Replace ✕ with ×

internal/fp.lua

@@ -210,7 +210,7 @@ end
 --
 -- @tparam fp2 a
 -- @tparam fp2 b
--- @treturn fp1 c ≡ a ✕ b (mod p).
+-- @treturn fp1 c ≡ a × b (mod p).
 --
 local function mul(a, b)
     local a00, a01, a02, a03, a04, a05, a06, a07, a08, a09, a10, a11 = unpack(a)
@@ -564,7 +564,7 @@ end
 --
 -- @tparam fp2 a
 -- @tparam number k A number k in [0..2²²).
--- @treturn fp1 c ≡ a ✕ k (mod p).
+-- @treturn fp1 c ≡ a × k (mod p).
 --
 local function kmul(a, k)
     local a00, a01, a02, a03, a04, a05, a06, a07, a08, a09, a10, a11 = unpack(a)

internal/fq.lua

@@ -61,7 +61,7 @@ local T1 = {
 
 --- Carries a number in base 2²⁴.
 --
--- @tparam {number...} a A number 0 <= a < 2 ^ (24 ✕ (#a + 1)) as limbs in
+-- @tparam {number...} a A number 0 <= a < 2 ^ (24 × (#a + 1)) as limbs in
 -- [-2⁵²..2⁵²].
 -- @treturn {number...} a as #a + 1 limbs in [0..2²⁴).
 --
@@ -98,7 +98,7 @@ end
 --
 -- @tparam {number...} a An array of 11 limbs in [0..2²⁴).
 -- @tparam {number...} b An array of 11 limbs in [0..2²⁴).
--- @treturn {number...} a ✕ b as 22 limbs in [0..2²⁴).
+-- @treturn {number...} a × b as 22 limbs in [0..2²⁴).
 --
 local function intMul(a, b)
     local c = {}
@@ -110,8 +110,8 @@ local function intMul(a, b)
         end
     end
 
-    -- {a, b} < 2²⁶⁴ means that c < 2⁵²⁸ = 2 ^ (24 ✕ (21 + 1)).
-    -- c's limbs are smaller than 2⁴⁸ ✕ 11 < 2⁵², since multiplication doubles
+    -- {a, b} < 2²⁶⁴ means that c < 2⁵²⁸ = 2 ^ (24 × (21 + 1)).
+    -- c's limbs are smaller than 2⁴⁸ × 11 < 2⁵², since multiplication doubles
     -- bit length, and 11 multiplied limbs are added together.
     return carry(c)
 end
@@ -138,7 +138,7 @@ local function reduce(a)
     end
 
     -- c >= q means c - q >= 0.
-    -- Since q < 2²⁸⁸, c < 2q means c - q < q < 2²⁸⁸ = 2^(24 ✕ (11 + 1)).
+    -- Since q < 2²⁸⁸, c < 2q means c - q < q < 2²⁸⁸ = 2^(24 × (11 + 1)).
     -- c's limbs fit in [-2²⁵..2²⁵], since subtraction adds at most one bit.
     local cc = carry(c)
     cc[12] = nil -- cc < q implies that cc[12] = 0.
@@ -148,7 +148,7 @@ end
 --- Adds two scalars mod q.
 --
 -- If the two operands are in Montgomery form, returns the correct result also
--- in Montgomery form, since (2²⁶⁴ ✕ a) + (2²⁶⁴ ✕ b) ≡ 2²⁶⁴ ✕ (a + b) (mod q).
+-- in Montgomery form, since (2²⁶⁴ × a) + (2²⁶⁴ × b) ≡ 2²⁶⁴ × (a + b) (mod q).
 --
 -- @tparam {number...} a A number a < q as 11 limbs in [0..2²⁴).
 -- @tparam {number...} b A number b < q as 11 limbs in [0..2²⁴).
@@ -169,7 +169,7 @@ local function neg(a)
         c[i] = Q[i] - a[i]
     end
 
-    -- 0 < c < q implies 0 < q - c < q < 2²⁸⁸ = 2^(24 ✕ (11 + 1)).
+    -- 0 < c < q implies 0 < q - c < q < 2²⁸⁸ = 2^(24 × (11 + 1)).
     -- c's limbs fit in [-2²⁵..2²⁵], since subtraction adds at most one bit.
     -- q - c < q also implies q - c < 2q.
     return reduce(carry(c))
@@ -177,8 +177,8 @@ end
 
 --- Given a scalar a, computes 2⁻²⁶⁴ a mod q.
 --
--- @tparam {number...} a A number a < 2²⁶⁴ ✕ q as 22 limbs in [0..2²⁴).
--- @treturn {number...} 2⁻²⁶⁴ ✕ a mod q as 11 limbs in [0..2²⁴).
+-- @tparam {number...} a A number a < 2²⁶⁴ × q as 22 limbs in [0..2²⁴).
+-- @treturn {number...} 2⁻²⁶⁴ × a mod q as 11 limbs in [0..2²⁴).
 --
 local function redc(a)
     local al = {unpack(a, 1, 11)}
@@ -192,29 +192,29 @@ end
 --- Converts a scalar into Montgomery form.
 --
 -- @tparam {number...} a A number a as 11 limbs in [0..2²⁴).
--- @treturn {number...} 2²⁶⁴ ✕ a mod q as 11 limbs in [0..2²⁴).
+-- @treturn {number...} 2²⁶⁴ × a mod q as 11 limbs in [0..2²⁴).
 --
 local function montgomery(a)
-    -- a < 2²⁶⁴ and T1 < q imply that a ✕ T1 < 2²⁶⁴ ✕ q.
+    -- a < 2²⁶⁴ and T1 < q imply that a × T1 < 2²⁶⁴ × q.
     return redc(intMul(a, T1))
 end
 
