Moving an object in the direction of the camera - c++

Question

I'm making a project where I need to move a player in any direction using an analog stick. I'm limited to specific functions and I only have the positions of the camera and the player and the analog stick. The camera is always pointed to the player.
vec2 &leftStick = getLeftStick(-1); // results in an x and a y, both ranging from -1 to 1.
vec3 *playerPos = getTrans(player);
vec3 *cameraPos = getCameraPos(player, 0);
playerPos->x += leftStick.x * 10.0f;
playerPos->z -= leftStick.y * 10.0f;
This code works to move the player, however its using the orientation of the world. I need it where holding up on the analog stick (left stick y = 1) makes the player go forward, no matter what way the player/camera are facing.

Answer 1

My solution, thank you #Borgleader for a majority of it.
I found an equation to find the distance and velocity for the x and z online, then I tested a bunch of combinations until it worked properly. Not a good way to do this but it worked out.
// this all replaces the last two lines of the previous code snippet
float speed = 30.0f;
float d = sqrt(powf(playerPos->x - cameraPos->x, 2) + powf(playerPos->z - cameraPos->z, 2));
float vx = (speed/d)*(playerPos->x - cameraPos->x);
float vz = (speed/d)*(playerPos->z - cameraPos->z);
playerPos->x -= leftStick.x * vz;
playerPos->z += leftStick.x * vx;
playerPos->x += leftStick.y * vx;
playerPos->z += leftStick.y * vz;