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Quickly converging computation of π
known as the Gauss–Euler, Brent–Salamin (or Salamin–Brent) algorithm; it was independently discovered in 1975 by Richard Brent and Eugene Salamin. It was
Gauss–Legendre_algorithm
Topics referred to by the same term
Brent's algorithm is either of the following: Brent's algorithm for cycle detection Brent's method for finding roots of functions of one real variable
Brent's_algorithm
On finding a repeating loop in a sequence
equal values. Alternatively, Brent's algorithm is based on the idea of exponential search. Both Floyd's and Brent's algorithms use only a constant number
Cycle_detection
well-known algorithms. Brent's algorithm: finds a cycle in function value iterations using only two iterators Floyd's cycle-finding algorithm: finds a cycle
List_of_algorithms
Root-finding algorithm
In numerical analysis, Brent's method is a hybrid root-finding algorithm combining the bisection method, the secant method and inverse quadratic interpolation
Brent's_method
Australian mathematician and computer scientist
analysis of algorithms. In 1973, he published a root-finding algorithm (an algorithm for solving equations numerically) which is now known as Brent's method
Richard_P._Brent
Integer factorization algorithm
Pollard's rho algorithm is an algorithm for integer factorization. It was invented by John Pollard in 1975. It uses only a small amount of space, and
Pollard's_rho_algorithm
The following timeline of algorithms outlines the development of algorithms (mainly "mathematical recipes") since their inception. Before – writing about
Timeline_of_algorithms
American mathematician
mathematician who discovered (independently with Richard Brent) the Salamin–Brent algorithm, used in high-precision calculation of pi. Eugene Salamin
Eugene Salamin (mathematician)
Eugene_Salamin_(mathematician)
Subfield of computer science
computer science, analysis of parallel algorithms is the process of finding the computational complexity of algorithms executed in parallel – the amount of
Analysis of parallel algorithms
Analysis_of_parallel_algorithms
Algorithm to multiply two numbers
multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient
Multiplication_algorithm
Decomposition of a number into a product
Floyd and one by Brent. Algebraic-group factorization algorithms, among which are Pollard's p − 1 algorithm, Williams' p + 1 algorithm, and Lenstra elliptic
Integer_factorization
Nehemiah Radian Ramanujan–Sato series Rhind Mathematical Papyrus Salamin–Brent algorithm Software for calculating π Squaring the circle Turn (geometry) Viète's
List_of_topics_related_to_π
Varying methods used to calculate pi
typically computed with the Gauss–Legendre algorithm and Borwein's algorithm; the Salamin–Brent algorithm, which was invented in 1976, has also been used
Approximations_of_pi
Fast method for calculating the digits of π
The Chudnovsky algorithm is a fast method for calculating the digits of π, based on Ramanujan's π formulae. Published by the Chudnovsky brothers in 1988
Chudnovsky_algorithm
Algorithm for computing the greatest common divisor
The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, is an algorithm that computes the greatest common divisor
Binary_GCD_algorithm
Technological phenomenon with social implications
Algorithmic bias describes systematic and repeatable harmful tendency in a computerized sociotechnical system to create "unfair" outcomes, such as "privileging"
Algorithmic_bias
Algorithmic runtime requirements for common math procedures
The following tables list the computational complexity of various algorithms for common mathematical operations. Here, complexity refers to the time complexity
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Algorithms for zeros of functions
In numerical analysis, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function
Root-finding_algorithm
Improvement of the coordinate descent algorithm
Adaptive coordinate descent is an improvement of the coordinate descent algorithm to non-separable optimization by the use of adaptive encoding. The adaptive
Adaptive_coordinate_descent
Method of solving equations
