Home » Archimedes archive » Acorn User » AU 1997-10 A.adf » Extras » Apple][e/PD/BOB/ARMBOB/!ArmBob/progs/ArithSqrt
Apple][e/PD/BOB/ARMBOB/!ArmBob/progs/ArithSqrt
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 User » AU 1997-10 A.adf » Extras |
| Filename: | Apple][e/PD/BOB/ARMBOB/!ArmBob/progs/ArithSqrt |
| Read OK: | ✔ |
| File size: | 0822 bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
/* ArithSqrt
Standard arithmetical integer square root algorithm
*/
main()
{
local i;
mode(27);
print( "Standard arithmetical integer square root algorithm\n\n" );
print( " ----- ArmBob -----\n" );
print( "integer N rounded �N sqrt(N) rdd(sqrt(N))\n" );
for (i = 1; i < 31; i ++)
{
N = (1 << i) - 1;
r = arithsqrt( N );
print( "\nN =",format( N,11,3 ));
print( " �N =",format( r,6,3 ));
s = sqrt( 1.0*N ); /* built-in sqrt() */
t = floor( s + 0.5 );
print(format( s,12,2 ));
print(format( t,8,3 ));
}
print( "\n" );
}
arithsqrt(b)
{
u = b;
v = 1 << 6;
n = 3;
repeat
{
u >>= 6;
if (u != 0)
{ n += 3; v <<= 6; }
}
until (u == 0);
if (n > 15)
{ v = 1 << 30; n = 15; }
v = 1 << 30; n = 15;
repeat
{
d = u + v;
u >>= 1;
if (b >= d) { b -= d; u += v; }
v >>= 2;
n --;
}
until (n < 0);
if (b > u) u ++;
return u;
}
format(n,l,p)
{
local dec,i,int,neg,s;
s = "";
switch (typeof(n))
{
case REAL:
if (neg = (n < 0.0)) n = -n;
int = floor(n);
if (neg) s = "-";
s += int_10(int);
s += ".";
dec = n - 1.0*int;
for (i = 0; i < p; i ++) dec *= 10.0;
dec = floor(dec + 0.5);
d = "";
for (i = 0;i < p; i ++)
{ d = '0' + dec%10 + d; dec /= 10; }
s += d;
break;
case INTEGER:
if (neg = (n < 0)) n = -n;
if (neg) s = "-";
s += int_10(n);
break;
case STRING:
s = n;
break;
default:
s = "first argument not real, integer or string";
}
for (i = l - sizeof(s); i > 0; i --) s = " " + s;
return s;
}
int_10(n)
{
local s;
s = "";
if (n == 0) s = "0";
else while(n) { s = '0' + n%10 + s; n /= 10; }
return s;
}
vdu(s)
{
local out,i;
out = fopen("rawvdu:","w");
for(i=0;i<sizeof(s);putc(s[i++],out));
fclose(out);
}
mode(n)
{ vdu(""+22+n); }
00000000 2f 2a 20 41 72 69 74 68 53 71 72 74 0a 20 53 74 |/* ArithSqrt. St|
00000010 61 6e 64 61 72 64 20 61 72 69 74 68 6d 65 74 69 |andard arithmeti|
00000020 63 61 6c 20 69 6e 74 65 67 65 72 20 73 71 75 61 |cal integer squa|
00000030 72 65 20 72 6f 6f 74 20 61 6c 67 6f 72 69 74 68 |re root algorith|
