/** Arbitrary-precision ('bignum') arithmetic.
*
* Performance is optimized for numbers below ~1000 decimal digits.
* For X86 machines, highly optimised assembly routines are used.
*
* The following algorithms are currently implemented:
* $(UL
* $(LI Karatsuba multiplication)
* $(LI Squaring is optimized independently of multiplication)
* $(LI Divide-and-conquer division)
* $(LI Binary exponentiation)
* )
*
* For very large numbers, consider using the $(HTTP gmplib.org, GMP library) instead.
*
* License: $(HTTP www.boost.org/LICENSE_1_0.txt, Boost License 1.0).
* Authors: Don Clugston
* Source: $(PHOBOSSRC std/bigint.d)
*/
/* Copyright Don Clugston 2008 - 2010.
* Distributed under the Boost Software License, Version 1.0.
* (See accompanying file LICENSE_1_0.txt or copy at
* http://www.boost.org/LICENSE_1_0.txt)
*/
module std.bigint;
import std.conv : ConvException;
import std.format.spec : FormatSpec;
import std.format : FormatException;
import std.internal.math.biguintcore;
import std.internal.math.biguintnoasm : BigDigit;
import std.range.primitives;
import std.traits;
/** A struct representing an arbitrary precision integer.
*
* All arithmetic operations are supported, except unsigned shift right (`>>>`).
* Bitwise operations (`|`, `&`, `^`, `~`) are supported, and behave as if BigInt was
* an infinite length 2's complement number.
*
* BigInt implements value semantics using copy-on-write. This means that
* assignment is cheap, but operations such as x++ will cause heap
* allocation. (But note that for most bigint operations, heap allocation is
* inevitable anyway.)
*/
struct BigInt
{
private:
BigUint data; // BigInt adds signed arithmetic to BigUint.
bool sign = false;
public:
/**
* Construct a `BigInt` from a decimal or hexadecimal string. The number must
* be in the form of a decimal or hex literal. It may have a leading `+`
* or `-` sign, followed by `0x` or `0X` if hexadecimal. Underscores are
* permitted in any location after the `0x` and/or the sign of the number.
*
* Params:
* s = a finite bidirectional range of any character type
*
* Throws:
* $(REF ConvException, std,conv) if the string doesn't represent a valid number
*/
this(Range)(Range s) if (
isBidirectionalRange!Range &&
isSomeChar!(ElementType!Range) &&
!isInfinite!Range &&
!isNarrowString!Range)
{
import std.algorithm.iteration : filterBidirectional;
import std.algorithm.searching : startsWith;
import std.conv : ConvException;
import std.exception : enforce;
import std.utf : byChar;
enforce!ConvException(!s.empty, "Can't initialize BigInt with an empty range");
bool neg = false;
bool ok;
data = 0UL;
// check for signs and if the string is a hex value
if (s.front == '+')
{
s.popFront(); // skip '+'
}
else if (s.front == '-')
{
neg = true;
s.popFront();
}
if (s.save.startsWith("0x".byChar) ||
s.save.startsWith("0X".byChar))
{
s.popFront;
s.popFront;
if (!s.empty)
ok = data.fromHexString(s.filterBidirectional!(a => a != '_'));
else
ok = false;
}
else
{
ok = data.fromDecimalString(s.filterBidirectional!(a => a != '_'));
}
enforce!ConvException(ok, "Not a valid numerical string");
if (isZero())
neg = false;
sign = neg;
}
/// ditto
this(Range)(Range s) pure
if (isNarrowString!Range)
{
import std.utf : byCodeUnit;
this(s.byCodeUnit);
}
@safe unittest
{
// system because of the dummy ranges eventually call std.array!string
import std.exception : assertThrown;
import std.internal.test.dummyrange;
auto r1 = new ReferenceBidirectionalRange!dchar("101");
auto big1 = BigInt(r1);
assert(big1 == BigInt(101));
auto r2 = new ReferenceBidirectionalRange!dchar("1_000");
auto big2 = BigInt(r2);
assert(big2 == BigInt(1000));
auto r3 = new ReferenceBidirectionalRange!dchar("0x0");
auto big3 = BigInt(r3);
assert(big3 == BigInt(0));
auto r4 = new ReferenceBidirectionalRange!dchar("0x");
assertThrown!ConvException(BigInt(r4));
}
/**
* Construct a `BigInt` from a sign and a magnitude.
*
* The magnitude is an $(REF_ALTTEXT input range, isInputRange, std,range,primitives)
* of unsigned integers that satisfies either $(REF hasLength, std,range,primitives)
* or $(REF isForwardRange, std,range,primitives). The first (leftmost)
* element of the magnitude is considered the most significant.
*
* Params:
* isNegative = true for negative, false for non-negative
* (ignored when magnitude is zero)
* magnitude = a finite range of unsigned integers
*/
this(Range)(bool isNegative, Range magnitude) if (
isInputRange!Range &&
isUnsigned!(ElementType!Range) &&
(hasLength!Range || isForwardRange!Range) &&
!isInfinite!Range)
{
data.fromMagnitude(magnitude);
sign = isNegative && !data.isZero;
}
///
pure @safe unittest
{
ubyte[] magnitude = [1, 2, 3, 4, 5, 6];
auto b1 = BigInt(false, magnitude);
assert(cast(long) b1 == 0x01_02_03_04_05_06L);
auto b2 = BigInt(true, magnitude);
assert(cast(long) b2 == -0x01_02_03_04_05_06L);
}
/// Construct a `BigInt` from a built-in integral type.
this(T)(T x) pure nothrow @safe if (isIntegral!T)
{
data = data.init; // @@@: Workaround for compiler bug
opAssign(x);
}
///
@safe unittest
{
ulong data = 1_000_000_000_000;
auto bigData = BigInt(data);
assert(bigData == BigInt("1_000_000_000_000"));
}
/// Construct a `BigInt` from another `BigInt`.
this(T)(T x) pure nothrow @safe if (is(immutable T == immutable BigInt))
{
opAssign(x);
}
///
@safe unittest
{
const(BigInt) b1 = BigInt("1_234_567_890");
BigInt b2 = BigInt(b1);
assert(b2 == BigInt("1_234_567_890"));
}
/// Assignment from built-in integer types.
BigInt opAssign(T)(T x) pure nothrow @safe if (isIntegral!T)
{
data = cast(ulong) absUnsign(x);
sign = (x < 0);
return this;
}
///
@safe unittest
{
auto b = BigInt("123");
b = 456;
assert(b == BigInt("456"));
}
/// Assignment from another BigInt.
BigInt opAssign(T:BigInt)(T x) pure @nogc @safe
{
data = x.data;
sign = x.sign;
return this;
}
///
@safe unittest
{
auto b1 = BigInt("123");
auto b2 = BigInt("456");
b2 = b1;
assert(b2 == BigInt("123"));
}
/**
* Implements assignment operators from built-in integers of the form
* `BigInt op= integer`.