the inverse of f. This algorithm is rarely used on its own, but it is important because it forms part of the popular Brent's method. The inverse quadratic
Inverse quadratic interpolation
Inverse_quadratic_interpolation
Topics referred to by the same term
International School, the Philippines Brent's method, a root-finding algorithm Brent railway station, South Devon, England Brent sidings, railway freight facility
Brent
An unrestricted algorithm is an algorithm for the computation of a mathematical function that puts no restrictions on the range of the argument or on
Unrestricted_algorithm
Arithmetic logic circuit
The Brent–Kung adder (BKA or BK), proposed in 1982, is an advanced binary adder design, having a gate level depth of O ( log 2 ( n ) ) {\displaystyle
Brent–Kung_adder
Task of computing complete subgraphs
time algorithm is known for this problem, more efficient algorithms than the brute-force search are known. For instance, the Bron–Kerbosch algorithm can
Clique_problem
Algorithm for finding a local minimum of a function
Powell's method, strictly Powell's conjugate direction method, is an algorithm proposed by Michael J. D. Powell for finding a local minimum of a function
Powell's_method
Process by which platform algorithms increase the reach of certain content
Algorithmic amplification is the process by which automated ranking and recommendation systems on digital platforms increase the visibility of certain
Algorithmic_amplification
Recursive algorighm in linear algebra
The algorithm runs in Θ(n2) time, which is a strong improvement over Gauss–Jordan elimination, which runs in Θ(n3). The Levinson–Durbin algorithm was
Levinson_recursion
System to predict users' preferences
called a recommendation algorithm, recommendation engine, recommendation platform, or in the context of social media, simply algorithm is a type of information
Recommender_system
Algorithm for computing trigonometric, hyperbolic, logarithmic and exponential functions
short for coordinate rotation digital computer, is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots
CORDIC
Rational number sequence
Bernoulli number Bn. Brent and Harvey give several algorithms for computing the Bernoulli numbers, including a simple algorithm that is faster and uses
Bernoulli_number
Algebraic-group factorisation algorithms are algorithms for factoring an integer N by working in an algebraic group defined modulo N whose group structure
Algebraic-group factorisation algorithm
Algebraic-group_factorisation_algorithm
Special-purpose algorithm for factoring integers
Pollard's p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974. It is a special-purpose algorithm, meaning
Pollard's_p_−_1_algorithm
Algorithm for integer factorization
elliptic-curve factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer factorization, which employs elliptic curves. For general-purpose
Lenstra elliptic-curve factorization
Lenstra_elliptic-curve_factorization
Technique for finding an extremum of a function
but very robust. The technique derives its name from the fact that the algorithm maintains the function values for four points whose three interval widths
Golden-section_search
Graph theory problem: find a matching containing the most edges
this algorithm is given by the more elaborate Hopcroft–Karp algorithm, which searches for multiple augmenting paths simultaneously. This algorithm runs
Maximum-cardinality_matching
Numerical method used to approximate solutions of univariate equations
falsi, method of false position, or false position method is a family of algorithms used to solve linear equations and smooth nonlinear equations for a single
Regula_falsi
Concept in modular arithmetic
cryptography and the RSA algorithm. A benefit for the computer implementation of these applications is that there exists a very fast algorithm (the extended Euclidean
Modular multiplicative inverse
Modular_multiplicative_inverse
Type system used in computer programming and mathematics
program without programmer-supplied type annotations or other hints. Algorithm W is an efficient type inference method in practice and has been successfully
Hindley–Milner_type_system
Arithmetic logic circuit
with carry-save adder. Parhami, Behrooz (2000). Computer arithmetic: Algorithms and Hardware Designs. Oxford University Press. p. 108. ISBN 0-19-512583-5
