pyth_sdk/

price.rs

use borsh::{
    BorshDeserialize,
    BorshSerialize,
};

use std::convert::TryFrom;

use schemars::JsonSchema;

use crate::{
    utils,
    UnixTimestamp,
};

// Constants for working with pyth's number representation
const PD_EXPO: i32 = -9;
const PD_SCALE: u64 = 1_000_000_000;
const MAX_PD_V_U64: u64 = (1 << 28) - 1;

/// A price with a degree of uncertainty at a certain time, represented as a price +- a confidence
/// interval.
///
/// Please refer to the documentation at https://docs.pyth.network/consumers/best-practices for
/// using this price safely.
///
/// The confidence interval roughly corresponds to the standard error of a normal distribution.
/// Both the price and confidence are stored in a fixed-point numeric representation, `x *
/// 10^expo`, where `expo` is the exponent. For example:
///
/// ```
/// use pyth_sdk::Price;
/// Price { price: 12345, conf: 267, expo: -2, publish_time: 100 }; // represents 123.45 +- 2.67 published at UnixTimestamp 100
/// Price { price: 123, conf: 1, expo: 2,  publish_time: 100 }; // represents 12300 +- 100 published at UnixTimestamp 100
/// ```
///
/// `Price` supports a limited set of mathematical operations. All of these operations will
/// propagate any uncertainty in the arguments into the result. However, the uncertainty in the
/// result may overestimate the true uncertainty (by at most a factor of `sqrt(2)`) due to
/// computational limitations. Furthermore, all of these operations may return `None` if their
/// result cannot be represented within the numeric representation (e.g., the exponent is so
/// small that the price does not fit into an i64). Users of these methods should (1) select
/// their exponents to avoid this problem, and (2) handle the `None` case gracefully.
#[derive(
    Clone,
    Copy,
    Default,
    Debug,
    PartialEq,
    Eq,
    BorshSerialize,
    BorshDeserialize,
    serde::Serialize,
    serde::Deserialize,
    JsonSchema,
)]
pub struct Price {
    /// Price.
    #[serde(with = "utils::as_string")] // To ensure accuracy on conversion to json.
    #[schemars(with = "String")]
    pub price:        i64,
    /// Confidence interval.
    #[serde(with = "utils::as_string")]
    #[schemars(with = "String")]
    pub conf:         u64,
    /// Exponent.
    pub expo:         i32,
    /// Publish time.
    pub publish_time: UnixTimestamp,
}

impl Price {
    /// Get the current price of this account in a different quote currency.
    ///
    /// If this account represents the price of the product X/Z, and `quote` represents the price
    /// of the product Y/Z, this method returns the price of X/Y. Use this method to get the
    /// price of e.g., mSOL/SOL from the mSOL/USD and SOL/USD accounts.
    ///
    /// `result_expo` determines the exponent of the result, i.e., the number of digits below the
    /// decimal point. This method returns `None` if either the price or confidence are too
    /// large to be represented with the requested exponent.
    ///
    /// Example:
    /// ```ignore
    /// let btc_usd: Price = ...;
    /// let eth_usd: Price = ...;
    /// // -8 is the desired exponent for the result
    /// let btc_eth: Price = btc_usd.get_price_in_quote(&eth_usd, -8);
    /// println!("BTC/ETH price: ({} +- {}) x 10^{}", price.price, price.conf, price.expo);
    /// ```
    pub fn get_price_in_quote(&self, quote: &Price, result_expo: i32) -> Option<Price> {
        self.div(quote)?.scale_to_exponent(result_expo)
    }

    /// Get the valuation of a collateral position according to:
    /// 1. the net amount currently deposited (across the protocol)
    /// 2. the deposits endpoint for the affine combination (across the protocol)
    /// 3. the initial (at 0 deposits) and final (at the deposits endpoint) valuation discount rates
    ///
    /// We use a linear interpolation between the the initial and final discount rates,
    /// scaled by the proportion of the deposits endpoint that has been deposited.
    /// This essentially assumes a linear liquidity cumulative density function,
    /// which has been shown to be a reasonable assumption for many crypto tokens in literature.
    /// For more detail on this: https://pythnetwork.medium.com/improving-lending-protocols-with-liquidity-oracles-fd1ea4f96f37
    ///
    /// If the assumptions of the liquidity curve hold true, we are obtaining a lower bound for the
    /// net price at which one can sell the quantity of token specified by deposits in the open
    /// markets. We value collateral according to the total deposits in the protocol due to the
    /// present intractability of assessing collateral at risk by price range.
    ///
    /// Args
    /// deposits: u64, quantity of token deposited in the protocol
    /// deposits_endpoint: u64, deposits right endpoint for the affine combination
    /// rate_discount_initial: u64, initial discounted rate at 0 deposits (units given by
    /// discount_exponent) rate_discount_final: u64, final discounted rate at deposits_endpoint
    /// deposits (units given by discount_exponent) discount_exponent: u64, the exponent to
    /// apply to the discounts above (e.g. if discount_final is 10 but meant to express 0.1/10%,
    /// exponent would be -2) note that if discount_initial is bigger than 100% per the discount
    /// exponent scale, then the initial valuation of the collateral will be higher than the oracle
    /// price
    pub fn get_collateral_valuation_price(
        &self,
        deposits: u64,
        deposits_endpoint: u64,
        rate_discount_initial: u64,
        rate_discount_final: u64,
        discount_exponent: i32,
    ) -> Option<Price> {
        // valuation price should not increase as amount of collateral grows, so
        // rate_discount_initial should >= rate_discount_final
        if rate_discount_initial < rate_discount_final {
            return None;
        }

        // get price versions of discounts
        let initial_percentage = Price {
            price:        i64::try_from(rate_discount_initial).ok()?,
            conf:         0,
            expo:         discount_exponent,
            publish_time: 0,
        };
        let final_percentage = Price {
            price:        i64::try_from(rate_discount_final).ok()?,
            conf:         0,
            expo:         discount_exponent,
            publish_time: 0,
        };

        // get the interpolated discount as a price
        let discount_interpolated = Price::affine_combination(
            0,
            initial_percentage,
            i64::try_from(deposits_endpoint).ok()?,
            final_percentage,
            i64::try_from(deposits).ok()?,
            -9,
        )?;

        let conf_orig = self.conf;
        let expo_orig = self.expo;

        // get price discounted, convert back to the original exponents we received the price in
        let price_discounted = self
            .mul(&discount_interpolated)?
            .scale_to_exponent(expo_orig)?;

        return Some(Price {
            price:        price_discounted.price,
            conf:         conf_orig,
            expo:         price_discounted.expo,
            publish_time: self.publish_time,
        });
    }

    /// Get the valuation of a borrow position according to:
    /// 1. the net amount currently borrowed (across the protocol)
    /// 2. the borrowed endpoint for the affine combination (across the protocol)
    /// 3. the initial (at 0 borrows) and final (at the borrow endpoint) valuation premiums
    ///
    /// We use a linear interpolation between the the initial and final premiums,
    /// scaled by the proportion of the borrows endpoint that has been borrowed out.
    /// This essentially assumes a linear liquidity cumulative density function,
    /// which has been shown to be a reasonable assumption for many crypto tokens in literature.
    /// For more detail on this: https://pythnetwork.medium.com/improving-lending-protocols-with-liquidity-oracles-fd1ea4f96f37
    ///
    /// If the assumptions of the liquidity curve hold true, we are obtaining an upper bound for the
    /// net price at which one can buy the quantity of token specified by borrows in the open
    /// markets. We value the borrows according to the total borrows out of the protocol due to
    /// the present intractability of assessing collateral at risk and repayment likelihood by
    /// price range.
    ///
    /// Args
    /// borrows: u64, quantity of token borrowed from the protocol
    /// borrows_endpoint: u64, borrows right endpoint for the affine combination
    /// rate_premium_initial: u64, initial premium at 0 borrows (units given by premium_exponent)
    /// rate_premium_final: u64, final premium at borrows_endpoint borrows (units given by
    /// premium_exponent) premium_exponent: u64, the exponent to apply to the premiums above
    /// (e.g. if premium_final is 50 but meant to express 0.05/5%, exponent would be -3)
    /// note that if premium_initial is less than 100% per the premium exponent scale, then the
    /// initial valuation of the borrow will be lower than the oracle price
    pub fn get_borrow_valuation_price(
        &self,
        borrows: u64,
        borrows_endpoint: u64,
        rate_premium_initial: u64,
        rate_premium_final: u64,
        premium_exponent: i32,
    ) -> Option<Price> {
        // valuation price should not decrease as amount of borrow grows, so rate_premium_initial
        // should <= rate_premium_final
        if rate_premium_initial > rate_premium_final {
            return None;
        }

        // get price versions of premiums
        let initial_percentage = Price {
            price:        i64::try_from(rate_premium_initial).ok()?,
            conf:         0,
            expo:         premium_exponent,
            publish_time: 0,
        };
        let final_percentage = Price {
            price:        i64::try_from(rate_premium_final).ok()?,
            conf:         0,
            expo:         premium_exponent,
            publish_time: 0,
        };

