var searchIndex = {};
searchIndex["num"] = {"doc":"A collection of numeric types and traits for Rust.","items":[[3,"BigInt","num","A big signed integer type.",null,null],[3,"BigUint","","A big unsigned integer type.",null,null],[6,"Rational","","",null,null],[6,"BigRational","","",null,null],[3,"Complex","","A complex number in Cartesian form.",null,null],[12,"re","","Real portion of the complex number",0,null],[12,"im","","Imaginary portion of the complex number",0,null],[8,"Integer","","",null,null],[10,"div_floor","","Floored integer division.",1,null],[10,"mod_floor","","Floored integer modulo, satisfying:",1,null],[10,"gcd","","Greatest Common Divisor (GCD).",1,null],[10,"lcm","","Lowest Common Multiple (LCM).",1,null],[10,"divides","","Deprecated, use `is_multiple_of` instead.",1,null],[10,"is_multiple_of","","Returns `true` if `other` is a multiple of `self`.",1,null],[10,"is_even","","Returns `true` if the number is even.",1,null],[10,"is_odd","","Returns `true` if the number is odd.",1,null],[10,"div_rem","","Simultaneous truncated integer division and modulus.\nReturns `(quotient, remainder)`.",1,null],[11,"div_mod_floor","","Simultaneous floored integer division and modulus.\nReturns `(quotient, remainder)`.",1,null],[5,"range","","Returns an iterator over the given range [start, stop) (that is, starting\nat start (inclusive), and ending at stop (exclusive)).",null,{"inputs":[{"name":"a"},{"name":"a"}],"output":{"name":"range"}}],[5,"range_inclusive","","Return an iterator over the range [start, stop]",null,{"inputs":[{"name":"a"},{"name":"a"}],"output":{"name":"rangeinclusive"}}],[5,"range_step","","Return an iterator over the range [start, stop) by `step`. It handles overflow by stopping.",null,{"inputs":[{"name":"a"},{"name":"a"},{"name":"a"}],"output":{"name":"rangestep"}}],[5,"range_step_inclusive","","Return an iterator over the range [start, stop] by `step`. It handles overflow by stopping.",null,{"inputs":[{"name":"a"},{"name":"a"},{"name":"a"}],"output":{"name":"rangestepinclusive"}}],[8,"Num","","The base trait for numeric types",null,null],[16,"FromStrRadixErr","","",2,null],[10,"from_str_radix","","Convert from a string and radix <= 36.",2,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[8,"Zero","","Defines an additive identity element for `Self`.",null,null],[10,"zero","","Returns the additive identity element of `Self`, `0`.",3,{"inputs":[],"output":{"name":"self"}}],[10,"is_zero","","Returns `true` if `self` is equal to the additive identity.",3,null],[8,"One","","Defines a multiplicative identity element for `Self`.",null,null],[10,"one","","Returns the multiplicative identity element of `Self`, `1`.",4,{"inputs":[],"output":{"name":"self"}}],[8,"Signed","","Useful functions for signed numbers (i.e. numbers that can be negative).",null,null],[10,"abs","","Computes the absolute value.",5,null],[10,"abs_sub","","The positive difference of two numbers.",5,null],[10,"signum","","Returns the sign of the number.",5,null],[10,"is_positive","","Returns true if the number is positive and false if the number is zero or negative.",5,null],[10,"is_negative","","Returns true if the number is negative and false if the number is zero or positive.",5,null],[8,"Unsigned","","A trait for values which cannot be negative",null,null],[8,"Bounded","","Numbers which have upper and lower bounds",null,null],[10,"min_value","","returns the smallest finite number this type can represent",6,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","returns the largest finite number this type can represent",6,{"inputs":[],"output":{"name":"self"}}],[8,"Saturating","","Saturating math operations",null,null],[10,"saturating_add","","Saturating addition operator.\nReturns a+b, saturating at the numeric bounds instead of overflowing.",7,null],[10,"saturating_sub","","Saturating subtraction operator.\nReturns a-b, saturating at the numeric bounds instead of overflowing.",7,null],[8,"CheckedAdd","","Performs addition that returns `None` instead of wrapping around on\noverflow.",null,null],[10,"checked_add","","Adds two numbers, checking for overflow. If overflow happens, `None` is\nreturned.",8,null],[8,"CheckedSub","","Performs subtraction that returns `None` instead of wrapping around on underflow.",null,null],[10,"checked_sub","","Subtracts two numbers, checking for underflow. If underflow happens,\n`None` is returned.",9,null],[8,"CheckedMul","","Performs multiplication that returns `None` instead of wrapping around on underflow or\noverflow.",null,null],[10,"checked_mul","","Multiplies two numbers, checking for underflow or overflow. If underflow\nor overflow happens, `None` is returned.",10,null],[8,"CheckedDiv","","Performs division that returns `None` instead of panicking on division by zero and instead of\nwrapping around on underflow and overflow.",null,null],[10,"checked_div","","Divides two numbers, checking for underflow, overflow and division by\nzero. If any of that happens, `None` is returned.",11,null],[8,"PrimInt","","",null,null],[10,"count_ones","","Returns the number of ones in the binary representation of `self`.",12,null],[10,"count_zeros","","Returns the number of zeros in the binary representation of `self`.",12,null],[10,"leading_zeros","","Returns the number of leading zeros in the binary representation\nof `self`.",12,null],[10,"trailing_zeros","","Returns the number of trailing zeros in the binary representation\nof `self`.",12,null],[10,"rotate_left","","Shifts the bits to the left by a specified amount amount, `n`, wrapping\nthe truncated bits to the end of the resulting integer.",12,null],[10,"rotate_right","","Shifts the bits to the right by a specified amount amount, `n`, wrapping\nthe truncated bits to the beginning of the resulting integer.",12,null],[10,"signed_shl","","Shifts the bits to the left by a specified amount amount, `n`, filling\nzeros in the least significant bits.",12,null],[10,"signed_shr","","Shifts the bits to the right by a specified amount amount, `n`, copying\nthe "sign bit" in the most significant bits even for unsigned types.",12,null],[10,"unsigned_shl","","Shifts the bits to the left by a specified amount amount, `n`, filling\nzeros in the least significant bits.",12,null],[10,"unsigned_shr","","Shifts the bits to the right by a specified amount amount, `n`, filling\nzeros in the most significant bits.",12,null],[10,"swap_bytes","","Reverses the byte order of the integer.",12,null],[10,"from_be","","Convert an integer from big endian to the target's endianness.",12,{"inputs":[{"name":"self"}],"output":{"name":"self"}}],[10,"from_le","","Convert an integer from little endian to the target's endianness.",12,{"inputs":[{"name":"self"}],"output":{"name":"self"}}],[10,"to_be","","Convert `self` to big endian from the target's endianness.",12,null],[10,"to_le","","Convert `self` to little endian from the target's endianness.",12,null],[10,"pow","","Raises self to the power of `exp`, using exponentiation by squaring.",12,null],[8,"Float","","",null,null],[10,"nan","","Returns the `NaN` value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"infinity","","Returns the infinite value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"neg_infinity","","Returns the negative infinite value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"neg_zero","","Returns `-0.0`.",13,{"inputs":[],"output":{"name":"self"}}],[10,"min_value","","Returns the smallest finite value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"min_positive_value","","Returns the smallest positive, normalized value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","Returns the largest finite value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"is_nan","","Returns `true` if this value is `NaN` and false otherwise.",13,null],[10,"is_infinite","","Returns `true` if this value is positive infinity or negative infinity and\nfalse otherwise.",13,null],[10,"is_finite","","Returns `true` if this number is neither infinite nor `NaN`.",13,null],[10,"is_normal","","Returns `true` if the number is neither zero, infinite,\n[subnormal][subnormal], or `NaN`.",13,null],[10,"classify","","Returns the floating point category of the number. If