schematic rounding modes

Author: milankl

Diff for: figs/schematic_all.jl

@@ -0,0 +1,102 @@
+using PyPlot
+using Statistics
+
+Statistics.mean(x::Real,y::Real) = (x+y)/2
+
+x = [0.5,1.0,2.0]
+xint = [mean(x[i],x[i+1]) for i in 1:length(x)-1]
+
+fig,(ax1,ax2,ax3,ax4,ax5) = subplots(5,1,figsize=(5,5),sharex=true)
+axs = [ax1,ax2,ax3,ax4,ax5]
+
+# BITSHAVE
+for i in 1:length(x)
+    ax1.scatter(x[i],0,20,color="C$(i-1)",edgecolor="k",zorder=10)
+end
+
+ax1.plot([0,x[1]],[0,0],"C5")
+ax1.plot([x[1],x[2]],[0,0],"C0")
+ax1.plot([x[2],x[3]],[0,0],"C1")
+ax1.plot([x[3],3],[0,0],"C2")
+ax1.set_yticks([])
+ax1.set_title("Bitshave (round-to-zero)",loc="left")
+
+ax1.plot([1.2,1.2],[-0.2,0.2],"k--",lw=0.5)
+ax1.text(1.22,-0.2,L"x is round to $x_2$")
+
+# BITSET
+for i in 1:length(x)-1
+    ax2.scatter(x[i+1]-0.02,0,20,color="C$(i-1)",edgecolor="k",zorder=10)
+end
+
+ax2.plot([0,x[1]],[0,0],"C5")
+ax2.plot([x[1],x[2]],[0,0],"C0")
+ax2.plot([x[2],x[3]],[0,0],"C1")
+ax2.plot([x[3],3],[0,0],"C2")
+ax2.set_yticks([])
+ax2.set_title("Bitset (round-away-from-zero)",loc="left")
+
+ax2.plot([1.2,1.2],[-0.2,0.2],"k--",lw=0.5)
+ax2.text(1.22,-0.2,L"x is round to $x_3^-$")
+
+# HALFSHAVE
+for i in 1:length(xint)
+    ax3.scatter(xint[i],0,20,color="C$(i-1)",edgecolor="k",zorder=10)
+end
+
+ax3.plot([0,x[1]],[0,0],"C5")
+ax3.plot([x[1],x[2]],[0,0],"C0")
+ax3.plot([x[2],x[3]],[0,0],"C1")
+ax3.plot([x[3],3],[0,0],"C2")
+ax3.set_yticks([])
+ax3.set_title("Halfshave",loc="left")
+
+ax3.plot([1.2,1.2],[-0.2,0.2],"k--",lw=0.5)
+ax3.text(1.22,-0.2,L"x is round to $x_2^*$")
+
+# ROUND NEAREST
+for i in 1:length(x)
+    ax4.scatter(x[i],0,20,color="C$(i-1)",edgecolor="k",zorder=10)
+end
+
+ax4.plot([0,xint[1]],[0,0],"C0")
+ax4.plot([xint[1],xint[2]],[0,0],"C1")
+ax4.plot([xint[2],3],[0,0],"C2")
+ax4.set_yticks([])
+ax4.set_title("Round-to-nearest",loc="left")
+
+ax4.plot([1.2,1.2],[-0.2,0.2],"k--",lw=0.5)
+ax4.text(1.22,-0.2,L"x is round to $x_2$")
+
+# STOCHASTIC ROUNDING
+ax5.plot([-0.5,0,x[1]],[0,1,0],"C5")
+ax5.plot([0,x[1],x[2]],[0,1,0],"C0")
+ax5.plot([x[1],x[2],x[3]],[0,1,0],"C1")
+ax5.plot([x[2],x[3],4],[0,1,0],"C2")
+ax5.plot([x[3],4,5],[0,1,0],"C4")
+
+for i in 1:length(x)
+    ax5.scatter(x[i],1,20,color="C$(i-1)",edgecolor="k",zorder=10)
+end
+
+ax5.plot([1.2,1.2],[0,1],"k--",lw=0.5)
+ax5.text(1.18,-0.3,L"x = ")
+ax5.text(1.31,-0.15,L"$x_2$ at 80%")
+ax5.text(1.31,-0.45,L"$x_3$ at 20% chance.")
+
+ax5.set_xlim(x[1]-0.2,x[3]+0.2)
+ax5.set_yticks([0,1])
+ax5.set_ylim([-0.1,1.1])
+ax5.set_yticklabels([L"0\%",L"100\%"])
+ax5.set_xticks(x)
+ax5.set_xticklabels([L"$x_1$",L"$x_2$",L"$x_3$"])
+ax5.set_title("Stochastic rounding",loc="left")
+
+for (iax,ax) in enumerate(axs)
+    ax.set_title(string(Char(iax+96)),loc="right",fontweight="bold")
+    ax.set_frame_on(false)
+end
+
+tight_layout()
+savefig("figs/schematic_all.pdf")
+savefig("figs/schematic_all.png",dpi=200)