00000040 6d 0a 2a 2f 0a 0a 6d 61 69 6e 28 29 0a 20 7b 0a |m.*/..main(). {.|
00000050 20 20 6c 6f 63 61 6c 20 69 3b 0a 20 20 6d 6f 64 | local i;. mod|
00000060 65 28 32 37 29 3b 0a 20 20 70 72 69 6e 74 28 20 |e(27);. print( |
00000070 22 53 74 61 6e 64 61 72 64 20 61 72 69 74 68 6d |"Standard arithm|
00000080 65 74 69 63 61 6c 20 69 6e 74 65 67 65 72 20 73 |etical integer s|
00000090 71 75 61 72 65 20 72 6f 6f 74 20 61 6c 67 6f 72 |quare root algor|
000000a0 69 74 68 6d 5c 6e 5c 6e 22 20 29 3b 0a 20 20 70 |ithm\n\n" );. p|
000000b0 72 69 6e 74 28 20 22 20 20 20 20 20 20 20 20 20 |rint( " |
000000c0 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 | |
000000d0 20 20 20 20 20 20 20 20 20 2d 2d 2d 2d 2d 20 20 | ----- |
000000e0 41 72 6d 42 6f 62 20 20 2d 2d 2d 2d 2d 5c 6e 22 |ArmBob -----\n"|
000000f0 20 29 3b 0a 20 20 70 72 69 6e 74 28 20 22 69 6e | );. print( "in|
00000100 74 65 67 65 72 20 4e 20 20 20 20 20 20 20 20 20 |teger N |
00000110 72 6f 75 6e 64 65 64 20 80 4e 20 20 20 20 20 20 |rounded .N |
00000120 73 71 72 74 28 4e 29 20 20 72 64 64 28 73 71 72 |sqrt(N) rdd(sqr|
00000130 74 28 4e 29 29 5c 6e 22 20 29 3b 0a 20 20 66 6f |t(N))\n" );. fo|
00000140 72 20 28 69 20 3d 20 31 3b 20 69 20 3c 20 33 31 |r (i = 1; i < 31|
00000150 3b 20 69 20 2b 2b 29 0a 20 20 20 7b 0a 20 20 20 |; i ++). {. |
00000160 20 4e 20 3d 20 28 31 20 3c 3c 20 69 29 20 2d 20 | N = (1 << i) - |
00000170 31 3b 0a 20 20 20 20 72 20 3d 20 61 72 69 74 68 |1;. r = arith|
00000180 73 71 72 74 28 20 4e 20 29 3b 0a 20 20 20 20 70 |sqrt( N );. p|
00000190 72 69 6e 74 28 20 22 5c 6e 4e 20 3d 22 2c 66 6f |rint( "\nN =",fo|
000001a0 72 6d 61 74 28 20 4e 2c 31 31 2c 33 20 29 29 3b |rmat( N,11,3 ));|
000001b0 0a 20 20 20 20 70 72 69 6e 74 28 20 22 20 20 20 |. print( " |
000001c0 20 80 4e 20 3d 22 2c 66 6f 72 6d 61 74 28 20 72 | .N =",format( r|
000001d0 2c 36 2c 33 20 29 29 3b 0a 20 20 20 20 73 20 3d |,6,3 ));. s =|
000001e0 20 73 71 72 74 28 20 31 2e 30 2a 4e 20 29 3b 20 | sqrt( 1.0*N ); |
000001f0 2f 2a 20 62 75 69 6c 74 2d 69 6e 20 73 71 72 74 |/* built-in sqrt|
00000200 28 29 20 2a 2f 0a 20 20 20 20 74 20 3d 20 66 6c |() */. t = fl|
00000210 6f 6f 72 28 20 73 20 2b 20 30 2e 35 20 29 3b 0a |oor( s + 0.5 );.|
00000220 20 20 20 20 70 72 69 6e 74 28 66 6f 72 6d 61 74 | print(format|
