var searchIndex = {};
searchIndex["num"] = {"doc":"A collection of numeric types and traits for Rust.","items":[[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"}}],[0,"bigint","","A Big integer (signed version: `BigInt`, unsigned version: `BigUint`).",null,null],[3,"BigUint","num::bigint","A big unsigned integer type.",null,null],[3,"BigInt","","A big signed integer type.",null,null],[4,"Sign","","A Sign is a `BigInt`'s composing element.",null,null],[13,"Minus","","",0,null],[13,"NoSign","","",0,null],[13,"Plus","","",0,null],[4,"ParseBigIntError","","",null,null],[13,"ParseInt","","",1,null],[13,"Other","","",1,null],[0,"big_digit","","",null,null],[5,"from_doublebigdigit","num::bigint::big_digit","Split one `DoubleBigDigit` into two `BigDigit`s.",null,null],[5,"to_doublebigdigit","","Join two `BigDigit`s into one `DoubleBigDigit`",null,{"inputs":[{"name":"bigdigit"},{"name":"bigdigit"}],"output":{"name":"doublebigdigit"}}],[17,"BITS","","",null,null],[17,"BASE","","",null,null],[6,"BigDigit","num::bigint","A `BigDigit` is a `BigUint`'s composing element.",null,null],[6,"DoubleBigDigit","","A `DoubleBigDigit` is the internal type used to do the computations.  Its\nsize is the double of the size of `BigDigit`.",null,null],[17,"ZERO_BIG_DIGIT","","",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`.",2,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`.",3,null],[8,"RandBigInt","","",null,null],[10,"gen_biguint","","Generate a random `BigUint` of the given bit size.",4,null],[10,"gen_bigint","","Generate a random BigInt of the given bit size.",4,null],[10,"gen_biguint_below","","Generate a random `BigUint` less than the given bound. Fails\nwhen the bound is zero.",4,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.",4,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.",4,null],[11,"hash","","",5,null],[11,"fmt","","",5,null],[11,"clone","","",5,null],[11,"decode","","",5,{"inputs":[{"name":"__d"}],"output":{"name":"result"}}],[11,"encode","","",5,null],[11,"eq","","",5,null],[11,"partial_cmp","","",5,null],[11,"cmp","","",5,null],[11,"default","","",5,{"inputs":[],"output":{"name":"biguint"}}],[11,"fmt","","",5,null],[11,"fmt","","",5,null],[11,"fmt","","",5,null],[11,"fmt","","",5,null],[11,"fmt","","",5,null],[11,"from_str","","",5,{"inputs":[{"name":"str"}],"output":{"name":"result"}}],[11,"from_str_radix","","Creates and initializes a `BigUint`.",5,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[11,"bitand","","",5,null],[11,"bitand","","",5,null],[11,"bitor","","",5,null],[11,"bitor","","",5,null],[11,"bitxor","","",5,null],[11,"bitxor","","",5,null],[11,"shl","","",5,null],[11,"shr","","",5,null],[11,"zero","","",5,{"inputs":[],"output":{"name":"biguint"}}],[11,"is_zero","","",5,null],[11,"one","","",5,{"inputs":[],"output":{"name":"biguint"}}],[11,"add","","",5,null],[11,"add","","",5,null],[11,"sub","","",5,null],[11,"sub","","",5,null],[11,"mul","","",5,null],[11,"mul","","",5,null],[11,"div","","",5,null],[11,"div","","",5,null],[11,"rem","","",5,null],[11,"rem","","",5,null],[11,"neg","","",5,null],[11,"checked_add","","",5,null],[11,"checked_sub","","",5,null],[11,"checked_mul","","",5,null],[11,"checked_div","","",5,null],[11,"div_rem","","",5,null],[11,"div_floor","","",5,null],[11,"mod_floor","","",5,null],[11,"div_mod_floor","","",5,null],[11,"gcd","","Calculates the Greatest Common Divisor (GCD) of the number and `other`.",5,null],[11,"lcm","","Calculates the Lowest Common Multiple (LCM) of the number and `other`.",5,null],[11,"divides","","Deprecated, use `is_multiple_of` instead.",5,null],[11,"is_multiple_of","","Returns `true` if the number is a multiple of `other`.",5,null],[11,"is_even","","Returns `true` if the number is divisible by `2`.",5,null],[11,"is_odd","","Returns `true` if the number is not divisible by `2`.",5,null],[11,"to_i64","","",5,null],[11,"to_u64","","",5,null],[11,"to_f32","","",5,null],[11,"to_f64","","",5,null],[11,"from_i64","","",5,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_u64","","",5,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f64","","",5,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[11,"from","","",5,{"inputs":[{"name":"u64"}],"output":{"name":"self"}}],[11,"from","","",5,{"inputs":[{"name":"u8"}],"output":{"name":"self"}}],[11,"from","","",5,{"inputs":[{"name":"u16"}],"output":{"name":"self"}}],[11,"from","","",5,{"inputs":[{"name":"u32"}],"output":{"name":"self"}}],[11,"from","","",5,{"inputs":[{"name":"usize"}],"output":{"name":"self"}}],[11,"to_biguint","","",6,null],[11,"to_biguint","","",5,null],[11,"new","","Creates and initializes a `BigUint`.",5,{"inputs":[{"name":"vec"}],"output":{"name":"biguint"}}],[11,"from_slice","","Creates and initializes a `BigUint`.",5,null],[11,"from_bytes_be","","Creates and initializes a `BigUint`.",5,null],[11,"from_bytes_le","","Creates and initializes a `BigUint`.",5,null],[11,"to_bytes_le","","Returns the byte representation of the `BigUint` in little-endian byte order.",5,null],[11,"to_bytes_be","","Returns the byte representation of the `BigUint` in big-endian byte order.",5,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]`.",5,null],[11,"parse_bytes","","Creates and initializes a `BigUint`.",5,null],[11,"bits","","Determines the fewest bits necessary to express the `BigUint`.",5,null],[11,"hash","","",0,null],[11,"fmt","","",0,null],[11,"clone","","",0,null],[11,"cmp","","",0,null],[11,"partial_cmp","","",0,null],[11,"eq","","",0,null],[11,"decode","","",0,{"inputs":[{"name":"__d"}],"output":{"name":"result"}}],[11,"encode","","",0,null],[11,"neg","","Negate Sign value.",0,null],[11,"mul","","",0,null],[11,"hash","","",6,null],[11,"fmt","","",6,null],[11,"clone","","",6,null],[11,"decode","","",6,{"inputs":[{"name":"__d"}],"output":{"name":"result"}}],[11,"encode","","",6,null],[11,"eq","","",6,null],[11,"partial_cmp","","",6,null],[11,"cmp","","",6,null],[11,"default","","",6,{"inputs":[],"output":{"name":"bigint"}}],[11,"fmt","","",6,null],[11,"fmt","","",6,null],[11,"fmt","","",6,null],[11,"fmt","","",6,null],[11,"fmt","","",6,null],[11,"from_str","","",6,{"inputs":[{"name":"str"}],"output":{"name":"result"}}],[11,"from_str_radix","","Creates and initializes a BigInt.",6,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[11,"shl","","",6,null],[11,"shr","","",6,null],[11,"zero","","",6,{"inputs":[],"output":{"name":"bigint"}}],[11,"is_zero","","",6,null],[11,"one","","",6,{"inputs":[],"output":{"name":"bigint"}}],[11,"abs","","",6,null],[11,"abs_sub","","",6,null],[11,"signum","","",6,null],[11,"is_positive","","",6,null],[11,"is_negative","","",6,null],[11,"add","","",6,null],[11,"add","","",6,null],[11,"sub","","",6,null],[11,"sub","","",6,null],[11,"mul","","",6,null],[11,"mul","","",6,null],[11,"div","","",6,null],[11,"div","","",6,null],[11,"rem","","",6,null],[11,"rem","","",6,null],[11,"neg","","",6,null],[11,"checked_add","","",6,null],[11,"checked_sub","","",6,null],[11,"checked_mul","","",6,null],[11,"checked_div","","",6,null],[11,"div_rem","","",6,null],[11,"div_floor","","",6,null],[11,"mod_floor","","",6,null],[11,"div_mod_floor","","",6,null],[11,"gcd","","Calculates the Greatest Common Divisor (GCD) of the number and `other`.",6,null],[11,"lcm","","Calculates the Lowest Common Multiple (LCM) of the number and `other`.",6,null],[11,"divides","","Deprecated, use `is_multiple_of` instead.",6,null],[11,"is_multiple_of","","Returns `true` if the number is a multiple of `other`.",6,null],[11,"is_even","","Returns `true` if the number is divisible by `2`.",6,null],[11,"is_odd","","Returns `true` if the number is not divisible by `2`.",6,null],[11,"to_i64","","",6,null],[11,"to_u64","","",6,null],[11,"to_f32","","",6,null],[11,"to_f64","","",6,null],[11,"from_i64","","",6,{"inputs":[{"name":"i64"}],"output":{"name":"option"}}],[11,"from_u64","","",6,{"inputs":[{"name":"u64"}],"output":{"name":"option"}}],[11,"from_f64","","",6,{"inputs":[{"name":"f64"}],"output":{"name":"option"}}],[11,"from","","",6,{"inputs":[{"name":"i64"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"i8"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"i16"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"i32"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"isize"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"u64"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"u8"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"u16"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"u32"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"usize"}],"output":{"name":"self"}}],[11,"from","","",6,{"inputs":[{"name":"biguint"}],"output":{"name":"self"}}],[11,"to_bigint","","",6,null],[11,"to_bigint","","",5,null],[11,"new","","Creates