*/
BigInt opOpAssign(string op, T)(T y) pure nothrow @safe return scope
if ((op=="+" || op=="-" || op=="*" || op=="/" || op=="%"
|| op==">>" || op=="<<" || op=="^^" || op=="|" || op=="&" || op=="^") && isIntegral!T)
{
ulong u = absUnsign(y);
static if (op=="+")
{
data = BigUint.addOrSubInt(data, u, sign != (y<0), sign);
}
else static if (op=="-")
{
data = BigUint.addOrSubInt(data, u, sign == (y<0), sign);
}
else static if (op=="*")
{
if (y == 0)
{
sign = false;
data = 0UL;
}
else
{
sign = ( sign != (y<0) );
data = BigUint.mulInt(data, u);
}
}
else static if (op=="/")
{
assert(y != 0, "Division by zero");
static if (T.sizeof <= uint.sizeof)
{
data = BigUint.divInt(data, cast(uint) u);
}
else
{
data = BigUint.divInt(data, u);
}
sign = data.isZero() ? false : sign ^ (y < 0);
}
else static if (op=="%")
{
assert(y != 0, "Division by zero");
static if (is(immutable(T) == immutable(long)) || is( immutable(T) == immutable(ulong) ))
{
this %= BigInt(y);
}
else
{
data = cast(ulong) BigUint.modInt(data, cast(uint) u);
if (data.isZero())
sign = false;
}
// x%y always has the same sign as x.
// This is not the same as mathematical mod.
}
else static if (op==">>" || op=="<<")
{
// Do a left shift if y>0 and <<, or
// if y<0 and >>; else do a right shift.
if (y == 0)
return this;
else if ((y > 0) == (op=="<<"))
{
// Sign never changes during left shift
data = data.opBinary!(op)(u);
}
else
{
data = data.opBinary!(op)(u);
if (data.isZero())
sign = false;
}
}
else static if (op=="^^")
{
sign = (y & 1) ? sign : false;
data = BigUint.pow(data, u);
}
else static if (op=="&")
{
if (y >= 0 && (y <= 1 || !sign)) // In these cases we can avoid some allocation.
{
static if (T.sizeof <= uint.sizeof && BigDigit.sizeof <= uint.sizeof)
data = cast(ulong) data.peekUint(0) & y;
else
data = data.peekUlong(0) & y;
sign = false;
}
else
{
BigInt b = y;
opOpAssign!op(b);
}
}
else static if (op=="|" || op=="^")
{
BigInt b = y;
opOpAssign!op(b);
}
else static assert(0, "BigInt " ~ op[0..$-1] ~ "= " ~ T.stringof ~ " is not supported");
return this;
}
///
@safe unittest
{
auto b = BigInt("1_000_000_000");
b += 12345;
assert(b == BigInt("1_000_012_345"));
b /= 5;
assert(b == BigInt("200_002_469"));
}
// https://issues.dlang.org/show_bug.cgi?id=16264
@safe unittest
{
auto a = BigInt(
`335690982744637013564796917901053301979460129353374296317539383938630086938` ~
`465898213033510992292836631752875403891802201862860531801760096359705447768` ~
`957432600293361240407059207520920532482429912948952142341440301429494694368` ~
`264560802292927144211230021750155988283029753927847924288850436812178022006` ~
`408597793414273953252832688620479083497367463977081627995406363446761896298` ~
`967177607401918269561385622811274398143647535024987050366350585544531063531` ~
`7118554808325723941557169427279911052268935775`);
auto b = BigInt(
`207672245542926038535480439528441949928508406405023044025560363701392340829` ~
`852529131306106648201340460604257466180580583656068555417076345439694125326` ~
`843947164365500055567495554645796102453565953360564114634705366335703491527` ~
`429426780005741168078089657359833601261803592920462081364401456331489106355` ~
`199133982282631108670436696758342051198891939367812305559960349479160308314` ~
`068518200681530999860641597181672463704794566473241690395901768680673716414` ~
`243691584391572899147223065906633310537507956952626106509069491302359792769` ~
`378934570685117202046921464019396759638376362935855896435623442486036961070` ~
`534574698959398017332214518246531363445309522357827985468581166065335726996` ~
`711467464306784543112544076165391268106101754253962102479935962248302404638` ~
`21737237102628470475027851189594709504`);
BigInt c = a * b; // Crashes
assert(c == BigInt(
`697137001950904057507249234183127244116872349433141878383548259425589716813` ~
`135440660252012378417669596912108637127036044977634382385990472429604619344` ~
`738746224291111527200379708978133071390303850450970292020176369525401803474` ~
`998613408923490273129022167907826017408385746675184651576154302536663744109` ~
`111018961065316024005076097634601030334948684412785487182572502394847587887` ~
`507385831062796361152176364659197432600147716058873232435238712648552844428` ~
`058885217631715287816333209463171932255049134340904981280717725999710525214` ~
`161541960645335744430049558161514565159449390036287489478108344584188898872` ~
`434914159748515512161981956372737022393466624249130107254611846175580584736` ~
`276213025837422102290580044755202968610542057651282410252208599309841499843` ~
`672251048622223867183370008181364966502137725166782667358559333222947265344` ~
`524195551978394625568228658697170315141077913403482061673401937141405425042` ~
`283546509102861986303306729882186190883772633960389974665467972016939172303` ~
`653623175801495207204880400522581834672918935651426160175413277309985678579` ~
`830872397214091472424064274864210953551447463312267310436493480881235642109` ~
`668498742629676513172286703948381906930297135997498416573231570483993847269` ~
`479552708416124555462530834668011570929850407031109157206202741051573633443` ~
`58105600`
));
}
/**
* Implements assignment operators of the form `BigInt op= BigInt`.
*/
BigInt opOpAssign(string op, T)(T y) pure nothrow @safe return scope
if ((op=="+" || op== "-" || op=="*" || op=="|" || op=="&" || op=="^" || op=="/" || op=="%")
&& is (T: BigInt))
{
static if (op == "+")
{
data = BigUint.addOrSub(data, y.data, sign != y.sign, sign);
}
else static if (op == "-")
{
data = BigUint.addOrSub(data, y.data, sign == y.sign, sign);
}
else static if (op == "*")
{
data = BigUint.mul(data, y.data);
sign = isZero() ? false : sign ^ y.sign;
}
else static if (op == "/")
{
y.checkDivByZero();
if (!isZero())
{
data = BigUint.div(data, y.data);
sign = isZero() ? false : sign ^ y.sign;
}
}
else static if (op == "%")
{
y.checkDivByZero();
if (!isZero())
{
data = BigUint.mod(data, y.data);
// x%y always has the same sign as x.
if (isZero())
sign = false;
}
}
else static if (op == "|" || op == "&" || op == "^")
{
data = BigUint.bitwiseOp!op(data, y.data, sign, y.sign, sign);
}
else static assert(0, "BigInt " ~ op[0..$-1] ~ "= " ~
T.stringof ~ " is not supported");
return this;
}
///
@safe unittest
{
auto x = BigInt("123");
auto y = BigInt("321");
x += y;
assert(x == BigInt("444"));
}
/**
* Implements binary operators between `BigInt`s.
