Actually my concern is that I am planning to apply xoshiro256+ for implementation of stream cipher https://prng.di.unimi.it/ for my cryptographic application. It passes the BigCrush tests. Will it provide me the same level of secuirty as any other cryptographically secure PRNG (CSPRNG)? On the webiste, they claim that xoshiro256+ is a general purpose PRNG and not to be used for cryptography. But I still want to find out how far this PRNG is from being CSPRNG, may be a mathematical expression because my limitation is speed and this seems to be very fast PRNG and remember that it passes BigCrush. My other question is that NIST statistical test suite https://www.nist.gov/publications/statistical-test-suite-random-and-pseudorandom-number-generators-cryptographic says that if a PRNG passes NIST tests then it is a CSPRNG. So how similar is BigCrush to NIST, again to know how far xoshiro256+ is from being CSPRNG?
P.S: I want to do a theoretical study of this issue as I am not well-versed in statistical testings practically on software.