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def sqr3(a,b,c): d=a+b+c #roughly 75% of cases exceed the original bit-width d*=d e=a-b+c #roughly 1/6 of the time this will exceed the original bit-width. However, whenever this exceeds the bit-width, then d also exceeds it. e*=e d=(d+e)/2 e=d-e f=(a+b-c)*(a-b-c) #it is never the case that both multiplicands exceed their original word width, but about 1/3 of the time, one of them exceeds it (~2/3 of the time, neither exceed). b*=(a-c) #neither multiplicand exceeds the original bit-width (though the second operand may become negative). b+=b a*=a e=(e+b)/2 b=e-b d=(d-f)/2 f+=d-a return [a,e,d,b,f]