*/
BigInt opBinary(string op, T)(T y) pure nothrow @safe const return scope
if ((op=="+" || op == "*" || op=="-" || op=="|" || op=="&" || op=="^" ||
op=="/" || op=="%")
&& is (T: BigInt))
{
BigInt r = this;
return r.opOpAssign!(op)(y);
}
///
@safe unittest
{
auto x = BigInt("123");
auto y = BigInt("456");
BigInt z = x * y;
assert(z == BigInt("56088"));
}
/**
* Implements binary operators between `BigInt`'s and built-in integers.
*/
BigInt opBinary(string op, T)(T y) pure nothrow @safe const return scope
if ((op=="+" || op == "*" || op=="-" || op=="/" || op=="|" || op=="&" ||
op=="^"|| op==">>" || op=="<<" || op=="^^")
&& isIntegral!T)
{
BigInt r = this;
r.opOpAssign!(op)(y);
return r;
}
///
@safe unittest
{
auto x = BigInt("123");
x *= 300;
assert(x == BigInt("36900"));
}
/**
Implements a narrowing remainder operation with built-in integer types.
This binary operator returns a narrower, built-in integer type
where applicable, according to the following table.
$(TABLE ,
$(TR $(TD `BigInt`) $(TD $(CODE_PERCENT)) $(TD `uint`) $(TD $(RARR)) $(TD `long`))
$(TR $(TD `BigInt`) $(TD $(CODE_PERCENT)) $(TD `long`) $(TD $(RARR)) $(TD `long`))
$(TR $(TD `BigInt`) $(TD $(CODE_PERCENT)) $(TD `ulong`) $(TD $(RARR)) $(TD `BigInt`))
$(TR $(TD `BigInt`) $(TD $(CODE_PERCENT)) $(TD other type) $(TD $(RARR)) $(TD `int`))
)
*/
auto opBinary(string op, T)(T y) pure nothrow @safe const
if (op == "%" && isIntegral!T)
{
assert(y != 0, "% 0 not allowed");
// BigInt % uint => long
// BigInt % long => long
// BigInt % ulong => BigInt
// BigInt % other_type => int
static if (is(immutable T == immutable long) || is(immutable T == immutable ulong))
{
auto r = this % BigInt(y);
static if (is(immutable T == immutable long))
{
return r.toLong();
}
else
{
// return as-is to avoid overflow
return r;
}
}
else
{
immutable uint u = absUnsign(y);
static if (is(immutable T == immutable uint))
alias R = long;
else
alias R = int;
R rem = BigUint.modInt(data, u);
// x%y always has the same sign as x.
// This is not the same as mathematical mod.
return sign ? -rem : rem;
}
}
///
@safe unittest
{
auto x = BigInt("1_000_000_500");
long l = 1_000_000L;
ulong ul = 2_000_000UL;
int i = 500_000;
short s = 30_000;
assert(is(typeof(x % l) == long) && x % l == 500L);
assert(is(typeof(x % ul) == BigInt) && x % ul == BigInt(500));
assert(is(typeof(x % i) == int) && x % i == 500);
assert(is(typeof(x % s) == int) && x % s == 10500);
}
/**
Implements operators with built-in integers on the left-hand side and
`BigInt` on the right-hand side.
*/
BigInt opBinaryRight(string op, T)(T y) pure nothrow @safe const
if ((op=="+" || op=="*" || op=="|" || op=="&" || op=="^") && isIntegral!T)
{
return opBinary!(op)(y);
}
///
@safe unittest
{
auto x = BigInt("100");
BigInt y = 123 + x;
assert(y == BigInt("223"));
BigInt z = 123 - x;
assert(z == BigInt("23"));
// Dividing a built-in integer type by BigInt always results in
// something that fits in a built-in type, so the built-in type is
// returned, not BigInt.
assert(is(typeof(1000 / x) == int));
assert(1000 / x == 10);
}
// BigInt = integer op BigInt
/// ditto
BigInt opBinaryRight(string op, T)(T y) pure nothrow @safe const
if (op == "-" && isIntegral!T)
{
ulong u = absUnsign(y);
BigInt r;
static if (op == "-")
{
r.sign = sign;
r.data = BigUint.addOrSubInt(data, u, sign == (y<0), r.sign);
r.negate();
}
return r;
}
// integer = integer op BigInt
/// ditto
T opBinaryRight(string op, T)(T x) pure nothrow @safe const
if ((op=="%" || op=="/") && isIntegral!T)
{
checkDivByZero();
static if (op == "%")
{
// x%y always has the same sign as x.
if (data.ulongLength > 1)
return x;
immutable u = absUnsign(x);
immutable rem = u % data.peekUlong(0);
// x%y always has the same sign as x.
return cast(T)((x<0) ? -rem : rem);
}
else static if (op == "/")
{
if (data.ulongLength > 1)
return 0;
return cast(T)(x / data.peekUlong(0));
}
}
// const unary operations
/**
Implements `BigInt` unary operators.
*/
BigInt opUnary(string op)() pure nothrow @safe const if (op=="+" || op=="-" || op=="~")
{
static if (op=="-")
{
BigInt r = this;
r.negate();
return r;
}
else static if (op=="~")
{
return -(this+1);
}
else static if (op=="+")
return this;
}
// non-const unary operations
/// ditto
BigInt opUnary(string op)() pure nothrow @safe if (op=="++" || op=="--")
{
static if (op=="++")
{
data = BigUint.addOrSubInt(data, 1UL, sign, sign);
return this;
}
else static if (op=="--")
{
data = BigUint.addOrSubInt(data, 1UL, !sign, sign);
return this;
}
}
///
@safe unittest
{
auto x = BigInt("1234");
assert(-x == BigInt("-1234"));
++x;
assert(x == BigInt("1235"));
}
/**
Implements `BigInt` equality test with other `BigInt`'s and built-in
numeric types.
*/
bool opEquals()(auto ref const BigInt y) const pure @nogc @safe
{
return sign == y.sign && y.data == data;
}
/// ditto
bool opEquals(T)(const T y) const pure nothrow @nogc @safe if (isIntegral!T)
{
if (sign != (y<0))
return 0;
return data.opEquals(cast(ulong) absUnsign(y));
}
/// ditto
bool opEquals(T)(const T y) const pure nothrow @nogc if (isFloatingPoint!T)
{
return 0 == opCmp(y);
}
///
@safe unittest
{
// Note that when comparing a BigInt to a float or double the
// full precision of the BigInt is always considered, unlike
// when comparing an int to a float or a long to a double.
assert(BigInt(123456789) != cast(float) 123456789);
}
@safe unittest
{
auto x = BigInt("12345");
auto y = BigInt("12340");
int z = 12345;
int w = 54321;
assert(x == x);
assert(x != y);
assert(x == y + 5);
assert(x == z);
assert(x != w);
}
@safe unittest
{
import std.math.operations : nextDown, nextUp;
const x = BigInt("0x1abc_de80_0000_0000_0000_0000_0000_0000");
BigInt x1 = x + 1;
BigInt x2 = x - 1;
const d = 0x1.abcde8p124;
assert(x == d);
assert(x1 != d);
assert(x2 != d);
assert(x != nextUp(d));
assert(x != nextDown(d));
assert(x != double.nan);
const dL = 0x1.abcde8p124L;
assert(x == dL);
assert(x1 != dL);
assert(x2 != dL);
assert(x != nextUp(dL));
assert(x != nextDown(dL));
assert(x != real.nan);
assert(BigInt(0) == 0.0f);
assert(BigInt(0) == 0.0);
assert(BigInt(0) == 0.0L);
assert(BigInt(0) == -0.0f);
assert(BigInt(0) == -0.0);
assert(BigInt(0) == -0.0L);
assert(BigInt("999_999_999_999_999_999_999_999_999_999_999_999_999") != float.infinity);
}
/**
Implements casting to `bool`.