only one property\nis going to be tested, it is generally faster to use the specific\npredicate instead.",13,null],[10,"floor","","Returns the largest integer less than or equal to a number.",13,null],[10,"ceil","","Returns the smallest integer greater than or equal to a number.",13,null],[10,"round","","Returns the nearest integer to a number. Round half-way cases away from\n`0.0`.",13,null],[10,"trunc","","Return the integer part of a number.",13,null],[10,"fract","","Returns the fractional part of a number.",13,null],[10,"abs","","Computes the absolute value of `self`. Returns `Float::nan()` if the\nnumber is `Float::nan()`.",13,null],[10,"signum","","Returns a number that represents the sign of `self`.",13,null],[10,"is_sign_positive","","Returns `true` if `self` is positive, including `+0.0` and\n`Float::infinity()`.",13,null],[10,"is_sign_negative","","Returns `true` if `self` is negative, including `-0.0` and\n`Float::neg_infinity()`.",13,null],[10,"mul_add","","Fused multiply-add. Computes `(self * a) + b` with only one rounding\nerror. This produces a more accurate result with better performance than\na separate multiplication operation followed by an add.",13,null],[10,"recip","","Take the reciprocal (inverse) of a number, `1/x`.",13,null],[10,"powi","","Raise a number to an integer power.",13,null],[10,"powf","","Raise a number to a floating point power.",13,null],[10,"sqrt","","Take the square root of a number.",13,null],[10,"exp","","Returns `e^(self)`, (the exponential function).",13,null],[10,"exp2","","Returns `2^(self)`.",13,null],[10,"ln","","Returns the natural logarithm of the number.",13,null],[10,"log","","Returns the logarithm of the number with respect to an arbitrary base.",13,null],[10,"log2","","Returns the base 2 logarithm of the number.",13,null],[10,"log10","","Returns the base 10 logarithm of the number.",13,null],[11,"to_degrees","","Converts radians to degrees.",13,null],[11,"to_radians","","Converts degrees to radians.",13,null],[10,"max","","Returns the maximum of the two numbers.",13,null],[10,"min","","Returns the minimum of the two numbers.",13,null],[10,"abs_sub","","The positive difference of two numbers.",13,null],[10,"cbrt","","Take the cubic root of a number.",13,null],[10,"hypot","","Calculate the length of the hypotenuse of a right-angle triangle given\nlegs of length `x` and `y`.",13,null],[10,"sin","","Computes the sine of a number (in radians).",13,null],[10,"cos","","Computes the cosine of a number (in radians).",13,null],[10,"tan","","Computes the tangent of a number (in radians).",13,null],[10,"asin","","Computes the arcsine of a number. Return value is in radians in\nthe range [-pi/2, pi/2] or NaN if the number is outside the range\n[-1, 1].",13,null],[10,"acos","","Computes the arccosine of a number. Return value is in radians in\nthe range [0, pi] or NaN if the number is outside the range\n[-1, 1].",13,null],[10,"atan","","Computes the arctangent of a number. Return value is in radians in the\nrange [-pi/2, pi/2];",13,null],[10,"atan2","","Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).",13,null],[10,"sin_cos","","Simultaneously computes the sine and cosine of the number, `x`. Returns\n`(sin(x), cos(x))`.",13,null],[10,"exp_m1","","Returns `e^(self) - 1` in a way that is accurate even if the\nnumber is close to zero.",13,null],[10,"ln_1p","","Returns `ln(1+n)` (natural logarithm) more accurately than if\nthe operations were performed separately.",13,null],[10,"sinh","","Hyperbolic sine function.",13,null],[10,"cosh","","Hyperbolic cosine function.",13,null],[10,"tanh","","Hyperbolic tangent function.",13,null],[10,"asinh","","Inverse hyperbolic sine function.",13,null],[10,"acosh","","Inverse hyperbolic cosine function.",13,null],[10,"atanh","","Inverse hyperbolic tangent function.",13,null],[10,"integer_decode","","Returns the mantissa, base 2 exponent, and sign as integers, respectively.\nThe original number can be recovered by `sign * mantissa * 2 ^ exponent`.\nThe floating point encoding is documented in the [Reference][floating-point].",13,null],[8,"ToPrimitive","","A generic trait for converting a value to a number.",null,null],[11,"to_isize","","Converts the value of `self` to an `isize`.",14,null],[11,"to_i8","","Converts the value of `self` to an `i8`.",14,null],[11,"to_i16","","Converts the value of `self` to an `i16`.",14,null],[11,"to_i32","","Converts the value of `self` to an `i32`.",14,null],[10,"to_i64","","Converts the value of `self` to an `i64`.",14,null],[11,"to_usize","","Converts the value of `self` to a `usize`.",14,null],[11,"to_u8","","Converts the value of `self` to an `u8`.",14,null],[11,"to_u16","","Converts the value of `self` to an `u16`.",14,null],[11,"to_u32","","Converts the value of `self` to an `u32`.",14,null],[10,"to_u64","","Converts the value of `self` to an `u64`.",14,null],[11,"to_f32","","Converts the value of `self` to an `f32`.",14,null],[11,"to_f64","","Converts the value of `self` to an `f64`.",14,null],[8,"FromPrimitive","","A generic trait for converting a number to a value.",null,null],[11,"from_isize","","Convert an `isize` to return an optional value of this type. If the\nvalue cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"isize"}],"output":{"name":"option"}}],[11,"from_i8","","Convert an `i8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i8"}],"output":{"name":"option"}}],[11,"from_i16","","Convert an `i16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i16"}],"output":{"name":"option"}}],[11,"from_i32","","Convert an `i32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i32"}],"output":{"name":"option"}}],[10,"from_i64","","Convert an `i64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_usize","","Convert a `usize` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"usize"}],"output":{"name":"option"}}],[11,"from_u8","","Convert an `u8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u8"}],"output":{"name":"option"}}],[11,"from_u16","","Convert an `u16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u16"}],"output":{"name":"option"}}],[11,"from_u32","","Convert an `u32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u32"}],"output":{"name":"option"}}],[10,"from_u64","","Convert an `u64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f32","","Convert a `f32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f32"}],"output":{"name":"option"}}],[11,"from_f64","","Convert a `f64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[8,"NumCast","","An interface for casting between machine scalars.",null,null],[10,"from","","Creates a number from another value that can be converted into\na primitive via the `ToPrimitive` trait.",16,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[0,"cast","","",null,null],[8,"ToPrimitive","num::cast","A generic trait for converting a value to a number.",null,null],[11,"to_isize","","Converts the value of `self` to an `isize`.",14,null],[11,"to_i8","","Converts the value of `self` to an `i8`.",14,null],[11,"to_i16","","Converts the value of `self` to an `i16`.",14,null],[11,"to_i32","","Converts the value of `self` to an `i32`.",14,null],[10,"to_i64","","Converts the value of `self` to an `i64`.",14,null],[11,"to_usize","","Converts the value of `self` to a `usize`.",14,null],[11,"to_u8","","Converts the value of `self` to an `u8`.",14,null],[11,"to_u16","","Converts the value of `self` to an `u16`.",14,null],[11,"to_u32","","Converts the value of `self` to an `u32`.",14,null],[10,"to_u64","","Converts the value of `self` to an `u64`.",14,null],[11,"to_f32","","Converts the value of `self` to an `f32`.",14,null],[11,"to_f64","","Converts the value of `self` to an `f64`.",14,null],[8,"FromPrimitive","","A generic trait for converting a number to a value.",null,null],[11,"from_isize","","Convert an `isize` to return an optional value of this type. If the\nvalue cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"isize"}],"output":{"name":"option"}}],[11,"from_i8","","Convert an `i8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i8"}],"output":{"name":"option"}}],[11,"from_i16","","Convert an `i16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i16"}],"output":{"name":"option"}}],[11,"from_i32","","Convert