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Optimize rpow(x,n,base) #78

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aaad4df
Optimize rpow(x,n,base) for the case x != 0 && n == 0 (291 gas vs 383…
k06a Oct 19, 2019
f71cd48
Simplify overflow check for squaring in rpow(x,n,base)
k06a Oct 19, 2019
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41 changes: 22 additions & 19 deletions src/jug.sol
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Original file line number Diff line number Diff line change
Expand Up @@ -38,27 +38,30 @@ contract Jug is DSNote {

// --- Math ---
function rpow(uint x, uint n, uint b) internal pure returns (uint z) {
assembly {
switch x case 0 {switch n case 0 {z := b} default {z := 0}}
default {
switch mod(n, 2) case 0 { z := b } default { z := x }
let half := div(b, 2) // for rounding.
for { n := div(n, 2) } n { n := div(n,2) } {
let xx := mul(x, x)
if iszero(eq(div(xx, x), x)) { revert(0,0) }
let xxRound := add(xx, half)
if lt(xxRound, xx) { revert(0,0) }
x := div(xxRound, b)
if mod(n,2) {
let zx := mul(z, x)
if and(iszero(iszero(x)), iszero(eq(div(zx, x), z))) { revert(0,0) }
let zxRound := add(zx, half)
if lt(zxRound, zx) { revert(0,0) }
z := div(zxRound, b)
assembly {
switch n case 0 { z := b }
default {
switch x case 0 { z := 0 }
default {
switch mod(n, 2) case 0 { z := b } default { z := x }
let half := div(b, 2) // for rounding.
for { n := div(n, 2) } n { n := div(n,2) } {
let xx := mul(x, x)
if shr(128, x) { revert(0,0) }
let xxRound := add(xx, half)
if lt(xxRound, xx) { revert(0,0) }
x := div(xxRound, b)
if mod(n,2) {
let zx := mul(z, x)
if and(iszero(iszero(x)), iszero(eq(div(zx, x), z))) { revert(0,0) }
let zxRound := add(zx, half)
if lt(zxRound, zx) { revert(0,0) }
z := div(zxRound, b)
}
}
}
}
}
}
}
}
uint256 constant ONE = 10 ** 27;
function add(uint x, uint y) internal pure returns (uint z) {
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33 changes: 18 additions & 15 deletions src/pot.sol
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Expand Up @@ -77,22 +77,25 @@ contract Pot is DSNote {
uint256 constant ONE = 10 ** 27;
function rpow(uint x, uint n, uint base) internal pure returns (uint z) {
assembly {
switch x case 0 {switch n case 0 {z := base} default {z := 0}}
switch n case 0 { z := base }
default {
switch mod(n, 2) case 0 { z := base } default { z := x }
let half := div(base, 2) // for rounding.
for { n := div(n, 2) } n { n := div(n,2) } {
let xx := mul(x, x)
if iszero(eq(div(xx, x), x)) { revert(0,0) }
let xxRound := add(xx, half)
if lt(xxRound, xx) { revert(0,0) }
x := div(xxRound, base)
if mod(n,2) {
let zx := mul(z, x)
if and(iszero(iszero(x)), iszero(eq(div(zx, x), z))) { revert(0,0) }
let zxRound := add(zx, half)
if lt(zxRound, zx) { revert(0,0) }
z := div(zxRound, base)
switch x case 0 { z := 0 }
default {
switch mod(n, 2) case 0 { z := base } default { z := x }
let half := div(base, 2) // for rounding.
for { n := div(n, 2) } n { n := div(n,2) } {
let xx := mul(x, x)
if shr(128, x) { revert(0,0) }
let xxRound := add(xx, half)
if lt(xxRound, xx) { revert(0,0) }
x := div(xxRound, base)
if mod(n,2) {
let zx := mul(z, x)
if and(iszero(iszero(x)), iszero(eq(div(zx, x), z))) { revert(0,0) }
let zxRound := add(zx, half)
if lt(zxRound, zx) { revert(0,0) }
z := div(zxRound, base)
}
}
}
}
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