awk — Number Theory

echo "48 18" | awk '{
    a=($1>$2)?$1:$2; b=($1>$2)?$2:$1
    while(b){t=b; b=a%b; a=t}
    printf "gcd(%d,%d) = %d\n", $1, $2, a
}'

awk 'function gcd(a,b){while(b){t=b;b=a%b;a=t}return a}
     NR==1{result=$1} NR>1{result=gcd(result,$1)}
     END{printf "gcd = %d\n", result}' <<'EOF'
120
84
36
EOF

echo "12 18" | awk '{
    a=$1; b=$2; p=a*b
    while(b){t=b; b=a%b; a=t}
    printf "lcm(%d,%d) = %d\n", $1, $2, p/a
}'

echo "15" | awk '{
    n=$1; a=0; b=1
    for(i=1;i<=n;i++){
        printf "%d ", a
        t=a+b; a=b; b=t
    }
    print ""
}'
# Output: 0 1 1 2 3 5 8 13 21 34 55 89 144 233 377

echo "97" | awk '{
    n=$1; prime=1
    if(n<2) prime=0
    for(i=2;i*i<=n;i++){
        if(n%i==0){prime=0; break}
    }
    printf "%d is %s\n", n, (prime?"prime":"not prime")
}'

echo "100" | awk '{
    n=$1
    for(i=2;i<=n;i++) s[i]=1
    for(i=2;i*i<=n;i++){
        if(s[i]) for(j=i*i;j<=n;j+=i) s[j]=0
    }
    for(i=2;i<=n;i++) if(s[i]) printf "%d ", i
    print ""
}'

echo "12" | awk '{
    n=$1; f=1
    for(i=2;i<=n;i++) f*=i
    printf "%d! = %d\n", n, f
}'
# Output: 12! = 479001600

echo "255" | awk '{
    n=$1; bits=""
    if(n==0) bits="0"
    while(n>0){bits=(n%2)bits; n=int(n/2)}
    printf "decimal %d = binary %s\n", $1, bits
}'

echo "11111111" | awk '{
    n=0; len=length($1)
    for(i=1;i<=len;i++){
        bit=substr($1,i,1)
        n=n*2+bit
    }
    printf "binary %s = decimal %d\n", $1, n
}'

awk 'BEGIN{
    for(d=0;d<=16;d++){
        n=d; bits=""
        if(n==0) bits="0"
        while(n>0){bits=(n%2)bits; n=int(n/2)}
        # Convert back
        dec=0; len=length(bits)
        for(i=1;i<=len;i++) dec=dec*2+substr(bits,i,1)
        printf "%3d -> %-8s -> %3d  %s\n", d, bits, dec, (d==dec?"OK":"FAIL")
    }
}'

awk '{
    pct=($2-$1)/$1*100
    printf "%s -> %s: %+.2f%%\n", $1, $2, pct
}' <<'EOF'
100 125
500 475
1024 2048
80 80
EOF

awk '{
    principal=$1; rate=$2/100; years=$3
    result=principal * (1+rate)^years
    printf "$%.2f at %.1f%% for %d years = $%.2f (gain: $%.2f)\n",
        principal, $2, years, result, result-principal
}' <<'EOF'
10000 5.0 10
25000 7.5 30
1000 3.2 5
EOF

awk '{
    rate=$1
    years=72/rate
    printf "At %.1f%% annual return: doubles in ~%.1f years\n", rate, years
}' <<'EOF'
3.0
5.0
7.0
10.0
EOF

awk '{
    val[NR]=$1; sum+=$1
    if(NR>=3){
        avg=(val[NR]+val[NR-1]+val[NR-2])/3
        if(NR>3) sum_old=(val[NR-1]+val[NR-2]+val[NR-3])/3
        printf "point %2d: value=%6.1f  3-pt avg=%6.2f\n", NR, $1, avg
    } else {
        printf "point %2d: value=%6.1f  (warming up)\n", NR, $1
    }
}' <<'EOF'
10.0
12.5
11.0
14.0
13.5
16.0
15.5
18.0
17.0
20.0
EOF

awk 'BEGIN{
    # Matrix A        Matrix B
    a11=1; a12=2;    b11=5; b12=6
    a21=3; a22=4;    b21=7; b22=8

    # C = A * B
    c11=a11*b11+a12*b21; c12=a11*b12+a12*b22
    c21=a21*b11+a22*b21; c22=a21*b12+a22*b22

    printf "A = |%d %d|  B = |%d %d|\n", a11, a12, b11, b12
    printf "    |%d %d|      |%d %d|\n", a21, a22, b21, b22
    printf "\n"
    printf "A*B = |%d %d|\n", c11, c12
    printf "      |%d %d|\n", c21, c22
}'
# Output:
# A = |1 2|  B = |5 6|
#     |3 4|      |7 8|
#
# A*B = |19 22|
#       |43 50|

awk 'BEGIN{
    pi=atan2(0,-1)
    # Rotate point (3,4) by 90 degrees
    x=3; y=4; deg=90
    rad=deg*pi/180
    rx=x*cos(rad)-y*sin(rad)
    ry=x*sin(rad)+y*cos(rad)
    printf "(%g,%g) rotated %d° = (%.4f, %.4f)\n", x, y, deg, rx, ry
}'
# Output: (3,4) rotated 90° = (-4.0000, 3.0000)