00000230 28 20 73 2c 31 32 2c 32 20 29 29 3b 0a 20 20 20 |( s,12,2 ));. |
00000240 20 70 72 69 6e 74 28 66 6f 72 6d 61 74 28 20 74 | print(format( t|
00000250 2c 38 2c 33 20 29 29 3b 0a 20 20 20 7d 0a 20 20 |,8,3 ));. }. |
00000260 20 70 72 69 6e 74 28 20 22 5c 6e 22 20 29 3b 0a | print( "\n" );.|
00000270 20 7d 0a 20 0a 61 72 69 74 68 73 71 72 74 28 62 | }. .arithsqrt(b|
00000280 29 0a 20 7b 0a 20 20 20 75 20 3d 20 62 3b 0a 20 |). {. u = b;. |
00000290 20 20 76 20 3d 20 31 20 3c 3c 20 36 3b 0a 20 20 | v = 1 << 6;. |
000002a0 20 6e 20 3d 20 33 3b 0a 20 20 20 72 65 70 65 61 | n = 3;. repea|
000002b0 74 0a 20 20 20 20 7b 0a 20 20 20 20 20 20 75 20 |t. {. u |
000002c0 3e 3e 3d 20 36 3b 0a 20 20 20 20 20 20 69 66 20 |>>= 6;. if |
000002d0 28 75 20 21 3d 20 30 29 0a 20 20 20 20 20 20 20 |(u != 0). |
000002e0 7b 20 6e 20 2b 3d 20 33 3b 20 76 20 3c 3c 3d 20 |{ n += 3; v <<= |
000002f0 36 3b 20 7d 0a 20 20 20 20 7d 0a 20 20 20 75 6e |6; }. }. un|
00000300 74 69 6c 20 28 75 20 3d 3d 20 30 29 3b 0a 20 20 |til (u == 0);. |
00000310 20 69 66 20 28 6e 20 3e 20 31 35 29 0a 20 20 20 | if (n > 15). |
00000320 20 7b 20 76 20 3d 20 31 20 3c 3c 20 33 30 3b 20 | { v = 1 << 30; |
00000330 6e 20 3d 20 31 35 3b 20 7d 0a 20 20 20 76 20 3d |n = 15; }. v =|
00000340 20 31 20 3c 3c 20 33 30 3b 20 6e 20 3d 20 31 35 | 1 << 30; n = 15|
00000350 3b 0a 20 20 20 72 65 70 65 61 74 0a 20 20 20 20 |;. repeat. |
00000360 7b 0a 20 20 20 20 20 20 64 20 3d 20 75 20 2b 20 |{. d = u + |
00000370 76 3b 0a 20 20 20 20 20 20 75 20 3e 3e 3d 20 31 |v;. u >>= 1|
00000380 3b 0a 20 20 20 20 20 20 69 66 20 28 62 20 3e 3d |;. if (b >=|
00000390 20 64 29 20 7b 20 62 20 2d 3d 20 64 3b 20 75 20 | d) { b -= d; u |
000003a0 2b 3d 20 76 3b 20 7d 0a 20 20 20 20 20 20 76 20 |+= v; }. v |
000003b0 3e 3e 3d 20 32 3b 0a 20 20 20 20 20 20 6e 20 2d |>>= 2;. n -|
000003c0 2d 3b 0a 20 20 20 20 7d 0a 20 20 20 75 6e 74 69 |-;. }. unti|
000003d0 6c 20 28 6e 20 3c 20 30 29 3b 0a 20 20 20 69 66 |l (n < 0);. if|
000003e0 20 28 62 20 3e 20 75 29 20 75 20 2b 2b 3b 0a 20 | (b > u) u ++;. |
000003f0 20 20 72 65 74 75 72 6e 20 75 3b 0a 20 7d 0a 20 | return u;. }. |
00000400 20 20 20 20 0a 66 6f 72 6d 61 74 28 6e 2c 6c 2c | .format(n,l,|
00000410 70 29 0a 7b 0a 20 20 6c 6f 63 61 6c 20 64 65 63 |p).{. local dec|
00000420 2c 69 2c 69 6e 74 2c 6e 65 67 2c 73 3b 0a 20 20 |,i,int,neg,s;. |
