Home » Archimedes archive » Acorn Computing » 1995 03.adf » 9503 » TechForum/FracRoot/Sqrt
TechForum/FracRoot/Sqrt
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Acorn Computing » 1995 03.adf » 9503 |
| Filename: | TechForum/FracRoot/Sqrt |
| Read OK: | ✔ |
| File size: | 072C bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
; sqrt16
; integer square root returning 16-bit fixed point number, assuming x is 16-bit fixed point
; ie returns 32 bit sqrt of (65536*x)
;
; It takes 6 parameters - all register names
;
; $x: x
; $r: result - may be the same as x
; $n: copy of x used during calculation
; $t: transient scratch
; $d: remainder
; $o: constant value of 1
;
MACRO
$label sqrt16 $x, $r, $n, $t, $d, $o
ASSERT $x <> $n
ASSERT $x <> $t
ASSERT $x <> $d
ASSERT $x <> $o
ASSERT $n <> $t
ASSERT $n <> $d
ASSERT $n <> $o
ASSERT $t <> $d
ASSERT $t <> $o
ASSERT $d <> $o
LCLA counter
$label MOV $n, $x
MOV $o, #1
MOV $x, #0
MOV $d, #0
AND $t, $n, #(3<<30)
MOV $t, $t, LSR #30
ORR $d, $d, $t
ADD $t, $o, $x, LSL #1
CMP $d, $t
SUBGE $d, $d, $t
ADDGE $x, $x, #1
counter SETA 28
WHILE counter < 32 ;want >= 0, however counter is unsigned, so after 0 it goes high, thus < 32 will catch it!
MOV $x, $x, LSL #1
MOV $d, $d, LSL #2
AND $t, $n, #(3<<counter)
[ counter <> 0
MOV $t, $t, LSR #counter
]
ORR $d, $d, $t
ADD $t, $o, $x, LSL #1
CMP $d, $t
SUBGE $d, $d, $t
ADDGE $x, $x, #1
counter SETA counter-2
WEND
counter SETA 14
WHILE counter < 32
MOV $x, $x, LSL #1
MOV $d, $d, LSL #2
ADD $t, $o, $x, LSL #1
CMP $d, $t
SUBGE $d, $d, $t
ADDGE $x, $x, #1
counter SETA counter-2
WEND
[ $r <> $x
MOV $r, $x
]
MEND
END
00000000 0a 3b 20 73 71 72 74 31 36 0a 3b 20 69 6e 74 65 |.; sqrt16.; inte| 00000010 67 65 72 20 73 71 75 61 72 65 20 72 6f 6f 74 20 |ger square root | 00000020 72 65 74 75 72 6e 69 6e 67 20 31 36 2d 62 69 74 |returning 16-bit| 00000030 20 66 69 78 65 64 20 70 6f 69 6e 74 20 6e 75 6d | fixed point num| 00000040 62 65 72 2c 20 61 73 73 75 6d 69 6e 67 20 78 20 |ber, assuming x | 00000050 69 73 20 31 36 2d 62 69 74 20 66 69 78 65 64 20 |is 16-bit fixed | 00000060 70 6f 69 6e 74 0a 3b 20 69 65 20 72 65 74 75 72 |point.; ie retur| 00000070 6e 73 20 33 32 20 62 69 74 20 73 71 72 74 20 6f |ns 32 bit sqrt o| 00000080 66 20 28 36 35 35 33 36 2a 78 29 0a 3b 0a 3b 20 |f (65536*x).;.; | 00000090 49 74 20 74 61 6b 65 73 20 36 20 70 61 72 61 6d |It takes 6 param| 000000a0 65 74 65 72 73 20 2d 20 61 6c 6c 20 72 65 67 69 |eters - all regi| 000000b0 73 74 65 72 20 6e 61 