Exponents and logarithms

packages/math/math.grnd

@@ -29,6 +29,10 @@ fun -double !pi
     return 3.141592653589793
 endfun
 
+fun -double !e
+    return 2.718281828459045
+endfun
+
 fun -double !intexp -double &base -int &power
     lesser $power 1 &store
     set &ans 1
@@ -206,8 +210,117 @@ fun -double !sqrt -double &in
     return $ans
 
     @error
-    error "Cannot find square root of a negative double"
+    error "Cannot find square root of a negative double" "mathError"
 endfun
 
-pusharg -0.5
-call !sqrt &store
+fun -double !abs -double &in
+    lesser $in 0 &store
+    if $store %negative
+    return $in
+
+    @negative
+    multiply $in -1 &in
+    return $in
+endfun
+
+fun -double !exp -double &in
+    call !e &e
+
+    lesser $in 0 &store
+    if $store %negative
+
+    # Find $in rounded down
+    pusharg $in
+    stod "1.00" &store
+    pusharg $store
+    call !mod &floorin
+    subtract $in $floorin &floorin
+    pusharg $floorin
+    call !dtoi &floorin
+    
+    # e^(a+x)=e^a*e^x
+    pusharg $e
+    pusharg $floorin
+    call !intexp &e^a
+
+    # Find e^($in - $floorin)
+    subtract $in $floorin &x
+
+    # e^x = 1 + x + x^2/2 + x^3/6 + ... + x^k/k!
+    set &idx 0
+    set &e^x 0
+    @loop
+        equal $idx 10 &store
+        if $store %return 
+
+        pusharg $x
+        pusharg $idx
+        call !intexp &store
+
+        pusharg $idx
+        call !factorial &fact
+
+        divide $store $fact &store
+
+        add $e^x $store &e^x
+        add $idx 1 &idx
+
+        jump %loop
+
+    @return
+    multiply $e^a $e^x &ans
+    return $ans
+
+    @negative
+    # e^-x = 1/e^x
+    multiply $in -1 &in
+    pusharg $in
+    call !exp &store
+    divide 1 $store &store
+    return $store
+
+endfun
+
+fun -double !ln -double &in
+    greater $in 0 &store
+    if $store %calculate
+    jump %error
+
+    @calculate
+    equal $in 1 &store
+    if $store %zero
+
+    # We will use Newton's method.
+    # ln(a) is the root of e^x-a
+    # Therefore x_k+1 = x_k - (e^x_k - a)/(e^x_k)
+
+    set &ans 0.9
+
+    @loop
+        pusharg $ans
+        call !exp &e^x
+        subtract $e^x $in &store
+        divide $store $e^x &store
+        subtract $ans $store &ans
+
+        pusharg $store
+        call !abs &store
+        lesser $store 0.000000000001 &store
+        if $store %return
+
+        jump %loop
+
+    @return
+    return $ans
+
+    @zero
+    stod "0" &zero
+    return $zero
+
+    @error
+    error "Cannot find ln of a non-positive double" "mathError"
+endfun
+
+pusharg 0.0000000000000000000000000000000000000000000001
+call !ln &store
+stdlnout $store

packages/math/readme.md

@@ -22,6 +22,14 @@ Gets the tan of input.
 
 Returns base^power, for positive integer values of power. Returns 1 if power is non-positive (and thus is inaccurate for negative values of power).
 
+### fun -double !exp -double &input
+
+Finds exp($input), where exp(x)=e^x, e is Euler's number = 2.718281828...
+
+### fun -double !ln -double &in
+
+Finds the natural log (log_e) of $input, i.e. finds x such that e^x = $input, e is Euler's number = 2.718281828...
+
 ### fun -double !sqrt -double &input
 
 Returns the positive value *x* that satisfies x^2 = input. Throws an error if input is negative.
@@ -30,6 +38,10 @@ Returns the positive value *x* that satisfies x^2 = input. Throws an error if in
 
 Returns *n* such that *n* is congruent to the input modulo $modulus, where *n* is at least 0 and less than $modulus.
 
+### fun -double !abs -double &in
+
+Returns the absolute value of *n*.
+
 ### fun -double !random -int &seed
 
 Gets a random double in the domain [0,1), using a LCG. A seed is required.