and initializes a BigInt.",6,{"inputs":[{"name":"sign"},{"name":"vec"}],"output":{"name":"bigint"}}],[11,"from_biguint","","Creates and initializes a `BigInt`.",6,{"inputs":[{"name":"sign"},{"name":"biguint"}],"output":{"name":"bigint"}}],[11,"from_slice","","Creates and initializes a `BigInt`.",6,null],[11,"from_bytes_be","","Creates and initializes a `BigInt`.",6,null],[11,"from_bytes_le","","Creates and initializes a `BigInt`.",6,null],[11,"to_bytes_le","","Returns the sign and the byte representation of the `BigInt` in little-endian byte order.",6,null],[11,"to_bytes_be","","Returns the sign and the byte representation of the `BigInt` in big-endian byte order.",6,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]`.",6,null],[11,"sign","","Returns the sign of the `BigInt` as a `Sign`.",6,null],[11,"parse_bytes","","Creates and initializes a `BigInt`.",6,null],[11,"to_biguint","","Converts this `BigInt` into a `BigUint`, if it's not negative.",6,null],[11,"checked_add","","",6,null],[11,"checked_sub","","",6,null],[11,"checked_mul","","",6,null],[11,"checked_div","","",6,null],[11,"eq","","",1,null],[11,"ne","","",1,null],[11,"fmt","","",1,null],[11,"fmt","","",1,null],[11,"description","","",1,null],[11,"from","","",1,{"inputs":[{"name":"parseinterror"}],"output":{"name":"parsebiginterror"}}],[0,"complex","num","Complex numbers.",null,null],[3,"Complex","num::complex","A complex number in Cartesian form.",null,null],[12,"re","","Real portion of the complex number",7,null],[12,"im","","Imaginary portion of the complex number",7,null],[6,"Complex32","","",null,null],[6,"Complex64","","",null,null],[11,"fmt","","",7,null],[11,"hash","","",7,null],[11,"clone","","",7,null],[11,"eq","","",7,null],[11,"ne","","",7,null],[11,"decode","","",7,{"inputs":[{"name":"__dt"}],"output":{"name":"result"}}],[11,"encode","","",7,null],[11,"new","","Create a new Complex",7,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"complex"}}],[11,"i","","Returns imaginary unit",7,{"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`.",7,null],[11,"scale","","Multiplies `self` by the scalar `t`.",7,null],[11,"unscale","","Divides `self` by the scalar `t`.",7,null],[11,"conj","","Returns the complex conjugate. i.e. `re - i im`",7,null],[11,"inv","","Returns `1/self`",7,null],[11,"norm","","Calculate |self|",7,null],[11,"arg","","Calculate the principal Arg of self.",7,null],[11,"to_polar","","Convert to polar form (r, theta), such that `self = r * exp(i\n* theta)`",7,null],[11,"from_polar","","Convert a polar representation into a complex number.",7,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"complex"}}],[11,"exp","","Computes `e^(self)`, where `e` is the base of the natural logarithm.",7,null],[11,"ln","","Computes the principal value of natural logarithm of `self`.",7,null],[11,"sqrt","","Computes the principal value of the square root of `self`.",7,null],[11,"sin","","Computes the sine of `self`.",7,null],[11,"cos","","Computes the cosine of `self`.",7,null],[11,"tan","","Computes the tangent of `self`.",7,null],[11,"asin","","Computes the principal value of the inverse sine of `self`.",7,null],[11,"acos","","Computes the principal value of the inverse cosine of `self`.",7,null],[11,"atan","","Computes the principal value of the inverse tangent of `self`.",7,null],[11,"sinh","","Computes the hyperbolic sine of `self`.",7,null],[11,"cosh","","Computes the hyperbolic cosine of `self`.",7,null],[11,"tanh","","Computes the hyperbolic tangent of `self`.",7,null],[11,"asinh","","Computes the principal value of inverse hyperbolic sine of `self`.",7,null],[11,"acosh","","Computes the principal value of inverse hyperbolic cosine