6d 65 73 0a 3b 0a 3b 20 24 |ster names.;.; $| 000000c0 78 3a 20 20 20 78 0a 3b 20 24 72 3a 20 20 20 72 |x: x.; $r: r| 000000d0 65 73 75 6c 74 20 2d 20 6d 61 79 20 62 65 20 74 |esult - may be t| 000000e0 68 65 20 73 61 6d 65 20 61 73 20 78 0a 3b 20 24 |he same as x.; $| 000000f0 6e 3a 20 20 20 63 6f 70 79 20 6f 66 20 78 20 75 |n: copy of x u| 00000100 73 65 64 20 64 75 72 69 6e 67 20 63 61 6c 63 75 |sed during calcu| 00000110 6c 61 74 69 6f 6e 0a 3b 20 24 74 3a 20 20 20 74 |lation.; $t: t| 00000120 72 61 6e 73 69 65 6e 74 20 73 63 72 61 74 63 68 |ransient scratch| 00000130 0a 3b 20 24 64 3a 20 20 20 72 65 6d 61 69 6e 64 |.; $d: remaind| 00000140 65 72 0a 3b 20 24 6f 3a 20 20 20 63 6f 6e 73 74 |er.; $o: const| 00000150 61 6e 74 20 76 61 6c 75 65 20 6f 66 20 31 0a 3b |ant value of 1.;| 00000160 0a 20 20 20 20 20 20 20 20 4d 41 43 52 4f 0a 24 |. MACRO.$| 00000170 6c 61 62 65 6c 20 20 73 71 72 74 31 36 20 20 24 |label sqrt16 $| 00000180 78 2c 20 24 72 2c 20 24 6e 2c 20 24 74 2c 20 24 |x, $r, $n, $t, $| 00000190 64 2c 20 24 6f 0a 0a 20 20 20 20 20 20 20 20 41 |d, $o.. A| 000001a0 53 53 45 52 54 20 20 24 78 20 3c 3e 20 24 6e 0a |SSERT $x <> $n.| 000001b0 20 20 20 20 20 20 20 20 41 53 53 45 52 54 20 20 | ASSERT | 000001c0 24 78 20 3c 3e 20 24 74 0a 20 20 20 20 20 20 20 |$x <> $t. | 000001d0 20 41 53 53 45 52 54 20 20 24 78 20 3c 3e 20 24 | ASSERT $x <> $| 000001e0 64 0a 20 20 20 20 20 20 20 20 41 53 53 45 52 54 |d. ASSERT| 000001f0 20 20 24 78 20 3c 3e 20 24 6f 0a 20 20 20 20 20 | $x <> $o. | 00000200 20 20 20 41 53 53 45 52 54 20 20 24 6e 20 3c 3e | ASSERT $n <>| 00000210 20 24 74 0a 20 20 20 20 20 20 20 20 41 53 53 45 | $t. ASSE| 00000220 52 54 20 20 24 6e 20 3c 3e 20 24 64 0a 20 20 20 |RT $n <> $d. | 00000230 20 20 20 20 20 41 53 53 45 52 54 20 20 24 6e 20 | ASSERT $n | 00000240 3c 3e 20 24 6f 0a 20 20 20 20 20 20 20 20 41 53 |<> $o. AS| 00000250 53 45 52 54 20 20 24 74 20 3c 3e 20 24 64 0a 20 |SERT $t <> $d. | 00000260 20 20 20 20 20 20 20 41 53 53 45 52 54 20 20 24 | ASSERT $| 00000270 74 20 3c 3e 20 24 6f 0a 20 20 20 20 20 20 20 20 |t <> $o. | 00000280 41 53 53 45 52 54 20 20 24 64 20 3c 3e 20 24 6f |ASSERT $d <> $o| 00000290 0a 0a 20 20 20 20 20 20 20 20 4c 43 4c 41 20 20 |.. LCLA | 000002a0 20 20 63 6f 75 6e 74 65 72 0a 0a 24 6c 61 62 65 | counter..$labe| 000002b0 6c 20 20 4d 4f 56 20 20 20 20 20 24 6e 2c 20 24 |l MOV $n, $| 000002c0 78 0a 20 20 20 20 20 20 20 20 4d 4f 56 20 20 20 |x. MOV | 000002d0 20 20 24 6f 2c 20 23 31 0a 20 20 20 20 20 20 20 | $o, #1. | 000002e0 20 4d 4f 56 20 20 20 20 20 24 78 2c 20 23 30 0a | MOV $x, #0.