 --- Converts a scalar from Montgomery form.
 --
 -- @tparam {number...} a A number a < q as 11 limbs in [0..2²⁴).
--- @treturn {number...} 2⁻²⁶⁴ ✕ a mod q as 11 limbs in [0..2²⁴).
+-- @treturn {number...} 2⁻²⁶⁴ × a mod q as 11 limbs in [0..2²⁴).
 --
 local function demontgomery(a)
     a = {unpack(a)}
     for i = 12, 22 do a[i] = 0 end
-    -- a < q < 2²⁶⁴ ✕ q.
+    -- a < q < 2²⁶⁴ × q.
     return redc(a)
 end
 
 --- Converts a Lua number to a scalar.
 --
 -- @tparam number n A number n in [0..2²⁴).
--- @treturn {number...} 2²⁶⁴ ✕ n mod q as 11 limbs in [0..2²⁴).
+-- @treturn {number...} 2²⁶⁴ × n mod q as 11 limbs in [0..2²⁴).
 --
 local function num(n)
     return montgomery({n, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0})
@@ -222,18 +222,18 @@ end
 
 --- Multiplies two scalars mod q.
 --
--- @tparam {number...} a 2²⁶⁴ ✕ a' mod q as 11 limbs in [0..2²⁴).
--- @tparam {number...} b 2²⁶⁴ ✕ b' mod q as 11 limbs in [0..2²⁴).
--- @treturn {number...} 2²⁶⁴ ✕ a' ✕ b' mod q as 11 limbs in [0..2²⁴).
+-- @tparam {number...} a 2²⁶⁴ × a' mod q as 11 limbs in [0..2²⁴).
+-- @tparam {number...} b 2²⁶⁴ × b' mod q as 11 limbs in [0..2²⁴).
+-- @treturn {number...} 2²⁶⁴ × a' × b' mod q as 11 limbs in [0..2²⁴).
 --
 local function mul(a, b)
-    -- {a, b} < q so a ✕ b < q² < 2²⁶⁴ ✕ q.
+    -- {a, b} < q so a × b < q² < 2²⁶⁴ × q.
     return redc(intMul(a, b))
 end
 
 --- Encodes a scalar.
 --
--- @tparam {number...} a A number 2²⁶⁴ ✕ a mod q as 11 limbs in [0..2²⁴).
+-- @tparam {number...} a A number 2²⁶⁴ × a mod q as 11 limbs in [0..2²⁴).
 -- @treturn string The 32-byte string encoding of a.
 --
 local function encode(a)
@@ -243,7 +243,7 @@ end
 --- Decodes a scalar.
 --
 -- @tparam string str A 32-byte string encoding some little-endian number a.
--- @treturn {number...} 2²⁶⁴ ✕ a mod q as 11 limbs in [0..2²⁴).
+-- @treturn {number...} 2²⁶⁴ × a mod q as 11 limbs in [0..2²⁴).
 --
 local function decode(str)
     local dec = {("<I3I3I3I3I3I3I3I3I3I3I2"):unpack(str)} dec[12] = nil
@@ -253,7 +253,7 @@ end
 --- Decodes a scalar from a "wide" string.
 --
 -- @tparam string str A 64-byte string encoding some little-endian number a.
--- @treturn {number...} 2²⁶⁴ ✕ a mod q as 11 limbs in [0..2²⁴).
+-- @treturn {number...} 2²⁶⁴ × a mod q as 11 limbs in [0..2²⁴).
 --
 local function decodeWide(str)
     local low = {("<I3I3I3I3I3I3I3I3I3I3I3"):unpack(str)} low[12] = nil
@@ -264,7 +264,7 @@ end
 --- Decodes a scalar using the X25519/Ed25519 bit clamping scheme.
 --
 -- @tparam string str A 32-byte string encoding some little-endian number a.
--- @treturn {number...} 2²⁶⁴ ✕ clamp(a) mod q as 11 limbs in [0..2²⁴).
+-- @treturn {number...} 2²⁶⁴ × clamp(a) mod q as 11 limbs in [0..2²⁴).
 --
 local function decodeClamped(str)
     -- Decode.
@@ -281,7 +281,7 @@ end
 --- Returns a scalar in binary.
 --
 -- @tparam {number...} a A number a < q as 11 limbs in [0..2²⁴).
--- @treturn {number...} 2⁻²⁶⁴ ✕ a mod q as 265 bits.
+-- @treturn {number...} 2⁻²⁶⁴ × a mod q as 265 bits.
 --
 local function bits(a)
     return util.rebaseLE(demontgomery(a), 2 ^ 24, 2)