of `self`.",7,null],[11,"atanh","","Computes the principal value of inverse hyperbolic tangent of `self`.",7,null],[11,"is_nan","","Checks if the given complex number is NaN",7,null],[11,"is_infinite","","Checks if the given complex number is infinite",7,null],[11,"is_finite","","Checks if the given complex number is finite",7,null],[11,"is_normal","","Checks if the given complex number is normal",7,null],[11,"from","","",7,{"inputs":[{"name":"t"}],"output":{"name":"complex"}}],[11,"from","","",7,{"inputs":[{"name":"t"}],"output":{"name":"complex"}}],[11,"add","","",7,null],[11,"add","","",7,null],[11,"sub","","",7,null],[11,"sub","","",7,null],[11,"mul","","",7,null],[11,"mul","","",7,null],[11,"div","","",7,null],[11,"div","","",7,null],[11,"neg","","",7,null],[11,"add","","",7,null],[11,"sub","","",7,null],[11,"mul","","",7,null],[11,"div","","",7,null],[11,"add","","",7,null],[11,"sub","","",7,null],[11,"mul","","",7,null],[11,"div","","",7,null],[11,"zero","","",7,{"inputs":[],"output":{"name":"complex"}}],[11,"is_zero","","",7,null],[11,"one","","",7,{"inputs":[],"output":{"name":"complex"}}],[11,"fmt","","",7,null],[0,"integer","num","Integer trait and functions.",null,null],[5,"div_rem","num::integer","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"}}],[8,"Integer","","",null,null],[10,"div_floor","","Floored integer division.",8,null],[10,"mod_floor","","Floored integer modulo, satisfying:",8,null],[10,"gcd","","Greatest Common Divisor (GCD).",8,null],[10,"lcm","","Lowest Common Multiple (LCM).",8,null],[10,"divides","","Deprecated, use `is_multiple_of` instead.",8,null],[10,"is_multiple_of","","Returns `true` if `other` is a multiple of `self`.",8,null],[10,"is_even","","Returns `true` if the number is even.",8,null],[10,"is_odd","","Returns `true` if the number is odd.",8,null],[10,"div_rem","","Simultaneous truncated integer division and modulus.\nReturns `(quotient, remainder)`.",8,null],[11,"div_mod_floor","","Simultaneous floored integer division and modulus.\nReturns `(quotient, remainder)`.",8,null],[0,"iter","num","External iterators for generic mathematics",null,null],[3,"Range","num::iter","An iterator over the range [start, stop)",null,null],[3,"RangeInclusive","","An iterator over the range [start, stop]",null,null],[3,"RangeStep","","An iterator over the range [start, stop) by `step`. It handles overflow by stopping.",null,null],[3,"RangeStepInclusive","","An iterator over the range [start, stop] by `step`. It handles overflow by stopping.",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"}}],[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"}}],[11,"clone","","",9,null],[11,"next","","",9,null],[11,"size_hint","","",9,null],[11,"next_back","","",9,null],[11,"clone","","",10,null],[11,"next","","",10,null],[11,"size_hint","","",10,null],[11,"next_back","","",10,null],[11,"clone","","",11,null],[11,"next","","",11,null],[11,"clone","","",12,null],[11,"next","","",12,null],[0,"traits","num","Numeric traits for generic mathematics",null,null],[3,"ParseFloatError","num::traits","",null,null],[12,"kind","","",13,null],[4,"FloatErrorKind","","",null,null],[13,"Empty","","",14,null],[13,"Invalid","","",14,null],[5,"cast","","Cast from one machine scalar to another.",null,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[8,"Num","","The base trait for numeric types",null,null],[16,"FromStrRadixErr","","Parse error for `from_str_radix`",15,null],[10,"from_str_radix","","Convert from a string and radix <= 36.",15,{"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`.",16,{"inputs":[],"output":{"name":"self"}}],[10,"is_zero","","Returns `true` if `self` is equal to the additive identity.",16,null],[8,"One","","Defines a multiplicative identity element for `Self`.",null,null],[10,"one","","Returns the multiplicative identity element of `Self`, `1`.",17,{"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.",18,null],[10,"abs_sub","","The positive difference of two numbers.",18,null],[10,"signum","","Returns the sign of the number.",18,null],[10,"is_positive","","Returns true if the number is positive and false if the number is zero or negative.",18,null],[10,"is_negative","","Returns true if the number is negative and false if the number is zero or positive.",18,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",19,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","returns the largest finite number this type can represent",19,{"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.",20,null],[10,"saturating_sub","","Saturating subtraction operator.