github.com/afumu/libc@v0.0.6/musl/src/math/acoshf.c (about)

     1  #include "libm.h"
     2  
     3  #if FLT_EVAL_METHOD==2
     4  #undef sqrtf
     5  #define sqrtf sqrtl
     6  #elif FLT_EVAL_METHOD==1
     7  #undef sqrtf
     8  #define sqrtf sqrt
     9  #endif
    10  
    11  /* acosh(x) = log(x + sqrt(x*x-1)) */
    12  float acoshf(float x)
    13  {
    14  	union {float f; uint32_t i;} u = {x};
    15  	uint32_t a = u.i & 0x7fffffff;
    16  
    17  	if (a < 0x3f800000+(1<<23))
    18  		/* |x| < 2, invalid if x < 1 or nan */
    19  		/* up to 2ulp error in [1,1.125] */
    20  		return log1pf(x-1 + sqrtf((x-1)*(x-1)+2*(x-1)));
    21  	if (a < 0x3f800000+(12<<23))
    22  		/* |x| < 0x1p12 */
    23  		return logf(2*x - 1/(x+sqrtf(x*x-1)));
    24  	/* x >= 0x1p12 */
    25  	return logf(x) + 0.693147180559945309417232121458176568f;
    26  }