Carry-skip_adder
2024 American TV series or program
Fumudoh as a customer service rep for an airline Dominique Jackson as the Algorithm Julia Fox as Mrs. Claus Aidy Bryant as Denise, a saleswoman for toilet
Fantasmas_(TV_series)
Algorithm that generates an approximation of a random number sequence
(PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the
Pseudorandom_number_generator
Number, approximately 3.14
Gauss–Legendre algorithm. As modified by Salamin and Brent, it is also referred to as the Brent–Salamin algorithm. The iterative algorithms were widely used
Pi
Intellectual isolation through internet algorithms
that arises when personalized searches, recommendation systems, and algorithmic curation selectively presents information to each user. The search results
Filter_bubble
Factorization algorithm
the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10100. Heuristically, its complexity
General_number_field_sieve
System that regulates the formation of blocks on a blockchain
through the idea of "reusable proof of work" using the 160-bit secure hash algorithm 1 (SHA-1). Proof of work was later popularized by Bitcoin as a foundation
Proof_of_work
Retrieved 2019-04-05. See Allan R. Andrews, "A Good Jump on the Ball: Algorithm in the Outfield", The American Reporter (8 October 1998) Archived 6 June
Glossary_of_baseball_terms
Combinational digital circuit
multiple-precision arithmetic is an algorithm that operates on integers which are larger than the ALU word size. To do this, the algorithm treats each integer as an
Arithmetic_logic_unit
Matrix with shifting rows
Brent, R. P. (1999), "Stability of fast algorithms for structured linear systems", in Kailath, T.; Sayed, A. H. (eds.), Fast Reliable Algorithms for
Toeplitz_matrix
Electronic circuit used to multiply binary numbers
product one at a time. Because some common digital signal processing algorithms spend most of their time multiplying, digital signal processor designers
Binary_multiplier
Efficient hardware implementation of a digital multiplier
than addition. From a complexity theoretic perspective, the Wallace tree algorithm puts multiplication in the class NC1. The downside of the Wallace tree
Wallace_tree
3D reconstruction technique
potential applications in computer graphics and content creation. The NeRF algorithm represents a scene as a radiance field parametrized by a deep neural network
Neural_radiance_field
Post-apocalyptic dystopian thriller TV series
decisions. In addition to keeping the train running, Javi uses computer algorithms and hacked satellites to predict the environment surrounding and ahead
Snowpiercer_(TV_series)
Arithmetic logic circuit
59–63, 114–116. Rojas, Raul (2014-06-07). "The Z1: Architecture and Algorithms of Konrad Zuse's First Computer". arXiv:1406.1886 [cs.AR]. Rosenberger
Carry-lookahead_adder
Arithmetic logic circuit
S. Stone, who published it in a seminal 1973 paper titled A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations
Kogge–Stone_adder
a description for a quantum Turing machine, as well as specifying an algorithm designed to run on a quantum computer Paul Dirac (1902–1984): British
List_of_agnostics
zero matrix Algorithms for matrix multiplication: Strassen algorithm Coppersmith–Winograd algorithm Cannon's algorithm — a distributed algorithm, especially
List of numerical analysis topics
List_of_numerical_analysis_topics
2026 film by Kane Parsons
the labyrinthine Backrooms and the COVID-19 lockdowns, recommendation algorithms, and generative AI. In May 2026, Parsons confirmed that he was not finished
Backrooms_(film)
Overview of the events of 2020 in science
events at the time. Researchers report to have developed a predictive algorithm which can show in visualizations how combinations of genetic mutations
April–June_2020_in_science
Computing circuit
Multiplication algorithm Booth's multiplication algorithm Wallace tree Dadda multiplier Booth encoding Divider (÷) Binary Divider Division algorithm Bitwise
Adder–subtractor
2025 suspension of an American talk show
requiring transparency from platforms about changes to recommendation algorithms and their decisions to block or demonetize users; and calling for ban
Suspension of Jimmy Kimmel Live!
Suspension_of_Jimmy_Kimmel_Live!