        // get the interpolated premium as a price
        let premium_interpolated = Price::affine_combination(
            0,
            initial_percentage,
            i64::try_from(borrows_endpoint).ok()?,
            final_percentage,
            i64::try_from(borrows).ok()?,
            -9,
        )?;

        let conf_orig = self.conf;
        let expo_orig = self.expo;

        // get price premium, convert back to the original exponents we received the price in
        let price_premium = self
            .mul(&premium_interpolated)?
            .scale_to_exponent(expo_orig)?;

        return Some(Price {
            price:        price_premium.price,
            conf:         conf_orig,
            expo:         price_premium.expo,
            publish_time: self.publish_time,
        });
    }

    /// affine_combination performs an affine combination of two prices located at x coordinates x1
    /// and x2, for query x coordinate x_query Takes in 2 points and a 3rd "query" x coordinate,
    /// to compute the value at x_query Effectively draws a line between the 2 points and then
    /// proceeds to interpolate/extrapolate to find the value at the query coordinate according
    /// to that line
    ///
    /// affine_combination gives you the Price, scaled to a specified exponent, closest to y2 *
    /// ((xq-x1)/(x2-x1)) + y1 * ((x2-x3)/(x2-x1)) If the numerators and denominators of the
    /// fractions there are both representable within 8 digits of precision and the fraction
    /// itself is also representable within 8 digits of precision, there is no loss due to taking
    /// the fractions. If the prices are normalized, then there is no loss in taking the
    /// products via mul. Otherwise, the prices will be converted to a form representable within
    /// 8 digits of precision. The scaling to the specified expo pre_add_expo introduces a max
    /// error of 2*10^pre_add_expo. If pre_add_expo is small enough relative to the products,
    /// then there is no loss due to scaling. If the fractions are expressable within 8 digits
    /// of precision, the ys are normalized, and the exponent is sufficiently small,
    /// then you get an exact result. Otherwise, your error is bounded as given below.
    ///
    /// Args
    /// x1: i64, the x coordinate of the first point
    /// y1: Price, the y coordinate of the first point, represented as a Price struct
    /// x2: i64, the x coordinate of the second point, must be greater than x1
    /// y2: Price, the y coordinate of the second point, represented as a Price struct
    /// x_query: i64, the query x coordinate, at which we wish to impute a y value
    /// pre_add_expo: i32, the exponent to scale to, before final addition; essentially the final
    /// precision you want
    ///
    /// Logic
    /// imputed y value = y2 * ((xq-x1)/(x2-x1)) + y1 * ((x2-x3)/(x2-x1))
    /// 1. compute A = xq-x1
    /// 2. compute B = x2-xq
    /// 3. compute C = x2-x1
    /// 4. compute D = A/C
    /// 5. compute E = B/C
    /// 6. compute F = y2 * D
    /// 7. compute G = y1 * E
    /// 8. compute H = F + G
    ///
    /// Bounds due to precision loss
    /// x = 10^(PD_EXPO+2)
    /// fraction (due to normalization & division) incurs max loss of x
    /// Thus, max loss here: Err(D), Err(E) <= x
    /// If y1, y2 already normalized, no additional error. O/w, Err(y1), Err(y2) with normalization
    /// <= x Err(F), Err(G) <= (1+x)^2 - 1 (in fractional terms) ~= 2x
    /// Err(H) <= 2*2x = 4x, when PD_EXPO = -9 ==> Err(H) <= 4*10^-7
    ///
    /// Scaling this back has error bounded by the expo (10^pre_add_expo).
    /// This is because reverting a potentially finer expo to a coarser grid has the potential to be
    /// off by the order of the atomic unit of the coarser grid.
    /// This scaling error combines with the previous error additively: Err <= 4x +
    /// 2*10^pre_add_expo But if pre_add_expo is reasonably small (<= -9), then other term will
    /// dominate
    ///
    /// Note that if the ys are unnormalized due to the confidence but not the price, the
    /// normalization could zero out the price fields. Based on this, it is recommended that
    /// input prices are normalized, or at least do not contain huge discrepancies between price and
    /// confidence.
    pub fn affine_combination(
        x1: i64,
        y1: Price,
        x2: i64,
        y2: Price,
        x_query: i64,
        pre_add_expo: i32,
    ) -> Option<Price> {
        if x2 <= x1 {
            return None;
        }

        // get the deltas for the x coordinates
        // 1. compute A = xq-x1
        let delta_q1 = x_query.checked_sub(x1)?;
        // 2. compute B = x2-xq
        let delta_2q = x2.checked_sub(x_query)?;
        // 3. compute C = x2-x1
        let delta_21 = x2.checked_sub(x1)?;

        // get the relevant fractions of the deltas, with scaling
        // 4. compute D = A/C, Err(D) <= x
        let frac_q1 = Price::fraction(delta_q1, delta_21)?;
        // 5. compute E = B/C, Err(E) <= x
        let frac_2q = Price::fraction(delta_2q, delta_21)?;

        // calculate products for left and right
        // 6. compute F = y2 * D, Err(F) <= (1+x)^2 - 1 ~= 2x
        let mut left = y2.mul(&frac_q1)?;
        // 7. compute G = y1 * E, Err(G) <= (1+x)^2 - 1 ~= 2x
        let mut right = y1.mul(&frac_2q)?;

        // Err(scaling) += 2*10^pre_add_expo
        left = left.scale_to_exponent(pre_add_expo)?;
        right = right.scale_to_exponent(pre_add_expo)?;

        // 8. compute H = F + G, Err(H) ~= 4x + 2*10^pre_add_expo
        return left.add(&right);
    }

    /// Get the price of a basket of currencies.
    ///
    /// Each entry in `amounts` is of the form `(price, qty, qty_expo)`, and the result is the sum
    /// of `price * qty * 10^qty_expo`. The result is returned with exponent `result_expo`.
    ///
    /// An example use case for this function is to get the value of an LP token.
    ///
    /// Example:
    /// ```ignore
    /// let btc_usd: Price = ...;
    /// let eth_usd: Price = ...;
    /// // Quantity of each asset in fixed-point a * 10^e.
    /// // This represents 0.1 BTC and .05 ETH.
    /// // -8 is desired exponent for result
    /// let basket_price: Price = Price::price_basket(&[
    ///     (btc_usd, 10, -2),
    ///     (eth_usd, 5, -2)
    ///   ], -8);
    /// println!("0.1 BTC and 0.05 ETH are worth: ({} +- {}) x 10^{} USD",
    ///          basket_price.price, basket_price.conf, basket_price.expo);
    /// ```
    pub fn price_basket(amounts: &[(Price, i64, i32)], result_expo: i32) -> Option<Price> {
        if amounts.is_empty() {
            return None;
        }

        let mut res = Price {
            price:        0,
            conf:         0,
            expo:         result_expo,
            publish_time: amounts[0].0.publish_time,
        };
        for amount in amounts {
            res = res.add(
                &amount
                    .0
                    .cmul(amount.1, amount.2)?
                    .scale_to_exponent(result_expo)?,
            )?
        }
        Some(res)
    }

    /// Divide this price by `other` while propagating the uncertainty in both prices into the
    /// result.
    ///
    /// This method will automatically select a reasonable exponent for the result. If both
    /// `self` and `other` are normalized, the exponent is `self.expo + PD_EXPO - other.expo`
    /// (i.e., the fraction has `PD_EXPO` digits of additional precision). If they are not
    /// normalized, this method will normalize them, resulting in an unpredictable result
    /// exponent. If the result is used in a context that requires a specific exponent,
    /// please call `scale_to_exponent` on it.
    pub fn div(&self, other: &Price) -> Option<Price> {
        // Price is not guaranteed to store its price/confidence in normalized form.
        // Normalize them here to bound the range of price/conf, which is required to perform
        // arithmetic operations.

        let base = self.normalize()?;
        let other = other.normalize()?;

        if other.price == 0 {
            return None;
        }

        // These use at most 27 bits each
        let (base_price, base_sign) = Price::to_unsigned(base.price);
        let (other_price, other_sign) = Price::to_unsigned(other.price);

        // Compute the midprice, base in terms of other.
        // Uses at most 57 bits
        let midprice = base_price.checked_mul(PD_SCALE)?.checked_div(other_price)?;
        let midprice_expo = base.expo.checked_sub(other.expo)?.checked_add(PD_EXPO)?;

        // Compute the confidence interval.
        // This code uses the 1-norm instead of the 2-norm for computational reasons.
        // Let p +- a and q +- b be the two arguments to this method. The correct
        // formula is p/q * sqrt( (a/p)^2 + (b/q)^2 ). This quantity
        // is difficult to compute due to the sqrt and overflow/underflow considerations.
        //
        // This code instead computes p/q * (a/p + b/q) = a/q + pb/q^2 .
        // This quantity is at most a factor of sqrt(2) greater than the correct result, which
        // shouldn't matter considering that confidence intervals are typically ~0.1% of the price.

