Received: from 173-13-139-235-sfba.hfc.comcastbusiness.net ([173.13.139.235]:36784 helo=jukni.digitalkingdom.org) by stodi.digitalkingdom.org with smtp (Exim 4.85) (envelope-from ) id 1aDREs-0002if-L4; Sun, 27 Dec 2015 22:25:08 -0800 Received: by jukni.digitalkingdom.org (sSMTP sendmail emulation); Sun, 27 Dec 2015 22:25:02 -0800 From: "Apache" Date: Sun, 27 Dec 2015 22:25:02 -0800 To: webmaster@lojban.org, curtis289@att.net Subject: [jvsw] Definition Edited At Word ji'i'u -- By gleki Bcc: jbovlaste-admin@lojban.org Message-ID: <5680d5be.QOaQi6DFe6KJCGfc%webmaster@lojban.org> User-Agent: Heirloom mailx 12.5 7/5/10 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Spam-Score: 0.5 (/) X-Spam_score: 0.5 X-Spam_score_int: 5 X-Spam_bar: / X-Spam-Report: Spam detection software, running on the system "stodi.digitalkingdom.org", has NOT identified this incoming email as spam. The original message has been attached to this so you can view it or label similar future email. If you have any questions, see the administrator of that system for details. Content preview: In jbovlaste, the user gleki has edited a definition of "ji'i'u" in the language "English". Differences: 5,5c5,5 < x must be a real number; n must be exactly one of exactly the following: -1, 0, 1; m must be 0 xor 1 if defined at all; t must be an integer if defined at all; the output is a real number. n does not have a contextless default value. m is defined iff n = 0; if m is undefined, then its slot is automatically and implicitly deleted from this word in that context (so the operator is at-most-3-ary and a third argument would fill the 't' slot under the condition that t is defined). If m is defined, then its contextless default value is m = 0. It first determines the base being used for interpretation of digit strings (determined by context or by explicit specification (JUHAU)) for x; this determination takes place even before inputs are accepted after x; let this base be represented by b throughout this description. If the base is not a positional system wherein each digit represents a corresponding multiple of a fixed natural number raised to the power of its position (as determined relative to the radix point) and wherein the overall number is the sum of these results/representands, then t is defined; if the base is sufficiently bad or unclear, then t is undefined; if t is undefined, then its slot is automatically and implicitly deleted from this word in that context (so the operator is at-most-3-ary and its input acceptance is terminated by the n or m slot, whichever one is later yet defined) and b = 1 for the purposes of this definition (but not for any digit-to-number interpretation/conversion!). If t is defined, then its contextless default value is t = 0. The rounding function, determined by n, is performed (b^(t))*x. If n = 1, then the rounding function is the ceiling function: (b^(t))*x is mapped to the least integer that is greater than or equal to it. If n = -1, then the rounding function is the floor function: (b^(t))*x is mapped to the greatest integer that is less than or equal to it. These integers are both determined by the ordering and metric. If n = 0, then the rounding function maps [...] Content analysis details: (0.5 points, 5.0 required) pts rule name description ---- ---------------------- -------------------------------------------------- 0.0 URIBL_BLOCKED ADMINISTRATOR NOTICE: The query to URIBL was blocked. See http://wiki.apache.org/spamassassin/DnsBlocklists#dnsbl-block for more information. [URIs: lojban.org] 1.4 RCVD_IN_BRBL_LASTEXT RBL: No description available. [173.13.139.235 listed in bb.barracudacentral.org] -1.9 BAYES_00 BODY: Bayes spam probability is 0 to 1% [score: 0.0016] 1.0 RDNS_DYNAMIC Delivered to internal network by host with dynamic-looking rDNS In jbovlaste, the user gleki has edited a definition of "ji'i'u" in the language "English". Differences: 5,5c5,5 < =09=09x must be a real number; n must be exactly one of exactly the f= ollowing: -1, 0, 1; m must be 0 xor 1 if defined at all; t must be an i= nteger if defined at all; the output is a real number. n does not have = a contextless default value. m is defined iff n =3D 0; if m is undefine= d, then its slot is automatically and implicitly deleted from this word= in that context (so the operator