authorgravatar for marc@tiehu.isMarc Tiehuis <marc@tiehu.is> 2018-07-21 23:33:28+12:00
committergravatar for marc@tiehu.isMarc Tiehuis <marc@tiehu.is> 2018-07-22 17:47:57+12:00
log07b6a3d335450778f69a6ee5afa5716e4fe83fe3
tree654aebd2f1216853efcff1a0176b02356241f759
parentbbd293355bf09f39d007370a7071dd581e6a64d1

Tighten Int.to bounds and add twos-complement bitcount

1 files changed, 91 insertions(+), 12 deletions(-)

std/math/big/int.zig+91-12
...@@ -115,13 +115,47 @@ pub const Int = struct {...@@ -115,13 +115,47 @@ pub const Int = struct {
115 return !r.isOdd();115 return !r.isOdd();
116 }116 }
117117
118 fn bitcount(self: Int) usize {118 // Returns the number of bits required to represent the absolute value of self.
119 const u_bit_count = (self.len - 1) * Limb.bit_count + (Limb.bit_count - @clz(self.limbs[self.len - 1]));119 fn bitCountAbs(self: Int) usize {
120 return usize(@boolToInt(!self.positive)) + u_bit_count;120 return (self.len - 1) * Limb.bit_count + (Limb.bit_count - @clz(self.limbs[self.len - 1]));
121 }121 }
122122
123 // Returns the number of bits required to represent the integer in twos-complement form.
124 //
125 // If the integer is negative the value returned is the number of bits needed by a signed
126 // integer to represent the value. If positive the value is the number of bits for an
127 // unsigned integer. Any unsigned integer will fit in the signed integer with bitcount
128 // one greater than the returned value.
129 //
130 // e.g. -127 returns 8 as it will fit in an i8. 127 returns 7 since it fits in a u7.
131 fn bitCountTwosComp(self: Int) usize {
132 var bits = self.bitCountAbs();
133
134 // If the entire value has only one bit set (e.g. 0b100000000) then the negation in twos
135 // complement requires one less bit.
136 if (!self.positive) block: {
137 bits += 1;
138
139 if (@popCount(self.limbs[self.len - 1]) == 1) {
140 for (self.limbs[0 .. self.len - 1]) |limb| {
141 if (@popCount(limb) != 0) {
142 break :block;
143 }
144 }
145
146 bits -= 1;
147 }
148 }
149
150 return bits;
151 }
152
153 // Returns the approximate size of the integer in the given base. Negative values accomodate for
154 // the minus sign. This is used for determining the number of characters needed to print the
155 // value. It is inexact and will exceed the given value by 1-2 digits.
123 pub fn sizeInBase(self: Int, base: usize) usize {156 pub fn sizeInBase(self: Int, base: usize) usize {
124 return (self.bitcount() / math.log2(base)) + 1;157 const bit_count = usize(@boolToInt(!self.positive)) + self.bitCountAbs();
158 return (bit_count / math.log2(base)) + 1;
125 }159 }
126160
127 pub fn set(self: *Int, value: var) Allocator.Error!void {161 pub fn set(self: *Int, value: var) Allocator.Error!void {
...@@ -189,9 +223,9 @@ pub const Int = struct {...@@ -189,9 +223,9 @@ pub const Int = struct {
189 pub fn to(self: Int, comptime T: type) ConvertError!T {223 pub fn to(self: Int, comptime T: type) ConvertError!T {
190 switch (@typeId(T)) {224 switch (@typeId(T)) {
191 TypeId.Int => {225 TypeId.Int => {
192 const UT = if (T.is_signed) @IntType(false, T.bit_count - 1) else T;226 const UT = @IntType(false, T.bit_count);
193227
194 if (self.bitcount() > 8 * @sizeOf(UT)) {228 if (self.bitCountTwosComp() > T.bit_count) {
