Merge pull request #9132 from JuliaLang/rf/randn-splitbranch

faster randn by separating out unlikely branch in a function

Author: ViralBShah

base/random.jl

@@ -56,6 +56,7 @@ type Close1Open2 <: FloatInterval end
 
 @inline rand_ui52_raw_inbounds(r::MersenneTwister) = reinterpret(UInt64, rand_inbounds(r, Close1Open2))
 @inline rand_ui52_raw(r::MersenneTwister) = (reserve_1(r); rand_ui52_raw_inbounds(r))
+@inline rand_ui52(r::MersenneTwister) = rand_ui52_raw(r) & 0x000fffffffffffff
 @inline rand_ui2x52_raw(r::MersenneTwister) = rand_ui52_raw(r) % UInt128 << 64 | rand_ui52_raw(r)
 
 function srand(r::MersenneTwister, seed::Vector{UInt32})
@@ -943,36 +944,37 @@ const ziggurat_nor_r      = 3.6541528853610087963519472518
 const ziggurat_nor_inv_r  = inv(ziggurat_nor_r)
 const ziggurat_exp_r      = 7.6971174701310497140446280481
 
-@inline randi(rng::MersenneTwister=GLOBAL_RNG) = reinterpret(Uint64, rand(rng, Close1Open2)) & 0x000fffffffffffff
 
 function randmtzig_randn(rng::MersenneTwister=GLOBAL_RNG)
     @inbounds begin
+        r = rand_ui52(rng)
+        rabs = int64(r>>1) # One bit for the sign
+        idx = rabs & 0xFF
+        x = ifelse(r % Bool, -rabs, rabs)*wi[idx+1]
+        rabs < ki[idx+1] && return x # 99.3% of the time we return here 1st try
+        return randmtzig_randn_unlikely(rng, idx, rabs, x)
+    end
+end
+
+# this unlikely branch is put in a separate function for better efficiency
+function randmtzig_randn_unlikely(rng, idx, rabs, x)
+    @inbounds if idx == 0
         while true
-            r = randi(rng)
-            rabs = int64(r>>1) # One bit for the sign
-            idx = rabs & 0xFF
-            x = ifelse(r % Bool, -rabs, rabs)*wi[idx+1]
-            if rabs < ki[idx+1]
-                return x # 99.3% of the time we return here 1st try
-            elseif idx == 0
-                while true
-                    xx = -ziggurat_nor_inv_r*log(rand(rng))
-                    yy = -log(rand(rng))
-                    if yy+yy > xx*xx
-                        return (rabs & 0x100) != 0x000000000 ? -ziggurat_nor_r-xx : ziggurat_nor_r+xx
-                    end
-                end
-            elseif (fi[idx] - fi[idx+1])*rand(rng) + fi[idx+1] < exp(-0.5*x*x)
-                return x # return from the triangular area
-            end
+            xx = -ziggurat_nor_inv_r*log(rand(rng))
+            yy = -log(rand(rng))
+            yy+yy > xx*xx && return (rabs >> 8) % Bool ? -ziggurat_nor_r-xx : ziggurat_nor_r+xx
         end
+    elseif (fi[idx] - fi[idx+1])*rand(rng) + fi[idx+1] < exp(-0.5*x*x)
+        return x # return from the triangular area
+    else
+        return randmtzig_randn(rng)
     end
 end
 
 function randmtzig_exprnd(rng::MersenneTwister=GLOBAL_RNG)
     @inbounds begin
         while true
-            ri = randi(rng)
+            ri = rand_ui52(rng)
             idx = ri & 0xFF
             x = ri*we[idx+1]
             if ri < ke[idx+1]