diff --git a/_test/gs_test.gno b/_test/gs_test.gno
index 7dd99713..a1fce6fb 100644
--- a/_test/gs_test.gno
+++ b/_test/gs_test.gno
@@ -74,16 +74,16 @@ func init() {
 	// println(govAddr, "// gov")
 }
 
-// 1. [POOL] Init
+// 1. [TC - POOL] Init
 func TestPoolInitManual(t *testing.T) {
 	std.TestSetOrigCaller(pc01)
 
 	pl.InitManual()
 
-	shouldPanicWithMsg(t, func() { pl.InitManual() }, "[POOl] pool_manager.gno__InitManual() || contract must not be initialized")
+	shouldPanicWithMsg(t, func() { pl.InitManual() }, "[TC - POOl] pool_manager.gno__InitManual() || contract must not be initialized")
 }
 
-// 2. [POOL] CreatePool
+// 2. [TC - POOL] CreatePool
 func TestPoolCreatePool(t *testing.T) {
 	std.TestSetOrigCaller(pc01)
 
@@ -99,7 +99,7 @@ func TestPoolCreatePool(t *testing.T) {
 	shouldEQ(t, tmpPool.GetTickSpacing(), bigint(10))
 }
 
-// 3. [POSITION] Mint LP
+// 3. [TC - POSITION] Mint LP
 func TestPositionMint(t *testing.T) {
 	tmpPool := pl.GetPool(pToken0, pToken1, pFee)
 
@@ -171,7 +171,7 @@ func TestPositionMint(t *testing.T) {
 	}
 }
 
-// 4. [STAKER] CreateExternalIncentive
+// 4. [TC - STAKER] CreateExternalIncentive
 // Internal incentive will automatcially created via init()
 func TestStakerCreateExternalIncentive(t *testing.T) {
 	std.TestSetOrigCaller(ci01)
@@ -190,11 +190,11 @@ func TestStakerCreateExternalIncentive(t *testing.T) {
 		func() {
 			stk.CreateExternalIncentive("bar_foo_500", "OBL", 10_000_000_000, GetTimestamp(), GetTimestamp()+(TIMESTAMP_30DAYS*2))
 		},
-		"[STAKER] staker.gno__CreateExternalIncentive() || incentive(YmFyX2Zvb181MDBfT0JM) already exists",
+		"[TC - STAKER] staker.gno__CreateExternalIncentive() || incentive(YmFyX2Zvb181MDBfT0JM) already exists",
 	)
 }
 
-// 5. [STAKER] StakeToken
+// 5. [TC - STAKER] StakeToken
 func TestStakerStakeToken(t *testing.T) {
 	// lp01 stakes tokenId '1'
 	std.TestSetPrevAddr(lp01) // r3v4_xxx: only test code, we need to call gnft.Approve directly from user
@@ -215,7 +215,7 @@ func TestStakerStakeToken(t *testing.T) {
 	shouldEQ(t, gnft.OwnerOf(bigint(2)), stakerAddr)
 }
 
-// 6. [POOL] SetFeeProtocol
+// 6. [TC - POOL] SetFeeProtocol
 func TestPoolSetFeeProtocol(t *testing.T) {
 	std.TestSetOrigCaller(pc01)
 
@@ -226,7 +226,7 @@ func TestPoolSetFeeProtocol(t *testing.T) {
 	shouldEQ(t, tmpPool.GetFeeProtocol(), bigint(134))
 }
 
-// 7. [POOL] Swap ( token0 -> token1 )
+// 7. [TC - POOL] Swap ( token0 -> token1 )
 func TestPoolSwap01(t *testing.T) {
 	tmpPool := pl.GetPool(pToken0, pToken1, pFee)
 	testPrice01 := bigint(MIN_SQRT_RATIO + 1)
@@ -283,7 +283,7 @@ func TestPoolSwap01(t *testing.T) {
 	shouldEQ(t, token1Balance(pc01), cAmount1)
 }
 