\nReturns a-b, saturating at the numeric bounds instead of overflowing.",20,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.",21,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.",22,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.",23,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.",24,null],[8,"PrimInt","","",null,null],[10,"count_ones","","Returns the number of ones in the binary representation of `self`.",25,null],[10,"count_zeros","","Returns the number of zeros in the binary representation of `self`.",25,null],[10,"leading_zeros","","Returns the number of leading zeros in the binary representation\nof `self`.",25,null],[10,"trailing_zeros","","Returns the number of trailing zeros in the binary representation\nof `self`.",25,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.",25,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.",25,null],[10,"signed_shl","","Shifts the bits to the left by a specified amount amount, `n`, filling\nzeros in the least significant bits.",25,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.",25,null],[10,"unsigned_shl","","Shifts the bits to the left by a specified amount amount, `n`, filling\nzeros in the least significant bits.",25,null],[10,"unsigned_shr","","Shifts the bits to the right by a specified amount amount, `n`, filling\nzeros in the most significant bits.",25,null],[10,"swap_bytes","","Reverses the byte order of the integer.",25,null],[10,"from_be","","Convert an integer from big endian to the target's endianness.",25,{"inputs":[{"name":"self"}],"output":{"name":"self"}}],[10,"from_le","","Convert an integer from little endian to the target's endianness.",25,{"inputs":[{"name":"self"}],"output":{"name":"self"}}],[10,"to_be","","Convert `self` to big endian from the target's endianness.",25,null],[10,"to_le","","Convert `self` to little endian from the target's endianness.",25,null],[10,"pow","","Raises self to the power of `exp`, using exponentiation by squaring.",25,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`.",26,null],[11,"to_i8","","Converts the value of `self` to an `i8`.",26,null],[11,"to_i16","","Converts the value of `self` to an `i16`.",26,null],[11,"to_i32","","Converts the value of `self` to an `i32`.",26,null],[10,"to_i64","","Converts the value of `self` to an `i64`.",26,null],[11,"to_usize","","Converts the value of `self` to a `usize`.",26,null],[11,"to_u8","","Converts the value of `self` to an `u8`.",26,null],[11,"to_u16","","Converts the value of `self` to an `u16`.",26,null],[11,"to_u32","","Converts the value of `self` to an `u32`.",26,null],[10,"to_u64","","Converts the value of `self` to an `u64`.",26,null],[11,"to_f32","","Converts the value of `self` to an `f32`.",26,null],[11,"to_f64","","Converts the value of `self` to an `f64`.",26,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.",27,{"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.",27,{"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.",27,{"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.",27,{"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.",27,{"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.",27,{"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.",27,{"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.",27,{"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.",27,{"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.",27,{"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.",27,{"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.",27,{"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.",28,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[8,"Float","","",null,null],[10,"nan","","Returns the `NaN` value.",29,{"inputs":[],"output":{"name":"self"}}],[10,"infinity","","Returns the infinite value.",29,{"inputs":[],"output":{"name":"self"}}],[10,"neg_infinity","","Returns the negative infinite value.",29,{"inputs":[],"output":{"name":"self"}}],[10,"neg_zero","","Returns `-0.0`.",29,{"inputs":[],"output":{"name":"self"}}],[10,"min_value","","Returns the smallest finite value that this type can represent.",29,{"inputs":[],"output":{"name":"self"}}],[10,"min_positive_value","","Returns the smallest positive, normalized value that this type can represent.",29,{"inputs":[],"output":{"name":"self"}}],[10,"max_value","","Returns the largest finite value that this type can represent.",29,{"inputs":[],"output":{"name":"self"}}],[10,"is_nan","","Returns `true` if this value is `NaN` and false otherwise.",29,null],[10,"is_infinite","","Returns `true` if this value is positive infinity or negative infinity and\nfalse otherwise.",29,null],[10,"is_finite","","Returns `true` if this number is neither infinite nor `NaN`.",29,null],[10,"is_normal","","Returns `true` if the number is neither zero, infinite,\n[subnormal][subnormal], or `NaN`.",29,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.",29,null],[10,"floor","","Returns the largest integer less than or equal to a number.",29,null],[10,"ceil","","Returns the smallest integer greater than or equal to a number.",29,null],[10,"round","","Returns the nearest integer to a number. Round half-way cases away from\n`0.0`.",29,null],[10,"trunc","","Return the integer part of a number.",29,null],[10,"fract","","Returns the fractional part of a number.",29,null],[10,"abs","","Computes the absolute value of `self`. Returns `Float::nan()` if the\nnumber is `Float::nan()`.",29,null],[10,"signum","","Returns a number that represents the sign of `self`.",29,null],[10,"is_sign_positive","","Returns `true` if `self` is positive, including `+0.0` and\n`Float::infinity()`.",29,null],[10,"is_sign_negative","","Returns `true` if `self` is negative, including `-0.0` and\n`Float::neg_infinity()`.",29,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.",29,null],[10,"recip","","Take the reciprocal (inverse) of a number, `1/x`.",29,null],[10,"powi","","Raise a number to an integer power.",29,null],[10,"powf","","Raise a number to a floating point power.",29,null],[10,"sqrt","","Take the square root of a number.",29,null],[10,"exp","","Returns `e^(self)`, (the exponential function).",29,null],[10,"exp2","","Returns `2^(self)`.",29,null],[10,"ln","","Returns the natural logarithm of the number.",29,null],[10,"log","","Returns the logarithm of the number with respect to an arbitrary base.",29,null],[10,"log2","","Returns the base 2 logarithm of the number.",29,null],[10,"log10","","Returns the base 10 logarithm of the number.",29,null],[10,"max","","Returns the maximum of the two numbers.",29,null],[10,"min","","Returns the minimum of the two numbers.",29,null],[10,"abs_sub","","The positive difference of two numbers.",29,null],[10,"cbrt","","Take the cubic root of a number.",29,null],[10,"hypot","","Calculate the length of the hypotenuse of a right-angle triangle given\nlegs of length `x` and `y`.",29,null],[10,"sin","","Computes the sine of a number (in radians).",29,null],[10,"cos","","Computes the cosine of a number (in radians).",29,null],[10,"tan","","Computes the tangent of a number (in radians).",29,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].",29,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].",29,null],[10,"atan","","Computes the arctangent of a number. Return value is in radians in the\nrange [-pi/2, pi/2];",29,null],[10,"atan2","","Computes the four quadrant arctangent of `self` (`y`) and `other` (`x`).",29,null],[10,"sin_cos","","Simultaneously computes the sine and cosine of the number, `x`. Returns\n`(sin(x), cos(x))`.",29,null],[10,"exp_m1","","Returns `e^(self) - 1` in a way that is accurate even if the\nnumber is close to zero.",29,null],[10,"ln_1p","","Returns `ln(1+n)` (natural logarithm) more accurately than if\nthe operations were performed separately.",29,null],[10,"sinh","","Hyperbolic sine function.",29,null],[10,"cosh","","Hyperbolic