From 6c9516300511aaa0d708e6582744c5b593c23df4 Mon Sep 17 00:00:00 2001
From: Andrew2 <andrew.xia@live.ca>
Date: Tue, 03 Dec 2013 03:48:04 +0000
Subject: Outlined in ticket 2697. Works by checking amount of digits in "x" then

rounding "x" to the appropriate amount of digits. Also added code to
return 0 when "x" is pi or pi/2 to the appropriate sin, cos or tan
function. Work by Andrew Xia
---
diff --git a/functions.py b/functions.py
index 8a737ff..f335d19 100644
--- a/functions.py
+++ b/functions.py
@@ -70,6 +70,7 @@ _FUNCTIONS = [
     _('tan'),
     _('tanh'),
     _('xor'),
+    _('countDigits')
     ]    
 
 def _d(val):
@@ -112,13 +113,17 @@ abs.__doc__ = _(
 'abs(x), return absolute value of x, which means -x for x < 0')
 
 def acos(x):
-    return _inv_scale_angle(math.acos(x))
+    n = countDigits(x)
+    x = _inv_scale_angle(math.acos(x))
+    return round(x, int(n - math.ceil(math.log10(abs(x)))))
 acos.__doc__ = _(
 'acos(x), return the arc cosine of x. This is the angle for which the cosine \
 is x. Defined for -1 <= x < 1')
 
 def acosh(x):
-    return math.acosh(x)
+    n = countDigits(x)
+    x = math.acosh(x)
+    return round(x, int(n - math.ceil(math.log10(abs(x)))))
 acosh.__doc__ = _(
 'acosh(x), return the arc hyperbolic cosine of x. This is the value y for \
 which the hyperbolic cosine equals x.')
@@ -136,25 +141,33 @@ def add(x, y):
 add.__doc__ = _('add(x, y), return x + y')
 
 def asin(x):
-    return _inv_scale_angle(math.asin(x))
+    n = countDigits(x)
+    x = _inv_scale_angle(math.asin(x))
+    return round(x, int(n - math.ceil(math.log10(abs(x)))))
 asin.__doc__ = _(
 'asin(x), return the arc sine of x. This is the angle for which the sine is x. \
 Defined for -1 <= x <= 1')
 
 def asinh(x):
-    return math.asinh(x)
+    n = countDigits(x)
+    x = math.asinh(x)
+    return round(x, int(n - math.ceil(math.log10(abs(x)))))
 asinh.__doc__ = _(
 'asinh(x), return the arc hyperbolic sine of x. This is the value y for \
 which the hyperbolic sine equals x.')
 
 def atan(x):
-    return _inv_scale_angle(math.atan(x))
+    n = countDigits(x)
+    x = _inv_scale_angle(math.atan(x))
+    return round(x, int(n - math.ceil(math.log10(abs(x)))))
 atan.__doc__ = _(
 'atan(x), return the arc tangent of x. This is the angle for which the tangent \
 is x. Defined for all x')
 
 def atanh(x):
-    return math.atanh(x)
+    n = countDigits(x)
+    x = math.atanh(x)
+    return round(x, int(n - math.ceil(math.log10(abs(x)))))
 atanh.__doc__ = _(
 'atanh(x), return the arc hyperbolic tangent of x. This is the value y for \
 which the hyperbolic tangent equals x.')
@@ -183,13 +196,19 @@ def ceil(x):
 ceil.__doc__ = _('ceil(x), return the smallest integer larger than x.')
 
 def cos(x):
-    return math.cos(_scale_angle(x))
+    if(x % (math.pi/2) == 0 and x % math.pi != 0):
+        return 0
+    n = countDigits(x)
+    x = math.cos(_scale_angle(x))
+    return round(x, int(n - math.ceil(math.log10(abs(x)))))
 cos.__doc__ = _(
 'cos(x), return the cosine of x. This is the x-coordinate on the unit circle \
 at the angle x')
 
 def cosh(x):
-    return math.cosh(x)
+    n = countDigits(x)
+    x = math.cosh(x)
+    return round(x, int(n - math.ceil(math.log10(abs(x)))))
 cosh.__doc__ = _(
 'cosh(x), return the hyperbolic cosine of x. Given by (exp(x) + exp(-x)) / 2')
 
@@ -371,9 +390,9 @@ rand_int.__doc__ = _(
 'rand_int([<maxval>]), return a random integer between 0 and <maxval>. \
 <maxval> is an optional argument and is set to 65535 by default.')
 
-def round(x):
+"""def round(x):
     return math.round(float(x))
-round.__doc__ = _('round(x), return the integer nearest to x.')
+round.__doc__ = _('round(x), return the integer nearest to x.')"""
 
 def shift_left(x, y):
     if is_int(x) and is_int(y):
@@ -392,20 +411,28 @@ shift_right.__doc__ = _(
 'shift_right(x, y), shift x by y bits to the right (divide by 2 per bit)')
 
 def sin(x):
-    return math.sin(_scale_angle(x))
+    if(x % math.pi == 0):
+        return 0
+    n = countDigits(x)
+    x = math.sin(_scale_angle(x))
+    return round(x, int(n - math.ceil(math.log10(abs(x)))))
 sin.__doc__ = _(
 'sin(x), return the sine of x. This is the y-coordinate on the unit circle at \
 the angle x')
 
 def sinh(x):
-    return math.sinh(x)
+    n = countDigits(x)
+    x = math.sinh(x)
+    return round(x, int(n - math.ceil(math.log10(abs(x)))))
 sinh.__doc__ = _(
 'sinh(x), return the hyperbolic sine of x. Given by (exp(x) - exp(-x)) / 2')
 
 def sinc(x):
     if float(x) == 0.0:
         return 1
-    return sin(x) / x
+    n = countDigits(x)
+    x = sin(x) / x
+    return round(x, int(n - math.ceil(math.log10(abs(x)))))
 sinc.__doc__ = _(
 'sinc(x), return the sinc of x. This is given by sin(x) / x.')
 
@@ -427,14 +454,20 @@ def sub(x, y):
 sub.__doc__ = _('sub(x, y), return x - y')
 
 def tan(x):
-    return math.tan(_scale_angle(x))
+    if(x % math.pi == 0):
+        return 0
+    n = countDigits(x)
+    x = math.tan(_scale_angle(x))
+    return round(x, int(n - math.ceil(math.log10(abs(x)))))
 tan.__doc__ = _(
 'tan(x), return the tangent of x. This is the slope of the line from the origin \
 of the unit circle to the point on the unit circle defined by the angle x. Given \
 by sin(x) / cos(x)')
 
 def tanh(x):
-    return math.tanh(x)
+    n = countDigits(x)
+    x = math.tanh(x)
+    return round(x, int(n - math.ceil(math.log10(abs(x)))))
 tanh.__doc__ = _(
 'tanh(x), return the hyperbolic tangent of x. Given by sinh(x) / cosh(x)')
 
@@ -444,3 +477,10 @@ xor.__doc__ = _(
 'xor(x, y), logical xor. Returns True if either x is True (and y is False) \
 or y is True (and x is False), else returns False')
 
+def countDigits(x):
+    if(x % 1 == 0):
+        return len(str(x))
+    else:
+        return len(str(x)) - 1
+countDigits.__doc__ = _(
+'Returns the number of digits in x')
--
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