        // This uses 57 bits and has an exponent of PD_EXPO.
        let other_confidence_pct: u64 =
            other.conf.checked_mul(PD_SCALE)?.checked_div(other_price)?;

        // first term is 57 bits, second term is 57 + 58 - 29 = 86 bits. Same exponent as the
        // midprice. Note: the computation of the 2nd term consumes about 3k ops. We may
        // want to optimize this.
        let conf = (base.conf.checked_mul(PD_SCALE)?.checked_div(other_price)? as u128)
            .checked_add(
                (other_confidence_pct as u128)
                    .checked_mul(midprice as u128)?
                    .checked_div(PD_SCALE as u128)?,
            )?;

        // Note that this check only fails if an argument's confidence interval was >> its price,
        // in which case None is a reasonable result, as we have essentially 0 information about the
        // price.
        if conf < (u64::MAX as u128) {
            Some(Price {
                price:        (midprice as i64)
                    .checked_mul(base_sign)?
                    .checked_mul(other_sign)?,
                conf:         conf as u64,
                expo:         midprice_expo,
                publish_time: self.publish_time.min(other.publish_time),
            })
        } else {
            None
        }
    }

    /// Add `other` to this, propagating uncertainty in both prices.
    ///
    /// Requires both `Price`s to have the same exponent -- use `scale_to_exponent` on
    /// the arguments if necessary.
    ///
    /// TODO: could generalize this method to support different exponents.
    pub fn add(&self, other: &Price) -> Option<Price> {
        assert_eq!(self.expo, other.expo);

        let price = self.price.checked_add(other.price)?;
        // The conf should technically be sqrt(a^2 + b^2), but that's harder to compute.
        let conf = self.conf.checked_add(other.conf)?;
        Some(Price {
            price,
            conf,
            expo: self.expo,
            publish_time: self.publish_time.min(other.publish_time),
        })
    }

    /// Multiply this `Price` by a constant `c * 10^e`.
    pub fn cmul(&self, c: i64, e: i32) -> Option<Price> {
        self.mul(&Price {
            price:        c,
            conf:         0,
            expo:         e,
            publish_time: self.publish_time,
        })
    }

    /// Multiply this `Price` by `other`, propagating any uncertainty.
    pub fn mul(&self, other: &Price) -> Option<Price> {
        // Price is not guaranteed to store its price/confidence in normalized form.
        // Normalize them here to bound the range of price/conf, which is required to perform
        // arithmetic operations.
        let base = self.normalize()?;
        let other = other.normalize()?;

        // These use at most 27 bits each
        let (base_price, base_sign) = Price::to_unsigned(base.price);
        let (other_price, other_sign) = Price::to_unsigned(other.price);

        // Uses at most 27*2 = 54 bits
        let midprice = base_price.checked_mul(other_price)?;
        let midprice_expo = base.expo.checked_add(other.expo)?;

        // Compute the confidence interval.
        // This code uses the 1-norm instead of the 2-norm for computational reasons.
        // Note that this simplifies: pq * (a/p + b/q) = qa + pb
        // 27*2 + 1 bits
        let conf = base
            .conf
            .checked_mul(other_price)?
            .checked_add(other.conf.checked_mul(base_price)?)?;

        Some(Price {
            price: (midprice as i64)
                .checked_mul(base_sign)?
                .checked_mul(other_sign)?,
            conf,
            expo: midprice_expo,
            publish_time: self.publish_time.min(other.publish_time),
        })
    }

    /// Get a copy of this struct where the price and confidence
    /// have been normalized to be between `MIN_PD_V_I64` and `MAX_PD_V_I64`.
    pub fn normalize(&self) -> Option<Price> {
        // signed division is very expensive in op count
        let (mut p, s) = Price::to_unsigned(self.price);
        let mut c = self.conf;
        let mut e = self.expo;

        while p > MAX_PD_V_U64 || c > MAX_PD_V_U64 {
            p = p.checked_div(10)?;
            c = c.checked_div(10)?;
            e = e.checked_add(1)?;
        }

        Some(Price {
            price:        (p as i64).checked_mul(s)?,
            conf:         c,
            expo:         e,
            publish_time: self.publish_time,
        })
    }

    /// Scale this price/confidence so that its exponent is `target_expo`.
    ///
    /// Return `None` if this number is outside the range of numbers representable in `target_expo`,
    /// which will happen if `target_expo` is too small.
    ///
    /// Warning: if `target_expo` is significantly larger than the current exponent, this
    /// function will return 0 +- 0.
    pub fn scale_to_exponent(&self, target_expo: i32) -> Option<Price> {
        let mut delta = target_expo.checked_sub(self.expo)?;
        if delta >= 0 {
            let mut p = self.price;
            let mut c = self.conf;
            // 2nd term is a short-circuit to bound op consumption
            while delta > 0 && (p != 0 || c != 0) {
                p = p.checked_div(10)?;
                c = c.checked_div(10)?;
                delta = delta.checked_sub(1)?;
            }

            Some(Price {
                price:        p,
                conf:         c,
                expo:         target_expo,
                publish_time: self.publish_time,
            })
        } else {
            let mut p = self.price;
            let mut c = self.conf;

            // Either p or c == None will short-circuit to bound op consumption
            while delta < 0 {
                p = p.checked_mul(10)?;
                c = c.checked_mul(10)?;
                delta = delta.checked_add(1)?;
            }

            Some(Price {
                price:        p,
                conf:         c,
                expo:         target_expo,
                publish_time: self.publish_time,
            })
        }
    }

    /// Helper function to convert signed integers to unsigned and a sign bit, which simplifies
    /// some of the computations above.
    fn to_unsigned(x: i64) -> (u64, i64) {
        if x == i64::MIN {
            // special case because i64::MIN == -i64::MIN
            (i64::MAX as u64 + 1, -1)
        } else if x < 0 {
            (-x as u64, -1)
        } else {
            (x as u64, 1)
        }
    }

    /// Helper function to create fraction
    ///
    /// fraction(x, y) gives you the unnormalized Price closest to x/y.
    /// This output could have arbitrary exponent due to the div, so you may need to call
    /// scale_to_exponent to scale to your desired expo. If you cannot represent x/y exactly
    /// within 8 digits of precision, it may zero out the remainder. In particular, if x and/or
    /// y cannot be represented within 8 digits of precision, potential for precision error.
    /// If x and y can both be represented within 8 digits of precision AND x/y can be represented
    /// within 8 digits, no precision loss.
    ///
    /// Error of normalizing x, y <= 10^(PD_EXPO+2) = 10^-7
    /// Inherits any bounded errors from normalization and div
    fn fraction(x: i64, y: i64) -> Option<Price> {
        // convert x and y to Prices
        let x_as_price = Price {
            price:        x,
            conf:         0,
            expo:         0,
            publish_time: 0,
        };
        let y_as_price = Price {
            price:        y,
            conf:         0,
            expo:         0,
            publish_time: 0,
        };

        // get the relevant fraction
        let frac = x_as_price.div(&y_as_price)?;

        return Some(frac);
    }
}

#[cfg(test)]
mod test {
    use quickcheck::TestResult;
    use quickcheck_macros::quickcheck;
    use std::convert::TryFrom;

    use crate::price::{
        Price,
        MAX_PD_V_U64,
        PD_EXPO,
        PD_SCALE,
    };

    const MAX_PD_V_I64: i64 = MAX_PD_V_U64 as i64;
    const MIN_PD_V_I64: i64 = -MAX_PD_V_I64;

    fn pc(price: i64, conf: u64, expo: i32) -> Price {
        Price {
            price,
            conf,
            expo,
            publish_time: 0,
        }
    }

    fn pc_scaled(price: i64, conf: u64, cur_expo: i32, expo: i32) -> Price {
        Price {
            price,
            conf,
            expo: cur_expo,
            publish_time: 0,
        }
        .scale_to_exponent(expo)
        .unwrap()
    }


    #[test]
    fn test_normalize() {
        fn succeeds(price1: Price, expected: Price) {
            assert_eq!(price1.normalize().unwrap(), expected);
        }

        fn fails(price1: Price) {
            assert_eq!(price1.normalize(), None);
        }

        succeeds(
            pc(2 * (PD_SCALE as i64), 3 * PD_SCALE, 0),
            pc(2 * (PD_SCALE as i64) / 100, 3 * PD_SCALE / 100, 2),
        );

        succeeds(
            pc(-2 * (PD_SCALE as i64), 3 * PD_SCALE, 0),
            pc(-2 * (PD_SCALE as i64) / 100, 3 * PD_SCALE / 100, 2),
        );

        // the i64 / u64 max values are a factor of 10^11 larger than MAX_PD_V
        let expo = -(PD_EXPO - 2);
        let scale_i64 = (PD_SCALE as i64) * 100;
        let scale_u64 = scale_i64 as u64;
        succeeds(pc(i64::MAX, 1, 0), pc(i64::MAX / scale_i64, 0, expo));
        succeeds(pc(i64::MIN, 1, 0), pc(i64::MIN / scale_i64, 0, expo));
        succeeds(pc(1, u64::MAX, 0), pc(0, u64::MAX / scale_u64, expo));