an `i32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i32"}],"output":{"name":"option"}}],[10,"from_i64","","Convert an `i64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_usize","","Convert a `usize` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"usize"}],"output":{"name":"option"}}],[11,"from_u8","","Convert an `u8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u8"}],"output":{"name":"option"}}],[11,"from_u16","","Convert an `u16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u16"}],"output":{"name":"option"}}],[11,"from_u32","","Convert an `u32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u32"}],"output":{"name":"option"}}],[10,"from_u64","","Convert an `u64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f32","","Convert a `f32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f32"}],"output":{"name":"option"}}],[11,"from_f64","","Convert a `f64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[5,"cast","","Cast from one machine scalar to another.",null,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[8,"NumCast","","An interface for casting between machine scalars.",null,null],[10,"from","","Creates a number from another value that can be converted into\na primitive via the `ToPrimitive` trait.",16,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[6,"BigDigit","num::bigint","",null,null],[6,"DoubleBigDigit","","",null,null],[17,"ZERO_BIG_DIGIT","","",null,null],[0,"big_digit","","",null,null],[17,"BITS","num::bigint::big_digit","",null,null],[17,"BASE","","",null,null],[5,"from_doublebigdigit","","Split one `DoubleBigDigit` into two `BigDigit`s.",null,null],[5,"to_doublebigdigit","","Join two `BigDigit`s into one `DoubleBigDigit`",null,{"inputs":[{"name":"u32"},{"name":"u32"}],"output":{"name":"u64"}}],[3,"BigUint","num::bigint","A big unsigned integer type.",null,null],[8,"ToBigUint","","A generic trait for converting a value to a `BigUint`.",null,null],[10,"to_biguint","","Converts the value of `self` to a `BigUint`.",17,null],[4,"Sign","","A Sign is a `BigInt`'s composing element.",null,null],[13,"Minus","","",18,null],[13,"NoSign","","",18,null],[13,"Plus","","",18,null],[3,"BigInt","","A big signed integer type.",null,null],[8,"ToBigInt","","A generic trait for converting a value to a `BigInt`.",null,null],[10,"to_bigint","","Converts the value of `self` to a `BigInt`.",19,null],[8,"RandBigInt","","",null,null],[10,"gen_biguint","","Generate a random `BigUint` of the given bit size.",20,null],[10,"gen_bigint","","Generate a random BigInt of the given bit size.",20,null],[10,"gen_biguint_below","","Generate a random `BigUint` less than the given bound. Fails\nwhen the bound is zero.",20,null],[10,"gen_biguint_range","","Generate a random `BigUint` within the given range. The lower\nbound is inclusive; the upper bound is exclusive. Fails when\nthe upper bound is not greater than the lower bound.",20,null],[10,"gen_bigint_range","","Generate a random `BigInt` within the given range. The lower\nbound is inclusive; the upper bound is exclusive. Fails when\nthe upper bound is not greater than the lower bound.",20,null],[4,"ParseBigIntError","","",null,null],[13,"ParseInt","","",21,null],[13,"Other","","",21,null],[3,"Complex","num::complex","A complex number in Cartesian form.",null,null],[12,"re","","Real portion of the complex number",0,null],[12,"im","","Imaginary portion of the complex number",0,null],[6,"Complex32","","",null,null],[6,"Complex64","","",null,null],[8,"Integer","num::integer","",null,null],[10,"div_floor","","Floored integer division.",1,null],[10,"mod_floor","","Floored integer modulo, satisfying:",1,null],[10,"gcd","","Greatest Common Divisor (GCD).",1,null],[10,"lcm","","Lowest Common Multiple (LCM).",1,null],[10,"divides","","Deprecated, use `is_multiple_of` instead.",1,null],[10,"is_multiple_of","","Returns `true` if `other` is a multiple of `self`.",1,null],[10,"is_even","","Returns `true` if the number is even.",1,null],[10,"is_odd","","Returns `true` if the number is odd.",1,null],[10,"div_rem","","Simultaneous truncated integer division and modulus.\nReturns `(quotient, remainder)`.",1,null],[11,"div_mod_floor","","Simultaneous floored integer division and modulus.\nReturns `(quotient, remainder)`.",1,null],[5,"div_rem","","Simultaneous integer division and modulus",null,null],[5,"div_floor","","Floored integer division",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[5,"mod_floor","","Floored integer modulus",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[5,"div_mod_floor","","Simultaneous floored integer division and modulus",null,null],[5,"gcd","","Calculates the Greatest Common Divisor (GCD) of the number and `other`. The\nresult is always positive.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[5,"lcm","","Calculates the Lowest Common Multiple (LCM) of the number and `other`.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[3,"Range","num::iter","An iterator over the range [start, stop)",null,null],[5,"range","","Returns an iterator over the given range [start, stop) (that is, starting\nat start (inclusive), and ending at stop (exclusive)).",null,{"inputs":[{"name":"a"},{"name":"a"}],"output":{"name":"range"}}],[3,"RangeInclusive","","An iterator over the range [start, stop]",null,null],[5,"range_inclusive","","Return an iterator over the range [start, stop]",null,{"inputs":[{"name":"a"},{"name":"a"}],"output":{"name":"rangeinclusive"}}],[3,"RangeStep","","An iterator over the range [start, stop) by `step`. It handles overflow by stopping.",null,null],[5,"range_step","","Return an iterator over the range [start, stop) by `step`. It handles overflow by stopping.",null,{"inputs":[{"name":"a"},{"name":"a"},{"name":"a"}],"output":{"name":"rangestep"}}],[3,"RangeStepInclusive","","An iterator over the range [start, stop] by `step`. It handles overflow by stopping.",null,null],[5,"range_step_inclusive","","Return an iterator over the range [start, stop] by `step`. It handles overflow by stopping.",null,{"inputs":[{"name":"a"},{"name":"a"},{"name":"a"}],"output":{"name":"rangestepinclusive"}}],[0,"identities","num::traits","",null,null],[8,"Zero","num::traits::identities","Defines an additive identity element for `Self`.",null,null],[10,"zero","","Returns the additive identity element of `Self`, `0`.",3,{"inputs":[],"output":{"name":"self"}}],[10,"is_zero","","Returns `true` if `self` is equal to the additive identity.",3,null],[8,"One","","Defines a multiplicative identity element for `Self`.",null,null],[10,"one","","Returns the multiplicative identity element of `Self`, `1`.",4,{"inputs":[],"output":{"name":"self"}}],[5,"zero","","Returns the additive identity, `0`.",null,{"inputs":[],"output":{"name":"t"}}],[5,"one","","Returns the multiplicative identity, `1`.",null,{"inputs":[],"output":{"name":"t"}}],[0,"sign","num::traits","",null,null],[8,"Signed","num::traits::sign","Useful functions for signed numbers (i.e. numbers that can be negative).",null,null],[10,"abs","","Computes the absolute value.",5,null],[10,"abs_sub","","The positive difference of two numbers.",5,null],[10,"signum","","Returns the sign of the number.",5,null],[10,"is_positive","","Returns true if the number is positive and false if the number is zero or negative.",5,null],[10,"is_negative","","Returns true if the number is negative and false if the number is zero or positive.",5,null],[5,"abs","","Computes the absolute value.",null,{"inputs":[{"name":"t"}],"output":{"name":"t"}}],[5,"abs_sub","","The positive difference of two numbers.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[5,"signum","","Returns the sign of the number.",null,{"inputs":[{"name":"t"}],"output":{"name":"t"}}],[8,"Unsigned","","A trait for values which cannot be negative",null,null],[0,"ops","num::traits","",null,null],[0,"saturating","num::traits::ops","",null,null],[8,"Saturating","num::traits::ops::saturating","Saturating math operations",null,null],[10,"saturating_add","","Saturating addition operator.\nReturns a+b, saturating at the numeric bounds instead of overflowing.",7,null],[10,"saturating_sub","","Saturating subtraction operator.