var searchIndex = {}; searchIndex["qrencode"] = {"doc":"","items":[[5,"main","qrencode","",null,{"inputs":[],"output":null}]],"paths":[]}; searchIndex["qrcode"] = {"doc":"QRCode encoder","items":[[3,"QrCode","qrcode","The encoded QR code symbol.",null,null],[0,"types","","",null,null],[4,"QrError","qrcode::types","`QrError` encodes the error encountered when generating a QR code.",null,null],[13,"DataTooLong","","The data is too long to encode into a QR code for the given version.",0,null],[13,"InvalidVersion","","The provided version / error correction level combination is invalid.",0,null],[13,"UnsupportedCharacterSet","","Some characters in the data cannot be supported by the provided QR code\nversion.",0,null],[13,"InvalidEciDesignator","","The provided ECI designator is invalid. A valid designator should be\nbetween 0 and 999999.",0,null],[13,"InvalidCharacter","","A character not belonging to the character set is found.",0,null],[4,"EcLevel","","The error correction level. It allows the original information be recovered\neven if parts of the code is damaged.",null,null],[13,"L","","Low error correction. Allows up to 7% of wrong blocks.",1,null],[13,"M","","Medium error correction (default). Allows up to 15% of wrong blocks.",1,null],[13,"Q","",""Quartile" error correction. Allows up to 25% of wrong blocks.",1,null],[13,"H","","High error correction. Allows up to 30% of wrong blocks.",1,null],[4,"Version","","In QR code terminology, `Version` means the size of the generated image.\nLarger version means the size of code is larger, and therefore can carry\nmore information.",null,null],[13,"Normal","","A normal QR code version. The parameter should be between 1 and 40.",2,null],[13,"Micro","","A Micro QR code version. The parameter should be between 1 and 4.",2,null],[4,"Mode","","The mode indicator, which specifies the character set of the encoded data.",null,null],[13,"Numeric","","The data contains only characters 0 to 9.",3,null],[13,"Alphanumeric","","The data contains only uppercase letters (A–Z), numbers (0–9) and a few\npunctuations marks (space, `$`, `%`, `*`, `+`, `-`, `.`, `/`, `:`).",3,null],[13,"Byte","","The data contains arbitrary binary data.",3,null],[13,"Kanji","","The data contains Shift-JIS-encoded double-byte text.",3,null],[6,"QrResult","","`QrResult` is a convenient alias for a QR code generation result.",null,null],[11,"clone","","",0,null],[11,"eq","","",0,null],[11,"fmt","","",0,null],[11,"fmt","","",0,null],[11,"cmp","","",1,null],[11,"partial_cmp","","",1,null],[11,"clone","","",1,null],[11,"eq","","",1,null],[11,"fmt","","",1,null],[11,"clone","","",2,null],[11,"eq","","",2,null],[11,"ne","","",2,null],[11,"fmt","","",2,null],[11,"width","","Get the number of "modules" on each size of the QR code, i.e. the width\nand height of the code.",2,null],[11,"fetch","","Obtains an object from a hard-coded table.",2,null],[11,"mode_bits_count","","The number of bits needed to encode the mode indicator.",2,null],[11,"is_micro","","Checks whether is version refers to a Micro QR code.",2,null],[11,"clone","","",3,null],[11,"eq","","",3,null],[11,"fmt","","",3,null],[11,"length_bits_count","","Computes the number of bits needed to encode the data length.",3,null],[11,"data_bits_count","","Computes the number of bits needed to some data of a given raw length.",3,null],[11,"max","","Find the lowest common mode which both modes are compatible with.",3,null],[11,"partial_cmp","","Defines a partial ordering between modes. If `a <= b`, then `b` contains\na superset of all characters supported by `a`.",3,null],[0,"bits","qrcode","The `bits` module encodes binary data into raw bits used in a QR code.",null,null],[3,"Bits","qrcode::bits","The `Bits` structure stores the encoded data for a QR code.",null,null],[4,"ExtendedMode","","An "extended" mode indicator, includes all indicators supported by QR code\nbeyond those bearing data.",null,null],[13,"Eci","","ECI mode indicator, to introduce an ECI designator.",4,null],[13,"Data","","The normal mode to introduce data.",4,null],[13,"Fnc1First","","FNC-1 mode in the first position.",4,null],[13,"Fnc1Second","","FNC-1 mode in the second position.",4,null],[13,"StructuredAppend","","Structured append.",4,null],[5,"encode_auto","","Automatically determines the minimum version to store the data, and encode\nthe result.",null,null],[11,"new","","Constructs a new, empty bits structure.",5,{"inputs":[{"name":"version"}],"output":{"name":"bits"}}],[11,"into_bytes","","Convert the bits into a bytes vector.",5,null],[11,"len","","Total number of bits currently pushed.",5,null],[11,"max_len","","The maximum number of bits allowed by the provided QR code version and\nerror correction level.",5,null],[11,"version","","Version of the QR code.",5,null],[11,"clone","","",4,null],[11,"push_mode_indicator","","Push the mode indicator to the end of the bits.",5,null],[11,"push_eci_designator","","Push an ECI (Extended Channel Interpretation) designator to the bits.",5,null],[11,"push_numeric_data","","Encodes a numeric string to the bits.",5,null],[11,"push_alphanumeric_data","","Encodes an alphanumeric string to the bits.",5,null],[11,"push_byte_data","","Encodes 8-bit byte data to the bits.",5,null],[11,"push_kanji_data","","Encodes Shift JIS double-byte data to the bits.",5,null],[11,"push_fnc1_first_position","","Encodes an indicator that the following data are formatted according to\nthe UCC/EAN Application Identifiers standard.",5,null],[11,"push_fnc1_second_position","","Encodes an indicator that the following data are formatted in accordance\nwith specific industry or application specifications previously agreed\nwith AIM International.",5,null],[11,"push_terminator","","Pushes the ending bits to indicate no more data.",5,null],[11,"push_segments","","Push a segmented data to the bits, and then terminate it.",5,null],[11,"push_optimal_data","","Pushes the data the bits, using the optimal encoding.",5,null],[0,"optimize","qrcode","Find the optimal data mode sequence to encode a piece of data.",null,null],[3,"Segment","qrcode::optimize","A segment of data committed to an encoding mode.",null,null],[12,"mode","","The encoding mode of the segment of data.",6,null],[12,"begin","","The start index of the segment.",6,null],[12,"end","","The end index (exclusive) of the segment.",6,null],[3,"Parser","","QR code data parser to classify the input into distinct segments.",null,null],[3,"Optimizer","","",null,null],[5,"total_encoded_len","","Computes the total encoded length of all segments.",null,null],[11,"clone","","",6,null],[11,"fmt","","",6,null],[11,"eq","","",6,null],[11,"ne","","",6,null],[11,"encoded_len","","Compute the number of bits (including the size of the mode indicator and\nlength bits) when this segment is encoded.",6,null],[11,"new","","Creates a new iterator which parse the data into segments that only\ncontains their exclusive subsets. No optimization is done at this point.",7,null],[11,"next","","",7,null],[11,"new","","Optimize the segments by