Does David's standing for prayer in the middle of the night contradict Allah's saying: "They used to sleep but little of the night"?

Prophet Dawud (peace be upon him) used to sleep the first half of the night, then pray for a third of the night, then sleep for a sixth of it. The Prophet (peace and blessings of Allah be upon him) praised this amount of prayer.

As for the Almighty's saying: (كَانُوا قَلِيلًا مِنَ اللَّيْلِ مَا يَهْجَعُونَ - They used to sleep but little of the night), exegetes have differed on its interpretation, holding two views:

1. That "ma" (ما) is a negating particle, and its meaning is: They slept but little of the night, meaning no night passed them by except that they prayed in it what Allah facilitated for them. 2. That "ma" (ما) is a a مصدرية (masdariyya) particle (forming a verbal noun), and its meaning is: Their sleep and slumber during the night was little, meaning their sleep at night was little compared to their standing in prayer and seeking forgiveness.

Reconciling the hadith and the verse is possible by understanding that the time of night extends from sunset to sunrise. One who prays the prayer of Dawud (peace be upon him) will have a sleeping time that is less than his time of wakefulness and worship, because he is awake from Maghrib until Isha, and from Fajr until sunrise. What remains is the time between Isha and Fajr, and he sleeps for half of that time. Thus, the duration of slumber is less than the duration of wakefulness.