| 000002f0 20 20 20 20 20 20 20 20 4d 4f 56 20 20 20 20 20 | MOV | 00000300 24 64 2c 20 23 30 0a 0a 20 20 20 20 20 20 20 20 |$d, #0.. | 00000310 41 4e 44 20 20 20 20 20 24 74 2c 20 24 6e 2c 20 |AND $t, $n, | 00000320 23 28 33 3c 3c 33 30 29 0a 20 20 20 20 20 20 20 |#(3<<30). | 00000330 20 4d 4f 56 20 20 20 20 20 24 74 2c 20 24 74 2c | MOV $t, $t,| 00000340 20 4c 53 52 20 23 33 30 0a 20 20 20 20 20 20 20 | LSR #30. | 00000350 20 4f 52 52 20 20 20 20 20 24 64 2c 20 24 64 2c | ORR $d, $d,| 00000360 20 24 74 0a 20 20 20 20 20 20 20 20 41 44 44 20 | $t. ADD | 00000370 20 20 20 20 24 74 2c 20 24 6f 2c 20 24 78 2c 20 | $t, $o, $x, | 00000380 4c 53 4c 20 23 31 0a 20 20 20 20 20 20 20 20 43 |LSL #1. C| 00000390 4d 50 20 20 20 20 20 24 64 2c 20 24 74 0a 20 20 |MP $d, $t. | 000003a0 20 20 20 20 20 20 53 55 42 47 45 20 20 20 24 64 | SUBGE $d| 000003b0 2c 20 24 64 2c 20 24 74 0a 20 20 20 20 20 20 20 |, $d, $t. | 000003c0 20 41 44 44 47 45 20 20 20 24 78 2c 20 24 78 2c | ADDGE $x, $x,| 000003d0 20 23 31 0a 0a 63 6f 75 6e 74 65 72 20 53 45 54 | #1..counter SET| 000003e0 41 20 20 20 20 32 38 0a 20 20 20 20 20 20 20 20 |A 28. | 000003f0 57 48 49 4c 45 20 20 20 63 6f 75 6e 74 65 72 20 |WHILE counter | 00000400 3c 20 33 32 20 20 20 20 20 20 20 20 20 20 20 20 |< 32 | 00000410 20 3b 77 61 6e 74 20 3e 3d 20 30 2c 20 68 6f 77 | ;want >= 0, how| 00000420 65 76 65 72 20 63 6f 75 6e 74 65 72 20 69 73 20 |ever counter is | 00000430 75 6e 73 69 67 6e 65 64 2c 20 73 6f 20 61 66 74 |unsigned, so aft| 00000440 65 72 20 30 20 69 74 20 67 6f 65 73 20 68 69 67 |er 0 it goes hig| 00000450 68 2c 20 74 68 75 73 20 3c 20 33 32 20 77 69 6c |h, thus < 32 wil| 00000460 6c 20 63 61 74 63 68 20 69 74 21 0a 20 20 20 20 |l catch it!. | 00000470 20 20 20 20 4d 4f 56 20 20 20 20 20 24 78 2c 20 | MOV $x, | 00000480 24 78 2c 20 4c 53 4c 20 23 31 0a 20 20 20 20 20 |$x, LSL #1. | 00000490 20 20 20 4d 4f 56 20 20 20 20 20 24 64 2c 20 24 | MOV $d, $| 000004a0 64 2c 20 4c 53 4c 20 23 32 0a 20 20 20 20 20 20 |d, LSL #2. | 000004b0 20 20 41 4e 44 20 20 20 20 20 24 74 2c 20 24 6e | AND $t, $n| 000004c0 2c 20 23 28 33 3c 3c 63 6f 75 6e 74 65 72 29 0a |, #(3<<counter).