-// 8. [POSITION] Collect
+// 8. [TC - POSITION] Collect
 // * collect fee from (swap token0 > token1)
 func TestPositionCollect01(t *testing.T) {
 	{
@@ -337,7 +337,7 @@ func TestPositionCollect01(t *testing.T) {
 	}
 }
 
-// 9. [POOL] Swap ( token1 -> token0 )
+// 9. [TC - POOL] Swap ( token1 -> token0 )
 func TestPoolSwap10(t *testing.T) {
 	tmpPool := pl.GetPool(pToken0, pToken1, pFee)
 	testPrice10 := bigint(MAX_SQRT_RATIO - 1)
@@ -393,7 +393,7 @@ func TestPoolSwap10(t *testing.T) {
 	shouldEQ(t, token1Balance(pc01), cAmount1)
 }
 
-// 10. [POSITION] Collect
+// 10. [TC - POSITION] Collect
 // * collect fee from (swap token1 > token0)
 func TestPositionCollect10(t *testing.T) {
 	{
@@ -447,7 +447,7 @@ func TestPositionCollect10(t *testing.T) {
 	}
 }
 
-// 11. [STAKER] UnstakeToken
+// 11. [TC - STAKER] UnstakeToken
 func TestStakerUnstakeToken(t *testing.T) {
 	{
 		// lp01 unstakes tokenId '1'
@@ -478,7 +478,7 @@ func TestStakerUnstakeToken(t *testing.T) {
 	}
 }
 
-// 12. [STAKER] EndExternalIncentive
+// 12. [TC - STAKER] EndExternalIncentive
 func TestStakerEndExternalIncentive(t *testing.T) {
 	std.TestSetOrigCaller(ci01)
 	std.TestSkipHeights(1036800)
@@ -494,7 +494,7 @@ func TestStakerEndExternalIncentive(t *testing.T) {
 	shouldPanicWithMsg(
 		t,
 		func() { stk.EndExternalIncentive("bar_foo_500", "OBL") },
-		"[STAKER] staker.gno__EndIncentive() || cannot end non existent incentive(YmFyX2Zvb181MDBfT0JM)",
+		"[TC - STAKER] staker.gno__EndIncentive() || cannot end non existent incentive(YmFyX2Zvb181MDBfT0JM)",
 	)
 }
 
@@ -513,7 +513,7 @@ func a2u(addr std.Address) users.AddressOrName {
 
 func tid(tokenId interface{}) grc721.TokenID {
 	if tokenId == nil {
-		panic("[POSITION] test_helper.gno__tid() || tokenId is nil")
+		panic("[TC - POSITION] test_helper.gno__tid() || tokenId is nil")
 	}
 
 	switch tokenId.(type) {
@@ -528,7 +528,7 @@ func tid(tokenId interface{}) grc721.TokenID {
 	case grc721.TokenID:
 		return tokenId.(grc721.TokenID)
 	default:
-		panic("[STAKER] utils.gno__tid() || unsupported tokenId type")
+		panic("[TC - STAKER] utils.gno__tid() || unsupported tokenId type")
 	}
 }
 
diff --git a/_test/phase_v1.mk b/_test/phase_v1.mk
index 95b02e6b..e2a9f277 100644
--- a/_test/phase_v1.mk
+++ b/_test/phase_v1.mk
@@ -116,7 +116,6 @@ approve-lp01:
 	$(info ************ [APPROVE] foo & bar from lp01 to pool ************)
 	@echo "" | gnokey maketx call -pkgpath gno.land/r/foo -func Approve -args $(ADDR_POOL) -args 50000000000 -insecure-password-stdin=true -remote $(GNOLAND_RPC_URL) -broadcast=true -chainid dev -gas-fee 1ugnot -gas-wanted 9000000 -memo "" lp01 > /dev/null
 	@echo "" | gnokey maketx call -pkgpath gno.land/r/bar -func Approve -args $(ADDR_POOL) -args 50000000000 -insecure-password-stdin=true -remote $(GNOLAND_RPC_URL) -broadcast=true -chainid dev -gas-fee 1ugnot -gas-wanted 9000000 -memo "" lp01 > /dev/null
-
 	@echo
 