combining adjacent segments when possible.",8,{"inputs":[{"name":"i"},{"name":"version"}],"output":{"name":"optimizer"}}],[11,"optimize","","",7,null],[11,"next","","",8,null],[0,"ec","qrcode","The `ec` module applies the Reed-Solomon error correction codes.",null,null],[5,"create_error_correction_code","qrcode::ec","Creates the error correction code in N bytes.",null,null],[5,"construct_codewords","","Constructs data and error correction codewords ready to be put in the QR\ncode matrix.",null,null],[5,"max_allowed_errors","","Computes the maximum allowed number of erratic modules can be introduced to\nthe QR code, before the data becomes truly corrupted.",null,{"inputs":[{"name":"version"},{"name":"eclevel"}],"output":{"name":"qrresult"}}],[0,"canvas","qrcode","The `canvas` module puts raw bits into the QR code canvas.",null,null],[3,"Canvas","qrcode::canvas","`Canvas` is an intermediate helper structure to render error-corrected data\ninto a QR code.",null,null],[4,"Module","","The color of a module (pixel) in the QR code.",null,null],[13,"Empty","","The module is empty.",9,null],[13,"Light","","The module is light (white), and cannot be masked. This mainly refers to\nmodules of functional patterns.",9,null],[13,"Dark","","The module is dark (black), and cannot be masked. This mainly refers to\nmodules of functional patterns.",9,null],[13,"LightUnmasked","","The module is light (white), but not yet masked. This mainly refers to\nmodules of data and error correction bits before masking.",9,null],[13,"DarkUnmasked","","The module is dark (black), but not yet masked. This mainly refers to\nmodules of data and error correction bits before masking.",9,null],[4,"MaskPattern","","The mask patterns. Since QR code and Micro QR code do not use the same\npattern number, we name them according to their shape instead of the number.",null,null],[13,"Checkerboard","","QR code pattern 000: `(x + y) % 2 == 0`.",10,null],[13,"HorizontalLines","","QR code pattern 001: `y % 2 == 0`.",10,null],[13,"VerticalLines","","QR code pattern 010: `x % 3 == 0`.",10,null],[13,"DiagonalLines","","QR code pattern 011: `(x + y) % 3 == 0`.",10,null],[13,"LargeCheckerboard","","QR code pattern 100: `((x/3) + (y/2)) % 2 == 0`.",10,null],[13,"Fields","","QR code pattern 101: `(x*y)%2 + (x*y)%3 == 0`.",10,null],[13,"Diamonds","","QR code pattern 110: `((x*y)%2 + (x*y)%3) % 2 == 0`.",10,null],[13,"Meadow","","QR code pattern 111: `((x+y)%2 + (x*y)%3) % 2 == 0`.",10,null],[5,"is_functional","","Gets whether the module at the given coordinates represents a functional\nmodule.",null,{"inputs":[{"name":"version"},{"name":"i16"},{"name":"i16"},{"name":"i16"}],"output":{"name":"bool"}}],[11,"fmt","","",9,null],[11,"clone","","",9,null],[11,"eq","","",9,null],[11,"is_dark","","Checks whether a module is dark.",9,null],[11,"mask","","Apply a mask to the unmasked modules.",9,null],[11,"clone","","",11,null],[11,"new","","Constructs a new canvas big enough for a QR code of the given version.",11,{"inputs":[{"name":"version"},{"name":"eclevel"}],"output":{"name":"canvas"}}],[11,"get","","Obtains a module at the given coordinates. For convenience, negative\ncoordinates will wrap around.",11,null],[11,"get_mut","","Obtains a mutable module at the given coordinates. For convenience,\nnegative coordinates will wrap around.",11,null],[11,"put","","Sets the color of a module at the given coordinates. For convenience,\nnegative coordinates will wrap around.",11,null],[11,"draw_all_functional_patterns","","Draw all functional patterns, before data placement.",11,null],[11,"draw_data","","Draws the encoded data and error correction codes to the empty modules.",11,null],[11,"clone","","",10,null],[11,"fmt","","",10,null],[11,"apply_mask","","Applies a mask to the canvas. This method will also draw the format info\npatterns.",11,null],[11,"apply_best_mask","","Construct a new canvas and apply the best masking that gives the lowest\npenalty score.",11,null],[11,"to_bools","","Convert the modules into a vector of booleans.",11,null],[11,"clone","qrcode","",12,null],[11,"new","","Constructs a new QR code which automatically encodes the given data.",12,{"inputs":[{"name":"d"}],"output":{"name":"qrresult"}}],[11,"with_error_correction_level","","Constructs a new QR code which automatically encodes the given data at a\nspecific error correction level.",12,{"inputs":[{"name":"d"},{"name":"eclevel"}],"output":{"name":"qrresult"}}],[11,"with_version","","Constructs a new QR code for the given version and error correction\nlevel.",12,{"inputs":[{"name":"d"},{"name":"version"},{"name":"eclevel"}],"output":{"name":"qrresult"}}],[11,"with_bits","","Constructs a new QR code with encoded bits.",12,{"inputs":[{"name":"bits"},{"name":"eclevel"}],"output":{"name":"qrresult"}}],[11,"version","","Gets the version of this QR code.",12,null],[11,"error_correction_level","","Gets the error correction level of this QR code.",12,null],[11,"width","","Gets the number of modules per side, i.e. the width of this QR code.",12,null],[11,"max_allowed_errors","","Gets the maximum number of allowed erratic modules can be introduced\nbefore the data becomes corrupted. Note that errors should not be\nintroduced to functional modules.",12,null],[11,"is_functional","","Checks whether a module at coordinate (x, y) is a functional module or\nnot.",12,null],[11,"to_debug_str","","Converts the QR code into a human-readable string. This is mainly for\ndebugging only.",12,null],[11,"to_vec","","Converts the QR code to a vector of booleans. Each entry represents the\ncolor of the module, with "true" means dark and "false" means light.",12,null],[11,"into_vec","","Converts the QR code to a vector of booleans. Each entry represents the\ncolor of the module, with "true" means dark and "false" means light.",12,null],[11,"index","","",12,null]],"paths":[[4,"QrError"],[4,"EcLevel"],[4,"Version"],[4,"Mode"],[4,"ExtendedMode"],[3,"Bits"],[3,"Segment"],[3,"Parser"],[3,"Optimizer"],[4,"Module"],[4,"MaskPattern"],[3,"Canvas"],[3,"QrCode"]]}; 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"]]}; searchIndex["rustc_serialize"] = {"doc":"Support code for encoding and decoding 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searchIndex["rand"] = {"doc":"Utilities for random number generation","items":[[3,"Generator","rand","Iterator which will generate a stream of random items.",null,null],[3,"AsciiGenerator","","Iterator which will continuously generate random ascii characters.",null,null],[3,"XorShiftRng","","An Xorshift[1] random number\ngenerator.",null,null],[3,"Open01","","A wrapper for generating floating point numbers uniformly in the\nopen interval `(0,1)` (not including either endpoint).",null,null],[12,"0","","",0,null],[3,"Closed01","","A wrapper for generating floating point numbers uniformly in the\nclosed interval `[0,1]` (including both endpoints).",null,null],[12,"0","","",1,null],[3,"StdRng","","The standard RNG. This is designed to be efficient on the current\nplatform.",null,null],[3,"ThreadRng","","The