00000430 73 20 3d 20 22 22 3b 0a 20 20 73 77 69 74 63 68 |s = "";. switch|
00000440 20 28 74 79 70 65 6f 66 28 6e 29 29 0a 20 20 20 | (typeof(n)). |
00000450 20 7b 0a 20 20 20 20 20 20 63 61 73 65 20 52 45 | {. case RE|
00000460 41 4c 3a 0a 20 20 20 20 20 20 20 20 69 66 20 28 |AL:. if (|
00000470 6e 65 67 20 3d 20 28 6e 20 3c 20 30 2e 30 29 29 |neg = (n < 0.0))|
00000480 20 6e 20 3d 20 2d 6e 3b 0a 20 20 20 20 20 20 20 | n = -n;. |
00000490 20 69 6e 74 20 3d 20 66 6c 6f 6f 72 28 6e 29 3b | int = floor(n);|
000004a0 0a 20 20 20 20 20 20 20 20 69 66 20 28 6e 65 67 |. if (neg|
000004b0 29 20 73 20 3d 20 22 2d 22 3b 0a 20 20 20 20 20 |) s = "-";. |
000004c0 20 20 20 73 20 2b 3d 20 69 6e 74 5f 31 30 28 69 | s += int_10(i|
000004d0 6e 74 29 3b 0a 20 20 20 20 20 20 20 20 73 20 2b |nt);. s +|
000004e0 3d 20 22 2e 22 3b 0a 20 20 20 20 20 20 20 20 64 |= ".";. d|
000004f0 65 63 20 3d 20 6e 20 2d 20 31 2e 30 2a 69 6e 74 |ec = n - 1.0*int|
00000500 3b 20 0a 20 20 20 20 20 20 20 20 66 6f 72 20 28 |; . for (|
00000510 69 20 3d 20 30 3b 20 69 20 3c 20 70 3b 20 69 20 |i = 0; i < p; i |
00000520 2b 2b 29 20 64 65 63 20 2a 3d 20 31 30 2e 30 3b |++) dec *= 10.0;|
00000530 0a 20 20 20 20 20 20 20 20 64 65 63 20 3d 20 66 |. dec = f|
00000540 6c 6f 6f 72 28 64 65 63 20 2b 20 30 2e 35 29 3b |loor(dec + 0.5);|
00000550 0a 20 20 20 20 20 20 20 20 64 20 3d 20 22 22 3b |. d = "";|
00000560 0a 20 20 20 20 20 20 20 20 66 6f 72 20 28 69 20 |. for (i |
00000570 3d 20 30 3b 69 20 3c 20 70 3b 20 69 20 2b 2b 29 |= 0;i < p; i ++)|
00000580 0a 20 20 20 20 20 20 20 20 20 20 7b 20 64 20 20 |. { d |
00000590 3d 20 27 30 27 20 2b 20 64 65 63 25 31 30 20 2b |= '0' + dec%10 +|
000005a0 20 64 3b 20 64 65 63 20 2f 3d 20 31 30 3b 20 7d | d; dec /= 10; }|
000005b0 0a 20 20 20 20 20 20 20 20 73 20 2b 3d 20 64 3b |. s += d;|
000005c0 0a 20 20 20 20 20 20 20 20 62 72 65 61 6b 3b 0a |. break;.|
000005d0 20 20 20 20 20 20 63 61 73 65 20 49 4e 54 45 47 | case INTEG|
000005e0 45 52 3a 0a 20 20 20 20 20 20 20 20 69 66 20 28 |ER:. if (|
000005f0 6e 65 67 20 3d 20 28 6e 20 3c 20 30 29 29 20 6e |neg = (n < 0)) n|
00000600 20 3d 20 2d 6e 3b 0a 20 20 20 20 20 20 20 20 69 | = -n;. i|
00000610 66 20 28 6e 65 67 29 20 73 20 3d 20 22 2d 22 3b |f (neg) s = "-";|
00000620 0a 20 20 20 20 20 20 20 20 73 20 2b 3d 20 69 6e |. s += in|
