Typo in nesting corrected

Author: czurnieden

mp_prime_is_prime.c

@@ -186,15 +186,15 @@ mp_err mp_prime_is_prime(const mp_int *a, int t, bool *result)
 
          This holds for a while. Next SPRPs < 2^35 to check for {2, 3, 1459}:
 
-                n          factors               log_2(n)            has a factor < 2^28
-            6770862367: 41143 164569    32.65669244751501848078             y
-            15579919981: 88261 176521   33.85896877256133553111             y
-            16149644101: 63541 254161   33.91078332064236217721             y
-            17849326081: 50497 353473   34.05515055377487005769             y
-            23510118061: 108421 216841  34.45256273267917105145             y
-            24988416967: 79039 316153   34.54054045749318459634             y
-            27031263841: 116257 232513  34.65390991522339129949             y
-            28448982721: 97381 292141   34.72765801442453753728             y
+                n          factors         log_2(n)    has a factor < 2^28
+            6770862367:  41143 164569      32.6567             y
+            15579919981: 88261 176521      33.859              y
+            16149644101: 63541 254161      33.9108             y
+            17849326081: 50497 353473      34.0556             y
+            23510118061: 108421 216841     34.4526             y
+            24988416967: 79039 316153      34.5405             y
+            27031263841: 116257 232513     34.6539             y
+            28448982721: 97381 292141      34.7276             y
 
        */
 #if ((defined S_MP_PRIME_IS_DIVISIBLE_C) && (MP_PRIME_TAB_SIZE >= 256))
@@ -216,38 +216,66 @@ mp_err mp_prime_is_prime(const mp_int *a, int t, bool *result)
          *result = res;
          goto LBL_B;
       }
-   }
 #else
       /* 2, 7, 61 found by Gerhard Jaeschke 1993 */
+      /*
+         Because we already have 2 and 3 at this point all four bases are good up to
+
+            33717240721: 129841 259681                     34.9728   y
+
+         This is the single SPRP up to 51706044253 (~2^35.5896). Next are
+
+            163204128181: 285661 571321                    37.2479   y
+            501086407781: 288989 1733929                   38.8663   y
+               ... 23588 others skipped ...
+            18441334942415579101: 876577981 21037871521    63.9996   n
+            18444384017352327673: 1920644893 9603224461    63.9998   n
+
+         Adding base 5 brings us to
+
+            10087771603687: 1588063 6352249                43.1977   y
+
+         The record for five bases is at 7999252175582851 for now, about 2^52.8288 bit large
+         but hase bases larger than 32 bit and none of the known 5-base records has bases
+         smaller than 28 bit.
+
+         Adding base 63803 (already > 2^15) brings us to
+
+           849491953715047: 14573023 58292089              49.5936   y
+
+         Record for 6 bases is at 585226005592931977  ~2^59.0217 but one base is over 60 bit
+         large.
+
+       */
       mp_digit bases32 = {7u, 61u};
 #endif
-   /* 2, 325, 9375, 28178, 450775, 9780504, 1795265022 found by Jim Sinclair 2011 */
-   mp_word bases64 = {325ull, 9375ull, 28178ull, 450775ull, 9780504ull, 1795265022ull};
-   if (bits < 32) {
-      for (ix = 0; ix < 2; ix++) {
-         mp_set(&b, bases32[ix]);
-         if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
-            goto LBL_B;
-         }
-         if (!res) {
-            goto LBL_B;
-         }
-      }
-      *result = true;
-      goto LBL_B;
-   } else if ((bits >= 32) && (bits < 64)) {
-      for (ix = 0; ix < 6; ix++) {
-         mp_set_u32(&b, bases64[ix]);
-         if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
-            goto LBL_B;
+      /* 2, 325, 9375, 28178, 450775, 9780504, 1795265022 found by Jim Sinclair 2011 */
+      mp_word bases64 = {325ull, 9375ull, 28178ull, 450775ull, 9780504ull, 1795265022ull};
+      if (bits < 32) {
+         for (ix = 0; ix < 2; ix++) {
+            mp_set(&b, bases32[ix]);
+            if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
+               goto LBL_B;
+            }
+            if (!res) {
+               goto LBL_B;
+            }
          }
-         if (!res) {
-            goto LBL_B;
+         *result = true;
+         goto LBL_B;
+      } else if ((bits >= 32) && (bits < 64)) {
+         for (ix = 0; ix < 6; ix++) {
+            mp_set_u32(&b, bases64[ix]);
+            if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
+               goto LBL_B;
+            }
+            if (!res) {
+               goto LBL_B;
+            }
          }
+         *result = true;
+         goto LBL_B;
       }
-      *result = true;
-      goto LBL_B;
-   }
 #endif
       /*
           Sorenson, Jonathan; Webster, Jonathan,  "Strong Pseudoprimes to Twelve Prime Bases". (2015) https://arxiv.org/abs/1509.00864
@@ -301,8 +329,7 @@ mp_err mp_prime_is_prime(const mp_int *a, int t, bool *result)
        Do "t" M-R tests with random bases between 3 and "a".
        See Fips 186.4 p. 126ff
    */
-   if (t > 0)
-   {
+   if (t > 0) {
       unsigned int mask;
       /*
        * The mp_digit's have a defined bit-size but the size of the