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Blake-MaddenBlake-Madden
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Add IPMT function
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‎TinyExprChanges.md‎

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@@ -52,6 +52,7 @@ The following are changes from the original TinyExpr C library:
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- `fact`: alias for `fac()`, like the *Excel* function.
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- `false`: returns `false` (i.e., `0`) in a boolean expression.
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- `fv`: returns the future value of an investment.
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- `ipmt`: returns the interest portion of a payment for a specified period of an investment.
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- `iserr`: returns true if an expression evaluates to NaN.
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- `iserror`: alias for `iserr`.
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- `iseven`: returns true if a number is even, false if odd.

‎docs/manual/functions.qmd‎

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@@ -127,6 +127,7 @@ Any subsequent arguments that evaluate to NaN will be ignored.
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| DB(Cost, Salvage, Lifetime, Period, Month) | Returns the depreciation of an asset for a specified period using the fixed-declining balance method. |
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| EFFECT(NominalRate, Periods) | Returns the effective annual interest rate, provided the nominal annual interest rate and the number of compounding periods per year.<br>\linebreak NaN will be returned if *Periods* is < 1 or if *NominalRate* <= 0. |
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| FV(Rate, Periods, Payment, [PresentValue], [Type]) | Returns the future value of an investment based on a constant interest rate, a fixed number of periods, and periodic payments.<br>\linebreak Note that *PresentValue* and *Type* are optional and default to 0.<br>\linebreak Also, *Type* specifies when payments are due: 0 = end of period, 1 = beginning of period.<br>\linebreak NaN will be returned if *Periods* <= 0 or if any required argument is not finite. |
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| IPMT(Rate, Period, Periods, PresentValue, [FutureValue], [Type]) | Returns the interest portion of a payment for a specified period of an investment.<br>\linebreak *FutureValue* and *Type* are optional and default to 0.<br>\linebreak *Type* specifies when payments are due: 0 = end of period, 1 = beginning of period. |
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| NOMINAL(EffectiveRate, Periods) | Returns the nominal annual interest rate, provided the effective rate and the number of compounding periods per year.<br>\linebreak NaN will be returned if *Periods* is < 1 or if *EffectiveRate* <= 0. |
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| NPER(Rate, Payment, PresentValue, [FutureValue], [Type]) | Returns the number of periods for an investment or loan based on a constant interest rate, periodic payments, and present and future values.<br>\linebreak Note that *FutureValue* and *Type* are optional and default to 0.<br>\linebreak Also, *Type* specifies when payments are due: 0 = end of period, 1 = beginning of period.<br>\linebreak NaN will be returned if any required argument is not finite or if the calculation is not defined. |
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| PMT(Rate, Periods, PresentValue, [FutureValue], [Type]) | Returns the periodic payment for an investment or loan based on a constant interest rate, a fixed number of periods, and a present value.<br>\linebreak Note that *FutureValue* and *Type* are optional and default to 0.<br>\linebreak Also, *Type* specifies when payments are due: 0 = end of period, 1 = beginning of period.<br>\linebreak NaN will be returned if *Periods* <= 0 or if any required argument is not finite. |

