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Source file src/math/tan.go

  // Copyright 2011 The Go Authors. All rights reserved.
  // Use of this source code is governed by a BSD-style
  // license that can be found in the LICENSE file.
  
  package math
  
  /*
  	Floating-point tangent.
  */
  
  // The original C code, the long comment, and the constants
  // below were from http://netlib.sandia.gov/cephes/cmath/sin.c,
  // available from http://www.netlib.org/cephes/cmath.tgz.
  // The go code is a simplified version of the original C.
  //
  //      tan.c
  //
  //      Circular tangent
  //
  // SYNOPSIS:
  //
  // double x, y, tan();
  // y = tan( x );
  //
  // DESCRIPTION:
  //
  // Returns the circular tangent of the radian argument x.
  //
  // Range reduction is modulo pi/4.  A rational function
  //       x + x**3 P(x**2)/Q(x**2)
  // is employed in the basic interval [0, pi/4].
  //
  // ACCURACY:
  //                      Relative error:
  // arithmetic   domain     # trials      peak         rms
  //    DEC      +-1.07e9      44000      4.1e-17     1.0e-17
  //    IEEE     +-1.07e9      30000      2.9e-16     8.1e-17
  //
  // Partial loss of accuracy begins to occur at x = 2**30 = 1.074e9.  The loss
  // is not gradual, but jumps suddenly to about 1 part in 10e7.  Results may
  // be meaningless for x > 2**49 = 5.6e14.
  // [Accuracy loss statement from sin.go comments.]
  //
  // Cephes Math Library Release 2.8:  June, 2000
  // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
  //
  // The readme file at http://netlib.sandia.gov/cephes/ says:
  //    Some software in this archive may be from the book _Methods and
  // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
  // International, 1989) or from the Cephes Mathematical Library, a
  // commercial product. In either event, it is copyrighted by the author.
  // What you see here may be used freely but it comes with no support or
  // guarantee.
  //
  //   The two known misprints in the book are repaired here in the
  // source listings for the gamma function and the incomplete beta
  // integral.
  //
  //   Stephen L. Moshier
  //   moshier@na-net.ornl.gov
  
  // tan coefficients
  var _tanP = [...]float64{
  	-1.30936939181383777646E4, // 0xc0c992d8d24f3f38
  	1.15351664838587416140E6,  // 0x413199eca5fc9ddd
  	-1.79565251976484877988E7, // 0xc1711fead3299176
  }
  var _tanQ = [...]float64{
  	1.00000000000000000000E0,
  	1.36812963470692954678E4,  //0x40cab8a5eeb36572
  	-1.32089234440210967447E6, //0xc13427bc582abc96
  	2.50083801823357915839E7,  //0x4177d98fc2ead8ef
  	-5.38695755929454629881E7, //0xc189afe03cbe5a31
  }
  
  // Tan returns the tangent of the radian argument x.
  //
  // Special cases are:
  //	Tan(±0) = ±0
  //	Tan(±Inf) = NaN
  //	Tan(NaN) = NaN
  func Tan(x float64) float64
  
  func tan(x float64) float64 {
  	const (
  		PI4A = 7.85398125648498535156E-1                             // 0x3fe921fb40000000, Pi/4 split into three parts
  		PI4B = 3.77489470793079817668E-8                             // 0x3e64442d00000000,
  		PI4C = 2.69515142907905952645E-15                            // 0x3ce8469898cc5170,
  		M4PI = 1.273239544735162542821171882678754627704620361328125 // 4/pi
  	)
  	// special cases
  	switch {
  	case x == 0 || IsNaN(x):
  		return x // return ±0 || NaN()
  	case IsInf(x, 0):
  		return NaN()
  	}
  
  	// make argument positive but save the sign
  	sign := false
  	if x < 0 {
  		x = -x
  		sign = true
  	}
  
  	j := int64(x * M4PI) // integer part of x/(Pi/4), as integer for tests on the phase angle
  	y := float64(j)      // integer part of x/(Pi/4), as float
  
  	/* map zeros and singularities to origin */
  	if j&1 == 1 {
  		j++
  		y++
  	}
  
  	z := ((x - y*PI4A) - y*PI4B) - y*PI4C
  	zz := z * z
  
  	if zz > 1e-14 {
  		y = z + z*(zz*(((_tanP[0]*zz)+_tanP[1])*zz+_tanP[2])/((((zz+_tanQ[1])*zz+_tanQ[2])*zz+_tanQ[3])*zz+_tanQ[4]))
  	} else {
  		y = z
  	}
  	if j&2 == 2 {
  		y = -1 / y
  	}
  	if sign {
  		y = -y
  	}
  	return y
  }
  

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