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diff --git a/api/nums.yaml b/api/nums.yaml new file mode 100644 index 00000000..d69a6b9e --- /dev/null +++ b/api/nums.yaml @@ -0,0 +1,978 @@ +Num.abs: + description: > + Calculates the absolute value of a number. + return: + type: 'Num' + description: > + The absolute value of `n`. + args: + n: + type: 'Num' + description: > + The number whose absolute value is to be computed. + example: | + >> (-3.5).abs() + = 3.5 + +Num.acos: + description: > + Computes the arc cosine of a number. + return: + type: 'Num' + description: > + The arc cosine of `x` in radians. + args: + x: + type: 'Num' + description: > + The number for which the arc cosine is to be calculated. + example: | + >> (0.0).acos() // -> (π/2) + = 1.5708 + +Num.acosh: + description: > + Computes the inverse hyperbolic cosine of a number. + return: + type: 'Num' + description: > + The inverse hyperbolic cosine of `x`. + args: + x: + type: 'Num' + description: > + The number for which the inverse hyperbolic cosine is to be calculated. + example: | + >> (1.0).acosh() + = 0 + +Num.asin: + description: > + Computes the arc sine of a number. + return: + type: 'Num' + description: > + The arc sine of `x` in radians. + args: + x: + type: 'Num' + description: > + The number for which the arc sine is to be calculated. + example: | + >> (0.5).asin() // -> (π/6) + = 0.5236 + +Num.asinh: + description: > + Computes the inverse hyperbolic sine of a number. + return: + type: 'Num' + description: > + The inverse hyperbolic sine of `x`. + args: + x: + type: 'Num' + description: > + The number for which the inverse hyperbolic sine is to be calculated. + example: | + >> (0.0).asinh() + = 0 + +Num.atan: + description: > + Computes the arc tangent of a number. + return: + type: 'Num' + description: > + The arc tangent of `x` in radians. + args: + x: + type: 'Num' + description: > + The number for which the arc tangent is to be calculated. + example: | + >> (1.0).atan() // -> (π/4) + = 0.7854 + +Num.atan2: + description: > + Computes the arc tangent of the quotient of two numbers. + return: + type: 'Num' + description: > + The arc tangent of `x/y` in radians. + args: + x: + type: 'Num' + description: > + The numerator. + y: + type: 'Num' + description: > + The denominator. + example: | + >> Num.atan2(1, 1) // -> (π/4) + = 0.7854 + +Num.atanh: + description: > + Computes the inverse hyperbolic tangent of a number. + return: + type: 'Num' + description: > + The inverse hyperbolic tangent of `x`. + args: + x: + type: 'Num' + description: > + The number for which the inverse hyperbolic tangent is to be calculated. + example: | + >> (0.5).atanh() + = 0.5493 + +Num.cbrt: + description: > + Computes the cube root of a number. + return: + type: 'Num' + description: > + The cube root of `x`. + args: + x: + type: 'Num' + description: > + The number for which the cube root is to be calculated. + example: | + >> (27.0).cbrt() + = 3 + +Num.ceil: + description: > + Rounds a number up to the nearest integer. + return: + type: 'Num' + description: > + The smallest integer greater than or equal to `x`. + args: + x: + type: 'Num' + description: > + The number to be rounded up. + example: | + >> (3.2).ceil() + = 4 + +Num.clamped: + description: > + Returns the given number clamped between two values so that it is within + that range. + return: + type: 'Num' + description: > + The first argument clamped between the other two arguments. + args: + x: + type: 'Num' + description: > + The number to clamp. + low: + type: 'Num' + description: > + The lowest value the result can take. + high: + type: 'Num' + description: > + The highest value the result can take. + example: | + >> (2.5).clamped(5.5, 10.5) + = 5.5 + +Num.copysign: + description: > + Copies the sign of one number to another. + return: + type: 'Num' + description: > + A number with the magnitude of `x` and the sign of `y`. + args: + x: + type: 'Num' + description: > + The number whose magnitude will be copied. + y: + type: 'Num' + description: > + The number whose sign will be copied. + example: | + >> (3.0).copysign(-1) + = -3 + +Num.cos: + description: > + Computes the cosine of a number (angle in radians). + return: + type: 'Num' + description: > + The cosine of `x`. + args: + x: + type: 'Num' + description: > + The angle in radians. + example: | + >> (0.0).cos() + = 1 + +Num.cosh: + description: > + Computes the hyperbolic cosine of a number. + return: + type: 'Num' + description: > + The hyperbolic cosine of `x`. + args: + x: + type: 'Num' + description: > + The number for which