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+// All code take from the HDLCon paper:
+// "Verilog Transcendental Functions for Numerical Testbenches"
+//
+// Authored by:
+// Mark G. Arnold marnold@co.umist.ac.uk,
+// Colin Walter c.walter@co.umist.ac.uk
+// Freddy Engineer freddy.engineer@xilinx.com
+//
+
+
+
+// The sine function is approximated with a polynomial which works
+// for -π/2 < x < π/2. (This polynomial, by itself, was used as a
+// Verilog example in [2]; unfortunately there was a typo with the
+// coefficients. The correct coefficients together with an error
+// analysis are given in [3].)   For arguments outside of -π/2 < x < π/2,
+// the identities sin(x) = -sin(-x) and sin(x) = -sin(x-π) allow the
+// argument to be shifted to be within this range.  The latter identity
+// can be applied repeatedly.  Doing so could cause inaccuracies for
+// very large arguments, but in practice the errors are acceptable
+// if the Verilog simulator uses double-precision floating point.
+
+function real sin;
+  input x;
+  real x;
+  real x1,y,y2,y3,y5,y7,sum,sign;
+  begin
+    sign = 1.0;
+    x1 = x;
+    if (x1<0)
+      begin
+        x1 = -x1;
+        sign = -1.0;
+      end
+    while (x1 > 3.14159265/2.0)
+      begin
+        x1 = x1 - 3.14159265;
+        sign = -1.0*sign;
+      end
+    y = x1*2/3.14159265;
+    y2 = y*y;
+    y3 = y*y2;
+    y5 = y3*y2;
+    y7 = y5*y2;
+    sum = 1.570794*y - 0.645962*y3 +
+           0.079692*y5 - 0.004681712*y7;
+    sin = sign*sum;
+  end
+endfunction
+
+// The cosine and tangent are computed from the sine:
+function real cos;
+  input x;
+  real x;
+  begin
+    cos = sin(x + 3.14159265/2.0);
+  end
+endfunction
+
+
+function real tan;
+  input x;
+  real x;
+  begin
+    tan = sin(x)/cos(x);
+  end
+endfunction
+
+// The base-two exponential (antilogarithm) function, 2x, is computed by
+// examining the bits of the argument, and for those bits of the argument
+// that are 1, multiplying the result by the corresponding power of a base
+//  very close to one.  For example,  if there were only two bits after
+// the radix point, the base would be the fourth root of two, 1.1892.
+// This number is squared on each iteration:  1.4142,  2.0,  4.0,  16.0.
+// So, if x is 101.112, the function computes 25.75 as 1.1892*1.4142*2.0*16.0 = 53.81.
+// In general, for k bits of precision, the base would be the 2k root of two.
+// Since we need about 23 bits of accuracy for our function, the base we use
+// is the 223 root of two, 1.000000082629586.  This constant poses a problem
+// to some Verilog parsers, so we construct it in two parts.  The following
+// function computes the appropriate root of two by repeatedly squaring this constant:
+
+function real rootof2;
+  input n;
+  integer n;
+  real power;
+  integer i;
+
+  begin
+    power = 0.82629586;
+    power = power / 10000000.0;
+    power = power + 1.0;
+    i = -23;
+
+    if (n >= 1)
+      begin
+        power = 2.0;
+        i = 0;
+      end
+
+    for (i=i; i< n; i=i+1)
+      begin
+        power = power * power;
+      end
+    rootof2 = power;
+  end
+endfunction // if
+
+// This function is used for computing both antilogarithms and logarithms.
+// This routine is never called with n less than -23, thus no validity check
+// need be performed. When n>0, the exponentiation begins with 2.0 in order to
+// improve accuracy.
+// For computing the antilogarithm, we make use of the identity ex = 2x/ln(2),
+// and then proceed as in the example above.  The constant 1/ln(2) = 1.44269504.
