From 07b6a3d335450778f69a6ee5afa5716e4fe83fe3 Mon Sep 17 00:00:00 2001
From: Marc Tiehuis <marctiehuis@gmail.com>
Date: Sat, 21 Jul 2018 23:33:28 +1200
Subject: [PATCH] Tighten Int.to bounds and add twos-complement bitcount

---
 std/math/big/int.zig | 103 ++++++++++++++++++++++++++++++++++++++-----
 1 file changed, 91 insertions(+), 12 deletions(-)

diff --git a/std/math/big/int.zig b/std/math/big/int.zig
index caa9d0a7e..026933bd6 100644
--- a/std/math/big/int.zig
+++ b/std/math/big/int.zig
@@ -115,13 +115,47 @@ pub const Int = struct {
         return !r.isOdd();
     }
 
-    fn bitcount(self: Int) usize {
-        const u_bit_count = (self.len - 1) * Limb.bit_count + (Limb.bit_count - @clz(self.limbs[self.len - 1]));
-        return usize(@boolToInt(!self.positive)) + u_bit_count;
+    // Returns the number of bits required to represent the absolute value of self.
+    fn bitCountAbs(self: Int) usize {
+        return (self.len - 1) * Limb.bit_count + (Limb.bit_count - @clz(self.limbs[self.len - 1]));
     }
 
+    // Returns the number of bits required to represent the integer in twos-complement form.
+    //
+    // If the integer is negative the value returned is the number of bits needed by a signed
+    // integer to represent the value. If positive the value is the number of bits for an
+    // unsigned integer. Any unsigned integer will fit in the signed integer with bitcount
+    // one greater than the returned value.
+    //
+    // e.g. -127 returns 8 as it will fit in an i8. 127 returns 7 since it fits in a u7.
+    fn bitCountTwosComp(self: Int) usize {
+        var bits = self.bitCountAbs();
+
+        // If the entire value has only one bit set (e.g. 0b100000000) then the negation in twos
+        // complement requires one less bit.
+        if (!self.positive) block: {
+            bits += 1;
+
+            if (@popCount(self.limbs[self.len - 1]) == 1) {
+                for (self.limbs[0 .. self.len - 1]) |limb| {
+                    if (@popCount(limb) != 0) {
+                        break :block;
+                    }
+                }
+
+                bits -= 1;
+            }
+        }
+
+        return bits;
+    }
+
+    // Returns the approximate size of the integer in the given base. Negative values accomodate for
+    // the minus sign. This is used for determining the number of characters needed to print the
+    // value. It is inexact and will exceed the given value by 1-2 digits.
     pub fn sizeInBase(self: Int, base: usize) usize {
-        return (self.bitcount() / math.log2(base)) + 1;
+        const bit_count = usize(@boolToInt(!self.positive)) + self.bitCountAbs();
+        return (bit_count / math.log2(base)) + 1;
     }
 
     pub fn set(self: *Int, value: var) Allocator.Error!void {
@@ -189,9 +223,9 @@ pub const Int = struct {
     pub fn to(self: Int, comptime T: type) ConvertError!T {
         switch (@typeId(T)) {
             TypeId.Int => {
-                const UT = if (T.is_signed) @IntType(false, T.bit_count - 1) else T;
+                const UT = @IntType(false, T.bit_count);
 
-                if (self.bitcount() > 8 * @sizeOf(UT)) {
+                if (self.bitCountTwosComp() > T.bit_count) {
                     return error.TargetTooSmall;
                 }
 
@@ -208,9 +242,17 @@ pub const Int = struct {
                 }
 
                 if (!T.is_signed) {
-                    return if (self.positive) r else error.NegativeIntoUnsigned;
+                    return if (self.positive) @intCast(T, r) else error.NegativeIntoUnsigned;
                 } else {
-                    return if (self.positive) @intCast(T, r) else -@intCast(T, r);
+                    if (self.positive) {
+                        return @intCast(T, r);
+                    } else {
+                        if (math.cast(T, r)) |ok| {
+                            return -ok;
+                        } else |_| {
+                            return @minValue(T);
+                        }
+                    }
                 }
             },
             else => {
@@ -1120,24 +1162,61 @@ test "big.int bitcount + sizeInBase" {
     var a = try Int.init(al);
 
     try a.set(0b100);
-    debug.assert(a.bitcount() == 3);
+    debug.assert(a.bitCountAbs() == 3);
     debug.assert(a.sizeInBase(2) >= 3);
     debug.assert(a.sizeInBase(10) >= 1);
 
+    a.negate();
+    debug.assert(a.bitCountAbs() == 3);
+    debug.assert(a.sizeInBase(2) >= 4);
+    debug.assert(a.sizeInBase(10) >= 2);
+
     try a.set(0xffffffff);
-    debug.assert(a.bitcount() == 32);
+    debug.assert(a.bitCountAbs() == 32);
     debug.assert(a.sizeInBase(2) >= 32);
     debug.assert(a.sizeInBase(10) >= 10);
 
     try a.shiftLeft(a, 5000);
-    debug.assert(a.bitcount() == 5032);
+    debug.assert(a.bitCountAbs() == 5032);
     debug.assert(a.sizeInBase(2) >= 5032);
     a.positive = false;
 
-    debug.assert(a.bitcount() == 5033);
+    debug.assert(a.bitCountAbs() == 5032);
     debug.assert(a.sizeInBase(2) >= 5033);
 }
 
+test "big.int bitcount/to" {
+    var a = try Int.init(al);
+
+    try a.set(0);
+    debug.assert(a.bitCountTwosComp() == 0);
+
+    // TODO: stack smashing
+    // debug.assert((try a.to(u0)) == 0);
+    // TODO: sigsegv
+    // debug.assert((try a.to(i0)) == 0);
+
+    try a.set(-1);
+    debug.assert(a.bitCountTwosComp() == 1);
+    debug.assert((try a.to(i1)) == -1);
+
+    try a.set(-8);
+    debug.assert(a.bitCountTwosComp() == 4);
+    debug.assert((try a.to(i4)) == -8);
+
+    try a.set(127);
+    debug.assert(a.bitCountTwosComp() == 7);
+    debug.assert((try a.to(u7)) == 127);
+
+    try a.set(-128);
+    debug.assert(a.bitCountTwosComp() == 8);
+    debug.assert((try a.to(i8)) == -128);
+
+    try a.set(-129);
+    debug.assert(a.bitCountTwosComp() == 9);
+    debug.assert((try a.to(i9)) == -129);
+}
+
 test "big.int string set" {
     var a = try Int.init(al);
     try a.setString(10, "120317241209124781241290847124");