}
/*
- * Propagate carries. Since the operation above really is a
- * truncature, followed by the addition of nonnegative values,
- * the result will be positive. Moreover, the carry cannot
- * exceed 5 bits (we performed 20 additions with values smaller
- * than 256 bits).
+ * Propagate carries. This is a signed propagation, and the
+ * result may be negative. The loop above may enlarge values,
+ * but not two much: worst case is the chain involving t[i - 3],
+ * in which a value may be added to itself up to 7 times. Since
+ * starting values are 13-bit each, all words fit on 20 bits
+ * (21 to account for the sign bit).
*/
cc = norm13(t, t, 20);
/*
* Perform modular reduction again for the bits beyond 256 (the carry
- * and the bits 256..259). This time, we can simply inject full
- * word values.
+ * and the bits 256..259). Since the largest shift below is by 10
+ * bits, and the values fit on 21 bits, values fit in 32-bit words,
+ * thereby allowing injecting full word values.
*/
cc = (cc << 4) | (t[19] >> 9);
t[19] &= 0x01FF;
}
/*
- * Propagate carries. Since the operation above really is a
- * truncature, followed by the addition of nonnegative values,
- * the result will be positive. Moreover, the carry cannot
- * exceed 5 bits (we performed 20 additions with values smaller
- * than 256 bits).
+ * Propagate carries. This is a signed propagation, and the
+ * result may be negative. The loop above may enlarge values,
+ * but not two much: worst case is the chain involving t[i - 3],
+ * in which a value may be added to itself up to 7 times. Since
+ * starting values are 13-bit each, all words fit on 20 bits
+ * (21 to account for the sign bit).
*/
cc = norm13(t, t, 20);
/*
* Perform modular reduction again for the bits beyond 256 (the carry
- * and the bits 256..259). This time, we can simply inject full
- * word values.
+ * and the bits 256..259). Since the largest shift below is by 10
+ * bits, and the values fit on 21 bits, values fit in 32-bit words,
+ * thereby allowing injecting full word values.
*/
cc = (cc << 4) | (t[19] >> 9);
t[19] &= 0x01FF;