        // exponent overflows
        succeeds(
            pc(i64::MAX, 1, i32::MAX - expo),
            pc(i64::MAX / scale_i64, 0, i32::MAX),
        );
        fails(pc(i64::MAX, 1, i32::MAX - expo + 1));
        succeeds(
            pc(i64::MAX, 1, i32::MIN),
            pc(i64::MAX / scale_i64, 0, i32::MIN + expo),
        );

        succeeds(
            pc(1, u64::MAX, i32::MAX - expo),
            pc(0, u64::MAX / scale_u64, i32::MAX),
        );
        fails(pc(1, u64::MAX, i32::MAX - expo + 1));

        // Check timestamp won't change after normalize
        let p = Price {
            publish_time: 100,
            ..Default::default()
        };

        assert_eq!(p.normalize().unwrap().publish_time, 100);
    }

    #[test]
    fn test_scale_to_exponent() {
        fn succeeds(price1: Price, target: i32, expected: Price) {
            assert_eq!(price1.scale_to_exponent(target).unwrap(), expected);
        }

        fn fails(price1: Price, target: i32) {
            assert_eq!(price1.scale_to_exponent(target), None);
        }

        succeeds(pc(1234, 1234, 0), 0, pc(1234, 1234, 0));
        succeeds(pc(1234, 1234, 0), 1, pc(123, 123, 1));
        succeeds(pc(1234, 1234, 0), 2, pc(12, 12, 2));
        succeeds(pc(-1234, 1234, 0), 2, pc(-12, 12, 2));
        succeeds(pc(1234, 1234, 0), 4, pc(0, 0, 4));
        succeeds(pc(1234, 1234, 0), -1, pc(12340, 12340, -1));
        succeeds(pc(1234, 1234, 0), -2, pc(123400, 123400, -2));
        succeeds(pc(1234, 1234, 0), -8, pc(123400000000, 123400000000, -8));
        // insufficient precision to represent the result in this exponent
        fails(pc(1234, 1234, 0), -20);
        fails(pc(1234, 0, 0), -20);
        fails(pc(0, 1234, 0), -20);

        // fails because exponent delta overflows
        fails(pc(1, 1, i32::MIN), i32::MAX);

        // Check timestamp won't change after scale to exponent
        let p = Price {
            publish_time: 100,
            ..pc(1234, 1234, 0)
        };

        assert_eq!(p.scale_to_exponent(2).unwrap().publish_time, 100);
    }

    #[test]
    fn test_div() {
        fn succeeds(price1: Price, price2: Price, expected: Price) {
            assert_eq!(price1.div(&price2).unwrap(), expected);
        }

        fn fails(price1: Price, price2: Price) {
            let result = price1.div(&price2);
            assert_eq!(result, None);
        }

        succeeds(pc(1, 1, 0), pc(1, 1, 0), pc_scaled(1, 2, 0, PD_EXPO));
        succeeds(pc(1, 1, -8), pc(1, 1, -8), pc_scaled(1, 2, 0, PD_EXPO));
        succeeds(pc(10, 1, 0), pc(1, 1, 0), pc_scaled(10, 11, 0, PD_EXPO));
        succeeds(pc(1, 1, 1), pc(1, 1, 0), pc_scaled(10, 20, 0, PD_EXPO + 1));
        succeeds(pc(1, 1, 0), pc(5, 1, 0), pc_scaled(20, 24, -2, PD_EXPO));

        // Negative numbers
        succeeds(pc(-1, 1, 0), pc(1, 1, 0), pc_scaled(-1, 2, 0, PD_EXPO));
        succeeds(pc(1, 1, 0), pc(-1, 1, 0), pc_scaled(-1, 2, 0, PD_EXPO));
        succeeds(pc(-1, 1, 0), pc(-1, 1, 0), pc_scaled(1, 2, 0, PD_EXPO));

        // Different exponents in the two inputs
        succeeds(
            pc(100, 10, -8),
            pc(2, 1, -7),
            pc_scaled(500_000_000, 300_000_000, -8, PD_EXPO - 1),
        );
        succeeds(
            pc(100, 10, -4),
            pc(2, 1, 0),
            pc_scaled(500_000, 300_000, -8, PD_EXPO + -4),
        );

        // Test with end range of possible inputs where the output should not lose precision.
        succeeds(
            pc(MAX_PD_V_I64, MAX_PD_V_U64, 0),
            pc(MAX_PD_V_I64, MAX_PD_V_U64, 0),
            pc_scaled(1, 2, 0, PD_EXPO),
        );
        succeeds(
            pc(MAX_PD_V_I64, MAX_PD_V_U64, 0),
            pc(1, 1, 0),
            pc_scaled(MAX_PD_V_I64, 2 * MAX_PD_V_U64, 0, PD_EXPO),
        );
        succeeds(
            pc(1, 1, 0),
            pc(MAX_PD_V_I64, MAX_PD_V_U64, 0),
            pc(
                (PD_SCALE as i64) / MAX_PD_V_I64,
                2 * (PD_SCALE / MAX_PD_V_U64),
                PD_EXPO,
            ),
        );

        succeeds(
            pc(MIN_PD_V_I64, MAX_PD_V_U64, 0),
            pc(MIN_PD_V_I64, MAX_PD_V_U64, 0),
            pc_scaled(1, 2, 0, PD_EXPO),
        );
        succeeds(
            pc(MIN_PD_V_I64, MAX_PD_V_U64, 0),
            pc(1, 1, 0),
            pc_scaled(MIN_PD_V_I64, 2 * MAX_PD_V_U64, 0, PD_EXPO),
        );
        succeeds(
            pc(1, 1, 0),
            pc(MIN_PD_V_I64, MAX_PD_V_U64, 0),
            pc(
                (PD_SCALE as i64) / MIN_PD_V_I64,
                2 * (PD_SCALE / MAX_PD_V_U64),
                PD_EXPO,
            ),
        );

        succeeds(
            pc(1, MAX_PD_V_U64, 0),
            pc(1, MAX_PD_V_U64, 0),
            pc_scaled(1, 2 * MAX_PD_V_U64, 0, PD_EXPO),
        );
        // This fails because the confidence interval is too large to be represented in PD_EXPO
        fails(pc(MAX_PD_V_I64, MAX_PD_V_U64, 0), pc(1, MAX_PD_V_U64, 0));

        // Unnormalized tests below here

        // More realistic inputs (get BTC price in ETH)
        let ten_e7: i64 = 10000000;
        let uten_e7: u64 = 10000000;
        succeeds(
            pc(520010 * ten_e7, 310 * uten_e7, -8),
            pc(38591 * ten_e7, 18 * uten_e7, -8),
            pc(1347490347, 1431804, -8),
        );

        // Test with end range of possible inputs to identify overflow
        // These inputs will lose precision due to the initial normalization.
        // Get the rounded versions of these inputs in order to compute the expected results.
        let normed = pc(i64::MAX, u64::MAX, 0).normalize().unwrap();

        succeeds(
            pc(i64::MAX, u64::MAX, 0),
            pc(i64::MAX, u64::MAX, 0),
            pc_scaled(1, 4, 0, PD_EXPO),
        );
        succeeds(
            pc(i64::MAX, u64::MAX, 0),
            pc(1, 1, 0),
            pc_scaled(
                normed.price,
                3 * (normed.price as u64),
                normed.expo,
                normed.expo + PD_EXPO,
            ),
        );
        succeeds(
            pc(1, 1, 0),
            pc(i64::MAX, u64::MAX, 0),
            pc(
                (PD_SCALE as i64) / normed.price,
                3 * (PD_SCALE / (normed.price as u64)),
                PD_EXPO - normed.expo,
            ),
        );

        succeeds(
            pc(i64::MAX, 1, 0),
            pc(i64::MAX, 1, 0),
            pc_scaled(1, 0, 0, PD_EXPO),
        );
        succeeds(
            pc(i64::MAX, 1, 0),
            pc(1, 1, 0),
            pc_scaled(
                normed.price,
                normed.price as u64,
                normed.expo,
                normed.expo + PD_EXPO,
            ),
        );
        succeeds(
            pc(1, 1, 0),
            pc(i64::MAX, 1, 0),
            pc(
                (PD_SCALE as i64) / normed.price,
                PD_SCALE / (normed.price as u64),
                PD_EXPO - normed.expo,
            ),
        );

        let normed = pc(i64::MIN, u64::MAX, 0).normalize().unwrap();
        let normed_c = (-normed.price) as u64;

        succeeds(
            pc(i64::MIN, u64::MAX, 0),
            pc(i64::MIN, u64::MAX, 0),
            pc_scaled(1, 4, 0, PD_EXPO),
        );
        succeeds(
            pc(i64::MIN, u64::MAX, 0),
            pc(i64::MAX, u64::MAX, 0),
            pc_scaled(-1, 4, 0, PD_EXPO),
        );
        succeeds(
            pc(i64::MIN, u64::MAX, 0),
            pc(1, 1, 0),
            pc_scaled(
                normed.price,
                3 * normed_c,
                normed.expo,
                normed.expo + PD_EXPO,
            ),
        );
        succeeds(
            pc(1, 1, 0),
            pc(i64::MIN, u64::MAX, 0),
            pc(
                (PD_SCALE as i64) / normed.price,
                3 * (PD_SCALE / normed_c),
                PD_EXPO - normed.expo,
            ),
        );

        succeeds(
            pc(i64::MIN, 1, 0),
            pc(i64::MIN, 1, 0),
            pc_scaled(1, 0, 0, PD_EXPO),
        );
        succeeds(
            pc(i64::MIN, 1, 0),
            pc(1, 1, 0),
            pc_scaled(normed.price, normed_c, normed.expo, normed.expo + PD_EXPO),
        );
        succeeds(
            pc(1, 1, 0),
            pc(i64::MIN, 1, 0),
            pc(
                (PD_SCALE as i64) / normed.price,
                PD_SCALE / (normed_c),
                PD_EXPO - normed.expo,
            ),
        );