thread-local RNG.",null,null],[5,"weak_rng","","Create a weak random number generator with a default algorithm and seed.",null,{"inputs":[],"output":{"name":"xorshiftrng"}}],[5,"thread_rng","","Retrieve the lazily-initialized thread-local random number\ngenerator, seeded by the system. Intended to be used in method\nchaining style, e.g. `thread_rng().gen::<i32>()`.",null,{"inputs":[],"output":{"name":"threadrng"}}],[5,"random","","Generates a random value using the thread-local random number generator.",null,{"inputs":[],"output":{"name":"t"}}],[5,"sample","","Randomly sample up to `amount` elements from an iterator.",null,{"inputs":[{"name":"r"},{"name":"i"},{"name":"usize"}],"output":{"name":"vec"}}],[0,"distributions","","Sampling from random distributions.",null,null],[3,"RandSample","rand::distributions","A wrapper for generating types that implement `Rand` via the\n`Sample` & `IndependentSample` traits.",null,null],[3,"Weighted","","A value with a particular weight for use with `WeightedChoice`.",null,null],[12,"weight","","The numerical weight of this item",2,null],[12,"item","","The actual item which is being weighted",2,null],[3,"WeightedChoice","","A distribution that selects from a finite collection of weighted items.",null,null],[0,"range","","Generating numbers between two others.",null,null],[3,"Range","rand::distributions::range","Sample values uniformly between two bounds.",null,null],[8,"SampleRange","","The helper trait for types that have a sensible way to sample\nuniformly between two values. This should not be used directly,\nand is only to facilitate `Range`.",null,null],[10,"construct_range","","Construct the `Range` object that `sample_range`\nrequires. This should not ever be called directly, only via\n`Range::new`, which will check that `low < high`, so this\nfunction doesn't have to repeat the check.",3,{"inputs":[{"name":"self"},{"name":"self"}],"output":{"name":"range"}}],[10,"sample_range","","Sample a value from the given `Range` with the given `Rng` as\na source of randomness.",3,{"inputs":[{"name":"range"},{"name":"r"}],"output":{"name":"self"}}],[11,"clone","","",4,null],[11,"new","","Create a new `Range` instance that samples uniformly from\n`[low, high)`. Panics if `low >= high`.",4,{"inputs":[{"name":"x"},{"name":"x"}],"output":{"name":"range"}}],[11,"sample","","",4,null],[11,"ind_sample","","",4,null],[0,"gamma","rand::distributions","The Gamma and derived distributions.",null,null],[3,"Gamma","rand::distributions::gamma","The Gamma distribution `Gamma(shape, scale)` distribution.",null,null],[3,"ChiSquared","","The chi-squared distribution `χ²(k)`, where `k` is the degrees of\nfreedom.",null,null],[3,"FisherF","","The Fisher F distribution `F(m, n)`.",null,null],[3,"StudentT","","The Student t distribution, `t(nu)`, where `nu` is the degrees of\nfreedom.",null,null],[11,"clone","","",5,null],[11,"new","","Construct an object representing the `Gamma(shape, scale)`\ndistribution.",5,{"inputs":[{"name":"f64"},{"name":"f64"}],"output":{"name":"gamma"}}],[11,"sample","","",5,null],[11,"ind_sample","","",5,null],[11,"clone","","",6,null],[11,"new","","Create a new chi-squared distribution with degrees-of-freedom\n`k`. Panics if `k < 0`.",6,{"inputs":[{"name":"f64"}],"output":{"name":"chisquared"}}],[11,"sample","","",6,null],[11,"ind_sample","","",6,null],[11,"clone","","",7,null],[11,"new","","Create a new `FisherF` distribution, with the given\nparameter. Panics if either `m` or `n` are not positive.",7,{"inputs":[{"name":"f64"},{"name":"f64"}],"output":{"name":"fisherf"}}],[11,"sample","","",7,null],[11,"ind_sample","","",7,null],[11,"clone","","",8,null],[11,"new","","Create a new Student t distribution with `n` degrees of\nfreedom. Panics if `n <= 0`.",8,{"inputs":[{"name":"f64"}],"output":{"name":"studentt"}}],[11,"sample","","",8,null],[11,"ind_sample","","",8,null],[0,"normal","rand::distributions","The normal and derived distributions.",null,null],[3,"StandardNormal","rand::distributions::normal","A wrapper around an `f64` to generate N(0, 1) random numbers\n(a.k.a. a standard normal, or Gaussian).",null,null],[12,"0","","",9,null],[3,"Normal","","The normal distribution `N(mean, std_dev**2)`.",null,null],[3,"LogNormal","","The log-normal distribution `ln N(mean, std_dev**2)`.",null,null],[11,"clone","","",9,null],[11,"rand","","",9,{"inputs":[{"name":"r"}],"output":{"name":"standardnormal"}}],[11,"clone","","",10,null],[11,"new","","Construct a new `Normal` distribution with the given mean and\nstandard deviation.",10,{"inputs":[{"name":"f64"},{"name":"f64"}],"output":{"name":"normal"}}],[11,"sample","","",10,null],[11,"ind_sample","","",10,null],[11,"clone","","",11,null],[11,"new","","Construct a new `LogNormal` distribution with the given mean\nand standard deviation.",11,{"inputs":[{"name":"f64"},{"name":"f64"}],"output":{"name":"lognormal"}}],[11,"sample","","",11,null],[11,"ind_sample","","",11,null],[0,"exponential","rand::distributions","The exponential distribution.",null,null],[3,"Exp1","rand::distributions::exponential","A wrapper around an `f64` to generate Exp(1) random numbers.",null,null],[12,"0","","",12,null],[3,"Exp","","The exponential distribution `Exp(lambda)`.",null,null],[11,"clone","","",12,null],[11,"rand","","",12,{"inputs":[{"name":"r"}],"output":{"name":"exp1"}}],[11,"clone","","",13,null],[11,"new","","Construct a new `Exp` with the given shape parameter\n`lambda`. Panics if `lambda <= 0`.",13,{"inputs":[{"name":"f64"}],"output":{"name":"exp"}}],[11,"sample","","",13,null],[11,"ind_sample","","",13,null],[8,"Sample","rand::distributions","Types that can be used to create a random instance of `Support`.",null,null],[10,"sample","","Generate a random value of `Support`, using `rng` as the\nsource of randomness.",14,null],[8,"IndependentSample","","`Sample`s that do not require keeping track of state.",null,null],[10,"ind_sample","","Generate a random value.",15,null],[11,"clone","","",16,null],[11,"sample","","",16,null],[11,"ind_sample","","",16,null],[11,"new","","",16,{"inputs":[],"output":{"name":"randsample"}}],[11,"clone","","",2,null],[11,"new","","Create a new `WeightedChoice`.",17,null],[11,"sample","","",17,null],[11,"ind_sample","","",17,null],[0,"isaac","rand","The ISAAC random number generator.",null,null],[3,"IsaacRng","rand::isaac","A random number generator that uses the ISAAC algorithm[1].",null,null],[3,"Isaac64Rng","","A random number generator that uses ISAAC-64[1], the 64-bit\nvariant of the ISAAC algorithm.",null,null],[11,"new_unseeded","","Create an ISAAC random number generator using the default\nfixed seed.",18,{"inputs":[],"output":{"name":"isaacrng"}}],[11,"clone","","",18,null],[11,"next_u32","","",18,null],[11,"reseed","","",18,null],[11,"from_seed","","Create an ISAAC random number generator with a seed. This can\nbe any length, although the maximum number of elements used is\n256 and any more will be silently ignored. A generator\nconstructed with a given seed will generate the same