*/
T opCast(T:bool)() pure nothrow @nogc @safe const
{
return !isZero();
}
///
@safe unittest
{
// Non-zero values are regarded as true
auto x = BigInt("1");
auto y = BigInt("10");
assert(x);
assert(y);
// Zero value is regarded as false
auto z = BigInt("0");
assert(!z);
}
/**
Implements casting to integer types.
Throws: $(REF ConvOverflowException, std,conv) if the number exceeds
the target type's range.
*/
T opCast(T:ulong)() pure @safe const
{
if (isUnsigned!T && sign)
{ /* throw */ }
else
if (data.ulongLength == 1)
{
ulong l = data.peekUlong(0);
if (isUnsigned!T || !sign)
{
if (l <= T.max)
return cast(T) l;
}
else
{
if (l <= ulong(T.max)+1)
return cast(T)-long(l); // -long.min == long.min
}
}
import std.conv : ConvOverflowException;
import std.string : format;
throw new ConvOverflowException(
"BigInt(%s) cannot be represented as a %s"
.format(this.toDecimalString, T.stringof));
}
///
@safe unittest
{
import std.conv : to, ConvOverflowException;
import std.exception : assertThrown;
assert(BigInt("0").to!int == 0);
assert(BigInt("0").to!ubyte == 0);
assert(BigInt("255").to!ubyte == 255);
assertThrown!ConvOverflowException(BigInt("256").to!ubyte);
assertThrown!ConvOverflowException(BigInt("-1").to!ubyte);
}
@safe unittest
{
import std.conv : to, ConvOverflowException;
import std.exception : assertThrown;
assert(BigInt("-1").to!byte == -1);
assert(BigInt("-128").to!byte == -128);
assert(BigInt("127").to!byte == 127);
assertThrown!ConvOverflowException(BigInt("-129").to!byte);
assertThrown!ConvOverflowException(BigInt("128").to!byte);
assert(BigInt("0").to!uint == 0);
assert(BigInt("4294967295").to!uint == uint.max);
assertThrown!ConvOverflowException(BigInt("4294967296").to!uint);
assertThrown!ConvOverflowException(BigInt("-1").to!uint);
assert(BigInt("-1").to!int == -1);
assert(BigInt("-2147483648").to!int == int.min);
assert(BigInt("2147483647").to!int == int.max);
assertThrown!ConvOverflowException(BigInt("-2147483649").to!int);
assertThrown!ConvOverflowException(BigInt("2147483648").to!int);
assert(BigInt("0").to!ulong == 0);
assert(BigInt("18446744073709551615").to!ulong == ulong.max);
assertThrown!ConvOverflowException(BigInt("18446744073709551616").to!ulong);
assertThrown!ConvOverflowException(BigInt("-1").to!ulong);
assert(BigInt("-1").to!long == -1);
assert(BigInt("-9223372036854775808").to!long == long.min);
assert(BigInt("9223372036854775807").to!long == long.max);
assertThrown!ConvOverflowException(BigInt("-9223372036854775809").to!long);
assertThrown!ConvOverflowException(BigInt("9223372036854775808").to!long);
}
/**
Implements casting to floating point types.
*/
T opCast(T)() @safe nothrow @nogc const if (isFloatingPoint!T)
{
return toFloat!(T, "nearest");
}
///
@system unittest
{
assert(cast(float) BigInt("35540592535949172786332045140593475584")
== 35540592535949172786332045140593475584.0f);
assert(cast(double) BigInt("35540601499647381470685035515422441472")
== 35540601499647381470685035515422441472.0);
assert(cast(real) BigInt("35540601499647381470685035515422441472")
== 35540601499647381470685035515422441472.0L);
assert(cast(float) BigInt("-0x1345_6780_0000_0000_0000_0000_0000") == -0x1.3456_78p+108f );
assert(cast(double) BigInt("-0x1345_678a_bcde_f000_0000_0000_0000") == -0x1.3456_78ab_cdefp+108 );
assert(cast(real) BigInt("-0x1345_678a_bcde_f000_0000_0000_0000") == -0x1.3456_78ab_cdefp+108L);
}
/// Rounding when casting to floating point
@system unittest
{
// BigInts whose values cannot be exactly represented as float/double/real
// are rounded when cast to float/double/real. When cast to float or
// double or 64-bit real the rounding is strictly defined. When cast
// to extended-precision real the rounding rules vary by environment.
// BigInts that fall somewhere between two non-infinite floats/doubles
// are rounded to the closer value when cast to float/double.
assert(cast(float) BigInt(0x1aaa_aae7) == 0x1.aaa_aaep+28f);
assert(cast(float) BigInt(0x1aaa_aaff) == 0x1.aaa_ab0p+28f);
assert(cast(float) BigInt(-0x1aaa_aae7) == -0x1.aaaaaep+28f);
assert(cast(float) BigInt(-0x1aaa_aaff) == -0x1.aaaab0p+28f);
assert(cast(double) BigInt(0x1aaa_aaaa_aaaa_aa77) == 0x1.aaa_aaaa_aaaa_aa00p+60);
assert(cast(double) BigInt(0x1aaa_aaaa_aaaa_aaff) == 0x1.aaa_aaaa_aaaa_ab00p+60);
assert(cast(double) BigInt(-0x1aaa_aaaa_aaaa_aa77) == -0x1.aaa_aaaa_aaaa_aa00p+60);
assert(cast(double) BigInt(-0x1aaa_aaaa_aaaa_aaff) == -0x1.aaa_aaaa_aaaa_ab00p+60);
// BigInts that fall exactly between two non-infinite floats/doubles
// are rounded away from zero when cast to float/double. (Note that
// in most environments this is NOT the same rounding rule rule used
// when casting int/long to float/double.)
assert(cast(float) BigInt(0x1aaa_aaf0) == 0x1.aaa_ab0p+28f);
assert(cast(float) BigInt(-0x1aaa_aaf0) == -0x1.aaaab0p+28f);
assert(cast(double) BigInt(0x1aaa_aaaa_aaaa_aa80) == 0x1.aaa_aaaa_aaaa_ab00p+60);
assert(cast(double) BigInt(-0x1aaa_aaaa_aaaa_aa80) == -0x1.aaa_aaaa_aaaa_ab00p+60);
// BigInts that are bounded on one side by the largest positive or
// most negative finite float/double and on the other side by infinity
// or -infinity are rounded as if in place of infinity was the value
// `2^^(T.max_exp)` when cast to float/double.