Website which tracks film box office revenue
industry data website that tracks box office revenue in a systematic, algorithmic way, a publication of Nash Information Services LLC. The company also
The_Numbers_(website)
Root-finding algorithm
method (Interpolate Truncate and Project method) is the first root-finding algorithm that achieves the superlinear convergence of the secant method while retaining
ITP_method
Right to have an algorithm explained
In the regulation of algorithms, particularly artificial intelligence and its subfield of machine learning, a right to [an] explanation is a right to be
Right_to_explanation
Collective perception of a group of people
indicates the correct answer. It was found that the "surprisingly popular" algorithm reduces errors by 21.3 percent in comparison to simple majority votes
Wisdom_of_the_crowd
2015 American film
Garriga to sabotage a rival team by selling them a faulty fuel-burning algorithm. There, he unexpectedly reunites with Jess, who is now romantically involved
Focus_(2015_film)
Digital circuit implementation method
Multiplication algorithm Booth's multiplication algorithm Wallace tree Dadda multiplier Booth encoding Divider (÷) Binary Divider Division algorithm Bitwise
Carry-select_adder
1941, MS 1942 Lloyd R. Welch, PhD 1958; co-inventor of the Baum-Welch algorithm Erik Winfree, PhD 1998; faculty; awarded MacArthur Fellowship W. Hugh
List of California Institute of Technology people
List_of_California_Institute_of_Technology_people
2025 Marvel Studios film
(May 24, 2023). "Poker Face DP Steve Yedlin on Creating His Own Imaging Algorithm, Drawing From '70s Influences, and Carving Out a Visual Niche for Himself"
Thunderbolts*
American YouTube channel for children
(FTC), YouTube began implementing major changes to its recommendation algorithm, data collection, and ad targeting for children's content. The changes
Cocomelon
American social networking service
mid-2008, an algorithmic lists of trending topics among users. A word or phrase mentioned can become "trending topic" based on an algorithm. Because a relatively
X_(social_network)
Root-finding algorithm in numerical analysis
In numerical analysis, Ridders' method is a root-finding algorithm based on the false position method and the use of an exponential function to successively
Ridders'_method
The predictions were then moderated by the regulator, Ofqual, using an algorithm designed to eliminate grade inflation. This gave an overall pass rate
2020_in_the_United_Kingdom
American media company
000 to the first developer of a video recommendation algorithm that could beat its existing algorithm Cinematch, at predicting customer ratings by more than
Netflix,_Inc.
EU regulation on information privacy
SSRN 2903469. Edwards, Lilian; Veale, Michael (2017). "Slave to the algorithm? Why a "right to an explanation" is probably not the remedy you are looking
General Data Protection Regulation
General_Data_Protection_Regulation
Integration of software development and operations
Thorne of Google". Retrieved 24 July 2024. Analyzing the DNA of DevOps, Brent Aaron Reed, Willy Schaub, 2018-11-14. Gene Kim; Patrick Debois; John Willis;
DevOps
Field of study to extract knowledge from data
computing, scientific methods, processing, scientific visualization, algorithms, coding (like Python, SQL, and R), and systems to extract or extrapolate
Data_science
Game engine
demo, was replaced with a similar but less computationally expensive algorithm due to performance concerns. On March 19, 2014, at the Game Developers
Unreal_Engine_4
Data ethics, artificial intelligence and robotics researcher
senior researcher in data ethics, artificial intelligence, robotics, algorithms and regulation at the Oxford Internet Institute. She is a former Fellow
Sandra_Wachter
2024 European Union regulation
fundamental rights before an AI system is deployed. Earlier work on algorithmic impact assessments has suggested that such tools should identify which
Artificial_Intelligence_Act
American computer scientist
significant new algorithms including the Jenkins–Traub algorithm for polynomial zeros, as well as the Shaw–Traub, Kung–Traub, and Brent–Traub algorithms. One of
Joseph_F._Traub
2025 music award ceremony
Night" (BJ the Chicago Kid and Coco Jones) (S) Dernst "D'Mile" Emile II Algorithm (Lucky Daye) (A) "Bar Song" (Koe Wetzel) (T) "Die with a Smile" (Lady
67th_Annual_Grammy_Awards
Ongoing theorised stock market bubble
Bunn, Philip; Davis, Steven J.; Foster, Kevin M.; Jalca, Aaron; Meyer, Brent H.; Mizen, Paul (February 2026), Firm Data on AI (Working Paper), Working
AI_bubble
Software for computational chemistry
systems on conventional computer clusters. The code uses novel parallel algorithms and numerical methods to achieve high performance on platforms containing
Desmond_(software)
