[builtins] Unify Cosh, Sinh and Tanh as exports from flibm

src/base/ieee754.cc

 // The following is adapted from fdlibm (http://www.netlib.org/fdlibm).
 //
 // ====================================================
 // Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 //
 // Developed at SunSoft, a Sun Microsystems, Inc. business.
 // Permission to use, copy, modify, and distribute this
 // software is freely granted, provided that this notice
 // is preserved.
 // ====================================================
@@ skipping 2290 matching lines @@
     /* tan(Inf or NaN) is NaN */
     return x - x; /* NaN */
   } else {
     /* argument reduction needed */
     n = __ieee754_rem_pio2(x, y);
     /* 1 -> n even, -1 -> n odd */
     return __kernel_tan(y[0], y[1], 1 - ((n & 1) << 1));
   }
 }
 
+/*
+ * ES6 draft 09-27-13, section 20.2.2.12.
+ * Math.cosh
+ * Method :
+ * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
+ *      1. Replace x by |x| (cosh(x) = cosh(-x)).
+ *      2.
+ *                                                      [ exp(x) - 1 ]^2
+ *          0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
+ *                                                         2*exp(x)
+ *
+ *                                                 exp(x) + 1/exp(x)
+ *          ln2/2    <= x <= 22     :  cosh(x) := -------------------
+ *                                                        2
+ *          22       <= x <= lnovft :  cosh(x) := exp(x)/2
+ *          lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
+ *          ln2ovft  <  x           :  cosh(x) := huge*huge (overflow)
+ *
+ * Special cases:
+ *      cosh(x) is |x| if x is +INF, -INF, or NaN.
+ *      only cosh(0)=1 is exact for finite x.
+ */
+double cosh(double x) {
+  static const double KCOSH_OVERFLOW = 710.4758600739439;
+  static const double one = 1.0, half = 0.5;
+  static volatile double huge = 1.0e+300;
+
+  int32_t ix;
+
+  /* High word of |x|. */
+  GET_HIGH_WORD(ix, x);
+  ix &= 0x7fffffff;
+
+  // |x| in [0,0.5*log2], return 1+expm1(|x|)^2/(2*exp(|x|))
+  if (ix < 0x3fd62e43) {
+    double t = expm1(fabs(x));
+    double w = one + t;
+    // For |x| < 2^-55, cosh(x) = 1
+    if (ix < 0x3c800000) return w;
+    return one + (t * t) / (w + w);
+  }
+
+  // |x| in [0.5*log2, 22], return (exp(|x|)+1/exp(|x|)/2
+  if (ix < 0x40360000) {
+    double t = exp(fabs(x));
+    return half * t + half / t;
+  }
+
+  // |x| in [22, log(maxdouble)], return half*exp(|x|)
+  if (ix < 0x40862e42) return half * exp(fabs(x));
+
+  // |x| in [log(maxdouble), overflowthreshold]
+  if (fabs(x) <= KCOSH_OVERFLOW) {
+    double w = exp(half * fabs(x));
+    double t = half * w;
+    return t * w;
+  }
+
+  /* x is INF or NaN */
+  if (ix >= 0x7ff00000) return x * x;
+
+  // |x| > overflowthreshold.
+  return huge * huge;
+}
+
+/*
+ * ES6 draft 09-27-13, section 20.2.2.30.
+ * Math.sinh
+ * Method :
+ * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
+ *      1. Replace x by |x| (sinh(-x) = -sinh(x)).
+ *      2.
+ *                                                  E + E/(E+1)
+ *          0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
+ *                                                      2
+ *
+ *          22       <= x <= lnovft :  sinh(x) := exp(x)/2
+ *          lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
+ *          ln2ovft  <  x           :  sinh(x) := x*shuge (overflow)
+ *
+ * Special cases:
+ *      sinh(x) is |x| if x is +Infinity, -Infinity, or NaN.
+ *      only sinh(0)=0 is exact for finite x.
+ */
+double sinh(double x) {
+  static const double KSINH_OVERFLOW = 710.4758600739439,
+                      TWO_M28 =
+                          3.725290298461914e-9,  // 2^-28, empty lower half
+      LOG_MAXD = 709.7822265625;  // 0x40862e42 00000000, empty lower half
+  static const double shuge = 1.0e307;
+
+  double h = (x < 0) ? -0.5 : 0.5;
+  // |x| in [0, 22]. return sign(x)*0.5*(E+E/(E+1))
+  double ax = fabs(x);
+  if (ax < 22) {
+    // For |x| < 2^-28, sinh(x) = x
+    if (ax < TWO_M28) return x;
+    double t = expm1(ax);
+    if (ax < 1) {
+      return h * (2 * t - t * t / (t + 1));
+    }
+    return h * (t + t / (t + 1));
+  }
+  // |x| in [22, log(maxdouble)], return 0.5 * exp(|x|)
+  if (ax < LOG_MAXD) return h * exp(ax);
+  // |x| in [log(maxdouble), overflowthreshold]
+  // overflowthreshold = 710.4758600739426
+  if (ax <= KSINH_OVERFLOW) {
+    double w = exp(0.5 * ax);
+    double t = h * w;
+    return t * w;
+  }
+  // |x| > overflowthreshold or is NaN.
+  // Return Infinity of the appropriate sign or NaN.
+  return x * shuge;
+}
+
+/* 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**-28 : tanh(x) := x with inexact if x != 0
+ *                                          -t
+ *      2**-28 <= x <  1      : tanh(x) := -----; t = expm1(-2x)
+ *                                         t + 2
+ *                                               2
+ *      1      <= x <  22     : tanh(x) := 1 - -----; t = expm1(2x)
+ *                                             t + 2
+ *      22     <= x <= INF    : tanh(x) := 1.
+ *
+ * Special cases:
+ *      tanh(NaN) is NaN;
+ *      only tanh(0)=0 is exact for finite argument.
+ */
+double tanh(double x) {
+  static const volatile double tiny = 1.0e-300;
+  static const double one = 1.0, two = 2.0, huge = 1.0e300;
+  double t, z;
+  int32_t jx, ix;
+
+  GET_HIGH_WORD(jx, x);
+  ix = jx & 0x7fffffff;
+
+  /* x is INF or NaN */
+  if (ix >= 0x7ff00000) {
+    if (jx >= 0)
+      return one / x + one; /* tanh(+-inf)=+-1 */
+    else
+      return one / x - one; /* tanh(NaN) = NaN */
+  }
+
+  /* |x| < 22 */
+  if (ix < 0x40360000) {            /* |x|<22 */
+    if (ix < 0x3e300000) {          /* |x|<2**-28 */
+      if (huge + x > one) return x; /* tanh(tiny) = tiny with inexact */
+    }
+    if (ix >= 0x3ff00000) { /* |x|>=1  */
+      t = expm1(two * fabs(x));
+      z = one - two / (t + two);
+    } else {
+      t = expm1(-two * fabs(x));
+      z = -t / (t + two);
+    }
+    /* |x| >= 22, return +-1 */
+  } else {
+    z = one - tiny; /* raise inexact flag */
+  }
+  return (jx >= 0) ? z : -z;
+}
+
 }  // namespace ieee754
 }  // namespace base
 }  // namespace v8