From deff5edd425bf9aee5ecf5439292347a75ce304f Mon Sep 17 00:00:00 2001
From: Russell O'Connor <roconnor@blockstream.io>
Date: Fri, 6 Jul 2018 07:53:32 -0400
Subject: [PATCH] Correct math typos in field_*.h

---
 src/field_10x26.h            | 4 +++-
 src/field_10x26_impl.h       | 3 ++-
 src/field_5x52.h             | 4 +++-
 src/field_5x52_int128_impl.h | 3 ++-
 4 files changed, 10 insertions(+), 4 deletions(-)

diff --git a/src/field_10x26.h b/src/field_10x26.h
index 727c5267fbb5f..5ff03c8abcc05 100644
--- a/src/field_10x26.h
+++ b/src/field_10x26.h
@@ -10,7 +10,9 @@
 #include <stdint.h>
 
 typedef struct {
-    /* X = sum(i=0..9, elem[i]*2^26) mod n */
+    /* X = sum(i=0..9, n[i]*2^(i*26)) mod p
+     * where p = 2^256 - 0x1000003D1
+     */
     uint32_t n[10];
 #ifdef VERIFY
     int magnitude;
diff --git a/src/field_10x26_impl.h b/src/field_10x26_impl.h
index 57613576d89de..d840825c3f461 100644
--- a/src/field_10x26_impl.h
+++ b/src/field_10x26_impl.h
@@ -486,7 +486,8 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint32_t *r, const uint32_t
     VERIFY_BITS(b[9], 26);
 
     /** [... a b c] is a shorthand for ... + a<<52 + b<<26 + c<<0 mod n.
-     *  px is a shorthand for sum(a[i]*b[x-i], i=0..x).
+     *  for 0 <= x <= 9, px is a shorthand for sum(a[i]*b[x-i], i=0..x).
+     *  for 9 <= x <= 18, px is a shorthand for sum(a[i]*b[x-i], i=(x-9)..9)
      *  Note that [x 0 0 0 0 0 0 0 0 0 0] = [x*R1 x*R0].
      */
 
diff --git a/src/field_5x52.h b/src/field_5x52.h
index bccd8feb4dde6..fc5bfe357e705 100644
--- a/src/field_5x52.h
+++ b/src/field_5x52.h
@@ -10,7 +10,9 @@
 #include <stdint.h>
 
 typedef struct {
-    /* X = sum(i=0..4, elem[i]*2^52) mod n */
+    /* X = sum(i=0..4, n[i]*2^(i*52)) mod p
+     * where p = 2^256 - 0x1000003D1
+     */
     uint64_t n[5];
 #ifdef VERIFY
     int magnitude;
diff --git a/src/field_5x52_int128_impl.h b/src/field_5x52_int128_impl.h
index 16f2caca7dead..bcbfb92ac265b 100644
--- a/src/field_5x52_int128_impl.h
+++ b/src/field_5x52_int128_impl.h
@@ -35,7 +35,8 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t
     VERIFY_CHECK(a != b);
 
     /*  [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
-     *  px is a shorthand for sum(a[i]*b[x-i], i=0..x).
+     *  for 0 <= x <= 4, px is a shorthand for sum(a[i]*b[x-i], i=0..x).
+     *  for 4 <= x <= 8, px is a shorthand for sum(a[i]*b[x-i], i=(x-4)..4)
      *  Note that [x 0 0 0 0 0] = [x*R].
      */