progs/perftest.c: Use from Glibc syscall numbers.

[catacomb] / math / gfreduce.h

diff --git a/math/gfreduce.h b/math/gfreduce.h
index 9f69585..539b7c1 100644 (file)
--- a/math/gfreduce.h
+++ b/math/gfreduce.h
@@ -91,7 +91,7 @@ extern void gfreduce_destroy(gfreduce */*r*/);
 
 /* --- @gfreduce_dump@ --- *
  *
- * Arguments:  @gfreduce *r@ = structure to dump
+ * Arguments:  @const gfreduce *r@ = structure to dump
  *             @FILE *fp@ = file to dump on
  *
  * Returns:    ---
@@ -99,44 +99,47 @@ extern void gfreduce_destroy(gfreduce */*r*/);
  * Use:                Dumps a reduction context.
  */
 
-extern void gfreduce_dump(gfreduce */*r*/, FILE */*fp*/);
+extern void gfreduce_dump(const gfreduce */*r*/, FILE */*fp*/);
 
 /* --- @gfreduce_do@ --- *
  *
- * Arguments:  @gfreduce *r@ = reduction context
+ * Arguments:  @const gfreduce *r@ = reduction context
  *             @mp *d@ = destination
  *             @mp *x@ = source
  *
  * Returns:    Destination, @x@ reduced modulo the reduction poly.
  */
 
-extern mp *gfreduce_do(gfreduce */*r*/, mp */*d*/, mp */*x*/);
+extern mp *gfreduce_do(const gfreduce */*r*/, mp */*d*/, mp */*x*/);
 
 /* --- @gfreduce_sqrt@ --- *
  *
- * Arguments:  @gfreduce *r@ = pointer to reduction context
+ * Arguments:  @const gfreduce *r@ = pointer to reduction context
  *             @mp *d@ = destination
  *             @mp *x@ = some polynomial
  *
  * Returns:    The square root of @x@ modulo @r->p@, or null.
  */
 
-extern mp *gfreduce_sqrt(gfreduce */*r*/, mp */*d*/, mp */*x*/);
+extern mp *gfreduce_sqrt(const gfreduce */*r*/, mp */*d*/, mp */*x*/);
 
 /* --- @gfreduce_trace@ --- *
  *
- * Arguments:  @gfreduce *r@ = pointer to reduction context
+ * Arguments:  @const gfreduce *r@ = pointer to reduction context
  *             @mp *x@ = some polynomial
  *
  * Returns:    The trace of @x@. (%$\Tr(x)=x + x^2 + \cdots + x^{2^{m-1}}$%
- *             if %$x \in \gf{2^m}$%).
+ *             if %$x \in \gf{2^m}$%).  Since the trace is invariant under
+ *             the Frobenius automorphism (i.e., %$\Tr(x)^2 = \Tr(x)$%), it
+ *             must be an element of the base field, i.e., %$\gf{2}$%, and
+ *             we only need a single bit to represent it.
  */
 
-extern int gfreduce_trace(gfreduce */*r*/, mp */*x*/);
+extern int gfreduce_trace(const gfreduce */*r*/, mp */*x*/);
 
 /* --- @gfreduce_halftrace@ --- *
  *
- * Arguments:  @gfreduce *r@ = pointer to reduction context
+ * Arguments:  @const gfreduce *r@ = pointer to reduction context
  *             @mp *d@ = destination
  *             @mp *x@ = some polynomial
  *
@@ -145,22 +148,33 @@ extern int gfreduce_trace(gfreduce */*r*/, mp */*x*/);
  *             if %$x \in \gf{2^m}$% with %$m$% odd).
  */
 
-extern mp *gfreduce_halftrace(gfreduce */*r*/, mp */*d*/, mp */*x*/);
+extern mp *gfreduce_halftrace(const gfreduce */*r*/, mp */*d*/, mp */*x*/);
 
 /* --- @gfreduce_quadsolve@ --- *
  *
- * Arguments:  @gfreduce *r@ = pointer to reduction context
+ * Arguments:  @const gfreduce *r@ = pointer to reduction context
  *             @mp *d@ = destination
  *             @mp *x@ = some polynomial
  *
  * Returns:    A polynomial @y@ such that %$y^2 + y = x$%, or null.
+ *
+ * Use:                Solves quadratic equations in a field with characteristic 2.
+ *             Suppose we have an equation %$y^2 + A y + B = 0$% where
+ *             %$A \ne 0$%.  (If %$A = 0$% then %$y = \sqrt{B}$% and you
+ *             want @gfreduce_sqrt@ instead.)  Use this function to solve
+ *             %$z^2 + z = B/A^2$%; then set %$y = A z$%, since
+ *             %$y^2 + y = A^2 z^2 + A^2 z = A^2 (z^2 + z) = B$% as
+ *             required.
+ *
+ *             The two roots are %$z$% and %$z + 1$%; this function always
+ *             returns the one with zero scalar coefficient.
  */
 
-extern mp *gfreduce_quadsolve(gfreduce */*r*/, mp */*d*/, mp */*x*/);
+extern mp *gfreduce_quadsolve(const gfreduce */*r*/, mp */*d*/, mp */*x*/);
 
 /* --- @gfreduce_exp@ --- *
  *
- * Arguments:  @gfreduce *gr@ = pointer to reduction context
+ * Arguments:  @const gfreduce *gr@ = pointer to reduction context
  *             @mp *d@ = fake destination
  *             @mp *a@ = base
  *             @mp *e@ = exponent
@@ -168,7 +182,8 @@ extern mp *gfreduce_quadsolve(gfreduce */*r*/, mp */*d*/, mp */*x*/);
  * Returns:    Result, %$a^e \bmod m$%.
  */
 
-extern mp *gfreduce_exp(gfreduce */*gr*/, mp */*d*/, mp */*a*/, mp */*e*/);
+extern mp *gfreduce_exp(const gfreduce */*gr*/, mp */*d*/,
+                       mp */*a*/, mp */*e*/);
 
 /*----- That's all, folks -------------------------------------------------*/