+// Here is the natural exponential function:
+
+function real exp;
+  input x;
+  real x;
+  real x1,power,prod;
+  integer i;
+  begin
+    x1 = fabs(x)*1.44269504;
+    if (x1 > 255.0)
+      begin
+        exp = 0.0;
+        if (x>0.0)
+          begin
+            $display("exp illegal argument:",x);
+            $stop;
+          end
+      end
+    else
+      begin
+        prod = 1.0;
+        power = 128.0;
+        for (i=7; i>=-23; i=i-1)
+          begin
+            if (x1 > power)
+              begin
+                prod = prod * rootof2(i);
+                x1 = x1 - power;
+              end
+            power = power / 2.0;
+          end
+        if (x < 0)
+          exp = 1.0/prod;
+        else
+          exp = prod;
+      end
+  end
+endfunction // fabs
+
+// The function prints an error message if the argument is too large
+// (greater than about 180).  All error messages in this package are
+// followed by $stop  to allow the designer to use the debugging
+// features of Verilog to determine the cause of the error, and
+// possibly to resume the simulation.  An argument of less than
+// about –180 simply returns zero with no error.  The main loop
+// assumes a positive argument.  A negative argument is computed as 1/e-x.
+// The logarithm function prints an error message for arguments less
+// than or equal to zero because the real-valued logarithm is not
+// defined for such arguments.  The loop here requires an argument
+// greater than or equal to one.  For arguments between zero and one,
+// this code uses the identity ln(1/x) = -ln(x).
+
+function real log;
+  input x;
+  real x;
+  real re,log2;
+  integer i;
+  begin
+    if (x <= 0.0)
+      begin
+        $display("log illegal argument:",x);
+        $stop;
+        log = 0;
+      end
+    else
+      begin
+        if (x<1.0)
+          re = 1.0/x;
+        else
+          re = x;
+        log2 = 0.0;
+        for (i=7; i>=-23; i=i-1)
+          begin
+            if (re > rootof2(i))
+              begin
+                re = re/rootof2(i);
+                log2 = 2.0*log2 + 1.0;
+              end
+            else
+              log2 = log2*2;
+          end
+        if (x < 1.0)
+          log = -log2/12102203.16;
+        else
+          log = log2/12102203.16;
+      end
+    end
+endfunction
+
+// The code only divides re by rootof2(i) when the re is larger
+// (so that the quotient will be greater than 1.0). Each time
+// such a division occurs, a bit that is 1 is recorded in the
+// whole number result (multiply by 2 and add 1).  Otherwise,
+// a zero is recorded (multiply by 2).  At the end of the loop,
+// log2 will contain 223 log2|x|.  We divide by 223 and use the
+// identity ln(x) = log2(x)/log2(e).  The constant 12102203.16 is 223  log2(e).
+// The log(x) and exp(x)functions are used to implement the pow(x,y) and sqrt(x) functions:
+
+function real pow;
+  input x,y;
+  real x,y;
+  begin
+    if (x<0.0)
+      begin
+        $display("pow illegal argument:",x);
+        $stop;
+      end
+    pow = exp(y*log(x));
+  end
+endfunction
+
+function real sqrt;
+  input x;
+  real x;
+  begin
+    if (x<0.0)
+      begin
+        $display("sqrt illegal argument:",x);
+        $stop;
+      end
+    sqrt = exp(0.5*log(x));
+  end
+endfunction
+
+// The arctangent [3,7] is computed as a continued fraction,
+// using the identities tan-1(x) = -tan-1(-x) and tan-1(x) = π/2 - tan-1(1/x)
+// to reduce the range to 0 < x < 1:
+
+function real atan;
+  input x;
+  real x;
+  real x1,x2,sign,bias;
+  real d3,s3;
+  begin
+    sign = 1.0;
+    bias = 0.0;
+    x1 = x;
+    if (x1 < 0.0)
+      begin
+	x1 = -x1;
+	sign = -1.0;
+      end
+    if (x1 > 1.0)
+      begin
+	x1 = 1.0/x1;
+	bias = sign*3.14159265/2.0;
+	sign = -1.0*sign;
+      end
+    x2 = x1*x1;
+    d3 = x2 + 1.44863154;
+    d3 = 0.26476862 / d3;
+    s3 = x2 + 3.3163354;
+    d3 = s3 - d3;
+    d3 = 7.10676 / d3;
+    s3 = 6.762139 + x2;
+    d3 = s3 - d3;
+    d3 = 3.7092563 / d3;
+    d3 = d3 + 0.17465544;
+    atan = sign*x1*d3+bias;
+  end
+endfunction
+
+// The other functions (asin(x) and acos(x)) are computed from the arctangent.