cosine function.",29,null],[10,"tanh","","Hyperbolic tangent function.",29,null],[10,"asinh","","Inverse hyperbolic sine function.",29,null],[10,"acosh","","Inverse hyperbolic cosine function.",29,null],[10,"atanh","","Inverse hyperbolic tangent function.",29,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].",29,null],[11,"fmt","","",13,null],[11,"fmt","","",14,null],[0,"rational","num","Rational numbers",null,null],[3,"Ratio","num::rational","Represents the ratio between 2 numbers.",null,null],[3,"ParseRatioError","","",null,null],[6,"Rational","","Alias for a `Ratio` of machine-sized integers.",null,null],[6,"Rational32","","",null,null],[6,"Rational64","","",null,null],[6,"BigRational","","Alias for arbitrary precision rationals.",null,null],[11,"fmt","","",30,null],[11,"hash","","",30,null],[11,"clone","","",30,null],[11,"decode","","",30,{"inputs":[{"name":"__dt"}],"output":{"name":"result"}}],[11,"encode","","",30,null],[11,"from_integer","","Creates a ratio representing the integer `t`.",30,{"inputs":[{"name":"t"}],"output":{"name":"ratio"}}],[11,"new_raw","","Creates a ratio without checking for `denom == 0` or reducing.",30,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"ratio"}}],[11,"new","","Create a new Ratio. Fails if `denom == 0`.",30,{"inputs":[{"name":"t"},{"name":"t"}],"output":{"name":"ratio"}}],[11,"to_integer","","Converts to an integer.",30,null],[11,"numer","","Gets an immutable reference to the numerator.",30,null],[11,"denom","","Gets an immutable reference to the denominator.",30,null],[11,"is_integer","","Returns true if the rational number is an integer (denominator is 1).",30,null],[11,"reduced","","Returns a `reduce`d copy of self.",30,null],[11,"recip","","Returns the reciprocal.",30,null],[11,"floor","","Rounds towards minus infinity.",30,null],[11,"ceil","","Rounds towards plus infinity.",30,null],[11,"round","","Rounds to the nearest integer. Rounds half-way cases away from zero.",30,null],[11,"trunc","","Rounds towards zero.",30,null],[11,"fract","","Returns the fractional part of a number.",30,null],[11,"pow","","Raises the ratio to the power of an exponent",30,null],[11,"from_float","","Converts a float into a rational number.",30,{"inputs":[{"name":"t"}],"output":{"name":"option"}}],[11,"eq","","",30,null],[11,"ne","","",30,null],[11,"lt","","",30,null],[11,"gt","","",30,null],[11,"le","","",30,null],[11,"ge","","",30,null],[11,"partial_cmp","","",30,null],[11,"cmp","","",30,null],[11,"mul","","",30,null],[11,"mul","","",30,null],[11,"div","","",30,null],[11,"div","","",30,null],[11,"add","","",30,null],[11,"add","","",30,null],[11,"sub","","",30,null],[11,"sub","","",30,null],[11,"rem","","",30,null],[11,"rem","","",30,null],[11,"neg","","",30,null],[11,"zero","","",30,{"inputs":[],"output":{"name":"ratio"}}],[11,"is_zero","","",30,null],[11,"one","","",30,{"inputs":[],"output":{"name":"ratio"}}],[11,"from_str_radix","","Parses `numer/denom` where the numbers are in base `radix`.",30,{"inputs":[{"name":"str"},{"name":"u32"}],"output":{"name":"result"}}],[11,"abs","","",30,null],[11,"abs_sub","","",30,null],[11,"signum","","",30,null],[11,"is_positive","","",30,null],[11,"is_negative","","",30,null],[11,"fmt","","Renders as `numer/denom`. If denom=1, renders as numer.",30,null],[11,"from_str","","Parses `numer/denom` or just `numer`.",30,{"inputs":[{"name":"str"}],"output":{"name":"result"}}],[11,"eq","","",31,null],[11,"ne","","",31,null],[11,"fmt","","",31,null],[11,"clone","","",31,null],[11,"fmt","","",31,null],[11,"description","","",31,null]],"paths":[[4,"Sign"],[4,"ParseBigIntError"],[8,"ToBigUint"],[8,"ToBigInt"],[8,"RandBigInt"],[3,"BigUint"],[3,"BigInt"],[3,"Complex"],[8,"Integer"],[3,"Range"],[3,"RangeInclusive"],[3,"RangeStep"],[3,"RangeStepInclusive"],[3,"ParseFloatError"],[4,"FloatErrorKind"],[8,"Num"],[8,"Zero"],[8,"One"],[8,"Signed"],[8,"Bounded"],[8,"Saturating"],[8,"CheckedAdd"],[8,"CheckedSub"],[8,"CheckedMul"],[8,"CheckedDiv"],[8,"PrimInt"],[8,"ToPrimitive"],[8,"FromPrimitive"],[8,"NumCast"],[8,"Float"],[3,"Ratio"],[3,"ParseRatioError"]]};
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