        // Price is zero pre-normalization
        succeeds(pc(0, 1, 0), pc(1, 1, 0), pc_scaled(0, 1, 0, PD_EXPO));
        succeeds(pc(0, 1, 0), pc(100, 1, 0), pc_scaled(0, 1, -2, PD_EXPO));
        fails(pc(1, 1, 0), pc(0, 1, 0));

        // Normalizing the input when the confidence is >> price produces a price of 0.
        fails(pc(1, 1, 0), pc(1, u64::MAX, 0));
        succeeds(
            pc(1, u64::MAX, 0),
            pc(1, 1, 0),
            pc_scaled(0, normed.conf, normed.expo, normed.expo + PD_EXPO),
        );

        // Exponent under/overflow.
        succeeds(
            pc(1, 1, i32::MAX),
            pc(1, 1, 0),
            pc(PD_SCALE as i64, 2 * PD_SCALE, i32::MAX + PD_EXPO),
        );
        fails(pc(1, 1, i32::MAX), pc(1, 1, -1));

        succeeds(
            pc(1, 1, i32::MIN - PD_EXPO),
            pc(1, 1, 0),
            pc(PD_SCALE as i64, 2 * PD_SCALE, i32::MIN),
        );
        succeeds(
            pc(1, 1, i32::MIN),
            pc(1, 1, PD_EXPO),
            pc(PD_SCALE as i64, 2 * PD_SCALE, i32::MIN),
        );
        fails(pc(1, 1, i32::MIN - PD_EXPO), pc(1, 1, 1));

        // Check timestamp will be the minimum after div
        let p1 = Price {
            publish_time: 100,
            ..pc(1234, 1234, 0)
        };

        let p2 = Price {
            publish_time: 200,
            ..pc(1234, 1234, 0)
        };

        assert_eq!(p1.div(&p2).unwrap().publish_time, 100);
        assert_eq!(p2.div(&p1).unwrap().publish_time, 100);
    }

    #[test]
    fn test_mul() {
        fn succeeds(price1: Price, price2: Price, expected: Price) {
            assert_eq!(price1.mul(&price2).unwrap(), expected);
        }

        fn fails(price1: Price, price2: Price) {
            let result = price1.mul(&price2);
            assert_eq!(result, None);
        }

        succeeds(pc(1, 1, 0), pc(1, 1, 0), pc(1, 2, 0));
        succeeds(pc(1, 1, -8), pc(1, 1, -8), pc(1, 2, -16));
        succeeds(pc(10, 1, 0), pc(1, 1, 0), pc(10, 11, 0));
        succeeds(pc(1, 1, 1), pc(1, 1, 0), pc(1, 2, 1));
        succeeds(pc(1, 1, 0), pc(5, 1, 0), pc(5, 6, 0));

        // Different exponents in the two inputs
        succeeds(pc(100, 10, -8), pc(2, 1, -7), pc(200, 120, -15));
        succeeds(pc(100, 10, -4), pc(2, 1, 0), pc(200, 120, -4));

        // Zero
        succeeds(pc(0, 10, -4), pc(2, 1, 0), pc(0, 20, -4));
        succeeds(pc(2, 1, 0), pc(0, 10, -4), pc(0, 20, -4));

        // Test with end range of possible inputs where the output should not lose precision.
        succeeds(
            pc(MAX_PD_V_I64, MAX_PD_V_U64, 0),
            pc(MAX_PD_V_I64, MAX_PD_V_U64, 0),
            pc(
                MAX_PD_V_I64 * MAX_PD_V_I64,
                2 * MAX_PD_V_U64 * MAX_PD_V_U64,
                0,
            ),
        );
        succeeds(
            pc(MAX_PD_V_I64, MAX_PD_V_U64, 0),
            pc(1, 1, 0),
            pc(MAX_PD_V_I64, 2 * MAX_PD_V_U64, 0),
        );
        succeeds(
            pc(1, MAX_PD_V_U64, 0),
            pc(3, 1, 0),
            pc(3, 1 + 3 * MAX_PD_V_U64, 0),
        );

        succeeds(
            pc(1, MAX_PD_V_U64, 0),
            pc(1, MAX_PD_V_U64, 0),
            pc(1, 2 * MAX_PD_V_U64, 0),
        );
        succeeds(
            pc(MAX_PD_V_I64, MAX_PD_V_U64, 0),
            pc(1, MAX_PD_V_U64, 0),
            pc(MAX_PD_V_I64, MAX_PD_V_U64 + MAX_PD_V_U64 * MAX_PD_V_U64, 0),
        );

        succeeds(
            pc(MIN_PD_V_I64, MAX_PD_V_U64, 0),
            pc(MIN_PD_V_I64, MAX_PD_V_U64, 0),
            pc(
                MIN_PD_V_I64 * MIN_PD_V_I64,
                2 * MAX_PD_V_U64 * MAX_PD_V_U64,
                0,
            ),
        );
        succeeds(
            pc(MIN_PD_V_I64, MAX_PD_V_U64, 0),
            pc(MAX_PD_V_I64, MAX_PD_V_U64, 0),
            pc(
                MIN_PD_V_I64 * MAX_PD_V_I64,
                2 * MAX_PD_V_U64 * MAX_PD_V_U64,
                0,
            ),
        );
        succeeds(
            pc(MIN_PD_V_I64, MAX_PD_V_U64, 0),
            pc(1, 1, 0),
            pc(MIN_PD_V_I64, 2 * MAX_PD_V_U64, 0),
        );
        succeeds(
            pc(MIN_PD_V_I64, MAX_PD_V_U64, 0),
            pc(1, MAX_PD_V_U64, 0),
            pc(MIN_PD_V_I64, MAX_PD_V_U64 + MAX_PD_V_U64 * MAX_PD_V_U64, 0),
        );

        // Unnormalized tests below here
        let ten_e7: i64 = 10000000;
        let uten_e7: u64 = 10000000;
        succeeds(
            pc(3 * (PD_SCALE as i64), 3 * PD_SCALE, PD_EXPO),
            pc(2 * (PD_SCALE as i64), 4 * PD_SCALE, PD_EXPO),
            pc(6 * ten_e7 * ten_e7, 18 * uten_e7 * uten_e7, -14),
        );

        // Test with end range of possible inputs to identify overflow
        // These inputs will lose precision due to the initial normalization.
        // Get the rounded versions of these inputs in order to compute the expected results.
        let normed = pc(i64::MAX, u64::MAX, 0).normalize().unwrap();

        succeeds(
            pc(i64::MAX, u64::MAX, 0),
            pc(i64::MAX, u64::MAX, 0),
            pc(
                normed.price * normed.price,
                4 * ((normed.price * normed.price) as u64),
                normed.expo * 2,
            ),
        );
        succeeds(
            pc(i64::MAX, u64::MAX, 0),
            pc(1, 1, 0),
            pc(normed.price, 3 * (normed.price as u64), normed.expo),
        );

        succeeds(
            pc(i64::MAX, 1, 0),
            pc(i64::MAX, 1, 0),
            pc(normed.price * normed.price, 0, normed.expo * 2),
        );
        succeeds(
            pc(i64::MAX, 1, 0),
            pc(1, 1, 0),
            pc(normed.price, normed.price as u64, normed.expo),
        );

        let normed = pc(i64::MIN, u64::MAX, 0).normalize().unwrap();
        let normed_c = (-normed.price) as u64;

        succeeds(
            pc(i64::MIN, u64::MAX, 0),
            pc(i64::MIN, u64::MAX, 0),
            pc(
                normed.price * normed.price,
                4 * (normed_c * normed_c),
                normed.expo * 2,
            ),
        );
        succeeds(
            pc(i64::MIN, u64::MAX, 0),
            pc(1, 1, 0),
            pc(normed.price, 3 * normed_c, normed.expo),
        );

        succeeds(
            pc(i64::MIN, 1, 0),
            pc(i64::MIN, 1, 0),
            pc(normed.price * normed.price, 0, normed.expo * 2),
        );
        succeeds(
            pc(i64::MIN, 1, 0),
            pc(1, 1, 0),
            pc(normed.price, normed_c, normed.expo),
        );

