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The multiplication by ksi computed 9a0 − a1 and 9a1 + a0 with a Montgomery multiplication by 9 followed by a modular subtraction or addition. Add modmuladd9(x, y, mod) computing (9x + y) % mod directly: the sum 9x + y is below 10·mod, so a quotient estimated from its top word is exact or one less, and one conditional subtraction completes the reduction. Multiplying by an integer keeps the Montgomery form, so it works on the internal representation as is. Field elements expose it through the `a * 9 + b` and `a * 9 - b` notation: `a * 9` returns a proxy reduced together with the following addition or subtraction. This reduces the ecpairing cycles by about 4.5% with GCC 15 and 5% with Clang 23.
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The multiplication by ksi computed 9a0 − a1 and 9a1 + a0 with
a Montgomery multiplication by 9 followed by a modular subtraction or
addition.
Add modmuladd9(x, y, mod) computing (9x + y) % mod directly: the sum
9x + y is below 10·mod, so a quotient estimated from its top word is
exact or one less, and one conditional subtraction completes the
reduction. Multiplying by an integer keeps the Montgomery form, so it
works on the internal representation as is.
Field elements expose it through the
a * 9 + banda * 9 - bnotation:
a * 9returns a proxy reduced together with the followingaddition or subtraction.
This reduces the ecpairing cycles by about 4.5% with GCC 15 and 5% with
Clang 23.