Java math library
optimization. It implements a parallel version of the adaptive strassen's algorithm for fast matrix multiplication. SuanShu has been quoted and used in a
SuanShu_numerical_library
I've Ever Had Making a Record": Natalie Imbruglia Announces New Album Algorithm". Rolling Stone Australia. Retrieved April 29, 2026. Hoess, Tabea (May
List_of_2026_albums
Israeli-American computer scientist
of PRAM algorithmic theory, Uzi Vishkin contributed the formative work-depth think-parallel framework, many fundamental parallel algorithms and the PRAM-on-chip
Uzi_Vishkin
First planet from the Sun
Retrieved March 19, 2023. Wagner, Sam; Wie, Bong (November 2015). "Hybrid Algorithm for Multiple Gravity-Assist and Impulsive Delta-V Maneuvers". Journal
Mercury_(planet)
Irish YouTuber (born 1990)
over algorithm tests". BBC News. Retrieved 28 May 2018. Weiss, Geoff (24 May 2018). "YouTube Confirms Test Of Subscriptions Feed Driven By Algorithm And
Jacksepticeye
services that "coordinate" rents through the passage of the Preventing the Algorithmic Facilitation of Rental Housing Cartels Act, and also call on Congress
2024 United States presidential election
2024_United_States_presidential_election
Operation of checking the integrity of file
File verification is the process of using an algorithm for verifying the integrity of a computer file, usually by checksum. This can be done by comparing
File_verification
Probability distribution
variates samples from a binomial distribution is to use an inversion algorithm. To do so, one must calculate the probability that Pr(X = k) for all values
Binomial_distribution
Prescription drug for pregnancy morning sickness
pregnancy. Evidence-based treatment algorithm" and "Treatment of nausea and vomiting in pregnancy. An updated algorithm," have subsequently come under critical
Pyridoxine/doxylamine
2017 American film by James Ponsoldt
from the original on January 4, 2017. Retrieved January 3, 2017. Lang, Brent (February 9, 2016). "EuropaCorp Buys Domestic Rights to 'The Circle' With
The_Circle_(2017_film)
Type of parallel computing architecture of tightly coupled nodes
multiplication or data sorting tasks. They are also used for dynamic programming algorithms, used in DNA and protein sequence analysis. A systolic array typically
Systolic_array
2022 American film by Steven Soderbergh
controversially makes use of human monitoring to improve the device's search algorithm. Amygdala plans to soon hold an initial public offering, which stands
Kimi_(film)
Season of television series
sues Pied Piper, alleging that Richard (Thomas Middleditch) created the algorithm on Hooli property during company time. Richard eventually decides to work
Silicon_Valley_season_2
institucional dificulta regulamentação da IA, alerta estudo" [Lack of algorithmic and institutional transparency hinders AI regulation, study warns]. SindPD
Donald_Trump_and_fascism
Hypothesis in computational complexity theory
Computational hardness assumptions are also useful for guiding algorithm designers: a simple algorithm is unlikely to refute a well-studied computational hardness
Computational hardness assumption
Computational_hardness_assumption
American visual effects and computer animation studio (1987–2021)
effects in manually; Troubetzkoy and Ludwig adapted MAGI's ray tracing, algorithms which simulate the physical properties of light in order to produce lighting
Blue_Sky_Studios
BRENTS ALGORITHM
BRENTS ALGORITHM
Male
Portuguese
Portuguese form of Celtic Brennus, BRENO means "king."
Girl/Female
American, Australian, Christian, Gaelic, Irish
Little Raven; Sword; Raven Maid; Dark-haired; Black Haired; Similar to Brenda; Beacon on the Hill
Male
English
Habitational surname transferred to forename use, composed of the Old English elements bryne, BRENTON means "fire, flame," and tun "enclosure, settlement, town," hence "fire town."
Boy/Male
American, Australian, British, Celtic, English
Hilltop; Mount; Variant of Brent
Male
English
English unisex name BRETT means, "a Breton."
Male
English
Variant spelling of English Brandt, BRANT means "blade, sword."
Surname or Lastname
English
English : variant of Brent.
Female
English
Altered form of Irish Prunty, a form of Gaelic Ó Proinntigh, BRONTE means "descendant of Proinnteach," a personal name that was originally a byname meaning "banquet hall (denoting a "generous person")." In Prunty's altered form (Bronte), the name is identical to the Sicilian place name and the name of a mythological horse of the Sun, meaning "thunder." But Prunty was probably purposely altered to Bronte by bearers of the name who admired Lord Nelson who was awarded the title of Duke of Bronte in 1799 by Ferdinand, King of the Two Sicilies.Â
Male
English
English topographic surname transferred to forename use, TRENT means "lives on the river-bank."