is at-most-3-ary and a third argument= would fill the 't' slot under the condition that t is defined). If m i= s defined, then its contextless default value is m =3D 0. It first dete= rmines the base being used for interpretation of digit strings (determi= ned by context or by explicit specification (JUHAU)) for x; this determ= ination takes place even before inputs are accepted after x; let this b= ase be represented by b throughout this description. If the base is not= a positional system wherein each digit represents a corresponding mult= iple of a fixed natural number raised to the power of its position (as = determined relative to the radix point) and wherein the overall number = is the sum of these results/representands, then t is defined; if the ba= se is sufficiently bad or unclear, then t is undefined; if t is undefin= ed, then its slot is automatically and implicitly deleted from this wor= d in that context (so the operator is at-most-3-ary and its input accep= tance is terminated by the n or m slot, whichever one is later yet defi= ned) and b =3D 1 for the purposes of this definition (but not for any d= igit-to-number interpretation/conversion!). If t is defined, then its c= ontextless default value is t =3D 0. The rounding function, determined= by n, is performed (b^(t))*x. If n =3D 1, then the rounding function i= s the ceiling function: (b^(t))*x is mapped to the least integer that i= s greater than or equal to it. If n =3D -1, then the rounding function= is the floor function: (b^(t))*x is mapped to the greatest integer tha= t is less than or equal to it. These integers are both determined by th= e ordering and metric. If n =3D 0, then the rounding function maps (b^(= t))*x to the integer that minimizes the metric distance between itself = and (b^(t))*x if a unique such integer exists (id est: (b^(t))*x is map= ped to the nearest integer, where "nearest"-ness is determined accordin= g to the order and metric); if no such unique integer exists, then (b^(= t))*x is mapped to the unique integer among these aforementioned option= s for which there exists an integer Z such that 2Z+m is the integer in = question; if no unique such integer exists, then the function is undefi= ned. Thus n =3D 0 produces the commonly used unbiased nearest-integer r= ounding function. In each of these cases, the output of the rounding f= unction is then multiplied by b^(-t). Thus, it rounds at the $t$th dig= it, so to speak. The order on, and the operators and metric endowing, t= he metric space and field of all real numbers is determined by context = or by explicit specification. --- > =09=09x must be a real number; n must be exactly one of exactly the f= ollowing: -1, 0, 1; m must be 0 xor 1 if defined at all; t must be an i= nteger if defined at all; the output is a real number. n does not have = a contextless default value. m is defined iff n =3D 0; if m is undefine= d, then its slot is automatically and implicitly deleted from this word= in that context (so the operator is at-most-3-ary and a third argument= would fill the 't' slot under the condition that t is defined). If m i= s defined, then its contextless default value is m =3D 0. It first dete= rmines the base being used for interpretation of digit strings (determi= ned by context or by explicit specification (JUHAU)) for x; this determ= ination takes place even before inputs are accepted after x; let this b= ase be represented by b throughout this description. If the base is not= a positional system wherein each digit represents a corresponding mult= iple of a fixed natural number raised to the power of its position (as = determined relative to the radix point) and wherein the overall number = is the sum of these results/representands, then t is defined; if the ba= se is sufficiently bad or unclear, then t is undefined; if t is undefin= ed, then its slot is automatically and implicitly deleted from this wor= d in that context (so the operator is at-most-3-ary and its input accep= tance is terminated by the n or m slot, whichever one is later yet defi= ned) and b =3D 1 for the purposes of this definition (but not for any d= igit-to-number interpretation/conversion!). If t is defined, then its c= ontextless default value is t =3D 0. The rounding function, determined= by n, is performed $(b^(t))*x$. If n =3D 1, then the rounding function= is the ceiling function: $(b^(t))*x$ is mapped to the least integer th= at is greater than or equal to it. If n =3D -1, then the rounding func= tion is the floor function: $(b^(t))*x$ is mapped to the greatest integ= er that is less than or equal to it. These integers are both determined= by the ordering and metric. If n =3D 0, then the rounding function map= s $(b^(t))*x$ to the integer that minimizes the metric distance between= itself and $(b^(t))*x$ if a unique such integer exists (id est: $(b^(t= ))*x$ is mapped to the nearest integer, where "nearest"-ness is determi= ned according to the order and metric); if no such unique integer exist= s, then $(b^(t))*x$ is mapped to the unique integer among these aforeme= ntioned options for which there exists an integer Z such that 2Z+m is t= he integer in question; if no unique such integer exists, then the func= tion is undefined. Thus n =3D 0 produces the commonly used unbiased nea= rest-integer rounding function. In each of these cases, the output of = the rounding function is then multiplied by $b^(-t)$. Thus, it rounds = at the $t$th digit, so to speak. The order on, and the operators and me= tric endowing, the metric space and field of all real numbers is determ= ined by context or by explicit specification. Old Data: =09Definition: =09=09mekso at-most-4-ary operator: a rounding function; ordered input = list is $(x,n,m,t)$ and the output is $b^{(-t)} *$ round($b^t * x$), wi= th rounding preference $n$ and where the fractional part of $b^t * x$ = being 1/2 causes the function to map $b^t * x$ to the nearest integer o= f form $2Z+m$, for base b and an integer Z determined by context =09Notes: =09=09x must be a real number; n must be exactly one of exactly the fol= lowing: -1, 0, 1; m must be 0 xor 1 if defined at all; t must be an int= eger if defined at all; the output is a real number. n does not have a = contextless default value. m is defined iff n =3D 0; if m is undefined,= then its slot is automatically and implicitly deleted from this word i= n that context (so the operator is at-most-3-ary and a third argument w= ould fill the 't' slot under the condition that t is defined). If m is = defined, then its contextless default value is m =3D 0. It first determ= ines the base being used for interpretation of digit strings (determine= d by context or by explicit specification (JUHAU)) for x; this determin= ation takes place even before inputs are accepted after x; let this bas= e be represented by b throughout this description. If the base is not a= positional system wherein each digit represents a corresponding multip= le of a fixed natural number raised to the power of its position (as de= termined relative to the radix point) and wherein the overall number is= the sum of these results/representands, then t is defined; if the base= is sufficiently bad or unclear, then t is undefined; if t is undefined= , then its slot is automatically and implicitly deleted from this word = in that context (so the operator is at-most-3-ary and its input accepta= nce is terminated by the n or m slot, whichever one is later yet define= d) and b =3D 1 for the purposes of this definition (but not for any dig= it-to-number interpretation/conversion!). If t is defined, then its con= textless default value is t =3D 0. The rounding function, determined b= y n, is performed (b^(t))*x. If n =3D 1, then the rounding function is = the ceiling function: (b^(t))*x is mapped to the least integer that is = greater than or equal to it. If n =3D -1, then the rounding function i= s the floor function: (b^(t))*x is mapped to the greatest integer that = is less than or equal to it. These integers are both determined by the = ordering and metric. If n =3D 0, then the rounding function maps (b^(t)= )*x to the integer that minimizes the metric distance between itself an= d (b^(t))*x if a unique such integer exists (id est: (b^(t))*x is mappe= d to the nearest integer, where "nearest"-ness is determined according = to the order and metric); if no such unique integer exists, then (b^(t)= )*x is mapped to the unique integer among these aforementioned options = for which there exists an integer Z such that 2Z+m is the integer in qu= estion; if no unique such integer exists, then the function is undefine= d. Thus