195 return error.TargetTooSmall;229 return error.TargetTooSmall;
196 }230 }
197231
...@@ -208,9 +242,17 @@ pub const Int = struct {...@@ -208,9 +242,17 @@ pub const Int = struct {
208 }242 }
209243
210 if (!T.is_signed) {244 if (!T.is_signed) {
211 return if (self.positive) r else error.NegativeIntoUnsigned;245 return if (self.positive) @intCast(T, r) else error.NegativeIntoUnsigned;
212 } else {246 } else {
213 return if (self.positive) @intCast(T, r) else -@intCast(T, r);247 if (self.positive) {
248 return @intCast(T, r);
249 } else {
250 if (math.cast(T, r)) |ok| {
251 return -ok;
252 } else |_| {
253 return @minValue(T);
254 }
255 }
214 }256 }
215 },257 },
216 else => {258 else => {
...@@ -1120,24 +1162,61 @@ test "big.int bitcount + sizeInBase" {...@@ -1120,24 +1162,61 @@ test "big.int bitcount + sizeInBase" {
1120 var a = try Int.init(al);1162 var a = try Int.init(al);
11211163
1122 try a.set(0b100);1164 try a.set(0b100);
1123 debug.assert(a.bitcount() == 3);1165 debug.assert(a.bitCountAbs() == 3);
1124 debug.assert(a.sizeInBase(2) >= 3);1166 debug.assert(a.sizeInBase(2) >= 3);
1125 debug.assert(a.sizeInBase(10) >= 1);1167 debug.assert(a.sizeInBase(10) >= 1);
11261168
1169 a.negate();
1170 debug.assert(a.bitCountAbs() == 3);
1171 debug.assert(a.sizeInBase(2) >= 4);
1172 debug.assert(a.sizeInBase(10) >= 2);
1173
1127 try a.set(0xffffffff);1174 try a.set(0xffffffff);
1128 debug.assert(a.bitcount() == 32);1175 debug.assert(a.bitCountAbs() == 32);
1129 debug.assert(a.sizeInBase(2) >= 32);1176 debug.assert(a.sizeInBase(2) >= 32);
1130 debug.assert(a.sizeInBase(10) >= 10);1177 debug.assert(a.sizeInBase(10) >= 10);
11311178
1132 try a.shiftLeft(a, 5000);1179 try a.shiftLeft(a, 5000);
1133 debug.assert(a.bitcount() == 5032);1180 debug.assert(a.bitCountAbs() == 5032);
1134 debug.assert(a.sizeInBase(2) >= 5032);1181 debug.assert(a.sizeInBase(2) >= 5032);
1135 a.positive = false;1182 a.positive = false;
11361183
1137 debug.assert(a.bitcount() == 5033);1184 debug.assert(a.bitCountAbs() == 5032);
1138 debug.assert(a.sizeInBase(2) >= 5033);1185 debug.assert(a.sizeInBase(2) >= 5033);
1139}1186}
11401187
1188test "big.int bitcount/to" {
1189 var a = try Int.init(al);
1190
1191 try a.set(0);
1192 debug.assert(a.bitCountTwosComp() == 0);
1193
1194 // TODO: stack smashing
1195 // debug.assert((try a.to(u0)) == 0);
1196 // TODO: sigsegv
1197 // debug.assert((try a.to(i0)) == 0);
1198
1199 try a.set(-1);
1200 debug.assert(a.bitCountTwosComp() == 1);
1201 debug.assert((try a.to(i1)) == -1);
1202
1203 try a.set(-8);
1204 debug.assert(a.bitCountTwosComp() == 4);
1205 debug.assert((try a.to(i4)) == -8);
1206
1207 try a.set(127);
1208 debug.assert(a.bitCountTwosComp() == 7);
1209 debug.assert((try a.to(u7)) == 127);
1210
1211 try a.set(-128);
1212 debug.assert(a.bitCountTwosComp() == 8);
1213 debug.assert((try a.to(i8)) == -128);
1214
1215 try a.set(-129);
1216 debug.assert(a.bitCountTwosComp() == 9);
1217 debug.assert((try a.to(i9)) == -129);
1218}
1219
1141test "big.int string set" {1220test "big.int string set" {
1142 var a = try Int.init(al);1221 var a = try Int.init(al);
1143 try a.setString(10, "120317241209124781241290847124");1222 try a.setString(10, "120317241209124781241290847124");