add make file for testing and doc

Makefile

@@ -0,0 +1,37 @@
+JL = julia --project
+
+default: init test
+
+init:
+	$(JL) -e 'using Pkg; Pkg.develop([Pkg.PackageSpec(path = joinpath("lib", pkg)) for pkg in ["YaoArrayRegister", "YaoBlocks", "YaoSym", "YaoPlots", "YaoAPI"]]); Pkg.precompile()'
+init-docs:
+	$(JL) -e 'using Pkg; Pkg.activate("docs"); Pkg.develop([Pkg.PackageSpec(path = joinpath("lib", pkg)) for pkg in ["YaoArrayRegister", "YaoBlocks", "YaoSym", "YaoPlots", "YaoAPI"]]); Pkg.precompile()'
+
+update:
+	$(JL) -e 'using Pkg; Pkg.update(); Pkg.precompile()'
+update-docs:
+	$(JL) -e 'using Pkg; Pkg.activate("docs"); Pkg.update(); Pkg.precompile()'
+
+test-Yao:
+	$(JL) -e 'using Pkg; Pkg.test("Yao")'
+test-CuYao:
+	$(JL) -e 'using Pkg; Pkg.activate("ext/CuYao/test"); Pkg.develop(path="."); Pkg.update()'
+	$(JL) -e 'using Pkg; Pkg.activate("ext/CuYao/test"); include("ext/CuYao/test/runtests.jl")'
+
+test-%:
+	$(JL) -e 'using Pkg; Pkg.test("$*")'
+
+test:
+	$(JL) -e 'using Pkg; Pkg.test(["YaoAPI", "YaoArrayRegister", "YaoBlocks", "YaoSym", "YaoPlots", "Yao"])'
+
+coverage:
+	$(JL) -e 'using Pkg; Pkg.test(["YaoAPI", "YaoArrayRegister", "YaoBlocks", "YaoSym", "YaoPlots", "Yao"]; coverage=true)'
+
+servedocs:
+	$(JL) -e 'using Pkg; Pkg.activate("docs"); using LiveServer; servedocs(;skip_dirs=["docs/src/assets", "docs/src/generated"])'
+
+clean:
+	rm -rf docs/build
+	find . -name "*.cov" -type f -print0 | xargs -0 /bin/rm -f
+
+.PHONY: init test

lib/YaoAPI/src/registers.jl

@@ -664,6 +664,8 @@ Trace distance is defined as following:
 \\frac{1}{2} || A - B ||_{\\rm tr}
 ```
 
+It takes values between 0 and 1.
+
 ### Examples
 
 ```jldoctest; setup=:(using Yao)
@@ -672,7 +674,7 @@ julia> reg1 = uniform_state(3);
 julia> reg2 = zero_state(3);
 
 julia> tracedist(reg1, reg2)
-0.9354143624774909
+0.9354143466934852
 ```
 
 ### References