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February 16, 2024 15:11
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/* | |
Multiplication using U15 Arithmetic | |
X = a*2^15 + b | |
Y = c*2^15 + d | |
Z = X*Y = e*2^45+f*2^30+g*2^15+h | |
Solve for e,f,g,h such that e,f,g,h are each less than 2^15 | |
h = (b*d).lo | |
g = ((a*d).lo+(b*d).hi)+(b*c).lo | |
f = ((((a*d).lo+(b*c).lo+(b*d).hi).carry+(b*c).hi)+(a*d).hi)+(a*c).lo | |
e = (a*c).hi + carries from f | |
then find Z.hi and Z.lo | |
*/ | |
<13371337>#X | |
<69696969>#Y | |
//X = a*2^15 + b | |
{X} | |
OP_SPLIT_U30#a,b | |
//Y = c*2^15 + d | |
{Y} | |
OP_SPLIT_U30#c,d | |
[b] | |
[d] | |
OP_MUL_U15_HI_LO#(b*d).hi,(b*d).lo | |
{(b*d).lo}#h | |
OP_TOALTSTACK // save h to alt stack | |
[a] | |
{d} | |
OP_MUL_U15_HI_LO#(a*d).hi,(a*d).lo | |
{(a*d).lo} | |
{(b*d).hi} | |
OP_ADD_U15_CARRY#carry1,((a*d).lo+(b*d).hi) | |
[c] | |
{b} | |
OP_MUL_U15_HI_LO#(b*c).hi,(b*c).lo | |
{(b*c).lo} | |
{((a*d).lo+(b*d).hi)} | |
OP_ADD_U15_CARRY#carry2,((a*d).lo+(b*d).hi)+(b*c).lo) | |
{((a*d).lo+(b*d).hi)+(b*c).lo)}#g | |
OP_TOALTSTACK //save g to alt stack | |
{carry1} | |
{carry2} | |
OP_ADD#((a*d).lo+(b*c).lo+(b*d).hi).carry | |
{((a*d).lo+(b*c).lo+(b*d).hi).carry} | |
{(b*c).hi} | |
OP_ADD_U15_CARRY#carry3,(((a*d).lo+(b*c).lo+(b*d).hi).carry+(b*c).hi) | |
{(((a*d).lo+(b*c).lo+(b*d).hi).carry+(b*c).hi)} | |
{(a*d).hi} | |
OP_ADD_U15_CARRY#carry4,((((a*d).lo+(b*c).lo+(b*d).hi).carry+(b*c).hi)+(a*d).hi) | |
{a} | |
{c} | |
OP_MUL_U15_HI_LO#(a*c).hi,(a*c).lo | |
{(a*c).lo} | |
{((((a*d).lo+(b*c).lo+(b*d).hi).carry+(b*c).hi)+(a*d).hi)} | |
OP_ADD_U15_CARRY#carry5,f | |
{f} | |
OP_TOALTSTACK // push f to alt stack | |
OP_ADD | |
OP_ADD | |
OP_ADD#e | |
OP_FROMALTSTACK | |
OP_FROMALTSTACK | |
OP_FROMALTSTACK | |
{h} | |
{g} | |
OP_JOIN_U15_HI_LO#Z.lo | |
{f} | |
{e} | |
OP_JOIN_U15_HI_LO#Z.hi | |
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