assert(cast(float) BigInt("999_999_999_999_999_999_999_999_999_999_999_999_999") == float.infinity);
assert(cast(float) BigInt("-999_999_999_999_999_999_999_999_999_999_999_999_999") == -float.infinity);
assert(cast(double) BigInt("999_999_999_999_999_999_999_999_999_999_999_999_999") < double.infinity);
assert(cast(real) BigInt("999_999_999_999_999_999_999_999_999_999_999_999_999") < real.infinity);
}
@safe unittest
{
// Test exponent overflow is correct.
assert(cast(float) BigInt(0x1fffffff) == 0x1.000000p+29f);
assert(cast(double) BigInt(0x1fff_ffff_ffff_fff0) == 0x1.000000p+61);
}
private T toFloat(T, string roundingMode)() @safe nothrow @nogc const
if (__traits(isFloating, T) && (roundingMode == "nearest" || roundingMode == "truncate"))
{
import core.bitop : bsr;
enum performRounding = (roundingMode == "nearest");
enum performTruncation = (roundingMode == "truncate");
static assert(performRounding || performTruncation, "unrecognized rounding mode");
enum int totalNeededBits = T.mant_dig + int(performRounding);
static if (totalNeededBits <= 64)
{
// We need to examine the top two 64-bit words, not just the top one,
// since the top word could have just a single significant bit.
const ulongLength = data.ulongLength;
const ulong w1 = data.peekUlong(ulongLength - 1);
if (w1 == 0)
return T(0); // Special: exponent should be all zero bits, plus bsr(w1) is undefined.
const ulong w2 = ulongLength < 2 ? 0 : data.peekUlong(ulongLength - 2);
const uint w1BitCount = bsr(w1) + 1;
ulong sansExponent = (w1 << (64 - w1BitCount)) | (w2 >>> (w1BitCount));
size_t exponent = (ulongLength - 1) * 64 + w1BitCount + 1;
static if (performRounding)
{
sansExponent += 1UL << (64 - totalNeededBits);
if (0 <= cast(long) sansExponent) // Use high bit to detect overflow.
{
// Do not bother filling in the high bit of sansExponent
// with 1. It will be discarded by float and double and 80
// bit real cannot be on this path with rounding enabled.
exponent += 1;
}
}
static if (T.mant_dig == float.mant_dig)
{
if (exponent >= T.max_exp)
return isNegative ? -T.infinity : T.infinity;
uint resultBits = (uint(isNegative) << 31) | // sign bit
((0xFF & (exponent - float.min_exp)) << 23) | // exponent
cast(uint) ((sansExponent << 1) >>> (64 - 23)); // mantissa.
// TODO: remove @trusted lambda after DIP 1000 is enabled by default.
return (() @trusted => *cast(float*) &resultBits)();
}
else static if (T.mant_dig == double.mant_dig)
{
if (exponent >= T.max_exp)
return isNegative ? -T.infinity : T.infinity;
ulong resultBits = (ulong(isNegative) << 63) | // sign bit
((0x7FFUL & (exponent - double.min_exp)) << 52) | // exponent
((sansExponent << 1) >>> (64 - 52)); // mantissa.
// TODO: remove @trusted lambda after DIP 1000 is enabled by default.
return (() @trusted => *cast(double*) &resultBits)();
}
else
{
import core.math : ldexp;
return ldexp(isNegative ? -cast(real) sansExponent : cast(real) sansExponent,
cast(int) exponent - 65);
}
}
else
{
import core.math : ldexp;
const ulongLength = data.ulongLength;
if ((ulongLength - 1) * 64L > int.max)
return isNegative ? -T.infinity : T.infinity;
int scale = cast(int) ((ulongLength - 1) * 64);
const ulong w1 = data.peekUlong(ulongLength - 1);
if (w1 == 0)
return T(0); // Special: bsr(w1) is undefined.
int bitsStillNeeded = totalNeededBits - bsr(w1) - 1;
T acc = ldexp(cast(T) w1, scale);
for (ptrdiff_t i = ulongLength - 2; i >= 0 && bitsStillNeeded > 0; i--)
{
ulong w = data.peekUlong(i);
// To round towards zero we must make sure not to use too many bits.
if (bitsStillNeeded >= 64)
{
acc += ldexp(cast(T) w, scale -= 64);
bitsStillNeeded -= 64;
}
else
{
w = (w >>> (64 - bitsStillNeeded)) << (64 - bitsStillNeeded);
acc += ldexp(cast(T) w, scale -= 64);
break;
}
}
if (isNegative)
acc = -acc;
return cast(T) acc;
}
}
/**
Implements casting to/from qualified `BigInt`'s.
Warning: Casting to/from `const` or `immutable` may break type
system guarantees. Use with care.
*/
T opCast(T)() pure nothrow @nogc const
if (is(immutable T == immutable BigInt))
{
return this;
}
///
@safe unittest
{
const(BigInt) x = BigInt("123");
BigInt y = cast() x; // cast away const
assert(y == x);
}
// Hack to make BigInt's typeinfo.compare work properly.
// Note that this must appear before the other opCmp overloads, otherwise
// DMD won't find it.
/**
Implements 3-way comparisons of `BigInt` with `BigInt` or `BigInt` with
built-in numeric types.
*/
int opCmp(ref const BigInt y) pure nothrow @nogc @safe const
{
// Simply redirect to the "real" opCmp implementation.
return this.opCmp!BigInt(y);
}
/// ditto
int opCmp(T)(const T y) pure nothrow @nogc @safe const if (isIntegral!T)
{
if (sign != (y<0) )
return sign ? -1 : 1;
int cmp = data.opCmp(cast(ulong) absUnsign(y));
return sign? -cmp: cmp;
}
/// ditto
int opCmp(T)(const T y) nothrow @nogc @safe const if (isFloatingPoint!T)
{
import core.bitop : bsr;
import std.math.operations : cmp;
import std.math.traits : isFinite;
const asFloat = toFloat!(T, "truncate");
if (asFloat != y)
return cmp(asFloat, y); // handles +/- NaN.
if (!isFinite(y))
return isNegative ? 1 : -1;
const ulongLength = data.ulongLength;
const w1 = data.peekUlong(ulongLength - 1);
if (w1 == 0)
return 0; // Special: bsr(w1) is undefined.
const numSignificantBits = (ulongLength - 1) * 64 + bsr(w1) + 1;
for (ptrdiff_t bitsRemainingToCheck = numSignificantBits - T.mant_dig, i = 0;
bitsRemainingToCheck > 0; i++, bitsRemainingToCheck -= 64)
{
auto word = data.peekUlong(i);
if (word == 0)
continue;
// Make sure we're only checking digits that are beyond
// the precision of `y`.
if (bitsRemainingToCheck < 64 && (word << (64 - bitsRemainingToCheck)) == 0)
break; // This can only happen on the last loop iteration.