 
@@ -124,7 +123,6 @@ approve-tr01:
 	$(info ************ [APPROVE] foo & bar from tr01 to pool ************)
 	@echo "" | gnokey maketx call -pkgpath gno.land/r/bar -func Approve -args $(ADDR_POOL) -args 50000000000 -insecure-password-stdin=true -remote $(GNOLAND_RPC_URL) -broadcast=true -chainid dev -gas-fee 1ugnot -gas-wanted 9000000 -memo "" tr01 > /dev/null
 	@echo "" | gnokey maketx call -pkgpath gno.land/r/foo -func Approve -args $(ADDR_POOL) -args 50000000000 -insecure-password-stdin=true -remote $(GNOLAND_RPC_URL) -broadcast=true -chainid dev -gas-fee 1ugnot -gas-wanted 9000000 -memo "" tr01 > /dev/null
-
 	@echo
 
 
diff --git a/pool/pool_multi_lp_fee_api_test.gno b/pool/pool_multi_lp_fee_api_test.gno
index e3160475..aa3df056 100644
--- a/pool/pool_multi_lp_fee_api_test.gno
+++ b/pool/pool_multi_lp_fee_api_test.gno
@@ -107,9 +107,8 @@ func TestSwap(t *testing.T) {
 
 	Swap(pToken0, pToken1, pFee, tr01, true, bigint(150000), test_price_01)
 	jsonStr = gjson.Parse(ApiGetPool("bar_foo_500"))
-	jsonStr = gjson.Parse(ApiGetPool("bar_foo_500"))
 	shouldEQ(t, jsonStr.Get("response.data.token0_balance").Int(), 3107550)
-	shouldEQ(t, jsonStr.Get("response.data.token1_balance").Int(), 8448096)
+	shouldEQ(t, jsonStr.Get("response.data.token1_balance").Int(), 7635058)
 	shouldEQ(t, jsonStr.Get("response.data.liquidity").Int(), 100000000)
 	shouldEQ(t, len(jsonStr.Get("response.data.positions").Array()), 1)
 
@@ -117,8 +116,8 @@ func TestSwap(t *testing.T) {
 	// Swap(pToken0, pToken1, pFee, tr01, true, bigint(1500000), test_price_01) // two iteration // s0: 1_500_000 // s1: -3_626_984 // currentTick: 7668
 	std.TestSkipHeights(1)
 	jsonStr = gjson.Parse(ApiGetPool("bar_foo_500"))
-	shouldEQ(t, jsonStr.Get("response.data.token0_balance").Int(), 4718682)
-	shouldEQ(t, jsonStr.Get("response.data.token1_balance").Int(), 9049947)
+	shouldEQ(t, jsonStr.Get("response.data.token0_balance").Int(), 1496418)
+	shouldEQ(t, jsonStr.Get("response.data.token1_balance").Int(), 8236909)
 	shouldEQ(t, jsonStr.Get("response.data.liquidity").Int(), 100000000)
 	shouldEQ(t, len(jsonStr.Get("response.data.positions").Array()), 1)
 
