X-Git-Url: https://git.distorted.org.uk/~mdw/catacomb/blobdiff_plain/12208248afbfcdedac9494a68ab83f203335c1a3..HEAD:/math/gfreduce.h

diff --git a/math/gfreduce.h b/math/gfreduce.h
index b60c8fab..539b7c14 100644
--- a/math/gfreduce.h
+++ b/math/gfreduce.h
@@ -60,7 +60,8 @@ typedef struct gfreduce {
   mpw mask;				/* Mask for degree word */
   mp *p;				/* Copy of the polynomial */
   size_t in;				/* Number of instruction words */
-  gfreduce_instr *iv, *liv;		/* Vector of instructions */
+  gfreduce_instr *iv;			/* Vector of instructions */
+  gfreduce_instr *fiv;			/* Final-pass instruction suffix */
 } gfreduce;
 
 /*----- Functions provided ------------------------------------------------*/
@@ -90,7 +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:	---
@@ -98,44 +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
  *
@@ -144,22 +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
@@ -167,7 +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 -------------------------------------------------*/