From f51aee83708673ef9941174951bec9aee80cb03c Mon Sep 17 00:00:00 2001
From: Gabriel Dos Reis <gdr@axiomatics.org>
Date: Thu, 31 Dec 2015 14:56:12 -0800
Subject: Avoid modulus bias in 'random()' usage.

---
 src/algebra/rep2.spad.pamphlet | 31 +++++++++++--------------------
 1 file changed, 11 insertions(+), 20 deletions(-)

(limited to 'src/algebra/rep2.spad.pamphlet')

diff --git a/src/algebra/rep2.spad.pamphlet b/src/algebra/rep2.spad.pamphlet
index 4219ab67..5524c72d 100644
--- a/src/algebra/rep2.spad.pamphlet
+++ b/src/algebra/rep2.spad.pamphlet
@@ -312,10 +312,10 @@ RepresentationPackage2(R): public == private where
     createRandomElement(aG,algElt) ==
       numberOfGenerators : NNI := #aG
       -- randomIndex := randnum numberOfGenerators
-      randomIndex := 1+(random()$Integer rem numberOfGenerators)
+      randomIndex := 1 + random(numberOfGenerators)$Integer
       algElt := algElt * aG.randomIndex
       -- randomIndxElement := randnum numberOfGenerators
-      randomIndex := 1+(random()$Integer rem numberOfGenerators)
+      randomIndex := 1 + random(numberOfGenerators)$Integer
       algElt + aG.randomIndex
  
  
@@ -481,8 +481,7 @@ RepresentationPackage2(R): public == private where
           -- fingerprint.
           x0,x1: M R
           if randomelements then   -- random should not be from I
-             --randomIndex  : I   := randnum numberOfGenerators
-             randomIndex := 1+(random()$Integer rem numberOfGenerators)
+             randomIndex := 1 + random(numberOfGenerators)$Integer
              x0 := aG0.randomIndex
              x1 := aG1.randomIndex
           n : NNI := #row(x0,1)   -- degree  of representation
@@ -496,12 +495,10 @@ RepresentationPackage2(R): public == private where
             -- chosen elements form "aG".
             if i = 7 then randomelements := true
             if randomelements then
-               --randomIndex := randnum numberOfGenerators
-               randomIndex := 1+(random()$Integer rem numberOfGenerators)
+               randomIndex := 1 + random(numberOfGenerators)$Integer
                x0 := x0 * aG0.randomIndex
                x1 := x1 * aG1.randomIndex
-               --randomIndex := randnum numberOfGenerators
-               randomIndex := 1+(random()$Integer rem numberOfGenerators)
+               randomIndex := 1 + random(numberOfGenerators)$Integer
                x0 := x0 + aG0.randomIndex
                x1 := x1 + aG1.randomIndex
             else
@@ -576,8 +573,7 @@ RepresentationPackage2(R): public == private where
         result : B := false
         numberOfGenerators  : NNI := #aG
         -- need a start value for creating random matrices:
-        -- randomIndex  : I   := randnum numberOfGenerators
-        randomIndex := 1+(random()$Integer rem numberOfGenerators)
+        randomIndex := 1 + random(numberOfGenerators)$Integer
         x : M R := aG.randomIndex
         n : NNI := #row(x,1)   -- degree  of representation
         foundResult : B := false
@@ -587,11 +583,9 @@ RepresentationPackage2(R): public == private where
           -- create random elements recursively:
           -- x_i+1 :=x_i * mr1 + mr2, where mr1 and mr2 are randomly
           -- chosen elements form "aG".
-          -- randomIndex := randnum numberOfGenerators
-          randomIndex := 1+(random()$Integer rem numberOfGenerators)
+          randomIndex := 1 + random(numberOfGenerators)$Integer
           x := x * aG.randomIndex
-          --randomIndex := randnum numberOfGenerators
-          randomIndex := 1+(random()$Integer rem numberOfGenerators)
+          randomIndex := 1 + random(numberOfGenerators)$Integer
           x := x + aG.randomIndex
           -- test whether rank of x is n-1
           rk : NNI := rank x
@@ -672,8 +666,7 @@ RepresentationPackage2(R): public == private where
           -- if we switch to randomelements later, we take the last
           -- fingerprint.
           if randomelements then   -- random should not be from I
-             --randomIndex  : I   := randnum numberOfGenerators
-             randomIndex := 1+(random()$Integer rem numberOfGenerators)
+             randomIndex := 1 + random(numberOfGenerators)$Integer
              x : M R := algebraGenerators.randomIndex
           foundResult : B := false
           for i in 1..numberOfTries until foundResult repeat
@@ -685,11 +678,9 @@ RepresentationPackage2(R): public == private where
             -- chosen elements form "algebraGenerators".
             if i = 7 then randomelements := true
             if randomelements then
-               --randomIndex := randnum numberOfGenerators
-               randomIndex := 1+(random()$Integer rem numberOfGenerators)
+               randomIndex := 1 + random(numberOfGenerators)$Integer
                x := x * algebraGenerators.randomIndex
-               --randomIndex := randnum numberOfGenerators
-               randomIndex := 1+(random()$Integer rem numberOfGenerators)
+               randomIndex := 1 + random(numberOfGenerators)$Integer
                x := x + algebraGenerators.randomIndex
             else
                x := fingerPrint (i, algebraGenerators.1,_
-- 
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