@@ -132,8 +131,8 @@ func TestSwap(t *testing.T) {
 	Collect(pToken0, pToken1, pFee, lp01, test_tickLower, test_tickUpper, 100000000, 100000000)
 	std.TestSkipHeights(1)
 	jsonStr = gjson.Parse(ApiGetPool("bar_foo_500"))
-	shouldEQ(t, jsonStr.Get("response.data.token0_balance").Int(), 4718608)
-	shouldEQ(t, jsonStr.Get("response.data.token1_balance").Int(), 9049647)
+	shouldEQ(t, jsonStr.Get("response.data.token0_balance").Int(), 1496344)
+	shouldEQ(t, jsonStr.Get("response.data.token1_balance").Int(), 8236609)
 	shouldEQ(t, jsonStr.Get("response.data.liquidity").Int(), 100000000)
 	shouldEQ(t, len(jsonStr.Get("response.data.positions").Array()), 1)
 }
diff --git a/pool/tick_bitmap.gno b/pool/tick_bitmap.gno
index 463a40bd..2530d7d3 100644
--- a/pool/tick_bitmap.gno
+++ b/pool/tick_bitmap.gno
@@ -15,7 +15,7 @@ func (pool *Pool) tickBitmapFlipTick(
 	tick int32,
 	tickSpacing int32,
 ) {
-	require(tick%tickSpacing == 0, ufmt.Sprintf("[POOL] tick_bitmap.gno__tickBitmapFlipTick() || tick MOD tickSpacing(%s) != 0", tick%tickSpacing))
+	require(tick%tickSpacing == 0, ufmt.Sprintf("[POOL] tick_bitmap.gno__tickBitmapFlipTick() || tick MOD tickSpacing(%d) != 0", tick%tickSpacing))
 	wordPos, bitPos := tickBitmapPosition(tick)
 	mask := bigint(1) << uint64(bitPos)
 	requireUnsigned(mask, ufmt.Sprintf("[POOL] tick_bitmap.gno__tickBitmapFlipTick() || mask(%s) > 0", mask))
diff --git a/position/consts.gno b/position/consts.gno
index ed0bee79..2e9f85a4 100644
--- a/position/consts.gno
+++ b/position/consts.gno
@@ -14,4 +14,6 @@ const (
 	// ETC
 	Q96  bigint = 79228162514264337593543950336           // 2 ** 96
 	Q128 bigint = 340282366920938463463374607431768211456 // 2 ** 128
+
+	MAX_UINT160 bigint = 1461501637330902918203684832716283019655932542975
 )
diff --git a/position/math_logic.gno b/position/math_logic.gno
new file mode 100644
index 00000000..8fc2753a
--- /dev/null
+++ b/position/math_logic.gno
@@ -0,0 +1,54 @@
+package position
+
+import (
+	p "gno.land/r/pool"
+)
+
+func DryMint(
+	tickCurrent int32,
+	tickLower int32,
+	tickUpper int32,
+	amount0Desired bigint,
+	amount1Desired bigint,
+) (amount0, amount1 bigint) {
+	sqrtRatioX96 := p.TickMathGetSqrtRatioAtTick(tickCurrent)
+	sqrtLowerX96 := p.TickMathGetSqrtRatioAtTick(tickLower)
+	sqrtUpperX96 := p.TickMathGetSqrtRatioAtTick(tickUpper)
+
+	liquidity := liquidityAmountsGetLiquidityForAmounts(
+		sqrtRatioX96,
+		sqrtLowerX96,
+		sqrtUpperX96,
+		amount0Desired,
+		amount1Desired,
+	)
+
+	if liquidity != 0 {
+		if tickCurrent < tickLower {
+			amount0 = sqrtPriceMathGetAmount0Delta(
+				sqrtLowerX96,
+				sqrtUpperX96,
+				liquidity,
+			)
+		} else if tickCurrent < tickUpper {
+			amount0 = sqrtPriceMathGetAmount0Delta(
+				sqrtRatioX96,
+				sqrtUpperX96,
+				liquidity,
+			)
+
+			amount1 = sqrtPriceMathGetAmount1Delta(
+				sqrtLowerX96,
+				sqrtRatioX96,
+				liquidity,
+			)
+		} else {
+			amount1 = sqrtPriceMathGetAmount1Delta(
+				sqrtLowerX96,
+				sqrtUpperX96,
+				liquidity,
+			)
+		}
+	}
+	return
+}
diff --git a/position/math_logic_test.gno b/position/math_logic_test.gno
new file mode 100644
index 00000000..be64d718
--- /dev/null
+++ b/position/math_logic_test.gno
@@ -0,0 +1,44 @@
+package position
+
+import (
+	"testing"
+)
+
+func TestDryMintInRange(t *testing.T) {
+	m0, m1 := DryMint(
+		10000, // tickCurrent int32
+		7000,  // tickLower int32
+		15000, // tickUpper int32
+		10000, // amount0Desired bigint
