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[Commit-gnuradio] r6532 - gnuradio/branches/developers/matt/u2f/models
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From: |
matt |
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Subject: |
[Commit-gnuradio] r6532 - gnuradio/branches/developers/matt/u2f/models |
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Date: |
Tue, 25 Sep 2007 12:18:55 -0600 (MDT) |
Author: matt
Date: 2007-09-25 12:18:47 -0600 (Tue, 25 Sep 2007)
New Revision: 6532
Added:
gnuradio/branches/developers/matt/u2f/models/math_real.v
Log:
copied from zhuochen's directory, originally by Brian Padalino (?)
Copied: gnuradio/branches/developers/matt/u2f/models/math_real.v (from rev
6531, gnuradio/branches/developers/zhuochen/simulations/burst_test/math_real.v)
===================================================================
--- gnuradio/branches/developers/matt/u2f/models/math_real.v
(rev 0)
+++ gnuradio/branches/developers/matt/u2f/models/math_real.v 2007-09-25
18:18:47 UTC (rev 6532)
@@ -0,0 +1,496 @@
+/*
+ * This is a general recreation of the VHDL ieee.math_real package.
+ */
+
+// Constants for use below and for general reference
+// TODO: Bring it out to 12 (or more???) places beyond the decimal?
+`define MATH_E 2.7182818284
+`define MATH_1_OVER_E 0.3678794411
+`define MATH_PI 3.1415926536
+`define MATH_2_PI 6.2831853071
+`define MATH_1_OVER_PI 0.3183098861
+`define MATH_PI_OVER_2 1.5707963267
+`define MATH_PI_OVER_3 1.0471975511
+`define MATH_PI_OVER_4 0.7853981633
+`define MATH_3_PI_OVER_2 4.7123889803
+`define MATH_LOG_OF_2 0.6931471805
+`define MATH_LOG_OF_10 2.3025850929
+`define MATH_LOG2_OF_E 1.4426950408
+`define MATH_LOG10_OF_E 0.4342944819
+`define MATH_SQRT_2 1.4142135623
+`define MATH_1_OVER_SQRT_2 0.7071067811
+`define MATH_SQRT_PI 1.7724538509
+`define MATH_DEG_TO_RAD 0.0174532925
+`define MATH_RAD_TO_DEG 57.2957795130
+
+// The number of iterations to do for the Taylor series approximations
+`define EXPLOG_ITERATIONS 19
+`define COS_ITERATIONS 13
+
+module math ;
+
+ /* Conversion Routines */
+
+ // Return the sign of a particular number.
+ function real sign ;
+ input real x ;
+ begin
+ sign = x < 0.0 ? 1.0 : 0.0 ;
+ end
+ endfunction
+
+ // Return the trunc function of a number
+ function real trunc ;
+ input real x ;
+ begin
+ trunc = x - mod(x,1.0) ;
+ end
+ endfunction
+
+ // Return the ceiling function of a number.
+ function real ceil ;
+ input real x ;
+ real retval ;
+ begin
+ retval = mod(x,1.0) ;
+ if( retval != 0.0 && x > 0.0 ) retval = x+1.0 ;
+ else retval = x ;
+ ceil = trunc(retval) ;
+ end
+ endfunction
+
+ // Return the floor function of a number
+ function real floor ;
+ input real x ;
+ real retval ;
+ begin
+ retval = mod(x,1.0) ;
+ if( retval != 0.0 && x < 0.0 ) retval = x - 1.0 ;
+ else retval = x ;
+ floor = trunc(retval) ;
+ end
+ endfunction
+
+ // Return the round function of a number
+ function real round ;
+ input real x ;
+ real retval ;
+ begin
+ retval = x > 0.0 ? x + 0.5 : x - 0.5 ;
+ round = trunc(retval) ;
+ end
+ endfunction
+
+ // Return the fractional remainder of (x mod m)
+ function real mod ;
+ input real x ;
+ input real m ;
+ real retval ;
+ begin
+ retval = x ;
+ if( retval > m ) begin
+ while( retval > m ) begin
+ retval = retval - m ;
+ end
+ end
+ else begin
+ while( retval < -m ) begin
+ retval = retval + m ;
+ end
+ end
+ mod = retval ;
+ end
+ endfunction
+
+ // Return the max between two real numbers
+ function real realmax ;
+ input real x ;