return isNegative ? -1 : 1;
}
return 0;
}
/// ditto
int opCmp(T:BigInt)(const T y) pure nothrow @nogc @safe const
{
if (sign != y.sign)
return sign ? -1 : 1;
immutable cmp = data.opCmp(y.data);
return sign? -cmp: cmp;
}
///
@safe unittest
{
auto x = BigInt("100");
auto y = BigInt("10");
int z = 50;
const int w = 200;
assert(y < x);
assert(x > z);
assert(z > y);
assert(x < w);
}
///
@safe unittest
{
auto x = BigInt("0x1abc_de80_0000_0000_0000_0000_0000_0000");
BigInt y = x - 1;
BigInt z = x + 1;
double d = 0x1.abcde8p124;
assert(y < d);
assert(z > d);
assert(x >= d && x <= d);
// Note that when comparing a BigInt to a float or double the
// full precision of the BigInt is always considered, unlike
// when comparing an int to a float or a long to a double.
assert(BigInt(123456789) < cast(float) 123456789);
}
@safe unittest
{
assert(BigInt("999_999_999_999_999_999_999_999_999_999_999_999_999") < float.infinity);
// Test `real` works.
auto x = BigInt("0x1abc_de80_0000_0000_0000_0000_0000_0000");
BigInt y = x - 1;
BigInt z = x + 1;
real d = 0x1.abcde8p124;
assert(y < d);
assert(z > d);
assert(x >= d && x <= d);
// Test comparison for numbers of 64 bits or fewer.
auto w1 = BigInt(0x1abc_de80_0000_0000);
auto w2 = w1 - 1;
auto w3 = w1 + 1;
assert(w1.ulongLength == 1);
assert(w2.ulongLength == 1);
assert(w3.ulongLength == 1);
double e = 0x1.abcde8p+60;
assert(w1 >= e && w1 <= e);
assert(w2 < e);
assert(w3 > e);
real eL = 0x1.abcde8p+60;
assert(w1 >= eL && w1 <= eL);
assert(w2 < eL);
assert(w3 > eL);
}
/**
Returns: The value of this `BigInt` as a `long`, or `long.max`/`long.min`
if outside the representable range.
*/
long toLong() @safe pure nothrow const @nogc
{
return (sign ? -1 : 1) *
(data.ulongLength == 1 && (data.peekUlong(0) <= sign+cast(ulong)(long.max)) // 1+long.max = |long.min|
? cast(long)(data.peekUlong(0))
: long.max);
}
///
@safe unittest
{
auto b = BigInt("12345");
long l = b.toLong();
assert(l == 12345);
}
/**
Returns: The value of this `BigInt` as an `int`, or `int.max`/`int.min` if outside
the representable range.
*/
int toInt() @safe pure nothrow @nogc const
{
return (sign ? -1 : 1) *
(data.uintLength == 1 && (data.peekUint(0) <= sign+cast(uint)(int.max)) // 1+int.max = |int.min|
? cast(int)(data.peekUint(0))
: int.max);
}
///
@safe unittest
{
auto big = BigInt("5_000_000");
auto i = big.toInt();
assert(i == 5_000_000);
// Numbers that are too big to fit into an int will be clamped to int.max.
auto tooBig = BigInt("5_000_000_000");
i = tooBig.toInt();
assert(i == int.max);
}
/// Number of significant `uint`s which are used in storing this number.
/// The absolute value of this `BigInt` is always < 2$(SUPERSCRIPT 32*uintLength)
@property size_t uintLength() @safe pure nothrow @nogc const
{
return data.uintLength;
}
/// Number of significant `ulong`s which are used in storing this number.
/// The absolute value of this `BigInt` is always < 2$(SUPERSCRIPT 64*ulongLength)
@property size_t ulongLength() @safe pure nothrow @nogc const
{
return data.ulongLength;
}
/** Convert the `BigInt` to `string`, passing it to the given sink.
*
* Params:
* sink = An OutputRange for accepting possibly piecewise segments of the
* formatted string.
* formatString = A format string specifying the output format.
*
* $(TABLE Available output formats:,
* $(TR $(TD "d") $(TD Decimal))
* $(TR $(TD "o") $(TD Octal))
* $(TR $(TD "x") $(TD Hexadecimal, lower case))
* $(TR $(TD "X") $(TD Hexadecimal, upper case))
* $(TR $(TD "s") $(TD Default formatting (same as "d") ))
* $(TR $(TD null) $(TD Default formatting (same as "d") ))
* )
*/
void toString(Writer)(scope ref Writer sink, string formatString) const
{
auto f = FormatSpec!char(formatString);
f.writeUpToNextSpec(sink);
toString!Writer(sink, f);
}
/// ditto
void toString(Writer)(scope ref Writer sink, scope const ref FormatSpec!char f) const
{
import std.range.primitives : put;
const spec = f.spec;
immutable hex = (spec == 'x' || spec == 'X');
if (!(spec == 's' || spec == 'd' || spec =='o' || hex))
throw new FormatException("Format specifier not understood: %" ~ spec);
char[] buff;
if (spec == 'X')
{
buff = data.toHexString(0, '_', 0, f.flZero ? '0' : ' ', LetterCase.upper);
}
else if (spec == 'x')
{
buff = data.toHexString(0, '_', 0, f.flZero ? '0' : ' ', LetterCase.lower);
}
else if (spec == 'o')
{
buff = data.toOctalString();
}
else
{
buff = data.toDecimalString(0);
}
assert(buff.length > 0, "Invalid buffer length");
char signChar = isNegative ? '-' : 0;
auto minw = buff.length + (signChar ? 1 : 0);
if (!hex && !signChar && (f.width == 0 || minw < f.width))
{
if (f.flPlus)
{
signChar = '+';
++minw;
}
else if (f.flSpace)
{
signChar = ' ';
++minw;
}
}
immutable maxw = minw < f.width ? f.width : minw;
immutable difw = maxw - minw;
if (!f.flDash && !f.flZero)
foreach (i; 0 .. difw)
put(sink, " ");
if (signChar)
{
scope char[1] buf = signChar;
put(sink, buf[]);
}
if (!f.flDash && f.flZero)
foreach (i; 0 .. difw)
put(sink, "0");
put(sink, buff);
if (f.flDash)
foreach (i; 0 .. difw)
put(sink, " ");
}
/**
`toString` is rarely directly invoked; the usual way of using it is via
$(REF format, std, format):
*/
@safe unittest
{
import std.format : format;
auto x = BigInt("1_000_000");
x *= 12345;
assert(format("%d", x) == "12345000000");
assert(format("%x", x) == "2_dfd1c040");
assert(format("%X", x) == "2_DFD1C040");
assert(format("%o", x) == "133764340100");
}
// for backwards compatibility, see unittest below
/// ditto
void toString(scope void delegate(scope const(char)[]) sink, string formatString) const
{
toString!(void delegate(scope const(char)[]))(sink, formatString);
}
// for backwards compatibility, see unittest below
/// ditto
void toString(scope void delegate(scope const(char)[]) sink, scope const ref FormatSpec!char f) const
{
toString!(void delegate(scope const(char)[]))(sink, f);
}
// Backwards compatibility test
// BigInt.toString used to only accept a delegate sink function, but this does not work
// well with attributes such as @safe. A template function toString was added that
// works on OutputRanges, but when a delegate was passed in the form of an untyped
// lambda such as `str => dst.put(str)` the parameter type was inferred as `void` and
// the function failed to instantiate.