        // Exponent under/overflow.
        succeeds(pc(1, 1, i32::MAX), pc(1, 1, 0), pc(1, 2, i32::MAX));
        succeeds(pc(1, 1, i32::MAX), pc(1, 1, -1), pc(1, 2, i32::MAX - 1));
        fails(pc(1, 1, i32::MAX), pc(1, 1, 1));

        succeeds(pc(1, 1, i32::MIN), pc(1, 1, 0), pc(1, 2, i32::MIN));
        succeeds(pc(1, 1, i32::MIN), pc(1, 1, 1), pc(1, 2, i32::MIN + 1));
        fails(pc(1, 1, i32::MIN), pc(1, 1, -1));

        // Check timestamp will be the minimum after mul
        let p1 = Price {
            publish_time: 100,
            ..pc(1234, 1234, 0)
        };

        let p2 = Price {
            publish_time: 200,
            ..pc(1234, 1234, 0)
        };

        assert_eq!(p1.mul(&p2).unwrap().publish_time, 100);
        assert_eq!(p2.mul(&p1).unwrap().publish_time, 100);
    }

    #[test]
    fn test_get_collateral_valuation_price() {
        fn succeeds(
            price: Price,
            deposits: u64,
            deposits_endpoint: u64,
            discount_initial: u64,
            discount_final: u64,
            discount_exponent: i32,
            expected: Price,
        ) {
            let price_collat = price
                .get_collateral_valuation_price(
                    deposits,
                    deposits_endpoint,
                    discount_initial,
                    discount_final,
                    discount_exponent,
                )
                .unwrap();

            assert_eq!(price_collat, expected);
        }

        fn fails(
            price: Price,
            deposits: u64,
            deposits_endpoint: u64,
            discount_initial: u64,
            discount_final: u64,
            discount_exponent: i32,
        ) {
            let result = price.get_collateral_valuation_price(
                deposits,
                deposits_endpoint,
                discount_initial,
                discount_final,
                discount_exponent,
            );
            assert_eq!(result, None);
        }

        // 0 deposits
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            0,
            100,
            100,
            90,
            -2,
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // half deposits
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            50,
            100,
            100,
            90,
            -2,
            pc(95 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // full deposits
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            100,
            100,
            100,
            90,
            -2,
            pc(90 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // 0 deposits, diff precision
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            0,
            100,
            1000,
            900,
            -3,
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // half deposits, diff precision
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            50,
            100,
            1000,
            900,
            -3,
            pc(95 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // full deposits, diff precision
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            100,
            100,
            1000,
            900,
            -3,
            pc(90 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // beyond final endpoint deposits
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            150,
            100,
            100,
            90,
            -2,
            pc(85 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // 0 deposits, staggered initial discount
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            0,
            100,
            98,
            90,
            -2,
            pc(98 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // half deposits, staggered initial discount
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            50,
            100,
            98,
            90,
            -2,
            pc(94 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // full deposits, staggered initial discount
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            100,
            100,
            98,
            90,
            -2,
            pc(90 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // test precision limits
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            0,
            1_000_000_000_000_000_000,
            100,
            90,
            -2,
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            1,
            1_000_000_000_000_000_000,
            100,
            90,
            -2,
            pc(100 * (PD_SCALE as i64) - 1000, 2 * PD_SCALE, -9),
        );
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            100_000_000,
            1_000_000_000_000_000_000,
            100,
            90,
            -2,
            pc(100 * (PD_SCALE as i64) - 1000, 2 * PD_SCALE, -9),
        );
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            1_000_000_000,
            1_000_000_000_000_000_000,
            100,
            90,
            -2,
            pc(100 * (PD_SCALE as i64) - 1000, 2 * PD_SCALE, -9),
        );
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            10_000_000_000,
            1_000_000_000_000_000_000,
            100,
            90,
            -2,
            pc(100 * (PD_SCALE as i64) - 1000, 2 * PD_SCALE, -9),
        );
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            100_000_000_000,
            1_000_000_000_000_000_000,
            100,
            90,
            -2,
            pc(100 * (PD_SCALE as i64) - 1000, 2 * PD_SCALE, -9),
        );
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            200_000_000_000,
            1_000_000_000_000_000_000,
            100,
            90,
            -2,
            pc(100 * (PD_SCALE as i64) - 2000, 2 * PD_SCALE, -9),
        );
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            1_000_000_000_000,
            1_000_000_000_000_000_000,
            100,
            90,
            -2,
            pc(100 * (PD_SCALE as i64) - 10000, 2 * PD_SCALE, -9),
        );

        // fails bc initial discount lower than final discount
        fails(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            50,
            100,
            89,
            90,
            -2,
        );
    }

    #[test]
    fn test_get_borrow_valuation_price() {
        fn succeeds(
            price: Price,
            borrows: u64,
            borrows_endpoint: u64,
            premium_initial: u64,
            premium_final: u64,
            premium_exponent: i32,
            expected: Price,
        ) {
            let price_borrow = price
                .get_borrow_valuation_price(
                    borrows,
                    borrows_endpoint,
                    premium_initial,
                    premium_final,
                    premium_exponent,
                )
                .unwrap();

            assert_eq!(price_borrow, expected);
        }

        fn fails(
            price: Price,
            borrows: u64,
            borrows_endpoint: u64,
            premium_initial: u64,
            premium_final: u64,
            premium_exponent: i32,
        ) {
            let result = price.get_borrow_valuation_price(
                borrows,
                borrows_endpoint,
                premium_initial,
                premium_final,
                premium_exponent,
            );
            assert_eq!(result, None);
        }

        // 0 borrows
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            0,
            100,
            100,
            110,
            -2,
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // half borrows
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            50,
            100,
            100,
            110,
            -2,
            pc(105 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // full borrows
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            100,
            100,
            100,
            110,
            -2,
            pc(110 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // 0 borrows, diff precision
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            0,
            100,
            1000,
            1100,
            -3,
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // half borrows, diff precision
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            50,
            100,
            1000,
            1100,
            -3,
            pc(105 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // full borrows, diff precision
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            100,
            100,
            1000,
            1100,
            -3,
            pc(110 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // beyond final endpoint borrows
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            150,
            100,
            100,
            110,
            -2,
            pc(115 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // 0 borrows, staggered initial premium
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            0,
            100,
            102,
            110,
            -2,
            pc(102 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // half borrows, staggered initial premium
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            50,
            100,
            102,
            110,
            -2,
            pc(106 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // full borrows, staggered initial premium
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            100,
            100,
            102,
            110,
            -2,
            pc(110 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );

        // test precision limits
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            1,
            1_000_000_000_000_000_000,
            100,
            110,
            -2,
            pc(100 * (PD_SCALE as i64 - 10), 2 * PD_SCALE, -9),
        );
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            100_000_000,
            1_000_000_000_000_000_000,
            100,
            110,
            -2,
            pc(100 * (PD_SCALE as i64 - 10), 2 * PD_SCALE, -9),
        );
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            1_000_000_000,
            1_000_000_000_000_000_000,
            100,
            110,
            -2,
            pc(100 * (PD_SCALE as i64 - 10), 2 * PD_SCALE, -9),
        );
        // interpolation now doesn't lose precision, but normalize in final multiply loses precision
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            10_000_000_000,
            1_000_000_000_000_000_000,
            100,
            110,
            -2,
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            20_000_000_000,
            1_000_000_000_000_000_000,
            100,
            110,
            -2,
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
        );
        // precision no longer lost
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            100_000_000_000,
            1_000_000_000_000_000_000,
            100,
            110,
            -2,
            pc(100 * (PD_SCALE as i64 + 10), 2 * PD_SCALE, -9),
        );
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            200_000_000_000,
            1_000_000_000_000_000_000,
            100,
            110,
            -2,
            pc(100 * (PD_SCALE as i64 + 20), 2 * PD_SCALE, -9),
        );
        succeeds(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            1_000_000_000_000,
            1_000_000_000_000_000_000,
            100,
            110,
            -2,
            pc(100 * (PD_SCALE as i64 + 100), 2 * PD_SCALE, -9),
        );

        // fails bc initial premium exceeds final premium
        fails(
            pc(100 * (PD_SCALE as i64), 2 * PD_SCALE, -9),
            50,
            100,
            111,
            110,
            -2,
        );
    }

    #[test]
    fn test_affine_combination() {
        fn succeeds(
            x1: i64,
            y1: Price,
            x2: i64,
            y2: Price,
            x_query: i64,
            pre_add_expo: i32,
            expected: Price,
        ) {
            let y_query = Price::affine_combination(x1, y1, x2, y2, x_query, pre_add_expo).unwrap();

            assert_eq!(y_query, expected);
        }

        fn fails(x1: i64, y1: Price, x2: i64, y2: Price, x_query: i64, pre_add_expo: i32) {
            let result = Price::affine_combination(x1, y1, x2, y2, x_query, pre_add_expo);
            assert_eq!(result, None);
        }