sequence\nof values as all other generators constructed with that seed.",18,null],[11,"rand","","",18,{"inputs":[{"name":"r"}],"output":{"name":"isaacrng"}}],[11,"new_unseeded","","Create a 64-bit ISAAC random number generator using the\ndefault fixed seed.",19,{"inputs":[],"output":{"name":"isaac64rng"}}],[11,"clone","","",19,null],[11,"next_u32","","",19,null],[11,"next_u64","","",19,null],[11,"reseed","","",19,null],[11,"from_seed","","Create an ISAAC random number generator with a seed. This can\nbe any length, although the maximum number of elements used is\n256 and any more will be silently ignored. A generator\nconstructed with a given seed will generate the same sequence\nof values as all other generators constructed with that seed.",19,null],[11,"rand","","",19,{"inputs":[{"name":"r"}],"output":{"name":"isaac64rng"}}],[0,"chacha","rand","The ChaCha random number generator.",null,null],[3,"ChaChaRng","rand::chacha","A random number generator that uses the ChaCha20 algorithm [1].",null,null],[11,"clone","","",20,null],[11,"new_unseeded","","Create an ChaCha random number generator using the default\nfixed key of 8 zero words.",20,{"inputs":[],"output":{"name":"chacharng"}}],[11,"set_counter","","Sets the internal 128-bit ChaCha counter to\na user-provided value. This permits jumping\narbitrarily ahead (or backwards) in the pseudorandom stream.",20,null],[11,"next_u32","","",20,null],[11,"reseed","","",20,null],[11,"from_seed","","Create a ChaCha generator from a seed,\nobtained from a variable-length u32 array.\nOnly up to 8 words are used; if less than 8\nwords are used, the remaining are set to zero.",20,null],[11,"rand","","",20,{"inputs":[{"name":"r"}],"output":{"name":"chacharng"}}],[0,"reseeding","rand","A wrapper around another RNG that reseeds it after it\ngenerates a certain number of random bytes.",null,null],[3,"ReseedingRng","rand::reseeding","A wrapper around any RNG which reseeds the underlying RNG after it\nhas generated a certain number of random bytes.",null,null],[12,"reseeder","","Controls the behaviour when reseeding the RNG.",21,null],[3,"ReseedWithDefault","","Reseed an RNG using a `Default` instance. This reseeds by\nreplacing the RNG with the result of a `Default::default` call.",null,null],[8,"Reseeder","","Something that can be used to reseed an RNG via `ReseedingRng`.",null,null],[10,"reseed","","Reseed the given RNG.",22,null],[11,"new","","Create a new `ReseedingRng` with the given parameters.",21,{"inputs":[{"name":"r"},{"name":"u64"},{"name":"rsdr"}],"output":{"name":"reseedingrng"}}],[11,"reseed_if_necessary","","Reseed the internal RNG if the number of bytes that have been\ngenerated exceed the threshold.",21,null],[11,"next_u32","","",21,null],[11,"next_u64","","",21,null],[11,"fill_bytes","","",21,null],[11,"reseed","","",21,null],[11,"from_seed","","Create a new `ReseedingRng` from the given reseeder and\nseed. This uses a default value for `generation_threshold`.",21,null],[11,"clone","","",23,null],[11,"reseed","","",23,null],[11,"default","","",23,{"inputs":[],"output":{"name":"reseedwithdefault"}}],[11,"rand","rand","",0,{"inputs":[{"name":"r"}],"output":{"name":"open01"}}],[11,"rand","","",1,{"inputs":[{"name":"r"}],"output":{"name":"closed01"}}],[11,"rand","","",0,{"inputs":[{"name":"r"}],"output":{"name":"open01"}}],[11,"rand","","",1,{"inputs":[{"name":"r"}],"output":{"name":"closed01"}}],[11,"rand","core::option","",24,{"inputs":[{"name":"r"}],"output":{"name":"option"}}],[0,"os","rand","Interfaces to the operating system provided random number\ngenerators.",null,null],[3,"OsRng","rand::os","A random number generator that retrieves randomness straight from\nthe operating system. Platform sources:",null,null],[11,"new","","Create a new `OsRng`.",25,{"inputs":[],"output":{"name":"result"}}],[11,"next_u32","","",25,null],[11,"next_u64","","",25,null],[11,"fill_bytes","","",25,null],[0,"read","rand","A wrapper around any Read to treat it as an RNG.",null,null],[3,"ReadRng","rand::read","An RNG that reads random bytes straight from a `Read`. This will\nwork best with an infinite reader, but this is not required.",null,null],[11,"new","","Create a new `ReadRng` from a `Read`.",26,{"inputs":[{"name":"r"}],"output":{"name":"readrng"}}],[11,"next_u32","","",26,null],[11,"next_u64","","",26,null],[11,"fill_bytes","","",26,null],[8,"Rand","rand","A type that can be randomly generated using an `Rng`.",null,null],[10,"rand","","Generates a random instance of this type using the specified source of\nrandomness.",27,{"inputs":[{"name":"r"}],"output":{"name":"self"}}],[8,"Rng","","A random number generator.",null,null],[10,"next_u32","","Return the next random u32.",28,null],[11,"next_u64","","Return the next random u64.",28,null],[11,"next_f32","","Return the next random f32 selected from the half-open\ninterval `[0, 1)`.",28,null],[11,"next_f64","","Return the next random f64 selected from the half-open\ninterval `[0, 1)`.",28,null],[11,"fill_bytes","","Fill `dest` with random data.",28,null],[11,"gen","","Return a random value of a `Rand` type.",28,null],[11,"gen_iter","","Return an iterator that will yield an infinite number of randomly\ngenerated items.",28,null],[11,"gen_range","","Generate a random value in the range [`low`, `high`).",28,null],[11,"gen_weighted_bool","","Return a bool with a 1 in n chance of true",28,null],[11,"gen_ascii_chars","","Return an iterator of random characters from the set A-Z,a-z,0-9.",28,null],[11,"choose","","Return a random element from `values`.",28,null],[11,"shuffle","","Shuffle a mutable slice in place.",28,null],[8,"SeedableRng","","A random number generator that can be explicitly seeded to produce\nthe same stream of randomness multiple times.",null,null],[10,"reseed","","Reseed an RNG with the given seed.",29,null],[10,"from_seed","","Create a new RNG with the given seed.",29,{"inputs":[{"name":"seed"}],"output":{"name":"self"}}],[11,"next_u32","alloc::boxed","",30,null],[11,"next_u64","","",30,null],[11,"next_f32","","",30,null],[11,"next_f64","","",30,null],[11,"fill_bytes","","",30,null],[11,"next","rand","",31,null],[11,"next","","",32,null],[11,"clone","","",33,null],[11,"new_unseeded","","Creates a new XorShiftRng instance which is not seeded.",33,{"inputs":[],"output":{"name":"xorshiftrng"}}],[11,"next_u32","","",33,null],[11,"reseed","","Reseed an XorShiftRng. This will panic if `seed` is entirely 0.",33,null],[11,"from_seed","","Create a new XorShiftRng. 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an instance of NonZero with the provided value.