\nReturns a-b, saturating at the numeric bounds instead of overflowing.",7,null],[0,"checked","num::traits::ops","",null,null],[8,"CheckedAdd","num::traits::ops::checked","Performs addition that returns `None` instead of wrapping around on\noverflow.",null,null],[10,"checked_add","","Adds two numbers, checking for overflow. If overflow happens, `None` is\nreturned.",8,null],[8,"CheckedSub","","Performs subtraction that returns `None` instead of wrapping around on underflow.",null,null],[10,"checked_sub","","Subtracts two numbers, checking for underflow. If underflow happens,\n`None` is returned.",9,null],[8,"CheckedMul","","Performs multiplication that returns `None` instead of wrapping around on underflow or\noverflow.",null,null],[10,"checked_mul","","Multiplies two numbers, checking for underflow or overflow. If underflow\nor overflow happens, `None` is returned.",10,null],[8,"CheckedDiv","","Performs division that returns `None` instead of panicking on division by zero and instead of\nwrapping around on underflow and overflow.",null,null],[10,"checked_div","","Divides two numbers, checking for underflow, overflow and division by\nzero. If any of that happens, `None` is returned.",11,null],[0,"bounds","num::traits","",null,null],[8,"Bounded","num::traits::bounds","Numbers which have upper and lower bounds",null,null],[10,"min_value","","returns the smallest finite number this type can represent",6,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","returns the largest finite number this type can represent",6,{"inputs":[],"output":{"name":"self"}}],[0,"float","num::traits","",null,null],[8,"Float","num::traits::float","",null,null],[10,"nan","","Returns the `NaN` value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"infinity","","Returns the infinite value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"neg_infinity","","Returns the negative infinite value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"neg_zero","","Returns `-0.0`.",13,{"inputs":[],"output":{"name":"self"}}],[10,"min_value","","Returns the smallest finite value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"min_positive_value","","Returns the smallest positive, normalized value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","Returns the largest finite value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"is_nan","","Returns `true` if this value is `NaN` and false otherwise.",13,null],[10,"is_infinite","","Returns `true` if this value is positive infinity or negative infinity and\nfalse otherwise.",13,null],[10,"is_finite","","Returns `true` if this number is neither infinite nor `NaN`.",13,null],[10,"is_normal","","Returns `true` if the number is neither zero, infinite,\n[subnormal][subnormal], or `NaN`.",13,null],[10,"classify","","Returns the floating point category of the number. If only one property\nis going to be tested, it is generally faster to use the specific\npredicate instead.",13,null],[10,"floor","","Returns the largest integer less than or equal to a number.",13,null],[10,"ceil","","Returns the smallest integer greater than or equal to a number.",13,null],[10,"round","","Returns the nearest integer to a number. Round half-way cases away from\n`0.0`.",13,null],[10,"trunc","","Return the integer part of a number.",13,null],[10,"fract","","Returns the fractional part of a number.",13,null],[10,"abs","","Computes the absolute value of `self`. Returns `Float::nan()` if the\nnumber is `Float::nan()`.",13,null],[10,"signum","","Returns a number that represents the sign of `self`.",13,null],[10,"is_sign_positive","","Returns `true` if `self` is positive, including `+0.0` and\n`Float::infinity()`.",13,null],[10,"is_sign_negative","","Returns `true` if `self` is negative, including `-0.0` and\n`Float::neg_infinity()`.",13,null],[10,"mul_add","","Fused multiply-add. Computes `(self * a) + b` with only one rounding\nerror. This produces a more accurate result with better performance than\na separate multiplication operation followed by an add.",13,null],[10,"recip","","Take the reciprocal (inverse) of a number, `1/x`.",13,null],[10,"powi","","Raise a number to an integer power.",13,null],[10,"powf","","Raise a number to a floating point power.",13,null],[10,"sqrt","","Take the square root of a number.",13,null],[10,"exp","","Returns `e^(self)`, (the exponential function).",13,null],[10,"exp2","","Returns `2^(self)`.",13,null],[10,"ln","","Returns the natural logarithm of the number.",13,null],[10,"log","","Returns the logarithm of the number with respect to an arbitrary base.",13,null],[10,"log2","","Returns the base 2 logarithm of the number.",13,null],[10,"log10","","Returns the base 10 logarithm of the number.",13,null],[11,"to_degrees","","Converts radians to degrees.",13,null],[11,"to_radians","","Converts degrees to radians.",13,null],[10,"max","","Returns the maximum of the two numbers.",13,null],[10,"min","","Returns the minimum of the two numbers.",13,null],[10,"abs_sub","","The positive difference of two numbers.",13,null],[10,"cbrt","","Take the cubic root of a number.",13,null],[10,"hypot","","Calculate the length of the hypotenuse of a right-angle triangle given\nlegs of length `x` and `y`.",13,null],[10,"sin","","Computes the sine of a number (in radians).",13,null],[10,"cos","","Computes the cosine of a number (in radians).",13,null],[10,"tan","","Computes the tangent of a number (in radians).",13,null],[10,"asin","","Computes the arcsine of a number. Return value is in radians in\nthe range [-pi/2, pi/2] or NaN if the number is outside the range\n[-1, 1].",13,null],[10,"acos","","Computes the arccosine of a number. Return value is in radians in\nthe range [0, pi] or NaN if the number is outside the range\n[-1, 1].",13,null],[10,"atan","","Computes the arctangent of a number. Return value is in radians in the\nrange [-pi/2, pi/2];",13,null],[10,"atan2","","Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).",13,null],[10,"sin_cos","","Simultaneously computes the sine and cosine of the number, `x`. Returns\n`(sin(x), cos(x))`.",13,null],[10,"exp_m1","","Returns `e^(self) - 1` in a way that is accurate even if the\nnumber is close to zero.",13,null],[10,"ln_1p","","Returns `ln(1+n)` (natural logarithm) more accurately than if\nthe operations were performed separately.",13,null],[10,"sinh","","Hyperbolic sine function.",13,null],[10,"cosh","","Hyperbolic cosine function.",13,null],[10,"tanh","","Hyperbolic tangent function.",13,null],[10,"asinh","","Inverse hyperbolic sine function.",13,null],[10,"acosh","","Inverse hyperbolic cosine function.",13,null],[10,"atanh","","Inverse hyperbolic tangent function.",13,null],[10,"integer_decode","","Returns the mantissa, base 2 exponent, and sign as integers, respectively.\nThe original number can be recovered by `sign * mantissa * 2 ^ exponent`.\nThe floating point encoding is documented in the [Reference][floating-point].",13,null],[0,"cast","num::traits","",null,null],[8,"ToPrimitive","num::traits::cast","A generic trait for converting a value to a number.",null,null],[11,"to_isize","","Converts the value of `self` to an `isize`.",14,null],[11,"to_i8","","Converts the value of `self` to an `i8`.",14,null],[11,"to_i16","","Converts the value of `self` to an `i16`.",14,null],[11,"to_i32","","Converts the value of `self` to an `i32`.",14,null],[10,"to_i64","","Converts the value of `self` to an `i64`.",14,null],[11,"to_usize","","Converts the value of `self` to a `usize`.",14,null],[11,"to_u8","","Converts the value of `self` to an `u8`.",14,null],[11,"to_u16","","Converts the value of `self` to an `u16`.",14,null],[11,"to_u32","","Converts the value of `self` to an `u32`.",14,null],[10,"to_u64","","Converts the value of `self` to an `u64`.",14,null],[11,"to_f32","","Converts the value of `self` to an `f32`.",14,null],[11,"to_f64","","Converts the value of `self` to an `f64`.",14,null],[8,"FromPrimitive","","A generic trait for converting a number to a value.",null,null],[11,"from_isize","","Convert an `isize` to return an optional value of this type. If the\nvalue cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"isize"}],"output":{"name":"option"}}],[11,"from_i8","","Convert an `i8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i8"}],"output":{"name":"option"}}],[11,"from_i16","","Convert an `i16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i16"}],"output":{"name":"option"}}],[11,"from_i32","","Convert an `i32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i32"}],"output":{"name":"option"}}],[10,"from_i64","","Convert an `i64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_usize","","Convert a `usize` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"usize"}],"output":{"name":"option"}}],[11,"from_u8","","Convert an `u8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u8"}],"output":{"name":"option"}}],[11,"from_u16","","Convert an `u16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u16"}],"output":{"name":"option"}}],[11,"from_u32","","Convert an `u32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u32"}],"output":{"name":"option"}}],[10,"from_u64","","Convert an `u64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f32","","Convert a `f32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f32"}],"output":{"name":"option"}}],[11,"from_f64","","Convert a `f64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[5,"cast","","Cast from one machine scalar to another.",null,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[8,"NumCast","","An interface for casting between machine scalars.",null,null],[10,"from","","Creates a number from another value that can be converted into\na primitive via the `ToPrimitive` trait.",16,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[0,"int","num::traits","",null,null],[8,"PrimInt","num::traits::int","",null,null],[10,"count_ones","","Returns the number of ones in the binary representation of `self`.",12,null],[10,"count_zeros","","Returns the number of zeros in the binary representation of `self`.",12,null],[10,"leading_zeros","","Returns the number of leading zeros in the binary representation\nof `self`.",12,null],[10,"trailing_zeros","","Returns the number of trailing zeros in the binary representation\nof `self`.",12,null],[10,"rotate_left","","Shifts the bits to the left by a specified amount amount, `n`, wrapping\nthe truncated bits to the end of the resulting integer.",12,null],[10,"rotate_right","","Shifts the bits to the right by a specified amount amount, `n`, wrapping\nthe truncated bits to the beginning of the resulting integer.",12,null],[10,"signed_shl","","Shifts the bits to the left by a specified amount amount, `n`, filling\nzeros in the least significant bits.",12,null],[10,"signed_shr","","Shifts the bits to the right by a specified amount amount, `n`, copying\nthe "sign bit" in the most significant bits even for unsigned types.",12,null],[10,"unsigned_shl","","Shifts the bits to the left by a specified amount amount, `n`, filling\nzeros in the least significant bits.",12,null],[10,"unsigned_shr","","Shifts the bits to the right by a specified amount amount, `n`, filling\nzeros in the most significant bits.",12,null],[10,"swap_bytes","","Reverses the byte order of the integer.",12,null],[10,"from_be","","Convert an integer from big endian to the target's endianness.",12,{"inputs":[{"name":"self"}],"output":{"name":"self"}}],[10,"from_le","","Convert an integer from little endian to the target's endianness.",12,{"inputs":[{"name":"self"}],"output":{"name":"self"}}],[10,"to_be","","Convert `self` to big endian from the target's endianness.",12,null],[10,"to_le","","Convert `self` to little endian from the target's endianness.",12,null],[10,"pow","","Raises self to the power of `exp`, using exponentiation by squaring.",12,null],[0,"pow","num::traits","",null,null],[5,"pow","num::traits::pow","Raises a value to the power of exp, using exponentiation by squaring.",null,{"inputs":[{"name":"t"},{"name":"usize"}],"output":{"name":"t"}}],[5,"checked_pow","","Raises a value to the power of exp, returning `None` if an overflow occurred.",null,{"inputs":[{"name":"t"},{"name":"usize"}],"output":{"name":"option"}}],[8,"Num","num::traits","The base trait for numeric types",null,null],[16,"FromStrRadixErr","","",2,null],[10,"from_str_radix","","Convert from a string and radix <= 36.",2,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[4,"FloatErrorKind","","",null,null],[13,"Empty","","",22,null],[13,"Invalid","","",22,null],[3,"ParseFloatError","","",null,null],[12,"kind","","",23,null],[8,"Bounded","","Numbers which have upper and lower bounds",null,null],[10,"min_value","","returns the smallest finite number this type can represent",6,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","returns the largest finite number this type can represent",6,{"inputs":[],"output":{"name":"self"}}],[5,"zero","","Returns the additive identity, `0`.",null,{"inputs":[],"output":{"name":"t"}}],[5,"checked_pow","","Raises a value to the power of exp, returning `None` if an overflow occurred.",null,{"inputs":[{"name":"t"},{"name":"usize"}],"output":{"name":"option"}}],[8,"ToPrimitive","","A generic trait for converting a value to a number.",null,null],[11,"to_isize","","Converts the value of `self` to an `isize`.",14,null],[11,"to_i8","","Converts the value of `self` to an `i8`.",14,null],[11,"to_i16","","Converts the value of `self` to an `i16`.",14,null],[11,"to_i32","","Converts the value of `self` to an `i32`.",14,null],[10,"to_i64","","Converts the value of `self` to an `i64`.",14,null],[11,"to_usize","","Converts the value of `self` to a `usize`.",14,null],[11,"to_u8","","Converts the value of `self` to an `u8`.",14,null],[11,"to_u16","","Converts the value of `self` to an `u16`.",14,null],[11,"to_u32","","Converts the value of `self` to an `u32`.",14,null],[10,"to_u64","","Converts the value of `self` to an `u64`.",14,null],[11,"to_f32","","Converts the value of `self` to an `f32`.",14,null],[11,"to_f64","","Converts the value of `self` to an `f64`.",14,null],[8,"PrimInt","","",null,null],[10,"count_ones","","Returns the number of ones in the binary representation of `self`.",12,null],[10,"count_zeros","","Returns the number of zeros in the binary representation of `self`.",12,null],[10,"leading_zeros","","Returns the number of leading zeros in the binary representation\nof `self`.",12,null],[10,"trailing_zeros","","Returns the number of trailing zeros in the binary representation\nof `self`.",12,null],[10,"rotate_left","","Shifts the bits to the left by a specified amount amount, `n`, wrapping\nthe truncated bits to the end of the resulting integer.",12,null],[10,"rotate_right","","Shifts the bits to the right by a specified amount amount, `n`, wrapping\nthe truncated bits to the beginning of the resulting integer.",12,null],[10,"signed_shl","","Shifts the bits to the left by a specified amount amount, `n`, filling\nzeros in the least significant bits.",12,null],[10,"signed_shr","","Shifts the bits to the right by a specified amount amount, `n`, copying\nthe "sign bit" in the most significant bits even for unsigned types.",12,null],[10,"unsigned_shl","","Shifts the bits to the left by a specified amount amount, `n`, filling\nzeros in the least significant bits.",12,null],[10,"unsigned_shr","","Shifts the bits to the right by a specified amount amount, `n`, filling\nzeros in the most significant bits.",12,null],[10,"swap_bytes","","Reverses the byte order of the integer.",12,null],[10,"from_be","","Convert an integer from big endian to the target's endianness.",12,{"inputs":[{"name":"self"}],"output":{"name":"self"}}],[10,"from_le","","Convert an integer from little endian to the target's endianness.",12,{"inputs":[{"name":"self"}],"output":{"name":"self"}}],[10,"to_be","","Convert `self` to big endian from the target's endianness.",12,null],[10,"to_le","","Convert `self` to little endian from the target's endianness.",12,null],[10,"pow","","Raises self to the power of `exp`, using exponentiation by squaring.",12,null],[5,"abs_sub","","The positive difference of two numbers.