n =3D 0 produces the commonly used unbiased nearest-integer rou= nding function. In each of these cases, the output of the rounding fun= ction is then multiplied by b^(-t). Thus, it rounds at the $t$th digit= , so to speak. The order on, and the operators and metric endowing, the= metric space and field of all real numbers is determined by context or= by explicit specification. =09Jargon: =09=09 =09Gloss Keywords: =09=09Word: ceiling function, In Sense:=20 =09=09Word: floor function, In Sense:=20 =09=09Word: nearest integer function, In Sense:=20 =09=09Word: rounding function, In Sense: rounds at given digit =09Place Keywords: New Data: =09Definition: =09=09mekso at-most-4-ary operator: a rounding function; ordered input = list is $(x,n,m,t)$ and the output is $b^{(-t)} *$ round($b^t * x$), wi= th rounding preference $n$ and where the fractional part of $b^t * x$ = being 1/2 causes the function to map $b^t * x$ to the nearest integer o= f form $2Z+m$, for base b and an integer Z determined by context =09Notes: =09=09x must be a real number; n must be exactly one of exactly the fol= lowing: -1, 0, 1; m must be 0 xor 1 if defined at all; t must be an int= eger if defined at all; the output is a real number. n does not have a = contextless default value. m is defined iff n =3D 0; if m is undefined,= then its slot is automatically and implicitly deleted from this word i= n that context (so the operator is at-most-3-ary and a third argument w= ould fill the 't' slot under the condition that t is defined). If m is = defined, then its contextless default value is m =3D 0. It first determ= ines the base being used for interpretation of digit strings (determine= d by context or by explicit specification (JUHAU)) for x; this determin= ation takes place even before inputs are accepted after x; let this bas= e be represented by b throughout this description. If the base is not a= positional system wherein each digit represents a corresponding multip= le of a fixed natural number raised to the power of its position (as de= termined relative to the radix point) and wherein the overall number is= the sum of these results/representands, then t is defined; if the base= is sufficiently bad or unclear, then t is undefined; if t is undefined= , then its slot is automatically and implicitly deleted from this word = in that context (so the operator is at-most-3-ary and its input accepta= nce is terminated by the n or m slot, whichever one is later yet define= d) and b =3D 1 for the purposes of this definition (but not for any dig= it-to-number interpretation/conversion!). If t is defined, then its con= textless default value is t =3D 0. The rounding function, determined b= y n, is performed $(b^(t))*x$. If n =3D 1, then the rounding function i= s the ceiling function: $(b^(t))*x$ is mapped to the least integer that= is greater than or equal to it. If n =3D -1, then the rounding functi= on is the floor function: $(b^(t))*x$ is mapped to the greatest integer= that is less than or equal to it. These integers are both determined b= y the ordering and metric. If n =3D 0, then the rounding function maps = $(b^(t))*x$ to the integer that minimizes the metric distance between i= tself and $(b^(t))*x$ if a unique such integer exists (id est: $(b^(t))= *x$ is mapped to the nearest integer, where "nearest"-ness is determine= d according to the order and metric); if no such unique integer exists,= then $(b^(t))*x$ is mapped to the unique integer among these aforement= ioned options for which there exists an integer Z such that 2Z+m is the= integer in question; if no unique such integer exists, then the functi= on is undefined. Thus n =3D 0 produces the commonly used unbiased neare= st-integer rounding function. In each of these cases, the output of th= e rounding function is then multiplied by $b^(-t)$. Thus, it rounds at= the $t$th digit, so to speak. The order on, and the operators and metr= ic endowing, the metric space and field of all real numbers is determin= ed by context or by explicit specification. =09Jargon: =09=09 =09Gloss Keywords: =09=09Word: ceiling function, In Sense:=20 =09=09Word: floor function, In Sense:=20 =09=09Word: nearest integer function, In Sense:=20 =09=09Word: rounding function, In Sense: rounds at given digit =09Place Keywords: You can go to to see it.