Some small performance improvements on 32-bit architectures.

src/int/i31_montmul.c

@@ -29,16 +29,45 @@ void
 br_i31_montymul(uint32_t *d, const uint32_t *x, const uint32_t *y,
 	const uint32_t *m, uint32_t m0i)
 {
+	/*
+	 * Each outer loop iteration computes:
+	 *   d <- (d + xu*y + f*m) / 2^31
+	 * We have xu <= 2^31-1 and f <= 2^31-1.
+	 * Thus, if d <= 2*m-1 on input, then:
+	 *   2*m-1 + 2*(2^31-1)*m <= (2^32)*m-1
+	 * and the new d value is less than 2*m.
+	 *
+	 * We represent d over 31-bit words, with an extra word 'dh'
+	 * which can thus be only 0 or 1.
+	 */
 	size_t len, len4, u, v;
-	uint64_t dh;
+	uint32_t dh;
 
 	len = (m[0] + 31) >> 5;
 	len4 = len & ~(size_t)3;
 	br_i31_zero(d, m[0]);
 	dh = 0;
 	for (u = 0; u < len; u ++) {
+		/*
+		 * The carry for each operation fits on 32 bits:
+		 *   d[v+1] <= 2^31-1
+		 *   xu*y[v+1] <= (2^31-1)*(2^31-1)
+		 *   f*m[v+1] <= (2^31-1)*(2^31-1)
+		 *   r <= 2^32-1
+		 *   (2^31-1) + 2*(2^31-1)*(2^31-1) + (2^32-1) = 2^63 - 2^31
+		 * After division by 2^31, the new r is then at most 2^32-1
+		 *
+		 * Using a 32-bit carry has performance benefits on 32-bit
+		 * systems; however, on 64-bit architectures, we prefer to
+		 * keep the carry (r) in a 64-bit register, thus avoiding some
+		 * "clear high bits" operations.
+		 */
 		uint32_t f, xu;
-		uint64_t r, zh;
+#if BR_64
+		uint64_t r;
+#else
+		uint32_t r;
+#endif
 
 		xu = x[u + 1];
 		f = MUL31_lo((d[1] + MUL31_lo(x[u + 1], y[1])), m0i);
@@ -73,9 +102,14 @@ br_i31_montymul(uint32_t *d, const uint32_t *x, const uint32_t *y,
 			d[v] = (uint32_t)z & 0x7FFFFFFF;
 		}
 
-		zh = dh + r;
-		d[len] = (uint32_t)zh & 0x7FFFFFFF;
-		dh = zh >> 31;
+		/*
+		 * Since the new dh can only be 0 or 1, the addition of
+		 * the old dh with the carry MUST fit on 32 bits, and
+		 * thus can be done into dh itself.
+		 */
+		dh += r;
+		d[len] = dh & 0x7FFFFFFF;
+		dh >>= 31;
 	}
 
 	/*