@system unittest
{
import std.format.spec : FormatSpec;
import std.array : appender;
BigInt num = 503;
auto dst = appender!string();
num.toString(str => dst.put(str), null);
assert(dst[] == "503");
num = 504;
auto f = FormatSpec!char("");
num.toString(str => dst.put(str), f);
assert(dst[] == "503504");
}
// Implement toHash so that BigInt works properly as an AA key.
/**
Returns: A unique hash of the `BigInt`'s value suitable for use in a hash
table.
*/
size_t toHash() const @safe pure nothrow @nogc
{
return data.toHash() + sign;
}
/**
`toHash` is rarely directly invoked; it is implicitly used when
BigInt is used as the key of an associative array.
*/
@safe pure unittest
{
string[BigInt] aa;
aa[BigInt(123)] = "abc";
aa[BigInt(456)] = "def";
assert(aa[BigInt(123)] == "abc");
assert(aa[BigInt(456)] == "def");
}
/**
* Gets the nth number in the underlying representation that makes up the whole
* `BigInt`.
*
* Params:
* T = the type to view the underlying representation as
* n = The nth number to retrieve. Must be less than $(LREF ulongLength) or
* $(LREF uintLength) with respect to `T`.
* Returns:
* The nth `ulong` in the representation of this `BigInt`.
*/
T getDigit(T = ulong)(size_t n) const
if (is(T == ulong) || is(T == uint))
{
static if (is(T == ulong))
{
assert(n < ulongLength(), "getDigit index out of bounds");
return data.peekUlong(n);
}
else
{
assert(n < uintLength(), "getDigit index out of bounds");
return data.peekUint(n);
}
}
///
@safe pure unittest
{
auto a = BigInt("1000");
assert(a.ulongLength() == 1);
assert(a.getDigit(0) == 1000);
assert(a.uintLength() == 1);
assert(a.getDigit!uint(0) == 1000);
auto b = BigInt("2_000_000_000_000_000_000_000_000_000");
assert(b.ulongLength() == 2);
assert(b.getDigit(0) == 4584946418820579328);
assert(b.getDigit(1) == 108420217);
assert(b.uintLength() == 3);
assert(b.getDigit!uint(0) == 3489660928);
assert(b.getDigit!uint(1) == 1067516025);
assert(b.getDigit!uint(2) == 108420217);
}
private:
void negate() @safe pure nothrow @nogc scope
{
if (!data.isZero())
sign = !sign;
}
bool isZero() pure const nothrow @nogc @safe scope
{
return data.isZero();
}
alias isNegative = sign;
// Generate a runtime error if division by zero occurs
void checkDivByZero() pure const nothrow @safe scope
{
assert(!isZero(), "BigInt division by zero");
}
}
///
@safe unittest
{
BigInt a = "9588669891916142";
BigInt b = "7452469135154800";
auto c = a * b;
assert(c == BigInt("71459266416693160362545788781600"));
auto d = b * a;
assert(d == BigInt("71459266416693160362545788781600"));
assert(d == c);
d = c * BigInt("794628672112");
assert(d == BigInt("56783581982794522489042432639320434378739200"));
auto e = c + d;
assert(e == BigInt("56783581982865981755459125799682980167520800"));
auto f = d + c;
assert(f == e);
auto g = f - c;
assert(g == d);
g = f - d;
assert(g == c);
e = 12345678;
g = c + e;
auto h = g / b;
auto i = g % b;
assert(h == a);
assert(i == e);
BigInt j = "-0x9A56_57f4_7B83_AB78";
BigInt k = j;
j ^^= 11;
assert(k ^^ 11 == j);
}
/**
Params:
x = The `BigInt` to convert to a decimal `string`.
Returns:
A `string` that represents the `BigInt` as a decimal number.
*/
string toDecimalString(const(BigInt) x) pure nothrow @safe
{
auto buff = x.data.toDecimalString(x.isNegative ? 1 : 0);
if (x.isNegative)
buff[0] = '-';
return buff;
}
///
@safe pure unittest
{
auto x = BigInt("123");
x *= 1000;
x += 456;
auto xstr = x.toDecimalString();
assert(xstr == "123456");
}
/**
Params:
x = The `BigInt` to convert to a hexadecimal `string`.
Returns:
A `string` that represents the `BigInt` as a hexadecimal (base 16)
number in upper case.
*/
string toHex(const(BigInt) x) pure @safe
{
import std.array : appender;
auto outbuff = appender!string();
x.toString(outbuff, "%X");
return outbuff[];
}
///
@safe unittest
{
auto x = BigInt("123");
x *= 1000;
x += 456;
auto xstr = x.toHex();
assert(xstr == "1E240");
}
/** Returns the absolute value of x converted to the corresponding unsigned
type.
Params:
x = The integral value to return the absolute value of.
Returns:
The absolute value of x.
*/
Unsigned!T absUnsign(T)(T x)
if (isIntegral!T)
{
static if (isSigned!T)
{
import std.conv : unsigned;
/* This returns the correct result even when x = T.min
* on two's complement machines because unsigned(T.min) = |T.min|
* even though -T.min = T.min.
