Update EIP-2537: rename PAIRING to PAIRING_CHECK; introduce PAIRING_PRODUCT precomiple

Merged by EIP-Bot.

Author: zhenfeizhang

EIPS/eip-2537.md

@@ -33,7 +33,7 @@ The motivation of this precompile is to add a cryptographic primitive that allow
 | BLS12_G2ADD         | 0x0e  | precompile address |
 | BLS12_G2MUL         | 0x0f  | precompile address |
 | BLS12_G2MSM         | 0x10  | precompile address |
-| BLS12_PAIRING       | 0x11  | precompile address |
+| BLS12_PAIRING_CHECK | 0x11  | precompile address |
 | BLS12_MAP_FP_TO_G1  | 0x12  | precompile address |
 | BLS12_MAP_FP2_TO_G2 | 0x13  | precompile address |
 
@@ -45,7 +45,7 @@ If `block.timestamp >= FORK_TIMESTAMP` we introduce *nine* separate precompiles
 - BLS12_G2ADD - to perform point addition in G2 (curve over quadratic extension of the base prime field) with a gas cost of `800` gas
 - BLS12_G2MUL - to perform point multiplication in G2 (curve over quadratic extension of the base prime field) with a gas cost of `45000` gas
 - BLS12_G2MSM - to perform multi-scalar-multiplication (MSM) in G2 (curve over quadratic extension of the base prime field) with a gas cost formula defined in the corresponding section
-- BLS12_PAIRING - to perform a pairing operations between a set of *pairs* of (G1, G2) points a gas cost formula defined in the corresponding section
+- BLS12_PAIRING_CHECK - to perform a pairing operations between a set of *pairs* of (G1, G2) points a gas cost formula defined in the corresponding section
 - BLS12_MAP_FP_TO_G1 - maps base field element into the G1 point with a gas cost of `5500` gas
 - BLS12_MAP_FP2_TO_G2 - maps extension field element into the G2 point with a gas cost of `75000` gas
 
@@ -115,7 +115,7 @@ On inputs that can not be a valid encodings of field elements the precompile *mu
 
 #### Encoding of points in G1/G2:
 
-Points of G1 and G2 are encoded as byte concatenation of the respective encodings of the `x` and `y` coordinates. Total encoding length for a  G1 point is thus `128` bytes and for a G2 point is `256` bytes.
+Points of G1 and G2 are encoded as byte concatenation of the respective encodings of the `x` and `y` coordinates. Total encoding length for a G1 point is thus `128` bytes and for a G2 point is `256` bytes.
 
 #### Point of infinity encoding:
 
@@ -203,9 +203,9 @@ Error cases:
 - An input is on the G2 elliptic curve but not in the correct subgroup
 - Input has invalid length
 
-#### ABI for pairing
+#### ABI for pairing check
 
-Pairing call expects `384*k`  (`k` being a **positive** integer)  bytes as an inputs that is interpreted as byte concatenation of `k` slices. Each slice has the following structure:
+Pairing check call expects `384*k`  (`k` being a **positive** integer)  bytes as an inputs that is interpreted as byte concatenation of `k` slices. Each slice has the following structure:
 
 - `128` bytes of G1 point encoding
 - `256` bytes of G2 point encoding
@@ -285,9 +285,9 @@ Discounts table as a vector of pairs `[k, discount]`:
 
 `max_discount = 174`
 
-#### Pairing operation
+#### Pairing check operation
 
-The cost of the pairing operation is `43000*k + 65000` where `k` is a number of pairs.
+The cost of the pairing check operation is `43000*k + 65000` where `k` is a number of pairs.
 
 #### Fp-to-G1 mapping operation