+		16000, // amount1Desired bigint
+	)
+
+	shouldEQ(t, m0, bigint(9347))
+	shouldEQ(t, m1, bigint(15999))
+}
+
+func TestDryMintLowerRange(t *testing.T) {
+	m0, m1 := DryMint(
+		7000,  // tickCurrent int32
+		5000,  // tickLower int32
+		6000,  // tickUpper int32
+		10000, // amount0Desired bigint
+		16000, // amount1Desired bigint
+	)
+
+	shouldEQ(t, m0, bigint(0))
+	shouldEQ(t, m1, bigint(15999))
+}
+
+func TestDryMintUpperRange(t *testing.T) {
+	m0, m1 := DryMint(
+		7000,  // tickCurrent int32
+		9000,  // tickLower int32
+		11000, // tickUpper int32
+		10000, // amount0Desired bigint
+		16000, // amount1Desired bigint
+	)
+
+	shouldEQ(t, m0, bigint(9999))
+	shouldEQ(t, m1, bigint(0))
+}
diff --git a/position/sqrt_price_math.gno b/position/sqrt_price_math.gno
new file mode 100644
index 00000000..3d6ed788
--- /dev/null
+++ b/position/sqrt_price_math.gno
@@ -0,0 +1,192 @@
+package position
+
+import "gno.land/p/demo/ufmt"
+
+func sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp(
+	sqrtPX96 bigint,
+	liquidity bigint,
+	amount bigint,
+	add bool,
+) bigint {
+	requireUnsigned(sqrtPX96, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp() || sqrtPX96(%s) >= 0", sqrtPX96))
+	requireUnsigned(liquidity, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp() || liquidity(%s) >= 0", liquidity))
+	requireUnsigned(amount, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp() || amount(%s) >= 0", amount))
+	if amount == 0 {
+		return sqrtPX96
+	}
+
+	numerator1 := liquidity << 96
+	requireUnsigned(numerator1, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp() || numerator1(%s) >= 0", numerator1))
+
+	product := amount * sqrtPX96
+	requireUnsigned(product, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp() || product(%s) >= 0", product))
+
+	var denominator bigint
+
+	if add {
+		if product/amount == sqrtPX96 {
+			denominator = numerator1 + product
+			requireUnsigned(denominator, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp() || denominator(%s) >= 0", denominator))
+
+			if denominator >= numerator1 {
+				requireUnsigned(numerator1*sqrtPX96/denominator, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp() || numerator1 * sqrtPX96 / denominator(%s) >= 0", numerator1*sqrtPX96/denominator))
+				return numerator1 * sqrtPX96 / denominator
+			}
+		}
+
+		requireUnsigned(numerator1/((numerator1/sqrtPX96)+amount), ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp() || numerator1 / ( (numerator1 / sqrtPX96) + amount(%s) >= 0", (numerator1/((numerator1/sqrtPX96)+amount))))
+		return numerator1 / ((numerator1 / sqrtPX96) + amount)
+	}
+	require(product/amount == sqrtPX96 && numerator1 > product, "[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp() || condition must return true")
+
+	denominator = numerator1 - product
+	requireUnsigned(denominator, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp() || denominator(%s) >= 0", denominator))
+
+	requireUnsigned(numerator1*sqrtPX96/denominator, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp() || numerator1 * sqrtPX96 / denominator(%s) >= 0", numerator1*sqrtPX96/denominator))
+	return numerator1 * sqrtPX96 / denominator
+}
+
+func sqrtPriceMathGetNextSqrtPriceFromAmount1RoundingDown(
+	sqrtPX96 bigint,
+	liquidity bigint,
+	amount bigint,
+	add bool,
+) bigint {
+	requireUnsigned(sqrtPX96, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount1RoundingDown() || sqrtPX96(%s) >= 0", sqrtPX96))