the hyperbolic cosine is to be calculated. + example: | + >> (0.0).cosh() + = 1 + +Num.erf: + description: > + Computes the error function of a number. + return: + type: 'Num' + description: > + The error function of `x`. + args: + x: + type: 'Num' + description: > + The number for which the error function is to be calculated. + example: | + >> (0.0).erf() + = 0 + +Num.erfc: + description: > + Computes the complementary error function of a number. + return: + type: 'Num' + description: > + The complementary error function of `x`. + args: + x: + type: 'Num' + description: > + The number for which the complementary error function is to be calculated. + example: | + >> (0.0).erfc() + = 1 + +Num.exp: + description: > + Computes the exponential function $e^x$ for a number. + return: + type: 'Num' + description: > + The value of $e^x$. + args: + x: + type: 'Num' + description: > + The exponent. + example: | + >> (1.0).exp() + = 2.7183 + +Num.exp2: + description: > + Computes $2^x$ for a number. + return: + type: 'Num' + description: > + The value of $2^x$. + args: + x: + type: 'Num' + description: > + The exponent. + example: | + >> (3.0).exp2() + = 8 + +Num.expm1: + description: > + Computes $e^x - 1$ for a number. + return: + type: 'Num' + description: > + The value of $e^x - 1$. + args: + x: + type: 'Num' + description: > + The exponent. + example: | + >> (1.0).expm1() + = 1.7183 + +Num.fdim: + description: > + Computes the positive difference between two numbers. + return: + type: 'Num' + description: > + The positive difference $\max(0, x - y)$. + args: + x: + type: 'Num' + description: > + The first number. + y: + type: 'Num' + description: > + The second number. + example: | + fd + + >> (5.0).fdim(3) + = 2 + +Num.floor: + description: > + Rounds a number down to the nearest integer. + return: + type: 'Num' + description: > + The largest integer less than or equal to `x`. + args: + x: + type: 'Num' + description: > + The number to be rounded down. + example: | + >> (3.7).floor() + = 3 + +Num.format: + description: > + Formats a number as a text with a specified precision. + return: + type: 'Text' + description: > + A text representation of the number with the specified precision. + args: + n: + type: 'Num' + description: > + The number to be formatted. + precision: + type: 'Int' + default: '0' + description: > + The number of decimal places. Default is `0`. + example: | + >> (3.14159).format(precision=2) + = "3.14" + +Num.hypot: + description: > + Computes the Euclidean norm, $\sqrt{x^2 + y^2}$, of two numbers. + return: + type: 'Num' + description: > + The Euclidean norm of `x` and `y`. + args: + x: + type: 'Num' + description: > + The first number. + y: + type: 'Num' + description: > + The second number. + example: | + >> Num.hypot(3, 4) + = 5 + +Num.isfinite: + description: > + Checks if a number is finite. + return: + type: 'Bool' + description: > + `yes` if `n` is finite, `no` otherwise. + args: + n: + type: 'Num' + description: > + The number to be checked. + example: | + >> (1.0).isfinite() + = yes + >> Num.INF.isfinite() + = no + +Num.is_between: + description: > + Determines if a number is between two numbers (inclusive). + return: + type: 'Bool' + description: > + `yes` if `low <= x and x <= high`, otherwise `no` + args: + x: + type: 'Num' + description: > + The integer to be checked. + low: + type: 'Num' + description: > + The lower bound to check (inclusive). + high: + type: 'Num' + description: > + The upper bound to check (inclusive). + example: | + >> (7.5).is_between(1, 10) + = yes + >> (7.5).is_between(100, 200) + = no + >> (7.5).is_between(1, 7.5) + = yes + +Num.isinf: + description: > + Checks if a number is infinite. + return: + type: 'Bool' + description: > + `yes` if `n` is infinite, `no` otherwise. + args: + n: + type: 'Num' + description: > + The number to be checked. + example: | + >> Num.INF.isinf() + = yes + >> (1.0).isinf() + = no + +Num.j0: + description: > + Computes the Bessel function of the first kind of order 0. + return: + type: 'Num' + description: > + The Bessel function of the first kind of order 0 of `x`. + args: + x: + type: 'Num' + description: > + The number for which the Bessel function is to be calculated. + example: | + >> (0.0).j0() + = 1 + +Num.j1: + description: > + Computes the Bessel function of the first kind of order 1. + return: + type: 'Num' + description: > + The Bessel function of the first kind of order 1 of `x`. + args: + x: + type: 'Num' + description: > + The number for which the Bessel function is to be calculated. + example: | + >> (0.0).j1() + = 0 + +Num.log: + description: > + Computes the natural logarithm (base $e$) of a number. + return: + type: 'Num' + description: > + The natural logarithm of `x`. + args: + x: + type: 'Num' + description: > + The number for which the natural logarithm is to be calculated. + example: | + >> Num.E.log() + = 1 + +Num.log10: + description: > + Computes the base-10 logarithm of a number. + return: + type: 'Num' + description: > + The base-10 logarithm of `x`. + args: + x: + type: 'Num' + description: > + The number for which the base-10 logarithm is to be calculated. + example: | + >> (100.0).log10() + = 2 + +Num.log1p: + description: > + Computes $\log(1 + x)$ for a number. + return: + type: 'Num' + description: > + The value of $\log(1 + x)$. + args: + x: + type: 'Num' + description: > + The number for which $\log(1 + x)$ is to be calculated. + example: | + >> (1.0).log1p() + = 0.6931 + +Num.log2: + description: > + Computes the base-2 logarithm of a number. + return: + type: 'Num' + description: > + The base-2 logarithm of `x`. + args: + x: + type: 'Num' + description: > + The number for which the base-2 logarithm is to be calculated. + example: | + >> (8.0).log2() + = 3 + +Num.logb: + description: > + Computes the binary exponent (base-2 logarithm) of a number. + return: + type: 'Num' + description: > + The binary exponent of `x`. + args: + x: + type: 'Num' + description: > + The number for which the binary exponent is to be calculated. + example: | + >> (8.0).logb() + = 3 + +Num.mix: + description: > + Interpolates between two numbers based on a given amount. + return: + type: 'Num' + description: > + The interpolated number between `x` and `y` based on `amount`. + args: + amount: + type: 'Num' + description: > + The interpolation factor (between `0` and `1`). + x: + type: 'Num' + description: > + The starting number. + y: + type: 'Num' + description: > + The ending number. + example: | + >> (0.5).mix(10, 20) + = 15 + >> (0.25).mix(10, 20) + = 12.5 + +Num.near: + description: > + Checks if two numbers are approximately equal within specified tolerances. If + two numbers are within an absolute difference or the ratio between the two is + small enough, they are considered near each other. + return: + type: 'Bool' + description: > + `yes` if `x` and `y` are approximately equal within the specified tolerances, `no` otherwise. + args: + x: + type: 'Num' + description: > + The first number. + y: + type: 'Num' + description: > + The second number. + ratio: + type: 'Num' + default: '1e-9' + description: > + The relative tolerance. Default is `1e-9`. + min_epsilon: + type: 'Num' + default: '1e-9' + description: > + The absolute tolerance. Default is `1e-9`. + example: | + >> (1.0).near(1.000000001) + = yes + + >> (100.0).near(110, ratio=0.1) + = yes + + >> (5.0).near(5.1, min_epsilon=0.1) + = yes + +Num.nextafter: + description: > + Computes the next representable value after a given number towards a specified direction. + return: + type: 'Num' + description: > + The next representable value after `x` in the direction of `y`. + args: + x: + type: 'Num' + description: > + The starting number. + y: + type: 'Num' + description: > + The direction towards which to find the next representable value. + example: | + >> (1.0).nextafter(1.1) + = 1.0000000000000002 + +Num.parse: + description: > + Converts a text representation of a number into a floating-point number. + return: + type: 'Num?' + description: > + The number represented by the text or `none` if the entire text can't be parsed + as a number. + args: + text: + type: 'Text' + description: > + The text containing the number. + example: | + >> Num.parse("3.14") + = 3.14 + >> Num.parse("1e3") + = 1000 + +Num.percent: + description: > + Convert a number into a percentage text with a percent sign. + return: + type: 'Text' + description: > + A text representation of the number as a percentage with a percent sign. + args: + n: + type: 'Num' + description: > + The number to be converted to a percent. + precision: + type: 'Int' + default: '0' + description: > + The number of decimal places. Default is `0`. + example: | + >> (0.5).percent() + = "50%" + >> (1./3.).percent(2) + = "33.33%" + +Num.rint: + description: > + Rounds a number to the nearest integer, with ties rounded to the nearest even integer. + return: + type: 'Num' + description: > + The nearest integer value of `x`. + args: + x: + type: 'Num' + description: > + The number to be rounded. + example: | + >> (3.5).rint() + = 4 + >> (2.5).rint() + = 2 + +Num.round: + description: > + Rounds a number to the nearest whole number