\nYou must indeed ensure that the value is actually "non-zero".",47,{"inputs":[{"name":"t"}],"output":{"name":"nonzero"}}],[11,"deref","","",47,null],[11,"new","core::ptr","Creates a new `Unique`.",48,null],[11,"get","","Dereferences the content.",48,null],[11,"get_mut","","Mutably dereferences the content.",48,null],[11,"deref","","",48,null],[11,"fmt","","",48,null],[11,"new","","Creates a new `Shared`.",49,null],[11,"clone","","",49,null],[11,"deref","","",49,null],[11,"fmt","","",49,null],[11,"hash","core::marker","",50,null],[11,"eq","","",50,null],[11,"partial_cmp","","",50,null],[11,"cmp","","",50,null],[11,"clone","","",50,null],[11,"default","","",50,{"inputs":[],"output":{"name":"phantomdata"}}],[11,"eq","core::ops","",51,null],[11,"clone","","",51,null],[11,"fmt","","",51,null],[11,"eq","","",52,null],[11,"ne","","",52,null],[11,"clone","","",52,null],[11,"fmt","","",52,null],[11,"contains","","# Examples",52,null],[11,"eq","","",53,null],[11,"ne","","",53,null],[11,"clone","","",53,null],[11,"fmt","","",53,null],[11,"contains","","# Examples",53,null],[11,"eq","","",54,null],[11,"ne","","",54,null],[11,"clone","","",54,null],[11,"fmt","","",54,null],[11,"contains","","# Examples",54,null],[11,"eq","","",55,null],[11,"ne","","",55,null],[11,"clone","","",55,null],[11,"fmt","","",55,null],[11,"from","","",55,{"inputs":[{"name":"range"}],"output":{"name":"rangeinclusive"}}],[11,"contains","","# Examples",55,null],[11,"eq","","",56,null],[11,"ne","","",56,null],[11,"clone","","",56,null],[11,"fmt","","",56,null],[11,"contains","","# Examples",56,null],[11,"hash","core::cmp","",57,null],[11,"fmt","","",57,null],[11,"eq","","",57,null],[11,"clone","","",57,null],[11,"reverse","","Reverse the `Ordering`.",57,null],[11,"cmp","","",57,null],[11,"partial_cmp","","",57,null],[11,"fmt","libc","",58,null],[11,"fmt","","",58,null],[11,"is","","Returns true if the boxed type is the same as `T`",58,null],[11,"downcast_ref","","Returns some reference to the boxed value if it is of type `T`, or\n`None` if it isn't.",58,null],[11,"downcast_mut","","Returns some mutable reference to the boxed value if it is of type `T`, or\n`None` if it isn't.",58,null],[11,"is","","Forwards to the method defined on the type `Any`.",58,null],[11,"downcast_ref","","Forwards to the method defined on the type `Any`.",58,null],[11,"downcast_mut","","Forwards to the method defined on the type `Any`.",58,null],[11,"hash","core::any","",59,null],[11,"fmt","","",59,null],[11,"eq","","",59,null],[11,"ne","","",59,null],[11,"clone","","",59,null],[11,"of","","Returns the `TypeId` of the type this generic function has been\ninstantiated with",59,{"inputs":[],"output":{"name":"typeid"}}],[11,"default","core::sync::atomic","",60,{"inputs":[],"output":{"name":"atomicbool"}}],[11,"default","","",61,{"inputs":[],"output":{"name":"atomicptr"}}],[11,"fmt","","",62,null],[11,"clone","","",62,null],[11,"new","","Creates a new `AtomicBool`.",60,{"inputs":[{"name":"bool"}],"output":{"name":"atomicbool"}}],[11,"load","","Loads a value from the bool.",60,null],[11,"store","","Stores a value into the bool.",60,null],[11,"swap","","Stores a value into the bool, returning the old value.",60,null],[11,"compare_and_swap","","Stores a value into the `bool` if the current value is the same as the `current` value.",60,null],[11,"compare_exchange","","Stores a value into the `bool` if the current value is the same as the `current` value.",60,null],[11,"compare_exchange_weak","","Stores a value into the `bool` if the current value is the same as the `current` value.",60,null],[11,"fetch_and","","Logical "and" with a boolean value.",60,null],[11,"fetch_nand","","Logical "nand" with a boolean value.",60,null],[11,"fetch_or","","Logical "or" with a boolean value.",60,null],[11,"fetch_xor","","Logical "xor" with a boolean value.",60,null],[11,"new","","Creates a new `AtomicPtr`.",61,null],[11,"load","","Loads a value from the pointer.",61,null],[11,"store","","Stores a value into the pointer.",61,null],[11,"swap","","Stores a value into the pointer, returning the old value.",61,null],[11,"compare_and_swap","","Stores a value into the pointer if the current value is the same as the `current` value.",61,null],[11,"compare_exchange","","Stores a value into the pointer if the current value is the same as the `current` value.",61,null],[11,"compare_exchange_weak","","Stores a value into the pointer if the current value is the same as the `current` value.",61,null],[11,"default","","",63,{"inputs":[],"output":{"name":"atomici8"}}],[11,"fmt","","",63,null],[11,"new","","Creates a new atomic integer.",63,{"inputs":[{"name":"i8"}],"output":{"name":"atomici8"}}],[11,"load","","Loads a value from the atomic integer.",63,null],[11,"store","","Stores a value into the atomic integer.",63,null],[11,"swap","","Stores a value into the atomic integer, returning the old value.",63,null],[11,"compare_and_swap","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",63,null],[11,"compare_exchange","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",63,null],[11,"compare_exchange_weak","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",63,null],[11,"fetch_add","","Add to the current value, returning the previous value.",63,null],[11,"fetch_sub","","Subtract from the current value, returning the previous value.",63,null],[11,"fetch_and","","Bitwise and with the current value, returning the previous value.",63,null],[11,"fetch_or","","Bitwise or with the current value, returning the previous value.",63,null],[11,"fetch_xor","","Bitwise xor with the current value, returning the previous value.",63,null],[11,"default","","",64,{"inputs":[],"output":{"name":"atomicu8"}}],[11,"fmt","","",64,null],[11,"new","","Creates a new atomic integer.",64,{"inputs":[{"name":"u8"}],"output":{"name":"atomicu8"}}],[11,"load","","Loads a value from the atomic integer.",64,null],[11,"store","","Stores a value into the atomic integer.",64,null],[11,"swap","","Stores a value into the atomic integer, returning the old value.",64,null],[11,"compare_and_swap","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",64,null],[11,"compare_exchange","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",64,null],[11,"compare_exchange_weak","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",64,null],[11,"fetch_add","","Add to the current value, returning the previous value.",64,null],[11,"fetch_sub","","Subtract from the current value, returning the previous value.",64,null],[11,"fetch_and","","Bitwise and with the current value, returning the previous value.",64,null],[11,"fetch_or","","Bitwise or with the current value, returning the previous value.",64,null],[11,"fetch_xor","","Bitwise xor with the current value, returning the previous value.",64,null],[11,"default","","",65,{"inputs":[],"output":{"name":"atomici16"}}],[11,"fmt","","",65,null],[11,"new","","Creates a new atomic integer.",65,{"inputs":[{"name":"i16"}],"output":{"name":"atomici16"}}],[11,"load","","Loads a value from the atomic integer.",65,null],[11,"store","","Stores a value into the atomic integer.",65,null],[11,"swap","","Stores a value into the atomic integer, returning the old value.",65,null],[11,"compare_and_swap","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",65,null],[11,"compare_exchange","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",65,null],[11,"compare_exchange_weak","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",65,null],[11,"fetch_add","","Add to the