+	requireUnsigned(liquidity, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount1RoundingDown() || liquidity(%s) >= 0", liquidity))
+	requireUnsigned(amount, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount1RoundingDown() || amount(%s) >= 0", amount))
+
+	var quotient bigint
+	if add {
+		if amount <= MAX_UINT160 {
+			quotient = (amount << 96) / liquidity
+		} else {
+			quotient = amount * Q96 / liquidity
+		}
+		requireUnsigned(quotient, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount1RoundingDown() || quotient(%s) >= 0", quotient))
+		return sqrtPX96 + quotient
+	} else {
+		if amount <= MAX_UINT160 {
+			quotient = (amount << 96) / liquidity
+		} else {
+			quotient = amount * Q96 / liquidity
+		}
+		requireUnsigned(quotient, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount1RoundingDown() || quotient(%s) >= 0", quotient))
+
+		require(sqrtPX96 > quotient, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromAmount1RoundingDown() || sqrtPX96(%s) must be greater than quotient(%s)", sqrtPX96, quotient))
+		return sqrtPX96 - quotient
+	}
+}
+
+func sqrtPriceMathGetNextSqrtPriceFromInput(
+	sqrtPX96 bigint,
+	liquidity bigint,
+	amountIn bigint,
+	zeroForOne bool,
+) (sqrtQ bigint) {
+	requireUnsigned(sqrtPX96, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromInput() || sqrtPX96(%s) >= 0", sqrtPX96))
+	requireUnsigned(liquidity, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromInput() || liquidity(%s) >= 0", liquidity))
+	requireUnsigned(amountIn, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromInput() || amountIn(%s) >= 0", amountIn))
+
+	if zeroForOne {
+		requireUnsigned(sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp(sqrtPX96, liquidity, amountIn, true), "[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromInput() || condition must return `v` >= 0__#1")
+		return sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp(sqrtPX96, liquidity, amountIn, true)
+	}
+
+	requireUnsigned(sqrtPriceMathGetNextSqrtPriceFromAmount1RoundingDown(sqrtPX96, liquidity, amountIn, true), "[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromInput() || condition must return `v` >= 0__#2")
+	return sqrtPriceMathGetNextSqrtPriceFromAmount1RoundingDown(sqrtPX96, liquidity, amountIn, true)
+}
+
+func sqrtPriceMathGetNextSqrtPriceFromOutput(
+	sqrtPX96 bigint,
+	liquidity bigint,
+	amountOut bigint,
+	zeroForOne bool,
+) (sqrtQ bigint) {
+	requireUnsigned(sqrtPX96, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromOutput() || sqrtPX96(%s) >= 0", sqrtPX96))
+	requireUnsigned(liquidity, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromOutput() || liquidity(%s) >= 0", liquidity))
+
+	if zeroForOne {
+		requireUnsigned(sqrtPriceMathGetNextSqrtPriceFromAmount1RoundingDown(sqrtPX96, liquidity, amountOut, false), "[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromOutput() || condition must return `v` >= 0__#1")
+		return sqrtPriceMathGetNextSqrtPriceFromAmount1RoundingDown(sqrtPX96, liquidity, amountOut, false)
+	}
+
+	requireUnsigned(sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp(sqrtPX96, liquidity, amountOut, false), "[POSITION] sqrt_price_math.gno__sqrtPriceMathGetNextSqrtPriceFromOutput() || condition must return `v` >= 0__#2")
+	return sqrtPriceMathGetNextSqrtPriceFromAmount0RoundingUp(sqrtPX96, liquidity, amountOut, false)
+}
+
+func sqrtPriceMathGetAmount0DeltaHelper(
+	sqrtRatioAX96 bigint,
