Interesting chip the HPI4081 for interfacing. To get more speed you have to sort out how to drive your stepper motor to its best advantage.
1. Stepper motors are speed power limited and should be connected to the load they are to drive when being set up. This is because the drive coils not only have an inductance but also generate a high back emf when the magnetic core spins which also reduces the input current.
2. The circuitry you are designing must take into account the maximum peak coil current rating of the motor. get this from the data sheet for the motor and do not exceed it unless you know what you are doing as the motors run hot and there is little margin.
3. The drive to a stepper motor is frequently pulse width modulated (PWM) to control the motor coil current. Look to feed back techniques to dynamically measure this.
4. Using micro stepping will limit the torque that can be generated and hence the top speed. Try and limit the micro stepping to a small value and use mechanical gearing to multiply the speed as this will give higher available torque and hence more speed.
5. Stepper motors come in a wide variety of shapes and differ a lot in their magnetic properties. In general the lower the inductance the better for a given current capability.
Do a search on stepper motors and speed as there is a lot of very good information available due to the generosity of this sites contributors.
Unfortunately generating the the sine and cosine values for the voltage drive is the easy bit. The problem is driving the highly inductive motor coils with current that results in a smooth turning force. You do not state what speed you are looking for. Stepper motors run out of torque rapidly with increasing speed. Look to remain sub 1000 rpm and try to get rid of all micro-stepping.
Sorry is this sounds tough but a reality check should help in the form of a comparison of stepper motor data sheets.
A. Use as high a voltage to drive the motor as practical (Chip and drive MOS limits apply - also back emf spikes must be taken into account as well as the breakdown voltage of the coil insulation. The inductance will determine the maximum voltage but think in terms of 50 volts as being typical with out getting too technical. ) See B. as the current must be limited to the safe value for the coil.
B. Use acive control of peak coil current to make safe and best use of the higher motor supply voltage.
C. The motor plate voltage and current is the safe voltage that can be applied for the coil's current limit. To get more power and hence speed you need to PWM the current at the safe limit from a high voltage source to give the maximum number of pulses per cycle.
D. Use mechanical gearing not microstepping when ever possible
E. Select motor for low inductance as well as speed v torque considerations - check maker's graphs. Frame size and length of the motor are factors that may limit the motor choice. Use modern high efficiency hybrid motors - the low inertia stepper motors are exotics and for normal purposes closed loop servo motor designs will give better results.
Regards - Pat