f rephrase ec arithmetic doc

Author: jonasnick

include/secp256k1.h

@@ -585,8 +585,8 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create(
  *  Args:   ctx:        pointer to a context object
  *  In/Out: seckey:     pointer to the 32-byte secret key to be negated. The secret
  *                      key should be valid according to secp256k1_ec_seckey_verify.
- *                      Value becomes undefined if this function returns 0.
- *                      (cannot be NULL)
+ *                      If this function returns 0, seckey will be some
+ *                      unspecified value. (cannot be NULL)
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_negate(
     const secp256k1_context* ctx,
@@ -605,15 +605,17 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_negate(
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
 
 /** Tweak a secret key by adding tweak to it.
- * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
- *          uniformly random 32-byte arrays, or if the given secret key is
- *          invalid according to secp256k1_ec_seckey_verify, or if the resulting
- *          secret key would be invalid (only when the tweak is the complement
- *          of the secret key). 1 otherwise.
+ * Returns: 0 if the resulting secret key would be invalid (only when the tweak
+ *          is the negation of the secret key). 1 otherwise.
  * Args:    ctx:    pointer to a context object (cannot be NULL).
- * In/Out:  seckey: pointer to a 32-byte secret key. Value becomes undefined if this
- *                  function returns 0. (cannot be NULL)
- * In:      tweak:  pointer to a 32-byte tweak.
+ * In/Out:  seckey: pointer to a 32-byte secret key. The secret key should be
+ *                  valid according to secp256k1_ec_seckey_verify. If this
+ *                  function returns 0, seckey will be some unspecified
+ *                  value. (cannot be NULL)
+ * In:       tweak: pointer to a 32-byte tweak. Must be in the same range as secret
+ *                  keys (see secp256k1_ec_seckey_verify). For uniformly random
+ *                  32-byte arrays the chance of being out of range is
+ *                  negligible (around 1 in 2^128). (cannot be NULL)
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add(
     const secp256k1_context* ctx,
@@ -622,16 +624,16 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_add(
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
 /** Tweak a public key by adding tweak times the generator to it.
- * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
- *          uniformly random 32-byte arrays, or if the given secret key is
- *          invalid according to secp256k1_ec_seckey_verify, or if the resulting
- *          public key would be invalid (only when the tweak is the complement
- *          of the corresponding secret key). 1 otherwise.
+ * Returns: 0 if the resulting public key would be invalid (only when the tweak
+ *          is the negation of the corresponding secret key). 1 otherwise.
  * Args:    ctx:    pointer to a context object initialized for validation
  *                  (cannot be NULL).
- * In/Out:  pubkey: pointer to a public key object. Value becomes undefined if this
- *                  function returns 0. (cannot be NULL).
- * In:      tweak:  pointer to a 32-byte tweak.
+ * In/Out:  pubkey: pointer to a public key object. If this function returns 0,
+ *                  pubkey will be invalid. (cannot be NULL).
+ * In:      tweak:  pointer to a 32-byte tweak. Must be in the same range as secret
+ *                  keys (see secp256k1_ec_seckey_verify). For uniformly random
+ *                  32-byte arrays the chance of being out of range is
+ *                  negligible (around 1 in 2^128). (cannot be NULL)
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add(
     const secp256k1_context* ctx,
@@ -640,12 +642,14 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add(
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
 /** Tweak a secret key by multiplying it by a tweak.
- * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
- *          uniformly random 32-byte arrays, or equal to zero. 1 otherwise.
+ * Returns: 0 if the arguments are invalid.. 1 otherwise.
  * Args:   ctx:    pointer to a context object (cannot be NULL).
- * In/Out: seckey: pointer to a 32-byte secret key. Value becomes undefined if this
- *                  function returns 0. (cannot be NULL).
- * In:     tweak:  pointer to a 32-byte tweak.
+ * In/Out: seckey: pointer to a 32-byte secret key. If this function returns 0,
+ *                 seckey will be some unspecified value. (cannot be NULL).
+ * In:     tweak:  pointer to a 32-byte tweak. Must be in the same range as secret
+ *                 keys (see secp256k1_ec_seckey_verify). For uniformly random
+ *                 32-byte arrays the chance of being out of range is
+ *                 negligible (around 1 in 2^128). (cannot be NULL)
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul(
     const secp256k1_context* ctx,
@@ -654,13 +658,15 @@ SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_privkey_tweak_mul(
 ) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
 
 /** Tweak a public key by multiplying it by a tweak value.
- * Returns: 0 if the tweak was out of range (chance of around 1 in 2^128 for
- *          uniformly random 32-byte arrays, or equal to zero. 1 otherwise.
+ * Returns: 0 if the arguments are invalid. 1 otherwise.
  * Args:    ctx:    pointer to a context object initialized for validation
- *                 (cannot be NULL).
- * In/Out:  pubkey: pointer to a public key object. Value becomes undefined if this
- *                  function returns 0. (cannot be NULL).
- * In:      tweak:  pointer to a 32-byte tweak.
+ *                  (cannot be NULL).
+ * In/Out:  pubkey: pointer to a public key object. If this function returns 0,
+ *                  pubkey will be invalid. (cannot be NULL).
+ * In:      tweak:  pointer to a 32-byte tweak. Must be in the same range as secret
+ *                  keys (see secp256k1_ec_seckey_verify). For uniformly random
+ *                  32-byte arrays the chance of being out of range is
+ *                  negligible (around 1 in 2^128). (cannot be NULL)
  */
 SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul(
     const secp256k1_context* ctx,