        // constant, in the bounds [x1, x2]
        succeeds(
            0,
            pc(100, 10, -4),
            10,
            pc(100, 10, -4),
            5,
            -9,
            pc(10_000_000, 1_000_000, -9),
        );

        // constant, outside the bounds
        succeeds(
            0,
            pc(100, 10, -4),
            10,
            pc(100, 10, -4),
            15,
            -9,
            pc(10_000_000, 2_000_000, -9),
        );

        // increasing, in the bounds
        succeeds(
            0,
            pc(90, 9, -4),
            10,
            pc(100, 10, -4),
            5,
            -9,
            pc(9_500_000, 950_000, -9),
        );

        // increasing, out of bounds
        succeeds(
            0,
            pc(90, 9, -4),
            10,
            pc(100, 10, -4),
            15,
            -9,
            pc(10_500_000, 1_950_000, -9),
        );

        // decreasing, in the bounds
        succeeds(
            0,
            pc(100, 10, -4),
            10,
            pc(80, 8, -4),
            5,
            -9,
            pc(9_000_000, 900_000, -9),
        );

        // decreasing, out of bounds
        succeeds(
            0,
            pc(100, 10, -4),
            10,
            pc(80, 8, -4),
            15,
            -9,
            pc(7_000_000, 1_700_000, -9),
        );

        // test with different pre_add_expos than -9
        succeeds(
            0,
            pc(100, 10, -2),
            100,
            pc(8000, 800, -4),
            50,
            -3,
            pc(900, 90, -3),
        );
        succeeds(
            100_000,
            pc(200_000, 20_000, -6),
            200_000,
            pc(-20_000_000_000, 2_000_000_000, -11),
            175_000,
            -4,
            pc(-1_000, 200, -4),
        );
        succeeds(
            2000,
            pc(75, 7, 3),
            10000,
            pc(675_000_000, 67_500_000, -3),
            6000,
            -2,
            pc(37_500_000, 3_725_000, -2),
        );
        succeeds(
            0,
            pc(100, 10, 2),
            100,
            pc(0, 0, -12),
            200,
            -12,
            pc(-10_000_000_000_000_000, 1_000_000_000_000_000, -12),
        );
        succeeds(
            0,
            pc(10, 1, 9),
            1000,
            pc(2, 0, 10),
            6000,
            6,
            pc(70_000, 5_000, 6),
        );

        // test loss due to scaling
        // lose more bc scaling to higher expo
        succeeds(
            0,
            pc(0, 0, -2),
            13,
            pc(10, 1, -2),
            1,
            -8,
            pc(769230, 76923, -8),
        );
        // lose less bc scaling to lower expo
        succeeds(
            0,
            pc(0, 0, -2),
            13,
            pc(10, 1, -2),
            1,
            -9,
            pc(7692307, 769230, -9),
        );
        // lose more bc need to increment expo more in scaling from original inputs
        succeeds(
            0,
            pc(0, 0, -3),
            13,
            pc(100, 10, -3),
            1,
            -9,
            pc(7692307, 769230, -9),
        );
        // lose less bc need to increment expo less in scaling from original inputs
        succeeds(
            0,
            pc(0, 0, -2),
            13,
            pc(100, 10, -2),
            1,
            -9,
            pc(76923076, 7692307, -9),
        );

        // Test with end range of possible inputs on endpoint xs
        succeeds(
            0,
            pc(100, 10, -9),
            i64::MAX,
            pc(0, 0, -9),
            i64::MAX / 10,
            -9,
            pc(90, 9, -9),
        );
        succeeds(
            i64::MIN,
            pc(100, 10, -9),
            i64::MIN / 2,
            pc(0, 0, -9),
            (i64::MIN / 4) * 3,
            -9,
            pc(50, 5, -9),
        );
        // test with xs that yield fractions with significantly different expos
        succeeds(
            0,
            pc(100_000_000, 10_000_000, -9),
            1_000_000_000_000_000,
            pc(0, 0, -9),
            10_000_000,
            -9,
            pc(99_999_999, 9_999_999, -9),
        );

        // Test with end range of possible inputs in prices to identify precision inaccuracy
        // precision inaccuracy due to loss in scaling
        succeeds(
            0,
            pc(MAX_PD_V_I64 - 10, 1000, -9),
            10,
            pc(MAX_PD_V_I64, 997, -9),
            5,
            -9,
            pc(MAX_PD_V_I64 - 6, 998, -9),
        );
        // precision inaccruacy due to loss in scaling
        succeeds(
            0,
            pc(MAX_PD_V_I64 - 1, 200, -9),
            10,
            pc(MAX_PD_V_I64, 191, -9),
            9,
            -9,
            pc(MAX_PD_V_I64 - 1, 191, -9),
        );
        // // test with max u64 in conf
        // // normalization to first price causes loss of price; loss in conf precision, only
        // preserve 8 digits of precision
        succeeds(
            0,
            pc(1000, u64::MAX, -9),
            1000,
            pc(-1000, 0, -9),
            500,
            -9,
            pc(-500, 92_23_372_000_000_000_000, -9),
        );
        // test with MAX_PD_V_U64 in conf--no loss in precision unlike above
        succeeds(
            0,
            pc(1000, MAX_PD_V_U64, -9),
            1000,
            pc(-1000, 0, -9),
            500,
            -9,
            pc(0, MAX_PD_V_U64 / 2, -9),
        );


        // Test with combinations of (in)exact fractions + (un)normalized ys; making pre_add_expo
        // very small to abstract away scaling error exact fraction, normalized ys --> exact
        // result
        succeeds(
            0,
            pc(0, 0, -9),
            512,
            pc(MAX_PD_V_I64 - 511, 512, -9),
            1,
            -18,
            pc(524_287_000_000_000, 1_000_000_000, -18),
        );
        // exact fraction, unnormalized ys, should be 524_289_000_000_000 exactly, but due to
        // normalization lose <= 2*10^(PD_EXPO+2) we see the actual result is off by <
        // 16_000_000, which corresponds to loss of ~= 1.6*10^-8 < 2*10^-7 as can be seen,
        // the normalization also messes with the final confidence precision
        succeeds(
            0,
            pc(0, 0, -9),
            512,
            pc(MAX_PD_V_I64 + 513, 512, -9),
            1,
            -18,
            pc(524_288_984_375_000, 996_093_750, -18),
        );
        // inexact fraciton, normalized ys, should be 262_143_000_000_000 exactly, but due to
        // fraction imprecision lose <= 2*10^(PD_EXPO+2) 1/1024 = 0.0009765625, but due to
        // imprecision --> 0.00976562; similar for 1023/1024 we see the actual result is off
        // by < 140_000_000, which corresponds to loss of 1.4*10^-7 < 2*10^-7
        // inexact fraction also messes with the final confidence precision
        succeeds(
            0,
            pc(0, 0, -9),
            1024,
            pc(MAX_PD_V_I64 - 1023, 1024, -9),
            1,
            -18,
            pc(262_142_865_782_784, 999_999_488, -18),
        );
        // inexact fraction, unnormalized ys, should be 262_145_000_000_000 exactly, but due to
        // normalization and fraction imprecision lose <= 4*10^(PD_EXPO+2) 1/1024 and
        // 1023/1024 precision losses described above + normalization of y2 actual result
        // off by < 140_000_000, which corresponds to loss of 1.4*10^-7 < 2*10^-7
        succeeds(
            0,
            pc(0, 0, -9),
            1024,
            pc(MAX_PD_V_I64 + 1025, 1024, -9),
            1,
            -18,
            pc(262_144_865_781_760, 996_093_240, -18),
        );
        // should be -267_912_190_000_000_000 exactly, but due to normalization and fraction
        // imprecision lose <= 4^10^(PD_EXPO+2) actual result off by < 2_000_000_000, which
        // corresponds to loss of 2*10^-7 < 4*10^-7 (counting figures from the start of the number)
        succeeds(
            0,
            pc(MIN_PD_V_I64 - 1025, 0, -9),
            1024,
            pc(MAX_PD_V_I64 + 1025, 0, -9),
            1,
            -18,
            pc(-267_912_188_120_944_640, 0, -18),
        );


        // test w confidence (same at both endpoints)--expect linear change btwn x1 and x2 and
        // growth in conf as distance from interval [x1, x2] increases
        succeeds(
            0,
            pc(90, 10, -4),
            10,
            pc(100, 10, -4),
            5,
            -9,
            pc(9_500_000, 1_000_000, -9),
        );

        // test w confidence (different at the endpoints)
        succeeds(
            0,
            pc(90, 10, -4),
            10,
            pc(100, 15, -4),
            5,
            -9,
            pc(9_500_000, 1_250_000, -9),
        );
        succeeds(
            0,
            pc(90, 10, -4),
            10,
            pc(100, 15, -4),
            8,
            -9,
            pc(9_800_000, 1_400_000, -9),
        );
        succeeds(
            0,
            pc(90, 10, -4),
            10,
            pc(100, 15, -4),
            15,
            -9,
            pc(10_500_000, 2_750_000, -9),
        );