+ input real y ;
+ begin
+ realmax = x > y ? x : y ;
+ end
+ endfunction
+
+ // Return the min between two real numbers
+ function real realmin ;
+ input real x ;
+ input real y ;
+ begin
+ realmin = x > y ? y : x ;
+ end
+ endfunction
+
+ /* Random Numbers */
+
+ // Generate Gaussian distributed variables
+ function real gaussian ;
+ input real mean ;
+ input real var ;
+ real u1, u2, v1, v2, s ;
+ begin
+ s = 1.0 ;
+ while( s >= 1.0 ) begin
+ // Two random numbers between 0 and 1
+ u1 = $random/4294967296.0 + 0.5 ;
+ u2 = $random/4294967296.0 + 0.5 ;
+ // Adjust to be between -1,1
+ v1 = 2*u1-1.0 ;
+ v2 = 2*u2-1.0 ;
+ // Polar mag squared
+ s = (v1*v1 + v2*v2) ;
+ end
+ gaussian = mean + sqrt((-2.0*log(s))/s) * v1 * sqrt(var) ;
+ // gaussian2 = mean + sqrt(-2*log(s)/s)*v2 * sqrt(var) ;
+ end
+ endfunction
+
+ /* Roots and Log Functions */
+
+ // Return the square root of a number
+ function real sqrt ;
+ input real x ;
+ real retval ;
+ begin
+ sqrt = (x == 0.0) ? 0.0 : powr(x,0.5) ;
+ end
+ endfunction
+
+ // Return the cube root of a number
+ function real cbrt ;
+ input real x ;
+ real retval ;
+ begin
+ cbrt = (x == 0.0) ? 0.0 : powr(x,1.0/3.0) ;
+ end
+ endfunction
+
+ // Return the absolute value of a real value
+ function real abs ;
+ input real x ;
+ begin
+ abs = (x > 0.0) ? x : -x ;
+ end
+ endfunction
+
+ // Return a real value raised to an integer power
+ function real pow ;
+ input real b ;
+ input integer x ;
+ integer absx ;
+ real retval ;
+ begin
+ retval = 1.0 ;
+ absx = abs(x) ;
+ repeat(absx) begin
+ retval = b*retval ;
+ end
+ pow = x < 0 ? (1.0/retval) : retval ;
+ end
+ endfunction
+
+ // Return a real value raised to a real power
+ function real powr ;
+ input real b ;
+ input real x ;
+ begin
+ powr = exp(x*log(b)) ;
+ end
+ endfunction
+
+ // Return the evaluation of e^x where e is the natural logarithm base
+ // NOTE: This is the Taylor series expansion of e^x
+ function real exp ;
+ input real x ;
+ real retval ;
+ integer i ;
+ real nm1_fact ;
+ real powm1 ;
+ begin
+ nm1_fact = 1.0 ;
+ powm1 = 1.0 ;
+ retval = 1.0 ;
+ for( i = 1 ; i < `EXPLOG_ITERATIONS ; i = i + 1 ) begin
+ powm1 = x*powm1 ;
+ nm1_fact = nm1_fact * i ;
+ retval = retval + powm1/nm1_fact ;
+ end
+ exp = retval ;
+ end
+ endfunction
+
+ // Return the evaluation log(x)
+ function real log ;
+ input real x ;
+ integer i ;
+ real whole ;
+ real xm1oxp1 ;
+ real retval ;
+ real newx ;
+ begin
+ retval = 0.0 ;
+ whole = 0.0 ;
+ newx = x ;
+ while( newx > `MATH_E ) begin
+ whole = whole + 1.0 ;
+ newx = newx / `MATH_E ;
+ end
+ xm1oxp1 = (newx-1.0)/(newx+1.0) ;
+ for( i = 0 ; i < `EXPLOG_ITERATIONS ; i = i + 1 ) begin
+ retval = retval + pow(xm1oxp1,2*i+1)/(2.0*i+1.0) ;
+ end
+ log = whole+2.0*retval ;
+ end
+ endfunction
+
+ // Return the evaluation ln(x) (same as log(x))
+ function real ln ;
+ input real x ;
+ begin
+ ln = log(x) ;
+ end
+ endfunction
+
+ // Return the evaluation log_2(x)
+ function real log2 ;
+ input real x ;
+ begin
+ log2 = log(x)/`MATH_LOG_OF_2 ;
+ end
+ endfunction
+
+ function real log10 ;
+ input real x ;
+ begin
+ log10 = log(x)/`MATH_LOG_OF_10 ;
+ end
+ endfunction
+
+ function real log_base ;
+ input real x ;
+ input real b ;
+ begin
+ log_base = log(x)/log(b) ;
+ end
+ endfunction
+
+ /* Trigonometric Functions */
+
+ // Internal function to reduce a value to be between [-pi:pi]
+ function real reduce ;
+ input real x ;
+ real retval ;
+ begin
+ retval = x ;
+ while( abs(retval) > `MATH_PI ) begin
+ retval = retval > `MATH_PI ?