current value, returning the previous value.",65,null],[11,"fetch_sub","","Subtract from the current value, returning the previous value.",65,null],[11,"fetch_and","","Bitwise and with the current value, returning the previous value.",65,null],[11,"fetch_or","","Bitwise or with the current value, returning the previous value.",65,null],[11,"fetch_xor","","Bitwise xor with the current value, returning the previous value.",65,null],[11,"default","","",66,{"inputs":[],"output":{"name":"atomicu16"}}],[11,"fmt","","",66,null],[11,"new","","Creates a new atomic integer.",66,{"inputs":[{"name":"u16"}],"output":{"name":"atomicu16"}}],[11,"load","","Loads a value from the atomic integer.",66,null],[11,"store","","Stores a value into the atomic integer.",66,null],[11,"swap","","Stores a value into the atomic integer, returning the old value.",66,null],[11,"compare_and_swap","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",66,null],[11,"compare_exchange","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",66,null],[11,"compare_exchange_weak","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",66,null],[11,"fetch_add","","Add to the current value, returning the previous value.",66,null],[11,"fetch_sub","","Subtract from the current value, returning the previous value.",66,null],[11,"fetch_and","","Bitwise and with the current value, returning the previous value.",66,null],[11,"fetch_or","","Bitwise or with the current value, returning the previous value.",66,null],[11,"fetch_xor","","Bitwise xor with the current value, returning the previous value.",66,null],[11,"default","","",67,{"inputs":[],"output":{"name":"atomici32"}}],[11,"fmt","","",67,null],[11,"new","","Creates a new atomic integer.",67,{"inputs":[{"name":"i32"}],"output":{"name":"atomici32"}}],[11,"load","","Loads a value from the atomic integer.",67,null],[11,"store","","Stores a value into the atomic integer.",67,null],[11,"swap","","Stores a value into the atomic integer, returning the old value.",67,null],[11,"compare_and_swap","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",67,null],[11,"compare_exchange","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",67,null],[11,"compare_exchange_weak","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",67,null],[11,"fetch_add","","Add to the current value, returning the previous value.",67,null],[11,"fetch_sub","","Subtract from the current value, returning the previous value.",67,null],[11,"fetch_and","","Bitwise and with the current value, returning the previous value.",67,null],[11,"fetch_or","","Bitwise or with the current value, returning the previous value.",67,null],[11,"fetch_xor","","Bitwise xor with the current value, returning the previous value.",67,null],[11,"default","","",68,{"inputs":[],"output":{"name":"atomicu32"}}],[11,"fmt","","",68,null],[11,"new","","Creates a new atomic integer.",68,{"inputs":[{"name":"u32"}],"output":{"name":"atomicu32"}}],[11,"load","","Loads a value from the atomic integer.",68,null],[11,"store","","Stores a value into the atomic integer.",68,null],[11,"swap","","Stores a value into the atomic integer, returning the old value.",68,null],[11,"compare_and_swap","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",68,null],[11,"compare_exchange","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",68,null],[11,"compare_exchange_weak","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",68,null],[11,"fetch_add","","Add to the current value, returning the previous value.",68,null],[11,"fetch_sub","","Subtract from the current value, returning the previous value.",68,null],[11,"fetch_and","","Bitwise and with the current value, returning the previous value.",68,null],[11,"fetch_or","","Bitwise or with the current value, returning the previous value.",68,null],[11,"fetch_xor","","Bitwise xor with the current value, returning the previous value.",68,null],[11,"default","","",69,{"inputs":[],"output":{"name":"atomici64"}}],[11,"fmt","","",69,null],[11,"new","","Creates a new atomic integer.",69,{"inputs":[{"name":"i64"}],"output":{"name":"atomici64"}}],[11,"load","","Loads a value from the atomic integer.",69,null],[11,"store","","Stores a value into the atomic integer.",69,null],[11,"swap","","Stores a value into the atomic integer, returning the old value.",69,null],[11,"compare_and_swap","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",69,null],[11,"compare_exchange","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",69,null],[11,"compare_exchange_weak","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",69,null],[11,"fetch_add","","Add to the current value, returning the previous value.",69,null],[11,"fetch_sub","","Subtract from the current value, returning the previous value.",69,null],[11,"fetch_and","","Bitwise and with the current value, returning the previous value.",69,null],[11,"fetch_or","","Bitwise or with the current value, returning the previous value.",69,null],[11,"fetch_xor","","Bitwise xor with the current value, returning the previous value.",69,null],[11,"default","","",70,{"inputs":[],"output":{"name":"atomicu64"}}],[11,"fmt","","",70,null],[11,"new","","Creates a new atomic integer.",70,{"inputs":[{"name":"u64"}],"output":{"name":"atomicu64"}}],[11,"load","","Loads a value from the atomic integer.",70,null],[11,"store","","Stores a value into the atomic integer.",70,null],[11,"swap","","Stores a value into the atomic integer, returning the old value.",70,null],[11,"compare_and_swap","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",70,null],[11,"compare_exchange","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",70,null],[11,"compare_exchange_weak","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",70,null],[11,"fetch_add","","Add to the current value, returning the previous value.",70,null],[11,"fetch_sub","","Subtract from the current value, returning the previous value.",70,null],[11,"fetch_and","","Bitwise and with the current value, returning the previous value.",70,null],[11,"fetch_or","","Bitwise or with the current value, returning the previous value.",70,null],[11,"fetch_xor","","Bitwise xor with the current value, returning the previous value.",70,null],[11,"default","","",71,{"inputs":[],"output":{"name":"atomicisize"}}],[11,"fmt","","",71,null],[11,"new","","Creates a new atomic integer.",71,{"inputs":[{"name":"isize"}],"output":{"name":"atomicisize"}}],[11,"load","","Loads a value from the atomic integer.",71,null],[11,"store","","Stores a value into the atomic integer.",71,null],[11,"swap","","Stores a value into the atomic integer, returning the old value.",71,null],[11,"compare_and_swap","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",71,null],[11,"compare_exchange","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",71,null],[11,"compare_exchange_weak","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",71,null],[11,"fetch_add","","Add to the current value, returning the previous value.",71,null],[11,"fetch_sub","","Subtract from the current