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[8,"CheckedMul","","Performs multiplication that returns `None` instead of wrapping around on underflow or\noverflow.",null,null],[10,"checked_mul","","Multiplies two numbers, checking for underflow or overflow. If underflow\nor overflow happens, `None` is returned.",10,null],[8,"FromPrimitive","","A generic trait for converting a number to a value.",null,null],[11,"from_isize","","Convert an `isize` to return an optional value of this type. If the\nvalue cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"isize"}],"output":{"name":"option"}}],[11,"from_i8","","Convert an `i8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i8"}],"output":{"name":"option"}}],[11,"from_i16","","Convert an `i16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i16"}],"output":{"name":"option"}}],[11,"from_i32","","Convert an `i32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i32"}],"output":{"name":"option"}}],[10,"from_i64","","Convert an `i64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_usize","","Convert a `usize` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"usize"}],"output":{"name":"option"}}],[11,"from_u8","","Convert an `u8` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u8"}],"output":{"name":"option"}}],[11,"from_u16","","Convert an `u16` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u16"}],"output":{"name":"option"}}],[11,"from_u32","","Convert an `u32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u32"}],"output":{"name":"option"}}],[10,"from_u64","","Convert an `u64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f32","","Convert a `f32` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f32"}],"output":{"name":"option"}}],[11,"from_f64","","Convert a `f64` to return an optional value of this type. If the\ntype cannot be represented by this value, the `None` is returned.",15,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[5,"one","","Returns the multiplicative identity, `1`.",null,{"inputs":[],"output":{"name":"t"}}],[8,"CheckedAdd","","Performs addition that returns `None` instead of wrapping around on\noverflow.",null,null],[10,"checked_add","","Adds two numbers, checking for overflow. If overflow happens, `None` is\nreturned.",8,null],[8,"Saturating","","Saturating math operations",null,null],[10,"saturating_add","","Saturating addition operator.\nReturns a+b, saturating at the numeric bounds instead of overflowing.",7,null],[10,"saturating_sub","","Saturating subtraction operator.\nReturns a-b, saturating at the numeric bounds instead of overflowing.",7,null],[8,"CheckedDiv","","Performs division that returns `None` instead of panicking on division by zero and instead of\nwrapping around on underflow and overflow.",null,null],[10,"checked_div","","Divides two numbers, checking for underflow, overflow and division by\nzero. If any of that happens, `None` is returned.",11,null],[5,"cast","","Cast from one machine scalar to another.",null,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[8,"Unsigned","","A trait for values which cannot be negative",null,null],[8,"CheckedSub","","Performs subtraction that returns `None` instead of wrapping around on underflow.",null,null],[10,"checked_sub","","Subtracts two numbers, checking for underflow. If underflow happens,\n`None` is returned.",9,null],[8,"One","","Defines a multiplicative identity element for `Self`.",null,null],[10,"one","","Returns the multiplicative identity element of `Self`, `1`.",4,{"inputs":[],"output":{"name":"self"}}],[8,"Zero","","Defines an additive identity element for `Self`.",null,null],[10,"zero","","Returns the additive identity element of `Self`, `0`.",3,{"inputs":[],"output":{"name":"self"}}],[10,"is_zero","","Returns `true` if `self` is equal to the additive identity.",3,null],[8,"Signed","","Useful functions for signed numbers (i.e. numbers that can be negative).",null,null],[10,"abs","","Computes the absolute value.",5,null],[10,"abs_sub","","The positive difference of two numbers.",5,null],[10,"signum","","Returns the sign of the number.",5,null],[10,"is_positive","","Returns true if the number is positive and false if the number is zero or negative.",5,null],[10,"is_negative","","Returns true if the number is negative and false if the number is zero or positive.",5,null],[5,"signum","","Returns the sign of the number.",null,{"inputs":[{"name":"t"}],"output":{"name":"t"}}],[8,"NumCast","","An interface for casting between machine scalars.",null,null],[10,"from","","Creates a number from another value that can be converted into\na primitive via the `ToPrimitive` trait.",16,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[5,"pow","","Raises a value to the power of exp, using exponentiation by squaring.",null,{"inputs":[{"name":"t"},{"name":"usize"}],"output":{"name":"t"}}],[8,"Float","","",null,null],[10,"nan","","Returns the `NaN` value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"infinity","","Returns the infinite value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"neg_infinity","","Returns the negative infinite value.",13,{"inputs":[],"output":{"name":"self"}}],[10,"neg_zero","","Returns `-0.0`.",13,{"inputs":[],"output":{"name":"self"}}],[10,"min_value","","Returns the smallest finite value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"min_positive_value","","Returns the smallest positive, normalized value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","Returns the largest finite value that this type can represent.",13,{"inputs":[],"output":{"name":"self"}}],[10,"is_nan","","Returns `true` if this value is `NaN` and false otherwise.",13,null],[10,"is_infinite","","Returns `true` if this value is positive infinity or negative infinity and\nfalse otherwise.",13,null],[10,"is_finite","","Returns `true` if this number is neither infinite nor `NaN`.",13,null],[10,"is_normal","","Returns `true` if the number is neither zero, infinite,\n[subnormal][subnormal], or `NaN`.",13,null],[10,"classify","","Returns the floating point category of the number. If only one property\nis going to be tested, it is generally faster to use the specific\npredicate instead.",13,null],[10,"floor","","Returns the largest integer less than or equal to a number.",13,null],[10,"ceil","","Returns the smallest integer greater than or equal to a number.",13,null],[10,"round","","Returns the nearest integer to a number. Round half-way cases away from\n`0.0`.",13,null],[10,"trunc","","Return the integer part of a number.",13,null],[10,"fract","","Returns the fractional part of a number.",13,null],[10,"abs","","Computes the absolute value of `self`. Returns `Float::nan()` if the\nnumber is `Float::nan()`.",13,null],[10,"signum","","Returns a number that represents the sign of `self`.",13,null],[10,"is_sign_positive","","Returns `true` if `self` is positive, including `+0.0` and\n`Float::infinity()`.",13,null],[10,"is_sign_negative","","Returns `true` if `self` is negative, including `-0.0` and\n`Float::neg_infinity()`.",13,null],[10,"mul_add","","Fused multiply-add. Computes `(self * a) + b` with only one rounding\nerror. This produces a more accurate result with better performance than\na separate multiplication operation followed by an add.",13,null],[10,"recip","","Take the reciprocal (inverse) of a number, `1/x`.",13,null],[10,"powi","","Raise a number to an integer power.",13,null],[10,"powf","","Raise a number to a floating point power.",13,null],[10,"sqrt","","Take the square root of a number.",13,null],[10,"exp","","Returns `e^(self)`, (the exponential function).",13,null],[10,"exp2","","Returns `2^(self)`.",13,null],[10,"ln","","Returns the natural logarithm of the number.",13,null],[10,"log","","Returns the logarithm of the number with respect to an arbitrary base.",13,null],[10,"log2","","Returns the base 2 logarithm of the number.",13,null],[10,"log10","","Returns the base 10 logarithm of the number.",13,null],[11,"to_degrees","","Converts radians to degrees.",13,null],[11,"to_radians","","Converts degrees to radians.",13,null],[10,"max","","Returns the maximum of the two numbers.",13,null],[10,"min","","Returns the minimum of the two numbers.",13,null],[10,"abs_sub","","The positive difference of two numbers.",13,null],[10,"cbrt","","Take the cubic root of a number.",13,null],[10,"hypot","","Calculate the length of the hypotenuse of a right-angle triangle given\nlegs of length `x` and `y`.",13,null],[10,"sin","","Computes the sine of a number (in