+ (retval - `MATH_2_PI) :
+ (retval + `MATH_2_PI) ;
+ end
+ reduce = retval ;
+ end
+ endfunction
+
+ // Return the cos of a number in radians
+ function real cos ;
+ input real x ;
+ integer i ;
+ integer sign ;
+ real newx ;
+ real retval ;
+ real xsqnm1 ;
+ real twonm1fact ;
+ begin
+ newx = reduce(x) ;
+ xsqnm1 = 1.0 ;
+ twonm1fact = 1.0 ;
+ retval = 1.0 ;
+ for( i = 1 ; i < `COS_ITERATIONS ; i = i + 1 ) begin
+ sign = -2*(i % 2)+1 ;
+ xsqnm1 = xsqnm1*newx*newx ;
+ twonm1fact = twonm1fact * (2.0*i) * (2.0*i-1.0) ;
+ retval = retval + sign*(xsqnm1/twonm1fact) ;
+ end
+ cos = retval ;
+ end
+ endfunction
+
+ // Return the sin of a number in radians
+ function real sin ;
+ input real x ;
+ begin
+ sin = cos(x - `MATH_PI_OVER_2) ;
+ end
+ endfunction
+
+ // Return the tan of a number in radians
+ function real tan ;
+ input real x ;
+ begin
+ tan = sin(x) / cos(x) ;
+ end
+ endfunction
+
+ // Return the arcsin in radians of a number
+ function real arcsin ;
+ input real x ;
+ begin
+ arcsin = 2.0*arctan(x/(1.0+sqrt(1.0-x*x))) ;
+ end
+ endfunction
+
+ // Return the arccos in radians of a number
+ function real arccos ;
+ input real x ;
+ begin
+ arccos = `MATH_PI_OVER_2-arcsin(x) ;
+ end
+ endfunction
+
+ // Return the arctan in radians of a number
+ // TODO: Make sure this REALLY does work as it is supposed to!
+ function real arctan ;
+ input real x ;
+ real retval ;
+ real y ;
+ real newx ;
+ real twoiotwoip1 ;
+ integer i ;
+ integer mult ;
+ begin
+ retval = 1.0 ;
+ twoiotwoip1 = 1.0 ;
+ mult = 1 ;
+ newx = abs(x) ;
+ while( newx > 1.0 ) begin
+ mult = mult*2 ;
+ newx = newx/(1.0+sqrt(1.0+newx*newx)) ;
+ end
+ y = 1.0 ;
+ for( i = 1 ; i < 2*`COS_ITERATIONS ; i = i + 1 ) begin
+ y = y*((newx*newx)/(1+newx*newx)) ;
+ twoiotwoip1 = twoiotwoip1 * (2.0*i)/(2.0*i+1.0) ;
+ retval = retval + twoiotwoip1*y ;
+ end
+ retval = retval * (newx/(1+newx*newx)) ;
+ retval = retval * mult ;
+
+ arctan = (x > 0.0) ? retval : -retval ;
+ end
+ endfunction
+
+ // Return the arctan in radians of a ratio x/y
+ // TODO: Test to make sure this works as it is supposed to!
+ function real arctan_xy ;
+ input real x ;
+ input real y ;
+ real retval ;
+ begin
+ retval = 0.0 ;
+ if( x < 0.0 ) retval = `MATH_PI - arctan(-abs(y)/x) ;
+ else if( x > 0.0 ) retval = arctan(abs(y)/x) ;
+ else if( x == 0.0 ) retval = `MATH_PI_OVER_2 ;
+ arctan_xy = (y < 0.0) ? -retval : retval ;
+ end
+ endfunction
+
+ /* Hyperbolic Functions */
+
+ // Return the sinh of a number
+ function real sinh ;
+ input real x ;
+ begin
+ sinh = (exp(x) - exp(-x))/2.0 ;
+ end
+ endfunction
+
+ // Return the cosh of a number
+ function real cosh ;
+ input real x ;
+ begin
+ cosh = (exp(x) + exp(-x))/2.0 ;
+ end
+ endfunction
+
+ // Return the tanh of a number
+ function real tanh ;
+ input real x ;
+ real e2x ;
+ begin
+ e2x = exp(2.0*x) ;
+ tanh = (e2x+1.0)/(e2x-1.0) ;
+ end
+ endfunction
+
+ // Return the arcsinh of a number
+ function real arcsinh ;
+ input real x ;
+ begin
+ arcsinh = log(x+sqrt(x*x+1.0)) ;
