text: #include "libm.h"
  
  #if FLT_EVAL_METHOD==2
  #undef sqrtf
  #define sqrtf sqrtl
  #elif FLT_EVAL_METHOD==1
  #undef sqrtf
  #define sqrtf sqrt
  #endif
  
  /* acosh(x) = log(x + sqrt(x*x-1)) */
  float acoshf(float x)
  {
  	union {float f; uint32_t i;} u = {x};
  	uint32_t a = u.i & 0x7fffffff;
  
  	if (a < 0x3f800000+(1<<23))
  		/* |x| < 2, invalid if x < 1 */
  		/* up to 2ulp error in [1,1.125] */
  		return log1pf(x-1 + sqrtf((x-1)*(x-1)+2*(x-1)));
  	if (u.i < 0x3f800000+(12<<23))
  		/* 2 <= x < 0x1p12 */
  		return logf(2*x - 1/(x+sqrtf(x*x-1)));
  	/* x >= 0x1p12 or x <= -2 or nan */
  	return logf(x) + 0.693147180559945309417232121458176568f;
  }
  