text: /**
   Copyright (c) 2014-present, Facebook, Inc.
   All rights reserved.
   
   This source code is licensed under the BSD-style license found in the
   LICENSE file in the root directory of this source tree. An additional grant
   of patent rights can be found in the PATENTS file in the same directory.
   */
  
  #import <Foundation/Foundation.h>
  
  #import <CoreGraphics/CoreGraphics.h>
  
  #import "POPDefines.h"
  #import "POPVector.h"
  
  NS_INLINE CGFloat sqrtr(CGFloat f)
  {
  #if CGFLOAT_IS_DOUBLE
    return sqrt(f);
  #else
    return sqrtf(f);
  #endif
  }
  
  // round to nearest sub; pass 2.0 to round to every 0.5 (eg: retina pixels)
  NS_INLINE CGFloat POPSubRound(CGFloat f, CGFloat sub)
  {
    return round(f * sub) / sub;
  }
  
  #define MIX(a, b, f) ((a) + (f) * ((b) - (a)))
  
  // the longer the duration, the higher the necessary precision
  #define SOLVE_EPS(dur) (1. / (1000. * (dur)))
  
  #define _EQLF_(x, y, epsilon) (fabsf ((x) - (y)) < epsilon)
  
  extern void POPInterpolateVector(NSUInteger count, CGFloat *dst, const CGFloat *from, const CGFloat *to, CGFloat f);
  
  extern double POPTimingFunctionSolve(const double vec[4], double t, double eps);
  
  // quadratic mapping of t [0, 1] to [start, end]
  extern double POPQuadraticOutInterpolation(double t, double start, double end);
  
  // normalize value to [0, 1] based on its range [startValue, endValue]
  extern double POPNormalize(double value, double startValue, double endValue);
  
  // project a normalized value [0, 1] to a given range [start, end]
  extern double POPProjectNormal(double n, double start, double end);
  
  // solve a quadratic equation of the form a * x^2 + b * x + c = 0
  extern void POPQuadraticSolve(CGFloat a, CGFloat b, CGFloat c, CGFloat &x1, CGFloat &x2);
  
  // for a given tension return the bouncy 3 friction that produces no bounce
  extern double POPBouncy3NoBounce(double tension);
  