/* Tanh(x) * Return the Hyperbolic Tangent of x * * Method : * x -x * e - e * 0. tanh(x) is defined to be ----------- * x -x * e + e * 1. reduce x to non-negative by tanh(-x) = -tanh(x). * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) * -t * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) * t + 2 * 2 * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) * t + 2 * 22.0 < x <= INF : tanh(x) := 1. * * Special cases: * tanh(NaN) is NaN; * only tanh(0)=0 is exact for finite argument. */ double __builtin_tanh(double x) { double t,z; int jx,ix; /* High word of |x|. */ jx = GET_HI(x); ix = jx&0x7fffffff; /* x is INF or NaN */ if(ix>=0x7ff00000) { if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ else return __builtin_nan(""); /* tanh(NaN) = NaN */ } /* |x| < 22 */ if (ix < 0x40360000) { /* |x|<22 */ if (ix<0x3c800000) /* |x|<2**-55 */ return x*(one+x); /* tanh(small) = small */ if (ix>=0x3ff00000) { /* |x|>=1 */ t = __builtin_expm1(two*__builtin_fabs(x)); z = one - two/(t+two); } else { t = __builtin_expm1(-two*__builtin_fabs(x)); z= -t/(t+two); } /* |x| > 22, return +-1 */ } else { z = one - tiny; /* raised inexact flag */ } return (jx>=0)? z: -z; }
void test_double_expm1 (void) { int i; for (i = 0; i < SIZE; i++) d1[i] = __builtin_expm1 (d2[i]); }