value, returning the previous value.",71,null],[11,"fetch_and","","Bitwise and with the current value, returning the previous value.",71,null],[11,"fetch_or","","Bitwise or with the current value, returning the previous value.",71,null],[11,"fetch_xor","","Bitwise xor with the current value, returning the previous value.",71,null],[11,"default","","",72,{"inputs":[],"output":{"name":"atomicusize"}}],[11,"fmt","","",72,null],[11,"new","","Creates a new atomic integer.",72,{"inputs":[{"name":"usize"}],"output":{"name":"atomicusize"}}],[11,"load","","Loads a value from the atomic integer.",72,null],[11,"store","","Stores a value into the atomic integer.",72,null],[11,"swap","","Stores a value into the atomic integer, returning the old value.",72,null],[11,"compare_and_swap","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",72,null],[11,"compare_exchange","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",72,null],[11,"compare_exchange_weak","","Stores a value into the atomic integer if the current value is the same as the\n`current` value.",72,null],[11,"fetch_add","","Add to the current value, returning the previous value.",72,null],[11,"fetch_sub","","Subtract from the current value, returning the previous value.",72,null],[11,"fetch_and","","Bitwise and with the current value, returning the previous value.",72,null],[11,"fetch_or","","Bitwise or with the current value, returning the previous value.",72,null],[11,"fetch_xor","","Bitwise xor with the current value, returning the previous value.",72,null],[11,"fmt","","",60,null],[11,"fmt","","",61,null],[11,"new","core::cell","Creates a new `Cell` containing the given value.",73,{"inputs":[{"name":"t"}],"output":{"name":"cell"}}],[11,"get","","Returns a copy of the contained value.",73,null],[11,"set","","Sets the contained value.",73,null],[11,"as_unsafe_cell","","Returns a reference to the underlying `UnsafeCell`.",73,null],[11,"get_mut","","Returns a mutable reference to the underlying data.",73,null],[11,"clone","","",73,null],[11,"default","","",73,{"inputs":[],"output":{"name":"cell"}}],[11,"eq","","",73,null],[11,"partial_cmp","","",73,null],[11,"lt","","",73,null],[11,"le","","",73,null],[11,"gt","","",73,null],[11,"ge","","",73,null],[11,"cmp","","",73,null],[11,"fmt","","",74,null],[11,"eq","","",74,null],[11,"clone","","",74,null],[11,"new","","Creates a new `RefCell` containing `value`.",75,{"inputs":[{"name":"t"}],"output":{"name":"refcell"}}],[11,"into_inner","","Consumes the `RefCell`, returning the wrapped value.",75,null],[11,"borrow_state","","Query the current state of this `RefCell`",75,null],[11,"borrow","","Immutably borrows the wrapped value.",75,null],[11,"borrow_mut","","Mutably borrows the wrapped value.",75,null],[11,"as_unsafe_cell","","Returns a reference to the underlying `UnsafeCell`.",75,null],[11,"get_mut","","Returns a mutable reference to the underlying data.",75,null],[11,"clone","","",75,null],[11,"default","","",75,{"inputs":[],"output":{"name":"refcell"}}],[11,"eq","","",75,null],[11,"partial_cmp","","",75,null],[11,"lt","","",75,null],[11,"le","","",75,null],[11,"gt","","",75,null],[11,"ge","","",75,null],[11,"cmp","","",75,null],[11,"deref","","",76,null],[11,"clone","","Copies a `Ref`.",76,{"inputs":[{"name":"ref"}],"output":{"name":"ref"}}],[11,"map","","Make a new `Ref` for a component of the borrowed data.",76,{"inputs":[{"name":"ref"},{"name":"f"}],"output":{"name":"ref"}}],[11,"filter_map","","Make a new `Ref` for an optional component of the borrowed data, e.g. an\nenum variant.",76,{"inputs":[{"name":"ref"},{"name":"f"}],"output":{"name":"option"}}],[11,"map","","Make a new `RefMut` for a component of the borrowed data, e.g. an enum\nvariant.",77,{"inputs":[{"name":"refmut"},{"name":"f"}],"output":{"name":"refmut"}}],[11,"filter_map","","Make a new `RefMut` for an optional component of the borrowed data, e.g.\nan enum variant.",77,{"inputs":[{"name":"refmut"},{"name":"f"}],"output":{"name":"option"}}],[11,"deref","","",77,null],[11,"deref_mut","","",77,null],[11,"new","","Constructs a new instance of `UnsafeCell` which will wrap the specified\nvalue.",78,{"inputs":[{"name":"t"}],"output":{"name":"unsafecell"}}],[11,"into_inner","","Unwraps the value.",78,null],[11,"get","","Gets a mutable pointer to the wrapped value.",78,null],[11,"default","","",78,{"inputs":[],"output":{"name":"unsafecell"}}],[11,"fmt","core::char","",79,null],[11,"clone","","",79,null],[11,"next","","",79,null],[11,"size_hint","","",79,null],[11,"count","","",79,null],[11,"last","","",79,null],[11,"len","","",79,null],[11,"fmt","","",80,null],[11,"clone","","",80,null],[11,"next","","",80,null],[11,"size_hint","","",80,null],[11,"count","","",80,null],[11,"nth","","",80,null],[11,"last","","",80,null],[11,"len","","",80,null],[11,"fmt","","",81,null],[11,"as_slice","","Returns the remaining bytes of this iterator as a slice.",81,null],[11,"next","","",81,null],[11,"size_hint","","",81,null],[11,"fmt","","",82,null],[11,"as_slice","","Returns the remaining bytes of this iterator as a slice.",82,null],[11,"next","","",82,null],[11,"size_hint","","",82,null],[11,"fmt","core::iter::range","",83,null],[11,"clone","","",83,null],[11,"step_by","core::ops","Creates an iterator starting at the same point, but stepping by\nthe given amount at each iteration.",53,null],[11,"step_by","","Creates an iterator with the same range, but stepping by the\ngiven amount at each iteration.",52,null],[11,"step_by","","Creates an iterator with the same range, but stepping by the\ngiven amount at each iteration.",55,null],[11,"next","core::iter::range","",83,null],[11,"size_hint","","",83,null],[11,"next","","",83,null],[11,"size_hint","","",83,null],[11,"next","","",83,null],[11,"size_hint","","",83,null],[11,"next","core::ops","",52,null],[11,"size_hint","","",52,null],[11,"next_back","","",52,null],[11,"next","","",53,null],[11,"next","","",55,null],[11,"size_hint","","",55,null],[11,"next_back","","",55,null],[11,"fmt","core::iter::sources","",84,null],[11,"clone","","",84,null],[11,"next","","",84,null],[11,"size_hint","","",84,null],[11,"next_back","","",84,null],[11,"fmt","","",85,null],[11,"next","","",85,null],[11,"size_hint","","",85,null],[11,"next_back","","",85,null],[11,"len","","",85,null],[11,"clone","","",85,null],[11,"default","","",85,{"inputs":[],"output":{"name":"empty"}}],[11,"fmt","","",86,null],[11,"clone","","",86,null],[11,"next","","",86,null],[11,"size_hint","","",86,null],[11,"next_back","","",86,null],[11,"len","","",86,null],[11,"fmt","core::iter","",87,null],[11,"clone","","",87,null],[11,"next","","",87,null],[11,"size_hint","","",87,null],[11,"next_back","","",87,null],[11,"fmt","","",88,null],[11,"clone","","",88,null],[11,"next","","",88,null],[11,"size_hint","","",88,null],[11,"next_back","","",88,null],[11,"fmt","","",89,null],[11,"clone","","",89,null],[11,"next","","",89,null],[11,"size_hint","","",89,null],[11,"fmt","","",90,null],[11,"clone","","",90,null],[11,"next","","",90,null],[11,"count","","",90,null],[11,"nth","","",90,null],[11,"find","","",90,null],[11,"last","","",90,null],[11,"size_hint","","",90,null],[11,"next_back","","",90,null],[11,"fmt","","",91,null],[11,"clone","","",91,null],[11,"next","","",91,null],[11,"size_hint","","",91,null],[11,"next_back","","",91,null],[11,"clone","","",92,null],[11,"fmt","","",92,null],[11,"next","","",92,null],[11,"size_hint","","",92,null],[11,"next_back","","",92,null],[11,"clone","","",93,null],[11,"fmt","","",93,null],[11,"next","","",93,null],[11,"size_hint","","",93,null],[11,"next_back","","",93,null],[11,"clone","","",94,null],[11,"fmt","","",94,null],[11,"next","","",94,null],[11,"size_hint","","",94,null],[11,"next_back","","",94,null],[11,"fmt","","",95,null],[11,"clone","","",95,null],[11,"next","","# Overflow