integer. + return: + type: 'Num' + description: > + The nearest integer value of `x`. + args: + x: + type: 'Num' + description: > + The number to be rounded. + example: | + >> (2.3).round() + = 2 + >> (2.7).round() + = 3 + +Num.scientific: + description: > + Formats a number in scientific notation with a specified precision. + return: + type: 'Text' + description: > + A text representation of the number in scientific notation with the specified precision. + args: + n: + type: 'Num' + description: > + The number to be formatted. + precision: + type: 'Int' + default: '0' + description: > + The number of decimal places. Default is `0`. + example: | + >> (12345.6789).scientific(precision=2) + = "1.23e+04" + +Num.significand: + description: > + Extracts the significand (or mantissa) of a number. + return: + type: 'Num' + description: > + The significand of `x`. + args: + x: + type: 'Num' + description: > + The number from which to extract the significand. + example: | + >> (1234.567).significand() + = 0.1234567 + +Num.sin: + description: > + Computes the sine of a number (angle in radians). + return: + type: 'Num' + description: > + The sine of `x`. + args: + x: + type: 'Num' + description: > + The angle in radians. + example: | + >> (0.0).sin() + = 0 + +Num.sinh: + description: > + Computes the hyperbolic sine of a number. + return: + type: 'Num' + description: > + The hyperbolic sine of `x`. + args: + x: + type: 'Num' + description: > + The number for which the hyperbolic sine is to be calculated. + example: | + >> (0.0).sinh() + = 0 + +Num.sqrt: + description: > + Computes the square root of a number. + return: + type: 'Num' + description: > + The square root of `x`. + args: + x: + type: 'Num' + description: > + The number for which the square root is to be calculated. + example: | + >> (16.0).sqrt() + = 4 + +Num.tan: + description: > + Computes the tangent of a number (angle in radians). + return: + type: 'Num' + description: > + The tangent of `x`. + args: + x: + type: 'Num' + description: > + The angle in radians. + example: | + >> (0.0).tan() + = 0 + +Num.tanh: + description: > + Computes the hyperbolic tangent of a number. + return: + type: 'Num' + description: > + The hyperbolic tangent of `x`. + args: + x: + type: 'Num' + description: > + The number for which the hyperbolic tangent is to be calculated. + example: | + >> (0.0).tanh() + = 0 + +Num.tgamma: + description: > + Computes the gamma function of a number. + return: + type: 'Num' + description: > + The gamma function of `x`. + args: + x: + type: 'Num' + description: > + The number for which the gamma function is to be calculated. + example: | + >> (1.0).tgamma() + = 1 + +Num.trunc: + description: > + Truncates a number to the nearest integer towards zero. + return: + type: 'Num' + description: > + The integer part of `x` towards zero. + args: + x: + type: 'Num' + description: > + The number to be truncated. + example: | + >> (3.7).trunc() + = 3 + >> (-3.7).trunc() + = -3 + +Num.y0: + description: > + Computes the Bessel function of the second kind of order 0. + return: + type: 'Num' + description: > + The Bessel function of the second kind of order 0 of `x`. + args: + x: + type: 'Num' + description: > + The number for which the Bessel function is to be calculated. + example: | + >> (1.0).y0() + = -0.7652 + +Num.y1: + description: > + Computes the Bessel function of the second kind of order 1. + return: + type: 'Num' + description: > + The Bessel function of the second kind of order 1 of `x`. + args: + x: + type: 'Num' + description: > + The number for which the Bessel function is to be calculated. + example: | + >> (1.0).y1() + = 0.4401 + + +Num.1_PI: + type: Num + description: > + The constant $\frac{1}{\pi}$. +Num.2_PI: + type: Num + description: > + The constant $2 \times \pi$. +Num.2_SQRTPI: + type: Num + description: > + The constant $2 \times \sqrt{\pi}$. +Num.E: + type: Num + description: > + The base of the natural logarithm ($e$). +Num.INF: + type: Num + description: > + Positive infinity. +Num.LN10: + type: Num + description: > + The natural logarithm of 10. +Num.LN2: + type: Num + description: > + The natural logarithm of 2. +Num.LOG2E: + type: Num + description: > + The base 2 logarithm of $e$ +Num.PI: + type: Num + description: > + Pi ($\pi$). +Num.PI_2: + type: Num + description: > + $\frac{\pi}{2}$ +Num.PI_4: + type: Num + description: > + $\frac{\pi}{4}$ +Num.SQRT1_2: + type: Num + description: > + $\sqrt{\frac{1}{2}}$ +Num.SQRT2: + type: Num + description: > + $\sqrt{2}$ +Num.TAU: + type: Num + description: > + Tau ($2 \times \pi$) |