dc.w $0518
dc.w $04c4
dc.w $0469
dc.w $0407
dc.w $039a
dc.w $031e
dc.w $028c
dc.w $01cc
dc.w $0000
--
*-------------------------------------------*---------------------------*
|Chris Green - Graphics Software Engineer - chrisg@commodore.COM f
| Commodore-Amiga - uunet!cbmvax!chrisg n
|My opinions are my own, and do not - icantforgettheimpression o
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