509 lines
12 KiB
Lua
509 lines
12 KiB
Lua
local unpack = unpack or table.unpack
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local function add(a, b)
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local a00, a01, a02, a03, a04, a05, a06, a07, a08, a09, a10, a11 = unpack(a)
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local b00, b01, b02, b03, b04, b05, b06, b07, b08, b09, b10, b11 = unpack(b)
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return {
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a00 + b00,
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a01 + b01,
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a02 + b02,
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a03 + b03,
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a04 + b04,
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a05 + b05,
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a06 + b06,
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a07 + b07,
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a08 + b08,
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a09 + b09,
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a10 + b10,
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a11 + b11,
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}
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end
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local function sub(a, b)
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local a00, a01, a02, a03, a04, a05, a06, a07, a08, a09, a10, a11 = unpack(a)
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local b00, b01, b02, b03, b04, b05, b06, b07, b08, b09, b10, b11 = unpack(b)
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return {
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a00 - b00,
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a01 - b01,
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a02 - b02,
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a03 - b03,
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a04 - b04,
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a05 - b05,
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a06 - b06,
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a07 - b07,
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a08 - b08,
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a09 - b09,
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a10 - b10,
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a11 - b11,
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}
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end
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local function kmul(a, k)
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local a00, a01, a02, a03, a04, a05, a06, a07, a08, a09, a10, a11 = unpack(a)
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local c00, c01, c02, c03, c04, c05, c06, c07, c08, c09, c10, c11
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-- Multiply.
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c00 = a00 * k
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c01 = a01 * k
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c02 = a02 * k
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c03 = a03 * k
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c04 = a04 * k
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c05 = a05 * k
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c06 = a06 * k
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c07 = a07 * k
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c08 = a08 * k
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c09 = a09 * k
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c10 = a10 * k
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c11 = a11 * k
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-- Carry and reduce.
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a11 = c11 % 2 ^ 255 c00 = c00 + (c11 - a11) * (19 / 2 ^ 255)
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a00 = c00 % 2 ^ 22 c01 = c01 + (c00 - a00)
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a01 = c01 % 2 ^ 43 c02 = c02 + (c01 - a01)
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a02 = c02 % 2 ^ 64 c03 = c03 + (c02 - a02)
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a03 = c03 % 2 ^ 85 c04 = c04 + (c03 - a03)
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a04 = c04 % 2 ^ 107 c05 = c05 + (c04 - a04)
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a05 = c05 % 2 ^ 128 c06 = c06 + (c05 - a05)
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a06 = c06 % 2 ^ 149 c07 = c07 + (c06 - a06)
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a07 = c07 % 2 ^ 170 c08 = c08 + (c07 - a07)
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a08 = c08 % 2 ^ 192 c09 = c09 + (c08 - a08)
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a09 = c09 % 2 ^ 213 c10 = c10 + (c09 - a09)
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a10 = c10 % 2 ^ 234 c11 = a11 + (c10 - a10)
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a11 = c11 % 2 ^ 255 a00 = a00 + (c11 - a11) * (19 / 2 ^ 255)
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return {a00, a01, a02, a03, a04, a05, a06, a07, a08, a09, a10, a11}
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end
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local function mul(a, b)
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local a00, a01, a02, a03, a04, a05, a06, a07, a08, a09, a10, a11 = unpack(a)
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local b00, b01, b02, b03, b04, b05, b06, b07, b08, b09, b10, b11 = unpack(b)
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local c00, c01, c02, c03, c04, c05, c06, c07, c08, c09, c10, c11
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-- Multiply high half.
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c00 = a11 * b01
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+ a10 * b02
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+ a09 * b03
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+ a08 * b04
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+ a07 * b05
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+ a06 * b06
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+ a05 * b07
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+ a04 * b08
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+ a03 * b09
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+ a02 * b10
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+ a01 * b11
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c01 = a11 * b02
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+ a10 * b03
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+ a09 * b04
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+ a08 * b05
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+ a07 * b06
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+ a06 * b07
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+ a05 * b08
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+ a04 * b09
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+ a03 * b10
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+ a02 * b11
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c02 = a11 * b03
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+ a10 * b04
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+ a09 * b05
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+ a08 * b06
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+ a07 * b07
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+ a06 * b08
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+ a05 * b09
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+ a04 * b10
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+ a03 * b11
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c03 = a11 * b04
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+ a10 * b05
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+ a09 * b06
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+ a08 * b07
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+ a07 * b08
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+ a06 * b09
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+ a05 * b10
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+ a04 * b11
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c04 = a11 * b05
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+ a10 * b06
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+ a09 * b07
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+ a08 * b08
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+ a07 * b09
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+ a06 * b10
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+ a05 * b11
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c05 = a11 * b06
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+ a10 * b07
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+ a09 * b08
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+ a08 * b09
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+ a07 * b10
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+ a06 * b11
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c06 = a11 * b07
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+ a10 * b08
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+ a09 * b09
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+ a08 * b10
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+ a07 * b11
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c07 = a11 * b08
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+ a10 * b09
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+ a09 * b10
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+ a08 * b11
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c08 = a11 * b09
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+ a10 * b10
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+ a09 * b11
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c09 = a11 * b10
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+ a10 * b11
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c10 = a11 * b11
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-- Multiply low half with reduction.