‎tests/tetests.cpp‎

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@@ -4193,6 +4193,133 @@ TEST_CASE("NaN Comparison", "[nan]")
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}
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// Financial functions
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// --------------------------------------------------
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// IPMT
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// --------------------------------------------------
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TEST_CASE("IPMT", "[finance]")
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{
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te_parser tep;
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// --------------------------------------------------
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// Excel Online Help example
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//
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// Data:
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// Annual interest rate: 10%
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// Number of years: 3
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// Present value: 8000
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//
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// Excel formula:
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// =IPMT(0.10/12, 1, 3*12, 8000)
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//
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// Excel result: -66.67
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// --------------------------------------------------
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CHECK_THAT(
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WITHIN_TYPE_CAST(tep.evaluate("IPMT(0.10/12, 1, 3*12, 8000)")),
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Catch::Matchers::WithinRel(
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WITHIN_TYPE_CAST(-66.67),
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WITHIN_TYPE_CAST(0.0001)));
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// --------------------------------------------------
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// Excel: =IPMT(0.10/12, 2, 3*12, 8000)
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// Interest portion for second period
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// Excel result: -65.0710764092997
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// --------------------------------------------------
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CHECK_THAT(
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WITHIN_TYPE_CAST(tep.evaluate("IPMT(0.10/12, 2, 3*12, 8000)")),
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Catch::Matchers::WithinRel(
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WITHIN_TYPE_CAST(-65.0710764092997),
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WITHIN_TYPE_CAST(0.0001)));
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// --------------------------------------------------
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// Excel: =IPMT(0.05/12, 1, 60, 10000)
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// First month's interest on a 5-year loan
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// Excel result: -41.67
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// --------------------------------------------------
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CHECK_THAT(
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WITHIN_TYPE_CAST(tep.evaluate("IPMT(0.05/12, 1, 60, 10000)")),
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Catch::Matchers::WithinRel(
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WITHIN_TYPE_CAST(-41.67),
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WITHIN_TYPE_CAST(0.0001)));
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// --------------------------------------------------
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// Excel: =IPMT(0.05/12, 12, 60, 10000)
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// Interest portion after one year
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// Excel result: -34.12
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// --------------------------------------------------
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CHECK_THAT(
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WITHIN_TYPE_CAST(tep.evaluate("IPMT(0.05/12, 12, 60, 10000)")),
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Catch::Matchers::WithinRel(
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WITHIN_TYPE_CAST(-34.7848954631707),
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WITHIN_TYPE_CAST(0.0001)));
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// --------------------------------------------------
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// Payments at beginning of period
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//
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// Excel: =IPMT(0.05/12, 1, 60, 10000, 0, 1)
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// First period interest is zero
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// --------------------------------------------------
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CHECK_THAT(
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WITHIN_TYPE_CAST(tep.evaluate("IPMT(0.05/12, 1, 60, 10000, 0, 1)")),
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Catch::Matchers::WithinRel(
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WITHIN_TYPE_CAST(0.0)));
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// --------------------------------------------------
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// Excel: =IPMT(0.05/12, 2, 60, 10000, 0, 1)
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// Interest starts accruing in second period
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// Excel result: -40.88
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// --------------------------------------------------
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CHECK_THAT(
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WITHIN_TYPE_CAST(tep.evaluate("IPMT(0.05/12, 2, 60, 10000, 0, 1)")),
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Catch::Matchers::WithinRel(
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WITHIN_TYPE_CAST(-40.8836279262513),
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WITHIN_TYPE_CAST(0.0000001)));
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// --------------------------------------------------
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// Zero interest rate
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//
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// Excel: =IPMT(0, 10, 60, 10000)
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// Excel result: 0
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// --------------------------------------------------
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CHECK_THAT(
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WITHIN_TYPE_CAST(tep.evaluate("IPMT(0, 10, 60, 10000)")),
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Catch::Matchers::WithinRel(
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WITHIN_TYPE_CAST(0.0)));
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CHECK_THAT(
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WITHIN_TYPE_CAST(tep.evaluate("=IPMT(0.05/12, 1.5, 60, 10000)")),
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Catch::Matchers::WithinRel(
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WITHIN_TYPE_CAST(-41.3606399677465),
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WITHIN_TYPE_CAST(0.0000001)));
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CHECK_THAT(
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WITHIN_TYPE_CAST(tep.evaluate("=IPMT(-1, 1, 60, 10000)")),
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Catch::Matchers::WithinRel(
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WITHIN_TYPE_CAST(10000),
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WITHIN_TYPE_CAST(0.0000001)));
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CHECK_THAT(
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WITHIN_TYPE_CAST(tep.evaluate("=IPMT(-1.1, 1, 60, 10000)")),
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Catch::Matchers::WithinRel(
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WITHIN_TYPE_CAST(11000),
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WITHIN_TYPE_CAST(0.0000001)));
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// --------------------------------------------------
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// Invalid inputs
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// --------------------------------------------------
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// period < 1
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CHECK(std::isnan(WITHIN_TYPE_CAST(tep.evaluate("IPMT(0.05/12, 0, 60, 10000)"))));
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// period > periods
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CHECK(std::isnan(WITHIN_TYPE_CAST(tep.evaluate("IPMT(0.05/12, 61, 60, 10000)"))));
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// non-finite args
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CHECK(std::isnan(WITHIN_TYPE_CAST(tep.evaluate("IPMT(NaN, 1, 60, 10000)"))));
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CHECK(std::isnan(WITHIN_TYPE_CAST(tep.evaluate("IPMT(0.05/12, NaN, 60, 10000)"))));
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CHECK(std::isnan(WITHIN_TYPE_CAST(tep.evaluate("IPMT(0.05/12, 1, NaN, 10000)"))));
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CHECK(std::isnan(WITHIN_TYPE_CAST(tep.evaluate("IPMT(0.05/12, 1, 60, NaN)"))));
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}
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// --------------------------------------------------
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// PV
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// --------------------------------------------------

