refactor(arithmetic): simplify initDifficulty and remove redundant input clamping

- drop redundant constrainDifficulty and initDifficultyRaw
- remove clamp from initDifficulty, apply constrainDifficulty at call sites matching py-fsrs approach
- remove redundant constrainDifficulty/constrainStability from nextRecallStability and nextForgetStability inputs

Author: cantalupo555

arithmetic.go

@@ -50,10 +50,6 @@ func (p *Parameters) initStability(r Rating) float64 {
 }
 
 func (p *Parameters) initDifficulty(r Rating) float64 {
-	return constrainDifficulty(p.W[4] - math.Exp(p.W[5]*float64(r-1)) + 1)
-}
-
-func (p *Parameters) initDifficultyRaw(r Rating) float64 {
 	return p.W[4] - math.Exp(p.W[5]*float64(r-1)) + 1
 }
 
@@ -77,7 +73,7 @@ func (p *Parameters) nextIntervalRaw(s float64) float64 {
 func (p *Parameters) nextDifficulty(d float64, r Rating) float64 {
 	deltaD := -p.W[6] * float64(r-3)
 	nextD := d + linearDamping(deltaD, d)
-	return constrainDifficulty(p.meanReversion(p.initDifficultyRaw(Easy), nextD))
+	return constrainDifficulty(p.meanReversion(p.initDifficulty(Easy), nextD))
 }
 
 func (p *Parameters) shortTermStability(s float64, r Rating) float64 {
@@ -94,9 +90,6 @@ func (p *Parameters) meanReversion(init float64, current float64) float64 {
 }
 
 func (p *Parameters) nextRecallStability(d float64, s float64, r float64, rating Rating) float64 {
-	d = constrainDifficulty(d)
-	s = constrainStability(s)
-
 	var hardPenalty, easyBonus float64
 	if rating == Hard {
 		hardPenalty = p.W[15]
@@ -119,9 +112,6 @@ func (p *Parameters) nextRecallStability(d float64, s float64, r float64, rating
 }
 
 func (p *Parameters) nextForgetStability(d float64, s float64, r float64) float64 {
-	d = constrainDifficulty(d)
-	s = constrainStability(s)
-
 	newS := p.W[11] *
 		math.Pow(d, -p.W[12]) *
 		(math.Pow(s+1, p.W[13]) - 1) *

fsrs_test.go

@@ -1118,8 +1118,8 @@ func TestNextStateElapsedZero(t *testing.T) {
 	if item.Memory.Stability != p.initStability(Good) {
 		t.Errorf("NextState new card: got stability=%v want=%v", item.Memory.Stability, p.initStability(Good))
 	}
-	if item.Memory.Difficulty != p.initDifficulty(Good) {
-		t.Errorf("NextState new card: got difficulty=%v want=%v", item.Memory.Difficulty, p.initDifficulty(Good))
+	if item.Memory.Difficulty != constrainDifficulty(p.initDifficulty(Good)) {
+		t.Errorf("NextState new card: got difficulty=%v want=%v", item.Memory.Difficulty, constrainDifficulty(p.initDifficulty(Good)))
 	}
 
 	current := &MemoryState{Stability: 5.0, Difficulty: 5.0}

parameters.go

@@ -78,7 +78,7 @@ func (p *Parameters) nextStateInner(current *MemoryState, desiredRetention, elap
 
 	if current == nil || current.Stability == 0 {
 		newS = p.initStability(grade)
-		newD = p.initDifficulty(grade)
+		newD = constrainDifficulty(p.initDifficulty(grade))
 	} else {
 		newD = p.nextDifficulty(current.Difficulty, grade)
 		if elapsed == 0 && p.EnableShortTerm {

scheduler_basic.go

@@ -43,7 +43,7 @@ func (bs basicScheduler) newState(grade Rating) SchedulingInfo {
 	}
 
 	next := bs.current
-	next.Difficulty = bs.parameters.initDifficulty(grade)
+	next.Difficulty = constrainDifficulty(bs.parameters.initDifficulty(grade))
 	next.Stability = bs.parameters.initStability(grade)
 	steps := bs.parameters.LearningSteps
 	elapsed := bs.elapsedDays()

scheduler_longterm.go

@@ -39,16 +39,16 @@ func (lts longTermScheduler) newState(grade Rating) SchedulingInfo {
 }
 
 func (lts longTermScheduler) initDs(nextAgain, nextHard, nextGood, nextEasy *Card) {
-	nextAgain.Difficulty = lts.parameters.initDifficulty(Again)
+	nextAgain.Difficulty = constrainDifficulty(lts.parameters.initDifficulty(Again))
 	nextAgain.Stability = lts.parameters.initStability(Again)
 
-	nextHard.Difficulty = lts.parameters.initDifficulty(Hard)
+	nextHard.Difficulty = constrainDifficulty(lts.parameters.initDifficulty(Hard))
 	nextHard.Stability = lts.parameters.initStability(Hard)
 
-	nextGood.Difficulty = lts.parameters.initDifficulty(Good)
+	nextGood.Difficulty = constrainDifficulty(lts.parameters.initDifficulty(Good))
 	nextGood.Stability = lts.parameters.initStability(Good)
 
-	nextEasy.Difficulty = lts.parameters.initDifficulty(Easy)
+	nextEasy.Difficulty = constrainDifficulty(lts.parameters.initDifficulty(Easy))
 	nextEasy.Stability = lts.parameters.initStability(Easy)
 }