{"action":"created","comment":{"url":"https://api.github.com/repos/JuliaLang/julia/pulls/comments/47266482","id":47266482,"diff_hunk":"@@ -404,13 +404,124 @@ invdigamma(x::Float32) = Float32(invdigamma(Float64(x)))\n invdigamma(x::Real) = invdigamma(Float64(x))\n @vectorize_1arg Real invdigamma\n \n-function beta(x::Number, w::Number)\n-    yx, sx = lgamma_r(x)\n-    yw, sw = lgamma_r(w)\n-    yxw, sxw = lgamma_r(x+w)\n-    return exp(yx + yw - yxw) * (sx*sw*sxw)\n+const MAXGAM = 171.624376956302725\n+const ASYMP_FACTOR = 1e6\n+\n+function beta(a::Number, b::Number)","path":"base/special/gamma.jl","position":12,"original_position":12,"commit_id":"86017108f88736c075193985dcc61687869221f5","original_commit_id":"86017108f88736c075193985dcc61687869221f5","user":{"login":"stevengj","id":2913679,"avatar_url":"https://avatars.githubusercontent.com/u/2913679?v=3","gravatar_id":"","url":"https://api.github.com/users/stevengj","html_url":"https://github.com/stevengj","followers_url":"https://api.github.com/users/stevengj/followers","following_url":"https://api.github.com/users/stevengj/following{/other_user}","gists_url":"https://api.github.com/users/stevengj/gists{/gist_id}","starred_url":"https://api.github.com/users/stevengj/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/stevengj/subscriptions","organizations_url":"https://api.github.com/users/stevengj/orgs","repos_url":"https://api.github.com/users/stevengj/repos","events_url":"https://api.github.com/users/stevengj/events{/privacy}","received_events_url":"https://api.github.com/users/stevengj/received_events","type":"User","site_admin":false},"body":"When you port something, you should always have a comment indicating the original source and the license thereof.","created_at":"2015-12-10T18:47:25Z","updated_at":"2015-12-10T18:47:25Z","html_url":"https://github.com/JuliaLang/julia/pull/14349#discussion_r47266482","pull_request_url":"https://api.github.com/repos/JuliaLang/julia/pulls/14349","_links":{"self":{"href":"https://api.github.com/repos/JuliaLang/julia/pulls/comments/47266482"},"html":{"href":"https://github.com/JuliaLang/julia/pull/14349#discussion_r47266482"},"pull_request":{"href":"https://api.github.com/repos/JuliaLang/julia/pulls/14349"}}},"pull_request":{"url":"https://api.github.com/repos/JuliaLang/julia/pulls/14349","id":53262353,"html_url":"https://github.com/JuliaLang/julia/pull/14349","diff_url":"https://github.com/JuliaLang/julia/pull/14349.diff","patch_url":"https://github.com/JuliaLang/julia/pull/14349.patch","issue_url":"https://api.github.com/repos/JuliaLang/julia/issues/14349","number":14349,"state":"open","locked":false,"title":"[WIP] port of Cephes implementation of Beta function (fixes #14256)","user":{"login":"CarloLucibello","id":7014210,"avatar_url":"https://avatars.githubusercontent.com/u/7014210?v=3","gravatar_id":"","url":"https://api.github.com/users/CarloLucibello","html_url":"https://github.com/CarloLucibello","followers_url":"https://api.github.com/users/CarloLucibello/followers","following_url":"https://api.github.com/users/CarloLucibello/following{/other_user}","gists_url":"https://api.github.com/users/CarloLucibello/gists{/gist_id}","starred_url":"https://api.github.com/users/CarloLucibello/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/CarloLucibello/subscriptions","organizations_url":"https://api.github.com/users/CarloLucibello/orgs","repos_url":"https://api.github.com/users/CarloLucibello/repos","events_url":"https://api.github.com/users/CarloLucibello/events{/privacy}","received_events_url":"https://api.github.com/users/CarloLucibello/received_events","type":"User","site_admin":false},"body":"port of https://github.com/scipy/scipy/blob/0cff7a5fe6226668729fc2551105692ce114c2b3/scipy/special/cephes/beta.c#L61-L133\r\n\r\nCopyright issues (none actually) are discussed in #14256 \r\n\r\nsee also #14165 for its relation with the binomial function\r\n\r\nComments appreciated @tkelman @stevengj @andreasnoack \r\n\r\n**TODO**\r\n- extend test coverage\r\n- check if it works correctly for complex arguments\r\n- address type instability (help needed here):\r\n```julia\r\njulia> @code_warntype beta(3.,2.)\r\nVariables:\r\n  a::Float64\r\n  b::Float64\r\n  #s5::Bool\r\n  #s8::Bool\r\n  #s1::Int64\r\n  y::Any\r\n  s::Any\r\n  #s6::Bool\r\n  #s7::Bool\r\n  #s2::Any\r\n  #s3::Any\r\n  yb::Any\r\n  sb::Any\r\n  #s4::Any\r\n  ya::Any\r\n  sa::Any\r\n  ######fy#1781#7325#7333::Float64\r\n  ######fy#1781#7325#7334::Float64\r\n\r\nBody:\r\n  begin  # /home/carlo/Git/julia/beta.jl, line 6:\r\n      NewvarNode(symbol(\"#s5\"))\r\n      NewvarNode(symbol(\"#s8\"))\r\n      NewvarNode(symbol(\"#s1\"))\r\n      NewvarNode(:y)\r\n      NewvarNode(:s)\r\n      NewvarNode(symbol(\"#s6\"))\r\n      NewvarNode(symbol(\"#s7\"))\r\n      NewvarNode(symbol(\"#s2\"))\r\n      NewvarNode(symbol(\"#s3\"))\r\n      NewvarNode(:yb)\r\n      NewvarNode(:sb)\r\n      NewvarNode(symbol(\"#s4\"))\r\n      NewvarNode(:ya)\r\n      NewvarNode(:sa)\r\n      unless (Base.le_float)(a::Float64,0.0)::Bool goto 1 # floatfuncs.jl, line 27: # float.jl, line 309: # float.jl, line 268:\r\n      ######fy#1781#7325#7333 = (Base.box)(Float64,(Base.sitofp)(Float64,0)) # float.jl, line 269:\r\n      unless (Base.box)(Base.Bool,(Base.and_int)((Base.eq_float)((Base.box)(Base.Float64,(Base.trunc_llvm)(a::Float64)),a::Float64)::Bool,(Base.box)(Base.Bool,(Base.and_int)((Base.eq_float)((Base.box)(Base.Float64,(Base.sub_float)(a::Float64,a::Float64)),######fy#1781#7325#7333::Float64)::Bool,0 === (Base.box)(Int64,(Base.fptosi)(Int64,######fy#1781#7325#7333::Float64))::Bool)))) goto 0\r\n      return (Main.beta_negint)(a::Float64,b::Float64)::Any\r\n      0: \r\n      goto 1\r\n      1:  # /home/carlo/Git/julia/beta.jl, line 7:\r\n      unless (Base.le_float)(b::Float64,0.0)::Bool goto 3 # floatfuncs.jl, line 27: # float.jl, line 309: # float.jl, line 268:\r\n      ######fy#1781#7325#7334 = (Base.box)(Float64,(Base.sitofp)(Float64,0)) # float.jl, line 269:\r\n      unless (Base.box)(Base.Bool,(Base.and_int)((Base.eq_float)((Base.box)(Base.Float64,(Base.trunc_llvm)(b::Float64)),b::Float64)::Bool,(Base.box)(Base.Bool,(Base.and_int)((Base.eq_float)((Base.box)(Base.Float64,(Base.sub_float)(b::Float64,b::Float64)),######fy#1781#7325#7334::Float64)::Bool,0 === (Base.box)(Int64,(Base.fptosi)(Int64,######fy#1781#7325#7334::Float64))::Bool)))) goto 2\r\n      return (Main.beta_negint)(b::Float64,a::Float64)::Any\r\n      2: \r\n      goto 3\r\n      3:  # /home/carlo/Git/julia/beta.jl, line 9:\r\n      unless (Base.lt_float)((Base.box)(Base.Float64,(Base.abs_float)(a::Float64)),(Base.box)(Base.Float64,(Base.abs_float)(b::Float64)))::Bool goto 4 # /home/carlo/Git/julia/beta.jl, line 10:\r\n      GenSym(0) = b::Float64\r\n      GenSym(1) = a::Float64\r\n      a = GenSym(0)\r\n      b = GenSym(1)\r\n      4:  # /home/carlo/Git/julia/beta.jl, line 13:\r\n      unless (Base.lt_float)((Base.box)(Base.Float64,(Base.mul_float)(Main.ASYMP_FACTOR,(Base.box)(Base.Float64,(Base.abs_float)(b::Float64)))),(Base.box)(Base.Float64,(Base.abs_float)(a::Float64)))::Bool goto 5\r\n      #s5 = (Base.lt_float)(Main.ASYMP_FACTOR,a::Float64)::Bool\r\n      goto 6\r\n      5: \r\n      #s5 = false\r\n      6: \r\n      unless #s5::Bool goto 7 # /home/carlo/Git/julia/beta.jl, line 15:\r\n      GenSym(2) = (Main.lbeta_asymp)(a::Float64,b::Float64)::Tuple{Any,Any}\r\n      #s1 = 1\r\n      GenSym(21) = (Base.getfield)(GenSym(2),1)::Any\r\n      GenSym(22) = (Base.box)(Base.Int,(Base.add_int)(1,1))\r\n      y = GenSym(21)\r\n      #s1 = GenSym(22)\r\n      GenSym(23) = (Base.getfield)(GenSym(2),2)::Any\r\n      GenSym(24) = (Base.box)(Base.Int,(Base.add_int)(2,1))\r\n      s = GenSym(23)\r\n      #s1 = GenSym(24) # /home/carlo/Git/julia/beta.jl, line 16:\r\n      return s * (Main.exp)(y)::Any::Any\r\n      7:  # /home/carlo/Git/julia/beta.jl, line 19:\r\n      y = (Base.box)(Base.Float64,(Base.add_float)(a::Float64,b::Float64)) # /home/carlo/Git/julia/beta.jl, line 20:\r\n      #s6 = (Base.lt_float)(Main.MAXGAM,(Base.box)(Base.Float64,(Base.abs_float)(y::Float64)))::Bool\r\n      unless #s6::Bool goto 8\r\n      #s8 = #s6::Bool\r\n      goto 10\r\n      8: \r\n      #s7 = (Base.lt_float)(Main.MAXGAM,(Base.box)(Base.Float64,(Base.abs_float)(a::Float64)))::Bool\r\n      unless #s7::Bool goto 9\r\n      #s8 = #s7::Bool\r\n      goto 10\r\n      9: \r\n      #s8 = (Base.lt_float)(Main.MAXGAM,(Base.box)(Base.Float64,(Base.abs_float)(b::Float64)))::Bool\r\n      10: \r\n      GenSym(5) = #s8::Bool\r\n      unless GenSym(5) goto 11 # /home/carlo/Git/julia/beta.jl, line 21:\r\n      GenSym(6) = (Main.lgamma_r)(y::Float64)::Any\r\n      #s2 = (top(start))(GenSym(6))::Any\r\n      GenSym(7) = (top(indexed_next))(GenSym(6),1,#s2)::Any\r\n      y = (top(getfield))(GenSym(7),1)::Any\r\n      #s2 = (top(getfield))(GenSym(7),2)::Any\r\n      GenSym(8) = (top(indexed_next))(GenSym(6),2,#s2)::Any\r\n      s = (top(getfield))(GenSym(8),1)::Any\r\n      #s2 = (top(getfield))(GenSym(8),2)::Any # /home/carlo/Git/julia/beta.jl, line 22:\r\n      GenSym(9) = (Main.lgamma_r)(b::Float64)::Any\r\n      #s3 = (top(start))(GenSym(9))::Any\r\n      GenSym(10) = (top(indexed_next))(GenSym(9),1,#s3)::Any\r\n      yb = (top(getfield))(GenSym(10),1)::Any\r\n      #s3 = (top(getfield))(GenSym(10),2)::Any\r\n      GenSym(11) = (top(indexed_next))(GenSym(9),2,#s3)::Any\r\n      sb = (top(getfield))(GenSym(11),1)::Any\r\n      #s3 = (top(getfield))(GenSym(11),2)::Any # /home/carlo/Git/julia/beta.jl, line 23:\r\n      y = yb - y::Any # /home/carlo/Git/julia/beta.jl, line 24:\r\n      GenSym(12) = (Main.lgamma_r)(a::Float64)::Any\r\n      #s4 = (top(start))(GenSym(12))::Any\r\n      GenSym(13) = (top(indexed_next))(GenSym(12),1,#s4)::Any\r\n      ya = (top(getfield))(GenSym(13),1)::Any\r\n      #s4 = (top(getfield))(GenSym(13),2)::Any\r\n      GenSym(14) = (top(indexed_next))(GenSym(12),2,#s4)::Any\r\n      sa = (top(getfield))(GenSym(14),1)::Any\r\n      #s4 = (top(getfield))(GenSym(14),2)::Any # /home/carlo/Git/julia/beta.jl, line 25:\r\n      y = ya + y::Any # /home/carlo/Git/julia/beta.jl, line 29:\r\n      return s * sa * sb * (Main.exp)(y)::Any::Any\r\n      11:  # /home/carlo/Git/julia/beta.jl, line 32: # special/gamma.jl, line 3:\r\n      GenSym(16) = (top(ccall))((top(tuple))(:tgamma,Base.Math.libm)::Tuple{Symbol,ASCIIString},Base.Math.Float64,(top(svec))(Base.Math.Float64)::SimpleVector,y::Float64,0)::Float64\r\n      y = (Base.Math.nan_dom_err)(GenSym(16),y::Float64)::Float64 # /home/carlo/Git/julia/beta.jl, line 33: # special/gamma.jl, line 3:\r\n      GenSym(18) = (top(ccall))((top(tuple))(:tgamma,Base.Math.libm)::Tuple{Symbol,ASCIIString},Base.Math.Float64,(top(svec))(Base.Math.Float64)::SimpleVector,a::Float64,0)::Float64\r\n      a = (Base.Math.nan_dom_err)(GenSym(18),a::Float64)::Float64 # /home/carlo/Git/julia/beta.jl, line 34: # special/gamma.jl, line 3:\r\n      GenSym(20) = (top(ccall))((top(tuple))(:tgamma,Base.Math.libm)::Tuple{Symbol,ASCIIString},Base.Math.Float64,(top(svec))(Base.Math.Float64)::SimpleVector,b::Float64,0)::Float64\r\n      b = (Base.Math.nan_dom_err)(GenSym(20),b::Float64)::Float64 # /home/carlo/Git/julia/beta.jl, line 35:\r\n      unless (Base.eq_float)(y::Float64,0.0)::Bool goto 12\r\n      return Main.Inf\r\n      12:  # /home/carlo/Git/julia/beta.jl, line 37:\r\n      unless (Base.lt_float)((Base.box)(Base.Float64,(Base.abs_float)((Base.box)(Base.Float64,(Base.sub_float)((Base.box)(Base.Float64,(Base.abs_float)(b::Float64)),(Base.box)(Base.Float64,(Base.abs_float)(y::Float64)))))),(Base.box)(Base.Float64,(Base.abs_float)((Base.box)(Base.Float64,(Base.sub_float)((Base.box)(Base.Float64,(Base.abs_float)(a::Float64)),(Base.box)(Base.Float64,(Base.abs_float)(y::Float64)))))))::Bool goto 13 # /home/carlo/Git/julia/beta.jl, line 38:\r\n      y = (Base.box)(Base.Float64,(Base.div_float)(b::Float64,y::Float64)) # /home/carlo/Git/julia/beta.jl, line 39:\r\n      y = (Base.box)(Base.Float64,(Base.mul_float)(y::Float64,a::Float64))\r\n      goto 14\r\n      13:  # /home/carlo/Git/julia/beta.jl, line 41:\r\n      y = (Base.box)(Base.Float64,(Base.div_float)(a::Float64,y::Float64)) # /home/carlo/Git/julia/beta.jl, line 