Behavior",95,null],[11,"size_hint","","",95,null],[11,"nth","","",95,null],[11,"count","","",95,null],[11,"next_back","","",95,null],[11,"fmt","","",96,null],[11,"clone","","",96,null],[11,"next","","",96,null],[11,"count","","",96,null],[11,"nth","","",96,null],[11,"last","","",96,null],[11,"size_hint","","",96,null],[11,"peek","","Returns a reference to the next() value without advancing the iterator.",96,null],[11,"is_empty","","Checks if the iterator has finished iterating.",96,null],[11,"clone","","",97,null],[11,"fmt","","",97,null],[11,"next","","",97,null],[11,"size_hint","","",97,null],[11,"clone","","",98,null],[11,"fmt","","",98,null],[11,"next","","",98,null],[11,"size_hint","","",98,null],[11,"fmt","","",99,null],[11,"clone","","",99,null],[11,"next","","",99,null],[11,"nth","","",99,null],[11,"count","","",99,null],[11,"last","","",99,null],[11,"size_hint","","",99,null],[11,"next_back","","",99,null],[11,"fmt","","",100,null],[11,"clone","","",100,null],[11,"next","","",100,null],[11,"nth","","",100,null],[11,"size_hint","","",100,null],[11,"clone","","",101,null],[11,"fmt","","",101,null],[11,"next","","",101,null],[11,"size_hint","","",101,null],[11,"clone","","",102,null],[11,"fmt","","",102,null],[11,"next","","",102,null],[11,"size_hint","","",102,null],[11,"next_back","","",102,null],[11,"fmt","","",103,null],[11,"clone","","",103,null],[11,"next","","",103,null],[11,"nth","","",103,null],[11,"last","","",103,null],[11,"count","","",103,null],[11,"size_hint","","",103,null],[11,"next_back","","",103,null],[11,"clone","","",104,null],[11,"fmt","","",104,null],[11,"next","","",104,null],[11,"size_hint","","",104,null],[11,"next_back","","",104,null],[11,"hash","core::option","",41,null],[11,"fmt","","",41,null],[11,"cmp","","",41,null],[11,"partial_cmp","","",41,null],[11,"lt","","",41,null],[11,"le","","",41,null],[11,"gt","","",41,null],[11,"ge","","",41,null],[11,"eq","","",41,null],[11,"ne","","",41,null],[11,"clone","","",41,null],[11,"default","","",41,{"inputs":[],"output":{"name":"option"}}],[11,"into_iter","","Returns a consuming iterator over the possibly contained value.",41,null],[11,"fmt","","",105,null],[11,"next","","",105,null],[11,"size_hint","","",105,null],[11,"next_back","","",105,null],[11,"clone","","",105,null],[11,"fmt","","",106,null],[11,"next","","",106,null],[11,"size_hint","","",106,null],[11,"next_back","","",106,null],[11,"fmt","","",107,null],[11,"clone","","",107,null],[11,"next","","",107,null],[11,"size_hint","","",107,null],[11,"next_back","","",107,null],[11,"from_iter","","Takes each element in the `Iterator`: if it is `None`, no further\nelements are taken, and the `None` is returned. Should no `None` occur, a\ncontainer with the values of each `Option` is returned.",41,{"inputs":[{"name":"i"}],"output":{"name":"option"}}],[11,"clone","core::raw","",108,null],[11,"clone","","",109,null],[11,"hash","core::result","",110,null],[11,"fmt","","",110,null],[11,"cmp","","",110,null],[11,"partial_cmp","","",110,null],[11,"lt","","",110,null],[11,"le","","",110,null],[11,"gt","","",110,null],[11,"ge","","",110,null],[11,"eq","","",110,null],[11,"ne","","",110,null],[11,"clone","","",110,null],[11,"is_ok","","Returns true if the result is `Ok`",110,null],[11,"is_err","","Returns true if the result is `Err`",110,null],[11,"ok","","Converts from `Result<T, E>` to `Option<T>`",110,null],[11,"err","","Converts from `Result<T, E>` to `Option<E>`",110,null],[11,"as_ref","","Converts from `Result<T, E>` to `Result<&T, &E>`",110,null],[11,"as_mut","","Converts from `Result<T, E>` to `Result<&mut T, &mut E>`",110,null],[11,"map","","Maps a `Result<T, E>` to `Result<U, E>` by applying a function to a\ncontained `Ok` value, leaving an `Err` value untouched.",110,null],[11,"map_err","","Maps a `Result<T, E>` to `Result<T, F>` by applying a function to a\ncontained `Err` value, leaving an `Ok` value untouched.",110,null],[11,"iter","","Returns an iterator over the possibly contained value.",110,null],[11,"iter_mut","","Returns a mutable iterator over the possibly contained value.",110,null],[11,"and","","Returns `res` if the result is `Ok`, otherwise returns the `Err` value of `self`.",110,null],[11,"and_then","","Calls `op` if the result is `Ok`, otherwise returns the `Err` value of `self`.",110,null],[11,"or","","Returns `res` if the result is `Err`, otherwise returns the `Ok` value of `self`.",110,null],[11,"or_else","","Calls `op` if the result is `Err`, otherwise returns the `Ok` value of `self`.",110,null],[11,"unwrap_or","","Unwraps a result, yielding the content of an `Ok`.\nElse it returns `optb`.",110,null],[11,"unwrap_or_else","","Unwraps a result, yielding the content of an `Ok`.\nIf the value is an `Err` then it calls `op` with its value.",110,null],[11,"unwrap","","Unwraps a result, yielding the content of an `Ok`.",110,null],[11,"expect","","Unwraps a result, yielding the content of an `Ok`.",110,null],[11,"unwrap_err","","Unwraps a result, yielding the content of an `Err`.",110,null],[11,"into_iter","","Returns a consuming iterator over the possibly contained value.",110,null],[11,"fmt","","",111,null],[11,"next","","",111,null],[11,"size_hint","","",111,null],[11,"next_back","","",111,null],[11,"clone","","",111,null],[11,"fmt","","",112,null],[11,"next","","",112,null],[11,"size_hint","","",112,null],[11,"next_back","","",112,null],[11,"fmt","","",113,null],[11,"next","","",113,null],[11,"size_hint","","",113,null],[11,"next_back","","",113,null],[11,"from_iter","","Takes each element in the `Iterator`: if it is an `Err`, no further\nelements are taken, and the `Err` is returned. Should no `Err` occur, a\ncontainer with the values of each `Result` is returned.",110,{"inputs":[{"name":"i"}],"output":{"name":"result"}}],[11,"fmt","core::slice","",114,null],[11,"as_slice","","View the underlying data as a subslice of the original data.",114,null],[11,"next","","",114,null],[11,"size_hint","","",114,null],[11,"count","","",114,null],[11,"nth","","",114,null],[11,"last","","",114,null],[11,"next_back","","",114,null],[11,"clone","","",114,null],[11,"fmt","","",115,null],[11,"into_slice","","View the underlying data as a subslice of the original 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