radians).",13,null],[10,"cos","","Computes the cosine of a number (in radians).",13,null],[10,"tan","","Computes the tangent of a number (in radians).",13,null],[10,"asin","","Computes the arcsine of a number. Return value is in radians in\nthe range [-pi/2, pi/2] or NaN if the number is outside the range\n[-1, 1].",13,null],[10,"acos","","Computes the arccosine of a number. Return value is in radians in\nthe range [0, pi] or NaN if the number is outside the range\n[-1, 1].",13,null],[10,"atan","","Computes the arctangent of a number. Return value is in radians in the\nrange [-pi/2, pi/2];",13,null],[10,"atan2","","Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).",13,null],[10,"sin_cos","","Simultaneously computes the sine and cosine of the number, `x`. Returns\n`(sin(x), cos(x))`.",13,null],[10,"exp_m1","","Returns `e^(self) - 1` in a way that is accurate even if the\nnumber is close to zero.",13,null],[10,"ln_1p","","Returns `ln(1+n)` (natural logarithm) more accurately than if\nthe operations were performed separately.",13,null],[10,"sinh","","Hyperbolic sine function.",13,null],[10,"cosh","","Hyperbolic cosine function.",13,null],[10,"tanh","","Hyperbolic tangent function.",13,null],[10,"asinh","","Inverse hyperbolic sine function.",13,null],[10,"acosh","","Inverse hyperbolic cosine function.",13,null],[10,"atanh","","Inverse hyperbolic tangent function.",13,null],[10,"integer_decode","","Returns the mantissa, base 2 exponent, and sign as integers, respectively.\nThe original number can be recovered by `sign * mantissa * 2 ^ exponent`.\nThe floating point encoding is documented in the [Reference][floating-point].",13,null],[5,"abs","","Computes the absolute value.",null,{"inputs":[{"name":"t"}],"output":{"name":"t"}}],[3,"Ratio","num::rational","Represents the ratio between 2 numbers.",null,null],[6,"Rational","","",null,null],[6,"Rational32","","",null,null],[6,"Rational64","","",null,null],[6,"BigRational","","",null,null],[3,"ParseRatioError","","",null,null],[5,"zero","num","Returns the additive identity, `0`.",null,{"inputs":[],"output":{"name":"t"}}],[5,"one","","Returns the multiplicative identity, `1`.",null,{"inputs":[],"output":{"name":"t"}}],[5,"abs","","Computes the absolute value.",null,{"inputs":[{"name":"t"}],"output":{"name":"t"}}],[5,"abs_sub","","The positive difference of two numbers.",null,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"t"}}],[5,"signum","","Returns the sign of the number.",null,{"inputs":[{"name":"t"}],"output":{"name":"t"}}],[5,"pow","","Raises a value to the power of exp, using exponentiation by squaring.",null,{"inputs":[{"name":"t"},{"name":"usize"}],"output":{"name":"t"}}],[5,"checked_pow","","Raises a value to the power of exp, returning `None` if an overflow occurred.",null,{"inputs":[{"name":"t"},{"name":"usize"}],"output":{"name":"option"}}],[11,"new","num::bigint","Creates and initializes a BigInt.",24,{"inputs":[{"name":"sign"},{"name":"vec"}],"output":{"name":"bigint"}}],[11,"from_biguint","","Creates and initializes a `BigInt`.",24,{"inputs":[{"name":"sign"},{"name":"biguint"}],"output":{"name":"bigint"}}],[11,"from_slice","","Creates and initializes a `BigInt`.",24,null],[11,"from_bytes_be","","Creates and initializes a `BigInt`.",24,null],[11,"from_bytes_le","","Creates and initializes a `BigInt`.",24,null],[11,"to_bytes_le","","Returns the sign and the byte representation of the `BigInt` in little-endian byte order.",24,null],[11,"to_bytes_be","","Returns the sign and the byte representation of the `BigInt` in big-endian byte order.",24,null],[11,"to_str_radix","","Returns the integer formatted as a string in the given radix.\n`radix` must be in the range `[2, 36]`.",24,null],[11,"sign","","Returns the sign of the `BigInt` as a `Sign`.",24,null],[11,"parse_bytes","","Creates and initializes a `BigInt`.",24,null],[11,"bits","","Determines the fewest bits necessary to express the `BigInt`,\nnot including the sign.",24,null],[11,"to_biguint","","Converts this `BigInt` into a `BigUint`, if it's not negative.",24,null],[11,"checked_add","","",24,null],[11,"checked_sub","","",24,null],[11,"checked_mul","","",24,null],[11,"checked_div","","",24,null],[11,"hash","","",25,null],[11,"fmt","","",25,null],[11,"clone","","",25,null],[11,"decode","","",25,{"inputs":[{"name":"__d"}],"output":{"name":"result"}}],[11,"encode","","",25,null],[11,"eq","","",25,null],[11,"partial_cmp","","",25,null],[11,"cmp","","",25,null],[11,"default","","",25,{"inputs":[],"output":{"name":"biguint"}}],[11,"fmt","","",25,null],[11,"fmt","","",25,null],[11,"fmt","","",25,null],[11,"fmt","","",25,null],[11,"fmt","","",25,null],[11,"from_str","","",25,{"inputs":[{"name":"str"}],"output":{"name":"result"}}],[11,"from_str_radix","","Creates and initializes a `BigUint`.",25,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[11,"bitand","","",25,null],[11,"bitand","","",25,null],[11,"bitor","","",25,null],[11,"bitor","","",25,null],[11,"bitxor","","",25,null],[11,"bitxor","","",25,null],[11,"shl","","",25,null],[11,"shr","","",25,null],[11,"zero","","",25,{"inputs":[],"output":{"name":"biguint"}}],[11,"is_zero","","",25,null],[11,"one","","",25,{"inputs":[],"output":{"name":"biguint"}}],[11,"add","","",25,null],[11,"add","","",25,null],[11,"sub","","",25,null],[11,"sub","","",25,null],[11,"mul","","",25,null],[11,"mul","","",25,null],[11,"div","","",25,null],[11,"div","","",25,null],[11,"rem","","",25,null],[11,"rem","","",25,null],[11,"neg","","",25,null],[11,"checked_add","","",25,null],[11,"checked_sub","","",25,null],[11,"checked_mul","","",25,null],[11,"checked_div","","",25,null],[11,"div_rem","","",25,null],[11,"div_floor","","",25,null],[11,"mod_floor","","",25,null],[11,"div_mod_floor","","",25,null],[11,"gcd","","Calculates the Greatest Common Divisor (GCD) of the number and `other`.",25,null],[11,"lcm","","Calculates the Lowest Common Multiple (LCM) of the number and `other`.",25,null],[11,"divides","","Deprecated, use `is_multiple_of` instead.",25,null],[11,"is_multiple_of","","Returns `true` if the number is a multiple of `other`.",25,null],[11,"is_even","","Returns `true` if the number is divisible by `2`.",25,null],[11,"is_odd","","Returns `true` if the number is not divisible by `2`.",25,null],[11,"to_i64","","",25,null],[11,"to_u64","","",25,null],[11,"to_f32","","",25,null],[11,"to_f64","","",25,null],[11,"from_i64","","",25,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_u64","","",25,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f64","","",25,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[11,"from","","",25,{"inputs":[{"name":"u64"}],"output":{"name":"biguint"}}],[11,"from","","",25,{"inputs":[{"name":"u8"}],"output":{"name":"biguint"}}],[11,"from","","",25,{"inputs":[{"name":"u16"}],"output":{"name":"biguint"}}],[11,"from","","",25,{"inputs":[{"name":"u32"}],"output":{"name":"biguint"}}],[11,"from","","",25,{"inputs":[{"name":"usize"}],"output":{"name":"biguint"}}],[11,"to_biguint","","",24,null],[11,"to_biguint","","",25,null],[11,"new","","Creates and initializes a `BigUint`.",25,{"inputs":[{"name":"vec"}],"output":{"name":"biguint"}}],[11,"from_slice","","Creates and initializes a `BigUint`.",25,null],[11,"from_bytes_be","","Creates and initializes a `BigUint`.",25,null],[11,"from_bytes_le","","Creates and initializes a `BigUint`.",25,null],[11,"to_bytes_le","","Returns the byte representation of the `BigUint` in little-endian byte order.",25,null],[11,"to_bytes_be","","Returns the byte representation of the `BigUint` in big-endian byte order.",25,null],[11,"to_str_radix","","Returns the integer formatted as a string in the given radix.