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c00 = c00 * (19 / 2 ^ 255)
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+ a00 * b00
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c01 = c01 * (19 / 2 ^ 255)
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+ a01 * b00
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+ a00 * b01
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c02 = c02 * (19 / 2 ^ 255)
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+ a02 * b00
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+ a01 * b01
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+ a00 * b02
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c03 = c03 * (19 / 2 ^ 255)
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+ a03 * b00
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+ a02 * b01
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+ a01 * b02
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+ a00 * b03
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c04 = c04 * (19 / 2 ^ 255)
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+ a04 * b00
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+ a03 * b01
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+ a02 * b02
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+ a01 * b03
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+ a00 * b04
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c05 = c05 * (19 / 2 ^ 255)
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+ a05 * b00
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+ a04 * b01
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+ a03 * b02
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+ a02 * b03
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+ a01 * b04
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+ a00 * b05
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c06 = c06 * (19 / 2 ^ 255)
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+ a06 * b00
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+ a05 * b01
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+ a04 * b02
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+ a03 * b03
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+ a02 * b04
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+ a01 * b05
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+ a00 * b06
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c07 = c07 * (19 / 2 ^ 255)
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+ a07 * b00
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+ a06 * b01
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+ a05 * b02
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+ a04 * b03
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+ a03 * b04
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+ a02 * b05
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+ a01 * b06
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+ a00 * b07
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c08 = c08 * (19 / 2 ^ 255)
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+ a08 * b00
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+ a07 * b01
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+ a06 * b02
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+ a05 * b03
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+ a04 * b04
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+ a03 * b05
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+ a02 * b06
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+ a01 * b07
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+ a00 * b08
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c09 = c09 * (19 / 2 ^ 255)
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+ a09 * b00
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+ a08 * b01
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+ a07 * b02
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+ a06 * b03
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+ a05 * b04
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+ a04 * b05
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+ a03 * b06
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+ a02 * b07
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+ a01 * b08
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+ a00 * b09
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c10 = c10 * (19 / 2 ^ 255)
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+ a10 * b00
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+ a09 * b01
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+ a08 * b02
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+ a07 * b03
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+ a06 * b04
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+ a05 * b05
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+ a04 * b06
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+ a03 * b07
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+ a02 * b08
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+ a01 * b09
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+ a00 * b10
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c11 = a11 * b00
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+ a10 * b01
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+ a09 * b02
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+ a08 * b03
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+ a07 * b04
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+ a06 * b05
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+ a05 * b06
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+ a04 * b07
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+ a03 * b08
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+ a02 * b09
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+ a01 * b10
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+ a00 * b11
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-- Carry and reduce.
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a10 = c10 % 2 ^ 234 c11 = c11 + (c10 - a10)
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a11 = c11 % 2 ^ 255 c00 = c00 + (c11 - a11) * (19 / 2 ^ 255)
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a00 = c00 % 2 ^ 22 c01 = c01 + (c00 - a00)
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a01 = c01 % 2 ^ 43 c02 = c02 + (c01 - a01)
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a02 = c02 % 2 ^ 64 c03 = c03 + (c02 - a02)
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a03 = c03 % 2 ^ 85 c04 = c04 + (c03 - a03)
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a04 = c04 % 2 ^ 107 c05 = c05 + (c04 - a04)
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a05 = c05 % 2 ^ 128 c06 = c06 + (c05 - a05)
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a06 = c06 % 2 ^ 149 c07 = c07 + (c06 - a06)
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a07 = c07 % 2 ^ 170 c08 = c08 + (c07 - a07)
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a08 = c08 % 2 ^ 192 c09 = c09 + (c08 - a08)
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a09 = c09 % 2 ^ 213 c10 = a10 + (c09 - a09)
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a10 = c10 % 2 ^ 234 c11 = a11 + (c10 - a10)
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a11 = c11 % 2 ^ 255 a00 = a00 + (c11 - a11) * (19 / 2 ^ 255)
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return {a00, a01, a02, a03, a04, a05, a06, a07, a08, a09, a10, a11}
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end
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local function square(a)
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local a00, a01, a02, a03, a04, a05, a06, a07, a08, a09, a10, a11 = unpack(a)
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local d00, d01, d02, d03, d04, d05, d06, d07, d08, d09, d10
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local c00, c01, c02, c03, c04, c05, c06, c07, c08, c09, c10, c11
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-- Compute 2a.