        // fails bc x1 > x2
        fails(20, pc(100, 10, -4), 10, pc(100, 20, -4), 15, -9);
        // fails bc x1 is MIN, x2-x1 --> overflow in delta
        fails(i64::MIN, pc(100, 20, -5), 10, pc(1000, 40, -5), 5, -9);
        // fails bc x2 is MAX, x1 is negative --> overflow in delta
        fails(-5, pc(100, 40, -4), i64::MAX, pc(1000, 10, -4), 5, -9);
        // fails bc of overflow in the checked_sub for x2-x1
        fails(
            i64::MIN / 2,
            pc(100, 20, -4),
            i64::MAX / 2 + 1,
            pc(100, 30, -4),
            5,
            -9,
        );
        // fails bc output price too small to be realized, cannot be scaled to fit with specified
        // pre_add_expo
        fails(0, pc(100, 0, -4), 10, pc(5, 50, -4), i64::MAX - 100, -9);
        // fails bc 0-i64::MIN > i64::MAX, so overflow
        fails(i64::MIN, pc(100, 10, -9), 0, pc(0, 12, -9), 0, -9);
    }

    pub fn construct_quickcheck_affine_combination_price(price: i64) -> Price {
        return Price {
            price:        price,
            conf:         0,
            expo:         -9,
            publish_time: 0,
        };
    }

    // quickcheck to confirm affine_combination introduces no error if normalization done
    // explicitly on prices first this quickcheck calls affine_combination with two sets of
    // almost identical inputs: the first set has potentially unnormalized prices, the second
    // set simply has the normalized versions of those prices this set of checks should pass
    // because normalization is automatically performed on the prices before they are
    // multiplied this set of checks passing indicates that it doesn't matter whether the
    // prices passed in are normalized
    #[quickcheck]
    fn quickcheck_affine_combination_normalize_prices(
        x1_inp: i32,
        p1: i32,
        x2_inp: i32,
        p2: i32,
        x_query_inp: i32,
    ) -> TestResult {
        // generating xs and prices from i32 to limit the range to reasonable values and guard
        // against overflow/bespoke constraint setting for quickcheck
        let y1 = construct_quickcheck_affine_combination_price(i64::try_from(p1).ok().unwrap());
        let y2 = construct_quickcheck_affine_combination_price(i64::try_from(p2).ok().unwrap());

        let x1 = i64::try_from(x1_inp).ok().unwrap();
        let x2 = i64::try_from(x2_inp).ok().unwrap();
        let x_query = i64::try_from(x_query_inp).ok().unwrap();

        // stick with single expo for ease of testing and generation
        let pre_add_expo = -9;

        // require x2 > x1, as needed for affine_combination
        if x1 >= x2 {
            return TestResult::discard();
        }

        // original result
        let result_orig = Price::affine_combination(x1, y1, x2, y2, x_query, pre_add_expo).unwrap();

        let y1_norm = y1.normalize().unwrap();
        let y2_norm = y2.normalize().unwrap();

        // result with normalized price inputs
        let result_norm =
            Price::affine_combination(x1, y1_norm, x2, y2_norm, x_query, pre_add_expo).unwrap();

        // results should match exactly
        TestResult::from_bool(result_norm == result_orig)
    }

    // quickcheck to confirm affine_combination introduces bounded error if close fraction x/y
    // passed in first this quickcheck calls affine_combination with two sets of similar inputs:
    // the first set has xs generated by the quickcheck generation process, leading to
    // potentially inexact fractions that don't fit within 8 digits of precision the second
    // set "normalizes" down to 8 digits of precision by setting x1 to 0, x2 to 100_000_000,
    // and xquery proportionally based on the bounds described in the docstring of
    // affine_combination, we expect error due to this to be leq 4*10^-7
    #[quickcheck]
    fn quickcheck_affine_combination_normalize_fractions(
        x1_inp: i32,
        p1: i32,
        x2_inp: i32,
        p2: i32,
        x_query_inp: i32,
    ) -> TestResult {
        // generating xs and prices from i32 to limit the range to reasonable values and guard
        // against overflow/bespoke constraint setting for quickcheck
        let y1 = construct_quickcheck_affine_combination_price(i64::try_from(p1).ok().unwrap());
        let y2 = construct_quickcheck_affine_combination_price(i64::try_from(p2).ok().unwrap());

        let x1 = i64::try_from(x1_inp).ok().unwrap();
        let x2 = i64::try_from(x2_inp).ok().unwrap();
        let x_query = i64::try_from(x_query_inp).ok().unwrap();

        // stick with single expo for ease of testing and generation
        let pre_add_expo = -9;

        // require x2 > x1, as needed for affine_combination
        if x1 >= x2 {
            return TestResult::discard();
        }

        // constrain x_query to be within 5 interval lengths of x1 or x2
        if (x_query > x2 + 5 * (x2 - x1)) || (x_query < x1 - 5 * (x2 - x1)) {
            return TestResult::discard();
        }

        // generate new xs based on scaling x_1 --> 0, x_2 --> 10^8
        let x1_new: i64;
        let xq_new: i64;
        let x2_new: i64;

        if x2 == 0 {
            x1_new = x1;
            xq_new = x_query;
            x2_new = x2;
        } else {
            let mut frac_q2 = Price::fraction(x_query - x1, x2 - x1).unwrap();
            frac_q2 = frac_q2.scale_to_exponent(-8).unwrap();

            x1_new = 0;
            xq_new = frac_q2.price;
            x2_new = 100_000_000 as i64;
        }

        // original result
        let result_orig = Price::affine_combination(x1, y1, x2, y2, x_query, pre_add_expo)
            .unwrap()
            .scale_to_exponent(-7)
            .unwrap();

        // xs "normalized" result
        let result_norm = Price::affine_combination(x1_new, y1, x2_new, y2, xq_new, pre_add_expo)
            .unwrap()
            .scale_to_exponent(-7)
            .unwrap();

        // compute difference in prices
        let price_diff = result_norm.add(&result_orig.cmul(-1, 0).unwrap()).unwrap();

        // results should differ by less than 4*10^-7
        TestResult::from_bool((price_diff.price < 4) && (price_diff.price > -4))
    }

    #[test]
    fn test_fraction() {
        fn succeeds(x: i64, y: i64, expected: Price) {
            let frac = Price::fraction(x, y).unwrap();

            assert_eq!(frac, expected);
        }

        fn fails(x: i64, y: i64) {
            let result = Price::fraction(x, y);

            assert_eq!(result, None);
        }

        // check basic tests of fraction division
        succeeds(100, 1000, pc(100_000_000, 0, -9));
        succeeds(1, 1_000_000_000, pc(10, 0, -10));
        // when x and y and x/y can be represented in 8 digits, no loss
        succeeds(10_000_001, 20_000_002, pc(500_000_000, 0, -9));
        succeeds(102, 3, pc(34_000_000_000, 0, -9));
        succeeds(11_111_111, 10_000_000, pc(1_111_111_100, 0, -9));

        // test loss due to big numer (x cannot be represented in 8 digits)--only preserves 8 digits
        // of precision
        succeeds(3_000_000_021_123, 1, pc(30_000_000_000_000_000, 0, -4));

        // test loss due to big denom (y cannot be represented in 8 digits)
        succeeds(1, 10_000_000_011, pc(10, 0, -11));

        // x and y representable within 8 digits, but x/y is not
        succeeds(1, 7, pc(142_857_142, 0, -9));

        // Test with big inputs where the output will lose precision.
        // x not representable within 8 digits
        succeeds(i64::MAX, 100, pc(922337200000000, 0, 2));
        succeeds(i64::MAX, 1, pc(92233720000000000, 0, 2));
        // Neither x nor y representable within 8 digits
        succeeds(
            i64::MAX - 10,
            i64::MAX - 10_000_000_000,
            pc(1000000000, 0, -9),
        );
        // Neither x nor y representable within 8 digits, but this subtraction actually influences
        // relevant digit for precision
        succeeds(
            i64::MAX - 10,
            i64::MAX - 100_000_000_000,
            pc(1_000_000_010, 0, -9),
        );

        // Test with end range of possible inputs where the output should not lose precision.
        succeeds(MAX_PD_V_I64, MAX_PD_V_I64, pc(1_000_000_000, 0, -9));
        succeeds(MAX_PD_V_I64, 1, pc(MAX_PD_V_I64 * 1_000_000_000, 0, -9));
        succeeds(MAX_PD_V_I64, MIN_PD_V_I64, pc(-1_000_000_000, 0, -9));
        succeeds(MIN_PD_V_I64, 1, pc(MIN_PD_V_I64 * 1_000_000_000, 0, -9));
        // test cases near the boundary where output should lose precision
        succeeds(
            MAX_PD_V_I64 + 1,
            1,
            pc(MAX_PD_V_I64 / 10 * 1_000_000_000, 0, -8),
        );
        succeeds(
            MAX_PD_V_I64 + 10,
            1,
            pc((MAX_PD_V_I64 / 10 + 1) * 1_000_000_000, 0, -8),
        );

        // fails due to div by 0
        fails(100, 0);
    }
}