Male
German
Variant spelling of Low German Bernd, BERNT means "bold as a bear."
Male
Portuguese
Pet form of Portuguese Benjamim, BENTO means "blessed."
Female
English
Feminine form of Irish Brian, BRENNA means "high hill."
Boy/Male
American, Australian, British, Celtic, Chinese, English
Hilltop; Variant of Brent
Boy/Male
Latin Russian
Victorious.
Male
Welsh
Welsh form of Celtic Brennus, BRENIN means "king."
Surname or Lastname
English
English : topographic name for someone who lived by a piece of ground that had been cleared by fire, from Middle English brend, past participle of brennen ‘to burn’.English : habitational name from any of the places in Devon and Somerset named Brent, probably from Old English brant ‘steep’, or from an old Celtic (British) word meaning ‘hill’, ‘high place’.English : byname or nickname for a criminal who had been branded; compare Henry Brendcheke (‘burned cheek’), recorded in Northumbria in 1279.English : Giles Brent (died 1672) came from Gloucestershire, England, to MD in 1638.
Female
English
 Old Irish and Scottish name believed to be of Scandinavian origin, from Old Norse brandr, BRENDA means "sword."Â
Boy/Male
American, Australian, British, Celtic, Chinese, Christian, English, Jamaican
Hilltop; Mount; Variant of Brent; Settlement Associated with Bryni; Fire; Flame
Male
English
Native of Brittany
Male
German
Variant form of German Bruno, BRUNS means "brown."
BRENTS ALGORITHM
BRENTS ALGORITHM
Girl/Female
British, English
Consecrated
Girl/Female
Australian, Greek
Light; Torch; Moon Elope
Boy/Male
Tamil
Honest, Sincere, One whos steadfast in happiness and sorrow
Boy/Male
Indian, Kannada, Tamil
Ruler of the Pandiya Naadu; Pron; Paandiyan
Boy/Male
Hindu
Kind hearted
Boy/Male
Hindu
Smiling girl, Cheerful, Joyful
Boy/Male
Hindu
Girl/Female
Indian
Snow queen.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Crystal Clear; Lord Krishna
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Kashmiri, Malayalam, Marathi, Sanskrit, Sindhi, Tamil, Telugu, Traditional
Ruler of the Gods; Lord Sun; Lord Shiva; Lord Indra; Lord Vishnu
BRENTS ALGORITHM
BRENTS ALGORITHM
BRENTS ALGORITHM
BRENTS ALGORITHM
BRENTS ALGORITHM
n.
The act of breathing naturally or freely; the power or capacity to breathe freely; as, I am out of breath.
n.
To grant the possession and enjoyment of, for a rent; to lease; as, the owwner of an estate or house rents it.
n.
The fore part of the body, between the neck and the belly; the chest; as, the breast of a man or of a horse.
n.
Anything resembling the human breast, or bosom; the front or forward part of anything; as, a chimney breast; a plow breast; the breast of a hill.
v. i.
To be leased, or let for rent; as, an estate rents for five hundred dollars a year.
a.
Deep as from the breast to the feet; as high as the breast.
n.
A species of wild goose (Branta bernicla) -- called also brent and brand goose. The name is also applied to other related species.
v. t.
To meet, with the breast; to struggle with or oppose manfully; as, to breast the storm or waves.
v. t.
The heat, or utmost violence, of an onset; the strength or greatest fury of any contention; as, the brunt of a battle.
n.
A brant. See Brant.
n.
To take and hold under an agreement to pay rent; as, the tennant rents an estate of the owner.
n.
One who, or that which, breeds, produces, brings up, etc.
a.
High as the breast.
v. t. & i.
Alt. of Brenne
n.
Alt. of Breast
a.
A bounding in bents, or the stalks of coarse, stiff, withered grass; as, benty fields.
n.
The power of singing; a musical voice; -- so called, probably, from the connection of the voice with the lungs, which lie within the breast.
imp. & p. p.
of Brenne
a.
Alt. of Brant