| 000004d0 20 20 20 20 20 20 20 20 5b 20 20 20 20 20 20 20 | [ | 000004e0 63 6f 75 6e 74 65 72 20 3c 3e 20 30 0a 20 20 20 |counter <> 0. | 000004f0 20 20 20 20 20 4d 4f 56 20 20 20 20 20 24 74 2c | MOV $t,| 00000500 20 24 74 2c 20 4c 53 52 20 23 63 6f 75 6e 74 65 | $t, LSR #counte| 00000510 72 0a 20 20 20 20 20 20 20 20 5d 0a 20 20 20 20 |r. ]. | 00000520 20 20 20 20 4f 52 52 20 20 20 20 20 24 64 2c 20 | ORR $d, | 00000530 24 64 2c 20 24 74 0a 20 20 20 20 20 20 20 20 41 |$d, $t. A| 00000540 44 44 20 20 20 20 20 24 74 2c 20 24 6f 2c 20 24 |DD $t, $o, $| 00000550 78 2c 20 4c 53 4c 20 23 31 0a 20 20 20 20 20 20 |x, LSL #1. | 00000560 20 20 43 4d 50 20 20 20 20 20 24 64 2c 20 24 74 | CMP $d, $t| 00000570 0a 20 20 20 20 20 20 20 20 53 55 42 47 45 20 20 |. SUBGE | 00000580 20 24 64 2c 20 24 64 2c 20 24 74 0a 20 20 20 20 | $d, $d, $t. | 00000590 20 20 20 20 41 44 44 47 45 20 20 20 24 78 2c 20 | ADDGE $x, | 000005a0 24 78 2c 20 23 31 0a 63 6f 75 6e 74 65 72 20 53 |$x, #1.counter S| 000005b0 45 54 41 20 20 20 20 63 6f 75 6e 74 65 72 2d 32 |ETA counter-2| 000005c0 0a 20 20 20 20 20 20 20 20 57 45 4e 44 0a 0a 63 |. WEND..c| 000005d0 6f 75 6e 74 65 72 20 53 45 54 41 20 20 20 20 31 |ounter SETA 1| 000005e0 34 0a 20 20 20 20 20 20 20 20 57 48 49 4c 45 20 |4. WHILE | 000005f0 20 20 63 6f 75 6e 74 65 72 20 3c 20 33 32 0a 20 | counter < 32. | 00000600 20 20 20 20 20 20 20 4d 4f 56 20 20 20 20 20 24 | MOV $| 00000610 78 2c 20 24 78 2c 20 4c 53 4c 20 23 31 0a 20 20 |x, $x, LSL #1. | 00000620 20 20 20 20 20 20 4d 4f 56 20 20 20 20 20 24 64 | MOV $d| 00000630 2c 20 24 64 2c 20 4c 53 4c 20 23 32 0a 20 20 20 |, $d, LSL #2. | 00000640 20 20 20 20 20 41 44 44 20 20 20 20 20 24 74 2c | ADD $t,| 00000650 20 24 6f 2c 20 24 78 2c 20 4c 53 4c 20 23 31 0a | $o, $x, LSL #1.| 00000660 20 20 20 20 20 20 20 20 43 4d 50 20 20 20 20 20 | CMP | 00000670 24 64 2c 20 24 74 0a 20 20 20 20 20 20 20 20 53 |$d, $t. S| 00000680 55 42 47 45 20 20 20 24 64 2c 20 24 64 2c 20 24 |UBGE $d, $d, $| 00000690 74 0a 20 20 20 20 20 20 20 20 41 44 44 47 45 20 |t. ADDGE | 000006a0 20 20 24 78 2c 20 24 78 2c 20 23 31 0a 63 6f 75 | $x, $x, #1.cou| 000006b0 6e 74 65 72 20 53 45 54 41 20 20 20 20 63 6f 75 |nter SETA cou| 000006c0 6e 74 65 72 2d 32 0a 20 20 20 20 20 20 20 20 57 |nter-2. W| 000006d0 45 4e 44 0a 0a 20 20 20 20 20 20 20 20 5b 20 20 |END.. [ | 000006e0 20 20 20 20 20 24 72 20 3c 3e 20 24 78 0a 20 20 | $r <> $x. | 000006f0 20 20 20 20 20 20 4d 4f 56 20 20 20 20 20 24 72 | MOV $r| 00000700 2c 20 24 78 0a 20 20 20 20 20 20 20 20 5d 0a 0a |, $x. ]..| 00000710 20 20 20 20 20 20 20 20 4d 45 4e 44 0a 0a 0a 0a | MEND....| 00000720 20 20 20 20 20 20 20 20 45 4e 44 0a | END.| 0000072c
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