‎tinyexpr.cpp‎

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@@ -392,6 +392,78 @@ namespace te_builtins
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((1 + (rate * type)) * (powVal - 1));
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}
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[[nodiscard]]
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static te_type te_ipmt(te_type rate, te_type period, te_type periods, te_type presentValue,
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te_type futureValue, te_type type)
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{
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if (!std::isfinite(rate) || !std::isfinite(period) || !std::isfinite(periods) ||
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!std::isfinite(presentValue))
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{
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return te_parser::te_nan;
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}
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if (!std::isfinite(futureValue))
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{
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futureValue = 0;
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}
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if (!std::isfinite(type))
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{
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type = 0;
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}
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type = (type != 0) ? 1 : 0;
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if (periods <= 0.0)
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{
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return te_parser::te_nan;
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}
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if (period < 1.0 || period > periods)
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{
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return te_parser::te_nan;
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}
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if (rate == 0.0)
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{
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return 0.0;
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}
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if (rate <= -1.0)
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{
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// Excel: linear interest regime for IPMT
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if (type != 0 && period == 1.0)
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{
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return 0.0;
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}
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return -presentValue * rate;
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}
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const te_type payment = te_pmt(rate, periods, presentValue, futureValue, type);
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if (!std::isfinite(payment))
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{
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return te_parser::te_nan;
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}
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te_type balance;
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if (type == 1)
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{
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if (period == 1.0)
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{
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return 0.0;
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}
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balance = -(presentValue * std::pow(1 + rate, period - 2) +
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payment * (std::pow(1 + rate, period - 2) - 1) / rate + payment);
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}
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else
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{
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balance = -(presentValue * std::pow(1 + rate, period - 1) +
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payment * (std::pow(1 + rate, period - 1) - 1) / rate);
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}
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return balance * rate;
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}
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[[nodiscard]]
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static te_type te_pv(te_type rate, te_type nper, te_type pmt, te_type futureValue, te_type type)
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{
@@ -1663,6 +1735,8 @@ const std::set<te_variable> te_parser::m_functions = { // NOLINT
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{ "if", static_cast<te_fun3>(te_builtins::te_if), TE_PURE },
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{ "ifs", static_cast<te_fun24>(te_builtins::te_ifs),
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static_cast<te_variable_flags>(TE_PURE | TE_VARIADIC) },
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{ "ipmt", static_cast<te_fun6>(te_builtins::te_ipmt),
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static_cast<te_variable_flags>(TE_PURE | TE_VARIADIC) },
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{ "ln", static_cast<te_fun1>(te_builtins::te_log), TE_PURE },
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{ "log10", static_cast<te_fun1>(te_builtins::te_log10), TE_PURE },
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{ "max", static_cast<te_fun24>(te_builtins::te_max),

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