Zoom to point

zoom.c

static float
scalbnf(float x, int n)
{
	union {float f; unsigned i;} u;
	float y = x;
	if (n > 127) {
		y *= 0x1p127f;
		n -= 127;
		if (n > 127) {
			y *= 0x1p127f;
			n -= 127;
			if (n > 127)
				n = 127;
		}
	} else if (n < -126) {
		y *= 0x1p-126f * 0x1p24f;
		n += 126 - 24;
		if (n < -126) {
			y *= 0x1p-126f * 0x1p24f;
			n += 126 - 24;
			if (n < -126)
				n = -126;
		}
	}
	u.i = (unsigned)(0x7f+n)<<23;
	x = y * u.f;
	return x;
}
static float
expf(float x)
{
	static const float half[2] = {0.5,-0.5};
	static const float ln2hi = 6.9314575195e-1f;  /* 0x3f317200 */
	static const float n2lo = 1.4286067653e-6f;  /* 0x35bfbe8e */
	static const float invln2 = 1.4426950216e+0f;  /* 0x3fb8aa3b */
 	/*
   	 * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
   	 * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
   	 */
  	static const float P1 =  1.6666625440e-1f; /*  0xaaaa8f.0p-26 */
  	static const float P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
	
  	float hi, lo, c, xx, y;
  	int k, sign;
  	unsigned hx;
  	union {float f; unsigned i;} u;
  	u.f = x; hx = u.i;

	sign = hx >> 31;   /* sign bit of x */
	hx &= 0x7fffffff;  /* high word of |x| */

	/* special cases */
	if (hx >= 0x42aeac50) {  /* if |x| >= -87.33655f or NaN */
		if (hx > 0x7f800000) /* NaN */
			return x;
		if (hx >= 0x42b17218 && !sign) {  /* x >= 88.722839f */
			/* overflow */
			x *= 0x1p127f;
			return x;
		}
		if (sign) {
			/* underflow */
      		volatile float __x = -0x1p-149f/x;
			if (hx >= 0x42cff1b5)  /* x <= -103.972084f */
				return 0;
		}
	}

	/* argument reduction */
	if (hx > 0x3eb17218) {  /* if |x| > 0.5 ln2 */
		if (hx > 0x3f851592)  /* if |x| > 1.5 ln2 */
			k = invln2*x + half[sign];
		else
			k = 1 - sign - sign;
		hi = x - k*ln2hi;  /* k*ln2hi is exact here */
		lo = k*ln2lo;
		x = hi - lo;
	} else if (hx > 0x39000000) {  /* |x| > 2**-14 */
		k = 0;
		hi = x;
		lo = 0;
	} else {
		/* raise inexact */
    	volatile float __x = 0x1p127f + x;
		return 1 + x;
	}

	/* x is now in primary range */
	xx = x*x;
	c = x - xx*(P1+xx*P2);
	y = 1 + (x*c/(2-c) - lo + hi);
	
	if (k == 0) return y;
	return scalbnf(y, k);
}
static void
pnt_view_to_img(float *out, const float *pnt,
                  float scaler, const float *off)
{
    out[0] = (pnt[0]+off[0])/scaler;
    out[1] = (pnt[1]+off[1])/scaler;
}
static void
zoom_to_pnt_off(float *off, const float *pnt,
                float old_scaler, float new_scaler)
{
    float img_pnt[2];
    pnt_view_to_img(img_pnt, pnt, old_scaler, off);
    off[0] = (img_pnt[0]*new_scaler)-pnt[0];
    off[1] = (img_pnt[1]*new_scaler)-pnt[1];
}
int main(int argc, char **argv)
{
    static const float zoom_fak = 0.2f;
    float off[2] = {0};
    float zoom = 0.0f;
    float scale = 1.0f; // expf(zoom);

    // ...
    {
        // mouse scroll handler
        zoom += scrl_wheel * zoom_fak;
        const float new_scale = expf(zoom);        
        zoom_to_pnt_off(off, view_rel_mouse_pos, scale, new_scale);
        scale = new_scale;
    }   
    // ...
    
    return 0;
}