Merge bitcoin#539: Assorted minor corrections

52ab96f clean dependendies in field_*_impl.h (Russell O'Connor)
deff5ed Correct math typos in field_*.h (Russell O'Connor)
4efb3f8 Add check that restrict pointers don't alias with all parameters. (Russell O'Connor)

Pull request description:

  * add more checks for restrict pointers.
  * correct math typos.
  * refine dependencies on "num.h"

Tree-SHA512: c368f577927db2ace3e7f46850cb2fdf9d7d169b698a9697767e1f82e9e7091f2b2fea0f7cf173048eb4c1bb56824c884fa849c04c595ee97766c01f346a54ec

Author: gmaxwell

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;

src/field_10x26_impl.h

@@ -8,7 +8,6 @@
 #define SECP256K1_FIELD_REPR_IMPL_H
 
 #include "util.h"
-#include "num.h"
 #include "field.h"
 
 #ifdef VERIFY
@@ -486,7 +485,8 @@ 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].
      */
 
@@ -1069,6 +1069,7 @@ static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp2
     secp256k1_fe_verify(a);
     secp256k1_fe_verify(b);
     VERIFY_CHECK(r != b);
+    VERIFY_CHECK(a != b);
 #endif
     secp256k1_fe_mul_inner(r->n, a->n, b->n);
 #ifdef VERIFY

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;

src/field_5x52_impl.h

@@ -12,7 +12,6 @@
 #endif
 
 #include "util.h"
-#include "num.h"
 #include "field.h"
 
 #if defined(USE_ASM_X86_64)
@@ -422,6 +421,7 @@ static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp2
     secp256k1_fe_verify(a);
     secp256k1_fe_verify(b);
     VERIFY_CHECK(r != b);
+    VERIFY_CHECK(a != b);
 #endif
     secp256k1_fe_mul_inner(r->n, a->n, b->n);
 #ifdef VERIFY

src/field_5x52_int128_impl.h

@@ -32,9 +32,11 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t
     VERIFY_BITS(b[3], 56);
     VERIFY_BITS(b[4], 52);
     VERIFY_CHECK(r != b);
+    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].
      */
 

src/field_impl.h

@@ -12,6 +12,7 @@
 #endif
 
 #include "util.h"
+#include "num.h"
 
 #if defined(USE_FIELD_10X26)
 #include "field_10x26_impl.h"