42:\r\n      y = (Base.box)(Base.Float64,(Base.mul_float)(y::Float64,b::Float64))\r\n      14:  # /home/carlo/Git/julia/beta.jl, line 45:\r\n      return y::Float64\r\n  end::Any\r\n```","created_at":"2015-12-10T14:07:13Z","updated_at":"2015-12-10T18:47:25Z","closed_at":null,"merged_at":null,"merge_commit_sha":"73a175ea0506391efaf92b33eb4ffd0e0470ed92","assignee":null,"milestone":null,"commits_url":"https://api.github.com/repos/JuliaLang/julia/pulls/14349/commits","review_comments_url":"https://api.github.com/repos/JuliaLang/julia/pulls/14349/comments","review_comment_url":"https://api.github.com/repos/JuliaLang/julia/pulls/comments{/number}","comments_url":"https://api.github.com/repos/JuliaLang/julia/issues/14349/comments","statuses_url":"https://api.github.com/repos/JuliaLang/julia/statuses/86017108f88736c075193985dcc61687869221f5","head":{"label":"CarloLucibello:beta","ref":"beta","sha":"86017108f88736c075193985dcc61687869221f5","user":{"login":"CarloLucibello","id":7014210,"avatar_url":"https://avatars.githubusercontent.com/u/7014210?v=3","gravatar_id":"","url":"https://api.github.com/users/CarloLucibello","html_url":"https://github.com/CarloLucibello","followers_url":"https://api.github.com/users/CarloLucibello/followers","following_url":"https://api.github.com/users/CarloLucibello/following{/other_user}","gists_url":"https://api.github.com/users/CarloLucibello/gists{/gist_id}","starred_url":"https://api.github.com/users/CarloLucibello/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/CarloLucibello/subscriptions","organizations_url":"https://api.github.com/users/CarloLucibello/orgs","repos_url":"https://api.github.com/users/CarloLucibello/repos","events_url":"https://api.github.com/users/CarloLucibello/events{/privacy}","received_events_url":"https://api.github.com/users/CarloLucibello/received_events","type":"User","site_admin":false},"repo":{"id":46961516,"name":"julia","full_name":"CarloLucibello/julia","owner":{"login":"CarloLucibello","id":7014210,"avatar_url":"https://avatars.githubusercontent.com/u/7014210?v=3","gravatar_id":"","url":"https://api.github.com/users/CarloLucibello","html_url":"https://github.com/CarloLucibello","followers_url":"https://api.github.com/users/CarloLucibello/followers","following_url":"https://api.github.com/users/CarloLucibello/following{/other_user}","gists_url":"https://api.github.com/users/CarloLucibello/gists{/gist_id}","starred_url":"https://api.github.com/users/CarloLucibello/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/CarloLucibello/subscriptions","organizations_url":"https://api.github.com/users/CarloLucibello/orgs","repos_url":"https://api.github.com/users/CarloLucibello/repos","events_url":"https://api.github.com/users/CarloLucibello/events{/privacy}","received_events_url":"https://api.github.com/users/CarloLucibello/received_events","type":"User","site_admin":false},"private":false,"html_url":"https://github.com/CarloLucibello/julia","description":"The 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