\n`radix` must be in the range `[2, 36]`.",25,null],[11,"parse_bytes","","Creates and initializes a `BigUint`.",25,null],[11,"bits","","Determines the fewest bits necessary to express the `BigUint`.",25,null],[11,"hash","","",18,null],[11,"fmt","","",18,null],[11,"clone","","",18,null],[11,"cmp","","",18,null],[11,"partial_cmp","","",18,null],[11,"eq","","",18,null],[11,"decode","","",18,{"inputs":[{"name":"__d"}],"output":{"name":"result"}}],[11,"encode","","",18,null],[11,"neg","","Negate Sign value.",18,null],[11,"mul","","",18,null],[11,"hash","","",24,null],[11,"fmt","","",24,null],[11,"clone","","",24,null],[11,"decode","","",24,{"inputs":[{"name":"__d"}],"output":{"name":"result"}}],[11,"encode","","",24,null],[11,"eq","","",24,null],[11,"partial_cmp","","",24,null],[11,"cmp","","",24,null],[11,"default","","",24,{"inputs":[],"output":{"name":"bigint"}}],[11,"fmt","","",24,null],[11,"fmt","","",24,null],[11,"fmt","","",24,null],[11,"fmt","","",24,null],[11,"fmt","","",24,null],[11,"from_str","","",24,{"inputs":[{"name":"str"}],"output":{"name":"result"}}],[11,"from_str_radix","","Creates and initializes a BigInt.",24,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[11,"shl","","",24,null],[11,"shr","","",24,null],[11,"zero","","",24,{"inputs":[],"output":{"name":"bigint"}}],[11,"is_zero","","",24,null],[11,"one","","",24,{"inputs":[],"output":{"name":"bigint"}}],[11,"abs","","",24,null],[11,"abs_sub","","",24,null],[11,"signum","","",24,null],[11,"is_positive","","",24,null],[11,"is_negative","","",24,null],[11,"add","","",24,null],[11,"add","","",24,null],[11,"sub","","",24,null],[11,"sub","","",24,null],[11,"mul","","",24,null],[11,"mul","","",24,null],[11,"div","","",24,null],[11,"div","","",24,null],[11,"rem","","",24,null],[11,"rem","","",24,null],[11,"neg","","",24,null],[11,"checked_add","","",24,null],[11,"checked_sub","","",24,null],[11,"checked_mul","","",24,null],[11,"checked_div","","",24,null],[11,"div_rem","","",24,null],[11,"div_floor","","",24,null],[11,"mod_floor","","",24,null],[11,"div_mod_floor","","",24,null],[11,"gcd","","Calculates the Greatest Common Divisor (GCD) of the number and `other`.",24,null],[11,"lcm","","Calculates the Lowest Common Multiple (LCM) of the number and `other`.",24,null],[11,"divides","","Deprecated, use `is_multiple_of` instead.",24,null],[11,"is_multiple_of","","Returns `true` if the number is a multiple of `other`.",24,null],[11,"is_even","","Returns `true` if the number is divisible by `2`.",24,null],[11,"is_odd","","Returns `true` if the number is not divisible by 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Rounds half-way cases away from zero.",26,null],[11,"trunc","","Rounds towards zero.",26,null],[11,"fract","","Returns the fractional part of a number.",26,null],[11,"pow","","Raises the ratio to the power of an exponent",26,null],[11,"from_float","","Converts a float into a rational number.",26,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[11,"cmp","","",26,null],[11,"partial_cmp","","",26,null],[11,"eq","","",26,null],[11,"mul","","",26,null],[11,"mul","","",26,null],[11,"div","","",26,null],[11,"div","","",26,null],[11,"add","","",26,null],[11,"add","","",26,null],[11,"sub","","",26,null],[11,"sub","","",26,null],[11,"rem","","",26,null],[11,"rem","","",26,null],[11,"neg","","",26,null],[11,"zero","","",26,{"inputs":[],"output":{"name":"ratio"}}],[11,"is_zero","","",26,null],[11,"one","","",26,{"inputs":[],"output":{"name":"ratio"}}],[11,"from_str_radix","","Parses `numer/denom` where the numbers are in base `radix`.",26,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[11,"abs","","",26,null],[11,"abs_sub","","",26,null],[11,"signum","","",26,null],[11,"is_positive","","",26,null],[11,"is_negative","","",26,null],[11,"fmt","","Renders as `numer/denom`. If denom=1, renders as numer.",26,null],[11,"from_str","","Parses `numer/denom` or just `numer`.",26,{"inputs":[{"name":"str"}],"output":{"name":"result"}}],[11,"eq","","",27,null],[11,"ne","","",27,null],[11,"fmt","","",27,null],[11,"clone","","",27,null],[11,"fmt","","",27,null],[11,"description","","",27,null],[11,"new","num::complex","Create a new Complex",0,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"complex"}}],[11,"i","","Returns imaginary unit",0,{"inputs":[],"output":{"name":"complex"}}],[11,"norm_sqr","","Returns the square of the norm (since `T` doesn't necessarily\nhave a sqrt function), i.e. `re^2 + im^2`.",0,null],[11,"scale","","Multiplies `self` by the scalar `t`.",0,null],[11,"unscale","","Divides `self` by the scalar `t`.",0,null],[11,"conj","","Returns the complex conjugate. i.e. `re - i im`",0,null],[11,"inv","","Returns `1/self`",0,null],[11,"norm","","Calculate |self|",0,null],[11,"arg","","Calculate the principal Arg of self.",0,null],[11,"to_polar","","Convert to polar form (r, theta), such that `self = r * exp(i\n* theta)`",0,null],[11,"from_polar","","Convert a polar representation into a complex number.",0,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"complex"}}],[11,"exp","","Computes `e^(self)`, where `e` is the base of the natural logarithm.",0,null],[11,"ln","","Computes the principal value of natural logarithm of `self`.",0,null],[11,"sqrt","","Computes the principal value of the square root of `self`.",0,null],[11,"powf","","Raises `self` to a floating point power.",0,null],[11,"log","","Returns the logarithm of `self` with respect to an arbitrary base.",0,null],[11,"powc","","Raises `self` to a complex power.",0,null],[11,"expf","","Raises a floating point number to the complex power `self`.",0,null],[11,"sin","","Computes the sine of `self`.",0,null],[11,"cos","","Computes the cosine of `self`.",0,null],[11,"tan","","Computes the tangent of `self`.",0,null],[11,"asin","","Computes the principal value of the inverse sine of `self`.",0,null],[11,"acos","","Computes the principal value of the inverse cosine of `self`.",0,null],[11,"atan","","Computes the principal value of the inverse tangent of `self`.",0,null],[11,"sinh","","Computes the hyperbolic sine of `self`.",0,null],[11,"cosh","","Computes the hyperbolic cosine of `self`.",0,null],[11,"tanh","","Computes the hyperbolic tangent of `self`.",0,null],[11,"asinh","","Computes the principal value of inverse hyperbolic sine of `self`.",0,null],[11,"acosh","","Computes the principal value of inverse hyperbolic cosine of `self`.",0,null],[11,"atanh","","Computes the principal value of inverse hyperbolic tangent of `self`.",0,null],[11,"is_nan","","Checks if the given complex number is NaN",0,null],[11,"is_infinite","","Checks if the given complex number is infinite",0,null],[11,"is_finite","","Checks if the given complex number is finite",0,null],[11,"is_normal","","Checks if the given complex number is normal",0,null],[11,"default","","",0,{"inputs":[],"output":{"name":"complex"}}],[11,"fmt","","",0,null],[11,"hash","","",0,null],[11,"clone","","",0,null],[11,"eq","","",0,null],[11,"ne","","",0,null],[11,"decode","","",0,{"inputs":[{"name":"__dt"}],"output":{"name":"result"}}],[11,"encode","","",0,null],[11,"from","","",0,{"inputs":[{"name":"t"}],"output":{"name":"complex"}}],[11,"from","","",0,{"inputs":[{"name":"t"}],"output":{"name":"complex"}}],[11,"add","","",0,null],[11,"add","","",0,null],[11,"sub","","",0,null],[11,"sub","","",0,null],[11,"mul","","",0,null],[11,"mul","","",0,null],[11,"div","","",0,null],[11,"div","","",0,null],[11,"neg","","",0,null],[11,"add","","",0,null],[11,"sub","","",0,null],[11,"mul","","",0,null],[11,"div","","",0,null],[11,"add","","",0,null],[11,"sub","","",0,null],[11,"mul","","",0,null],[11,"div","","",0,null],[11,"zero","","",0,{"inputs":[],"output":{"name":"complex"}}],[11,"is_zero","","",0,null],[11,"one","","",0,{"inputs":[],"output":{"name":"complex"}}],[11,"fmt","","",0,null],[11,"fmt","num::traits","",22,null],[11,"fmt","","",23,null],[11,"clone","num::iter","",28,null],[11,"next","","",28,null],[11,"size_hint","","",28,null],[11,"next_back","","",28,null],[11,"clone","","",29,null],[11,"next","","",29,null],[11,"size_hint","","",29,null],[11,"next_back","","",29,null],[11,"clone","","",30,null],[11,"next","","",30,null],[11,"clone","","",31,null],[11,"next","","",31,null]],"paths":[[3,"Complex"],[8,"Integer"],[8,"Num"],[8,"Zero"],[8,"One"],[8,"Signed"],[8,"Bounded"],[8,"Saturating"],[8,"CheckedAdd"],[8,"CheckedSub"],[8,"CheckedMul"],[8,"CheckedDiv"],[8,"PrimInt"],[8,"Float"],[8,"ToPrimitive"],[8,"FromPrimitive"],[8,"NumCast"],[8,"ToBigUint"],[4,"Sign"],[8,"ToBigInt"],[8,"RandBigInt"],[4,"ParseBigIntError"],[4,"FloatErrorKind"],[3,"ParseFloatError"],[3,"BigInt"],[3,"BigUint"],[3,"Ratio"],[3,"ParseRatioError"],[3,"Range"],[3,"RangeInclusive"],[3,"RangeStep"],[3,"RangeStepInclusive"]]};
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