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Pushing the bulk of UHD-3.7.0 code.

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Original-commit: ff1546f8137f7f92bb250f685561b0c34cc0e053
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Ben Hilburn
2014-02-14 12:05:07 -08:00
parent 29086f9001
commit fbbc991a7d
2194 changed files with 1489297 additions and 1084 deletions
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sim/math.v
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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.