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d00 = a00 + a00
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d01 = a01 + a01
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d02 = a02 + a02
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d03 = a03 + a03
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d04 = a04 + a04
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d05 = a05 + a05
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d06 = a06 + a06
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d07 = a07 + a07
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d08 = a08 + a08
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d09 = a09 + a09
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d10 = a10 + a10
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-- Multiply high half.
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c00 = a11 * d01
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+ a10 * d02
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+ a09 * d03
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+ a08 * d04
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+ a07 * d05
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+ a06 * a06
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c01 = a11 * d02
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+ a10 * d03
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+ a09 * d04
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+ a08 * d05
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+ a07 * d06
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c02 = a11 * d03
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+ a10 * d04
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+ a09 * d05
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+ a08 * d06
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+ a07 * a07
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c03 = a11 * d04
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+ a10 * d05
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+ a09 * d06
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+ a08 * d07
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c04 = a11 * d05
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+ a10 * d06
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+ a09 * d07
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+ a08 * a08
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c05 = a11 * d06
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+ a10 * d07
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+ a09 * d08
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c06 = a11 * d07
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+ a10 * d08
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+ a09 * a09
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c07 = a11 * d08
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+ a10 * d09
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c08 = a11 * d09
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+ a10 * a10
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c09 = a11 * d10
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c10 = a11 * a11
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-- Multiply low half with reduction.
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c00 = c00 * (19 / 2 ^ 255)
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+ a00 * a00
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c01 = c01 * (19 / 2 ^ 255)
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+ a01 * d00
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c02 = c02 * (19 / 2 ^ 255)
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+ a02 * d00
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+ a01 * a01
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c03 = c03 * (19 / 2 ^ 255)
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+ a03 * d00
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+ a02 * d01
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c04 = c04 * (19 / 2 ^ 255)
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+ a04 * d00
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+ a03 * d01
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+ a02 * a02
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c05 = c05 * (19 / 2 ^ 255)
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+ a05 * d00
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+ a04 * d01
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+ a03 * d02
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c06 = c06 * (19 / 2 ^ 255)
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+ a06 * d00
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+ a05 * d01
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+ a04 * d02
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+ a03 * a03
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c07 = c07 * (19 / 2 ^ 255)
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+ a07 * d00
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+ a06 * d01
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+ a05 * d02
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+ a04 * d03
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c08 = c08 * (19 / 2 ^ 255)
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+ a08 * d00
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+ a07 * d01
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+ a06 * d02
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+ a05 * d03
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+ a04 * a04
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c09 = c09 * (19 / 2 ^ 255)
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+ a09 * d00
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+ a08 * d01
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+ a07 * d02
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+ a06 * d03
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+ a05 * d04
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c10 = c10 * (19 / 2 ^ 255)
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+ a10 * d00
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+ a09 * d01
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+ a08 * d02
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+ a07 * d03
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+ a06 * d04
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+ a05 * a05
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c11 = a11 * d00
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+ a10 * d01
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+ a09 * d02
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+ a08 * d03
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+ a07 * d04
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+ a06 * d05
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-- Carry and reduce.
