  An all-optical method for directly reconstructing the spectral phase of
isolated attosecond pulse (IAP) has been proposed recently [New J. Phys. 25,
083003 (2023)]. This method is based on the high-harmonic generation (HHG)
streaking spectra generated by an IAP and a time-delayed intense infrared (IR)
laser, which can be accurately simulated by an extended quantitative
rescattering model. Here we extend the retrieval algorithm in this method to
successfully retrieve the spectral phase of an shaped IAP, which has a spectral
minimum, a phase jump about $\pi$, and a "split" temporal profile. We then
reconstruct the carrier-envelope phase of IR laser from HHG streaking spectra.
And we finally discuss the retrieval of the phase of high harmonics by the
intense IR laser alone using the Fourier transform of HHG streaking spectra.