+	sqrtRatioBX96 bigint,
+	liquidity bigint,
+) bigint {
+	requireUnsigned(sqrtRatioAX96, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetAmount0DeltaHelper() || sqrtRatioAX96(%s) >= 0", sqrtRatioAX96))
+	requireUnsigned(sqrtRatioBX96, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetAmount0DeltaHelper() || sqrtRatioBX96(%s) >= 0", sqrtRatioBX96))
+	requireUnsigned(liquidity, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetAmount0DeltaHelper() || liquidity(%s) >= 0", liquidity))
+
+	if sqrtRatioAX96 > sqrtRatioBX96 {
+		sqrtRatioAX96, sqrtRatioBX96 = sqrtRatioBX96, sqrtRatioAX96
+	}
+	requireUnsigned(sqrtRatioAX96, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetAmount0DeltaHelper() || sqrtRatioAX96(%s) >= 0", sqrtRatioAX96))
+
+	numerator1 := liquidity << 96
+	requireUnsigned(numerator1, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetAmount0DeltaHelper() || numerator1(%s) >= 0", numerator1))
+
+	numerator2 := sqrtRatioBX96 - sqrtRatioAX96
+	requireUnsigned(numerator2, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetAmount0DeltaHelper() || numerator2(%s) >= 0", numerator2))
+
+	requireUnsigned((numerator1*numerator2/sqrtRatioBX96)/sqrtRatioAX96, "[POSITION] sqrt_price_math.gno__sqrtPriceMathGetAmount0DeltaHelper() || condition must return `v` >= 0")
+	return (numerator1 * numerator2 / sqrtRatioBX96) / sqrtRatioAX96
+}
+
+func sqrtPriceMathGetAmount1DeltaHelper(
+	sqrtRatioAX96 bigint,
+	sqrtRatioBX96 bigint,
+	liquidity bigint,
+) bigint {
+	requireUnsigned(sqrtRatioAX96, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetAmount1DeltaHelper() || sqrtRatioAX96(%s) >= 0", sqrtRatioAX96))
+	requireUnsigned(sqrtRatioBX96, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetAmount1DeltaHelper() || sqrtRatioBX96(%s) >= 0", sqrtRatioBX96))
+	requireUnsigned(liquidity, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetAmount1DeltaHelper() || liquidity(%s) >= 0", liquidity))
+
+	if sqrtRatioAX96 > sqrtRatioBX96 {
+		sqrtRatioAX96, sqrtRatioBX96 = sqrtRatioBX96, sqrtRatioAX96
+	}
+
+	return liquidity * (sqrtRatioBX96 - sqrtRatioAX96) / Q96
+}
+
+func sqrtPriceMathGetAmount0Delta(
+	sqrtRatioAX96 bigint,
+	sqrtRatioBX96 bigint,
+	liquidity bigint,
+) bigint {
+	requireUnsigned(sqrtRatioAX96, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetAmount0Delta() || sqrtRatioAX96(%s) >= 0", sqrtRatioAX96))
+	requireUnsigned(sqrtRatioBX96, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetAmount0Delta() || sqrtRatioBX96(%s) >= 0", sqrtRatioBX96))
+
+	if liquidity < 0 {
+		return -sqrtPriceMathGetAmount0DeltaHelper(sqrtRatioAX96, sqrtRatioBX96, -liquidity)
+	}
+
+	return sqrtPriceMathGetAmount0DeltaHelper(sqrtRatioAX96, sqrtRatioBX96, liquidity)
+}
+
+func sqrtPriceMathGetAmount1Delta(
+	sqrtRatioAX96 bigint,
+	sqrtRatioBX96 bigint,
+	liquidity bigint,
+) bigint {
+	requireUnsigned(sqrtRatioAX96, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetAmount1Delta() || sqrtRatioAX96(%s) >= 0", sqrtRatioAX96))
+	requireUnsigned(sqrtRatioBX96, ufmt.Sprintf("[POSITION] sqrt_price_math.gno__sqrtPriceMathGetAmount1Delta() || sqrtRatioBX96(%s) >= 0", sqrtRatioBX96))
+
+	if liquidity < 0 {
+		return -sqrtPriceMathGetAmount1DeltaHelper(sqrtRatioAX96, sqrtRatioBX96, -liquidity)
+	}
+
+	return sqrtPriceMathGetAmount1DeltaHelper(sqrtRatioAX96, sqrtRatioBX96, liquidity)
+}
+
+func requireUnsigned(x bigint, msg string) {
+	if x < 0 {
+		panic(msg)
+	}
+}