+ end
+ endfunction
+
+ // Return the arccosh of a number
+ function real arccosh ;
+ input real x ;
+ begin
+ arccosh = ln(x+sqrt(x*x-1.0)) ;
+ end
+ endfunction
+
+ // Return the arctanh of a number
+ function real arctanh ;
+ input real x ;
+ begin
+ arctanh = 0.5*ln((1.0+x)/(1.0-x)) ;
+ end
+ endfunction
+ /*
+ initial begin
+ $display( "cos(MATH_PI_OVER_3): %f", cos(`MATH_PI_OVER_3) ) ;
+ $display( "sin(MATH_PI_OVER_3): %f", sin(`MATH_PI_OVER_3) ) ;
+ $display( "sign(-10): %f", sign(-10) ) ;
+ $display( "realmax(MATH_PI,MATH_E): %f", realmax(`MATH_PI,`MATH_E) ) ;
+ $display( "realmin(MATH_PI,MATH_E): %f", realmin(`MATH_PI,`MATH_E) ) ;
+ $display( "mod(MATH_PI,MATH_E): %f", mod(`MATH_PI,`MATH_E) ) ;
+ $display( "ceil(-MATH_PI): %f", ceil(-`MATH_PI) ) ;
+ $display( "ceil(4.0): %f", ceil(4.0) ) ;
+ $display( "ceil(3.99999999999999): %f", ceil(3.99999999999999) ) ;
+ $display( "pow(MATH_PI,2): %f", pow(`MATH_PI,2) ) ;
+ $display( "gaussian(1.0,1.0): %f", gaussian(1.0,1.0) ) ;
+ $display( "round(MATH_PI): %f", round(`MATH_PI) ) ;
+ $display( "trunc(-MATH_PI): %f", trunc(-`MATH_PI) ) ;
+ $display( "ceil(-MATH_PI): %f", ceil(-`MATH_PI) ) ;
+ $display( "floor(MATH_PI): %f", floor(`MATH_PI) ) ;
+ $display( "round(e): %f", round(`MATH_E)) ;
+ $display( "ceil(-e): %f", ceil(-`MATH_E)) ;
+ $display( "exp(MATH_PI): %f", exp(`MATH_PI) ) ;
+ $display( "log2(MATH_PI): %f", log2(`MATH_PI) ) ;
+ $display( "log_base(pow(2,32),2): %f", log_base(pow(2,32),2) ) ;
+ $display( "ln(0.1): %f", log(0.1) ) ;
+ $display( "cbrt(7): %f", cbrt(7) ) ;
+ $display( "cos(`MATH_2_PI): %f", cos(20*`MATH_2_PI) ) ;
+ $display( "sin(-`MATH_2_PI): %f", sin(-50*`MATH_2_PI) ) ;
+ $display( "sinh(`MATH_E): %f", sinh(`MATH_E) ) ;
+ $display( "cosh(`MATH_2_PI): %f", cosh(`MATH_2_PI) ) ;
+ $display( "arctan_xy(-4,3): %f", arctan_xy(-4,3) ) ;
+ $display( "arctan(MATH_PI): %f", arctan(`MATH_PI) ) ;
+ $display( "arctan(-MATH_E/2): %f", arctan(-`MATH_E/2) ) ;
+ $display( "arctan(MATH_PI_OVER_2): %f", arctan(`MATH_PI_OVER_2) ) ;
+ $display( "arctan(1/7) = %f", arctan(1.0/7.0) ) ;
+ $display( "arctan(3/79) = %f", arctan(3.0/79.0) ) ;
+ $display( "pi/4 ?= %f", 5*arctan(1.0/7.0)+2*arctan(3.0/79.0) ) ;
+ $display( "arcsin(1.0): %f", arcsin(1.0) ) ;
+ $display( "cos(pi/2): %f", cos(`MATH_PI_OVER_2)) ;
+ $display( "arccos(cos(pi/2)): %f", arccos(cos(`MATH_PI_OVER_2)) ) ;
+ $display( "cos(0): %f", cos(0) ) ;
+ $display( "cos(`MATH_PI_OVER_4): %f", cos(`MATH_PI_OVER_4) ) ;
+ $display( "cos(`MATH_PI_OVER_2): %f", cos(`MATH_PI_OVER_2) ) ;
+ $display( "cos(3*`MATH_PI_OVER_4): %f", cos(3*`MATH_PI_OVER_4) ) ;
+ $display( "cos(`MATH_PI): %f", cos(`MATH_PI) ) ;
+ $display( "cos(5*`MATH_PI_OVER_4): %f", cos(5*`MATH_PI_OVER_4) ) ;
+ $display( "cos(6*`MATH_PI_OVER_4): %f", cos(6*`MATH_PI_OVER_4) ) ;
+ $display( "cos(7*`MATH_PI_OVER_4): %f", cos(7*`MATH_PI_OVER_4) ) ;
+ $display( "cos(8*`MATH_PI_OVER_4): %f", cos(8*`MATH_PI_OVER_4) ) ;
+ end*/
+
+endmodule
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