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a10 = c10 % 2 ^ 234 c11 = c11 + (c10 - a10)
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a11 = c11 % 2 ^ 255 c00 = c00 + (c11 - a11) * (19 / 2 ^ 255)
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a00 = c00 % 2 ^ 22 c01 = c01 + (c00 - a00)
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a01 = c01 % 2 ^ 43 c02 = c02 + (c01 - a01)
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a02 = c02 % 2 ^ 64 c03 = c03 + (c02 - a02)
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a03 = c03 % 2 ^ 85 c04 = c04 + (c03 - a03)
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a04 = c04 % 2 ^ 107 c05 = c05 + (c04 - a04)
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a05 = c05 % 2 ^ 128 c06 = c06 + (c05 - a05)
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a06 = c06 % 2 ^ 149 c07 = c07 + (c06 - a06)
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a07 = c07 % 2 ^ 170 c08 = c08 + (c07 - a07)
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a08 = c08 % 2 ^ 192 c09 = c09 + (c08 - a08)
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a09 = c09 % 2 ^ 213 c10 = a10 + (c09 - a09)
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a10 = c10 % 2 ^ 234 c11 = a11 + (c10 - a10)
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a11 = c11 % 2 ^ 255 a00 = a00 + (c11 - a11) * (19 / 2 ^ 255)
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return {a00, a01, a02, a03, a04, a05, a06, a07, a08, a09, a10, a11}
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end
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local function nsquare(a, n)
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for _ = 1, n do a = square(a) end
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return a
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end
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local function invert(a)
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local a2 = square(a)
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local a9 = mul(a, nsquare(a2, 2))
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local a11 = mul(a9, a2)
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local x5 = mul(square(a11), a9)
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local x10 = mul(nsquare(x5, 5), x5)
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local x20 = mul(nsquare(x10, 10), x10)
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local x40 = mul(nsquare(x20, 20), x20)
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local x50 = mul(nsquare(x40, 10), x10)
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local x100 = mul(nsquare(x50, 50), x50)
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local x200 = mul(nsquare(x100, 100), x100)
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local x250 = mul(nsquare(x200, 50), x50)
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return mul(nsquare(x250, 5), a11)
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end
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local function encode(a)
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local a00, a01, a02, a03, a04, a05, a06, a07, a08, a09, a10, a11 = unpack(a)
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-- Canonicalize.
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if a11 == (2 ^ 21 - 1) * 2 ^ 234
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and a10 == (2 ^ 21 - 1) * 2 ^ 213
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and a09 == (2 ^ 21 - 1) * 2 ^ 192
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and a08 == (2 ^ 22 - 1) * 2 ^ 170
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and a07 == (2 ^ 21 - 1) * 2 ^ 149
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and a06 == (2 ^ 21 - 1) * 2 ^ 128
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and a05 == (2 ^ 21 - 1) * 2 ^ 107
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and a04 == (2 ^ 22 - 1) * 2 ^ 85
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and a03 == (2 ^ 21 - 1) * 2 ^ 64
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and a02 == (2 ^ 21 - 1) * 2 ^ 43
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and a01 == (2 ^ 21 - 1) * 2 ^ 22
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and a00 >= 2 ^ 22 - 19
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then
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a11 = 0
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a10 = 0
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a09 = 0
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a08 = 0
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a07 = 0
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a06 = 0
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a05 = 0
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a04 = 0
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a03 = 0
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a02 = 0
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a01 = 0
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a00 = a00 - (2 ^ 22 - 19)
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end
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-- Encode.
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-- TODO this can be improved.
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local bytes = {}
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local acc = a00
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local function putBytes(n)
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for _ = 1, n do
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local byte = acc % 256
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bytes[#bytes + 1] = byte
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acc = (acc - byte) / 256
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end
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end
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putBytes(2) acc = acc + a01 / 2 ^ 16
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putBytes(3) acc = acc + a02 / 2 ^ 40
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putBytes(3) acc = acc + a03 / 2 ^ 64
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putBytes(2) acc = acc + a04 / 2 ^ 80
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putBytes(3) acc = acc + a05 / 2 ^ 104
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putBytes(3) acc = acc + a06 / 2 ^ 128
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putBytes(2) acc = acc + a07 / 2 ^ 144
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putBytes(3) acc = acc + a08 / 2 ^ 168
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putBytes(3) acc = acc + a09 / 2 ^ 192
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putBytes(2) acc = acc + a10 / 2 ^ 208
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putBytes(3) acc = acc + a11 / 2 ^ 232
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putBytes(3)
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return string.char(unpack(bytes))
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end
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local function decode(b)
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local w00, w01, w02, w03, w04, w05, w06, w07, w08, w09, w10, w11 =
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("<I3I3I2I3I3I2I3I3I2I3I3I2"):unpack(b)
|
|
|
|
w11 = w11 % 2 ^ 15
|
|
|
|
local out = {
|
|
w00,
|
|
w01 * 2 ^ 24,
|
|
w02 * 2 ^ 48,
|
|
w03 * 2 ^ 64,
|
|
w04 * 2 ^ 88,
|
|
w05 * 2 ^ 112,
|
|
w06 * 2 ^ 128,
|
|
w07 * 2 ^ 152,
|
|
w08 * 2 ^ 176,
|
|
w09 * 2 ^ 192,
|
|
w10 * 2 ^ 216,
|
|
w11 * 2 ^ 240,
|
|
}
|
|
|
|
return kmul(out, 1)
|
|
end
|
|
|
|
return {
|
|
add = add,
|
|
sub = sub,
|
|
kmul = kmul,
|
|
mul = mul,
|
|
square = square,
|
|
invert = invert,
|
|
encode = encode,
|
|
decode = decode,
|
|
}
|