fusl/src/math/tanh.c

#include "libm.h"

/* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x))
 *         = (exp(2*x) - 1)/(exp(2*x) - 1 + 2)
 *         = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2)
 */
double tanh(double x) {
  union {
    double f;
    uint64_t i;
  } u = {.f = x};
  uint32_t w;
  int sign;
  double_t t;

  /* x = |x| */
  sign = u.i >> 63;
  u.i &= (uint64_t)-1 / 2;
  x = u.f;
  w = u.i >> 32;

  if (w > 0x3fe193ea) {
    /* |x| > log(3)/2 ~= 0.5493 or nan */
    if (w > 0x40340000) {
      /* |x| > 20 or nan */
      /* note: this branch avoids raising overflow */
      t = 1 - 0 / x;
    } else {
      t = expm1(2 * x);
      t = 1 - 2 / (t + 2);
    }
  } else if (w > 0x3fd058ae) {
    /* |x| > log(5/3)/2 ~= 0.2554 */
    t = expm1(2 * x);
    t = t / (t + 2);
  } else if (w >= 0x00100000) {
    /* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */
    t = expm1(-2 * x);
    t = -t / (t + 2);
  } else {
    /* |x| is subnormal */
    /* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022)
     */
    FORCE_EVAL((float)x);
    t = x;
  }
  return sign ? -t : t;
}