00000630 74 5f 31 30 28 6e 29 3b 0a 20 20 20 20 20 20 20 |t_10(n);. |
00000640 20 62 72 65 61 6b 3b 0a 20 20 20 20 20 20 63 61 | break;. ca|
00000650 73 65 20 53 54 52 49 4e 47 3a 0a 20 20 20 20 20 |se STRING:. |
00000660 20 20 20 73 20 3d 20 6e 3b 20 20 20 20 20 20 20 | s = n; |
00000670 20 0a 20 20 20 20 20 20 20 20 62 72 65 61 6b 3b | . break;|
00000680 0a 20 20 20 20 20 20 64 65 66 61 75 6c 74 3a 0a |. default:.|
00000690 20 20 20 20 20 20 20 20 73 20 3d 20 22 66 69 72 | s = "fir|
000006a0 73 74 20 61 72 67 75 6d 65 6e 74 20 6e 6f 74 20 |st argument not |
000006b0 72 65 61 6c 2c 20 69 6e 74 65 67 65 72 20 6f 72 |real, integer or|
000006c0 20 73 74 72 69 6e 67 22 3b 20 20 20 20 20 20 20 | string"; |
000006d0 20 0a 20 20 20 20 7d 0a 20 20 66 6f 72 20 28 69 | . }. for (i|
000006e0 20 3d 20 6c 20 2d 20 73 69 7a 65 6f 66 28 73 29 | = l - sizeof(s)|
000006f0 3b 20 69 20 3e 20 30 3b 20 69 20 2d 2d 29 20 73 |; i > 0; i --) s|
00000700 20 3d 20 22 20 22 20 2b 20 73 3b 0a 20 20 72 65 | = " " + s;. re|
00000710 74 75 72 6e 20 73 3b 0a 7d 0a 20 0a 69 6e 74 5f |turn s;.}. .int_|
00000720 31 30 28 6e 29 0a 7b 0a 20 20 6c 6f 63 61 6c 20 |10(n).{. local |
00000730 73 3b 0a 20 20 73 20 3d 20 22 22 3b 0a 20 20 69 |s;. s = "";. i|
00000740 66 20 28 6e 20 3d 3d 20 30 29 20 73 20 3d 20 22 |f (n == 0) s = "|
00000750 30 22 3b 0a 20 20 65 6c 73 65 20 77 68 69 6c 65 |0";. else while|
00000760 28 6e 29 20 7b 20 73 20 3d 20 27 30 27 20 2b 20 |(n) { s = '0' + |
00000770 6e 25 31 30 20 2b 20 73 3b 20 6e 20 2f 3d 20 31 |n%10 + s; n /= 1|
00000780 30 3b 20 7d 0a 20 20 72 65 74 75 72 6e 20 73 3b |0; }. return s;|
00000790 0a 7d 0a 0a 76 64 75 28 73 29 0a 20 7b 0a 20 20 |.}..vdu(s). {. |
000007a0 6c 6f 63 61 6c 20 6f 75 74 2c 69 3b 0a 20 20 6f |local out,i;. o|
000007b0 75 74 20 3d 20 66 6f 70 65 6e 28 22 72 61 77 76 |ut = fopen("rawv|
000007c0 64 75 3a 22 2c 22 77 22 29 3b 0a 20 20 66 6f 72 |du:","w");. for|
000007d0 28 69 3d 30 3b 69 3c 73 69 7a 65 6f 66 28 73 29 |(i=0;i<sizeof(s)|
000007e0 3b 70 75 74 63 28 73 5b 69 2b 2b 5d 2c 6f 75 74 |;putc(s[i++],out|
000007f0 29 29 3b 0a 20 20 66 63 6c 6f 73 65 28 6f 75 74 |));. fclose(out|
00000800 29 3b 0a 20 7d 0a 0a 6d 6f 64 65 28 6e 29 0a 20 |);. }..mode(n). |
00000810 7b 20 76 64 75 28 22 22 2b 32 32 2b 6e 29 3b 20 |{ vdu(""+22+n); |
00000820 7d 0a |}.|
00000822 
.