*/
return unsigned((x < 0) ? cast(T)(0-x) : x);
}
else
{
return x;
}
}
///
nothrow pure @safe
unittest
{
assert((-1).absUnsign == 1);
assert(1.absUnsign == 1);
}
nothrow pure @safe
unittest
{
BigInt a, b;
a = 1;
b = 2;
auto c = a + b;
assert(c == 3);
}
nothrow pure @safe
unittest
{
long a;
BigInt b;
auto c = a + b;
assert(c == 0);
auto d = b + a;
assert(d == 0);
}
nothrow pure @safe
unittest
{
BigInt x = 1, y = 2;
assert(x < y);
assert(x <= y);
assert(y >= x);
assert(y > x);
assert(x != y);
long r1 = x.toLong;
assert(r1 == 1);
BigInt r2 = 10 % x;
assert(r2 == 0);
BigInt r3 = 10 / y;
assert(r3 == 5);
BigInt[] arr = [BigInt(1)];
auto incr = arr[0]++;
assert(arr == [BigInt(2)]);
assert(incr == BigInt(1));
}
@safe unittest
{
// Radix conversion
assert( toDecimalString(BigInt("-1_234_567_890_123_456_789"))
== "-1234567890123456789");
assert( toHex(BigInt("0x1234567890123456789")) == "123_45678901_23456789");
assert( toHex(BigInt("0x00000000000000000000000000000000000A234567890123456789"))
== "A23_45678901_23456789");
assert( toHex(BigInt("0x000_00_000000_000_000_000000000000_000000_")) == "0");
assert(BigInt(-0x12345678).toInt() == -0x12345678);
assert(BigInt(-0x12345678).toLong() == -0x12345678);
assert(BigInt(0x1234_5678_9ABC_5A5AL).ulongLength == 1);
assert(BigInt(0x1234_5678_9ABC_5A5AL).toLong() == 0x1234_5678_9ABC_5A5AL);
assert(BigInt(-0x1234_5678_9ABC_5A5AL).toLong() == -0x1234_5678_9ABC_5A5AL);
assert(BigInt(0xF234_5678_9ABC_5A5AL).toLong() == long.max);
assert(BigInt(-0x123456789ABCL).toInt() == -int.max);
char[] s1 = "123".dup; // https://issues.dlang.org/show_bug.cgi?id=8164
assert(BigInt(s1) == 123);
char[] s2 = "0xABC".dup;
assert(BigInt(s2) == 2748);
assert((BigInt(-2) + BigInt(1)) == BigInt(-1));
BigInt a = ulong.max - 5;
auto b = -long.max % a;
assert( b == -long.max % (ulong.max - 5));
b = long.max / a;
assert( b == long.max /(ulong.max - 5));
assert(BigInt(1) - 1 == 0);
assert((-4) % BigInt(5) == -4); // https://issues.dlang.org/show_bug.cgi?id=5928
assert(BigInt(-4) % BigInt(5) == -4);
assert(BigInt(2)/BigInt(-3) == BigInt(0)); // https://issues.dlang.org/show_bug.cgi?id=8022
assert(BigInt("-1") > long.min); // https://issues.dlang.org/show_bug.cgi?id=9548
assert(toDecimalString(BigInt("0000000000000000000000000000000000000000001234567"))
== "1234567");
}
@safe unittest // Minimum signed value bug tests.
{
assert(BigInt("-0x8000000000000000") == BigInt(long.min));
assert(BigInt("-0x8000000000000000")+1 > BigInt(long.min));
assert(BigInt("-0x80000000") == BigInt(int.min));
assert(BigInt("-0x80000000")+1 > BigInt(int.min));
assert(BigInt(long.min).toLong() == long.min); // lossy toLong bug for long.min
assert(BigInt(int.min).toInt() == int.min); // lossy toInt bug for int.min
assert(BigInt(long.min).ulongLength == 1);
assert(BigInt(int.min).uintLength == 1); // cast/sign extend bug in opAssign
BigInt a;
a += int.min;
assert(a == BigInt(int.min));
a = int.min - BigInt(int.min);
assert(a == 0);
a = int.min;
assert(a == BigInt(int.min));
assert(int.min % (BigInt(int.min)-1) == int.min);
assert((BigInt(int.min)-1)%int.min == -1);
}
// Recursive division (https://issues.dlang.org/show_bug.cgi?id=5568)
@safe unittest
{
enum Z = 4843;
BigInt m = (BigInt(1) << (Z*8) ) - 1;
m -= (BigInt(1) << (Z*6)) - 1;
BigInt oldm = m;
BigInt a = (BigInt(1) << (Z*4) )-1;
BigInt b = m % a;
m /= a;
m *= a;
assert( m + b == oldm);
m = (BigInt(1) << (4846 + 4843) ) - 1;
a = (BigInt(1) << 4846 ) - 1;
b = (BigInt(1) << (4846*2 + 4843)) - 1;
BigInt c = (BigInt(1) << (4846*2 + 4843*2)) - 1;
BigInt w = c - b + a;
assert(w % m == 0);
// https://issues.dlang.org/show_bug.cgi?id=6819
BigInt z1 = BigInt(10)^^64;
BigInt w1 = BigInt(10)^^128;
assert(z1^^2 == w1);
BigInt z2 = BigInt(1)<<64;
BigInt w2 = BigInt(1)<<128;
assert(z2^^2 == w2);
// https://issues.dlang.org/show_bug.cgi?id=7993
BigInt n7793 = 10;
assert( n7793 / 1 == 10);
// https://issues.dlang.org/show_bug.cgi?id=7973
auto a7973 = 10_000_000_000_000_000;
const c7973 = 10_000_000_000_000_000;
immutable i7973 = 10_000_000_000_000_000;
BigInt v7973 = 2551700137;
v7973 %= a7973;
assert(v7973 == 2551700137);
v7973 %= c7973;
assert(v7973 == 2551700137);
v7973 %= i7973;
assert(v7973 == 2551700137);
// https://issues.dlang.org/show_bug.cgi?id=8165
BigInt[2] a8165;
a8165[0] = a8165[1] = 1;
}
@safe unittest
{
import std.array;
import std.format.write : formattedWrite;
immutable string[][] table = [
/* fmt, +10 -10 */
["%d", "10", "-10"],
["%+d", "+10", "-10"],
["%-d", "10", "-10"],
["%+-d", "+10", "-10"],
["%4d", " 10", " -10"],
["%+4d", " +10", " -10"],
["%-4d", "10 ", "-10 "],
["%+-4d", "+10 ", "-10 "],
["%04d", "0010", "-010"],
["%+04d", "+010", "-010"],
["%-04d", "10 ", "-10 "],
["%+-04d", "+10 ", "-10 "],
["% 04d", " 010", "-010"],
["%+ 04d", "+010", "-010"],
["%- 04d", " 10 ", "-10 "],
["%+- 04d", "+10 ", "-10 "],
];
auto w1 = appender!(char[])();
auto w2 = appender!(char[])();
foreach (entry; table)
{
immutable fmt = entry[0];
formattedWrite(w1, fmt, BigInt(10));
formattedWrite(w2, fmt, 10);
assert(w1.data == w2.data);
assert(w1.data == entry[1]);
w1.clear();
w2.clear();
formattedWrite(w1, fmt, BigInt(-10));
formattedWrite(w2, fmt, -10);
assert(w1.data == w2.data);
assert(w1.data == entry[2]);
w1.clear();
w2.clear();
}
}
@safe unittest
{
import std.array;
import std.format.write : formattedWrite;
immutable string[][] table = [
/* fmt, +10 -10 */
["%x", "a", "-a"],
["%+x", "a", "-a"],
["%-x", "a", "-a"],
["%+-x", "a", "-a"],
["%4x", " a", " -a"],
["%+4x", " a", " -a"],
["%-4x", "a ", "-a "],
["%+-4x", "a ", "-a "],
["%04x", "000a", "-00a"],
["%+04x", "000a", "-00a"],
["%-04x", "a ", "-a "],
["%+-04x", "a ", "-a "],
["% 04x", "000a", "-00a"],
["%+ 04x", "000a", "-00a"],
["%- 04x", "a ", "-a "],
["%+- 04x", "a ", "-a "],
];
auto w1 = appender!(char[])();
auto w2 = appender!(char[])();
foreach (entry; table)
{
immutable fmt = entry[0];
formattedWrite(w1, fmt, BigInt(10));
formattedWrite(w2, fmt, 10);
assert(w1.data == w2.data); // Equal only positive BigInt
assert(w1.data == entry[1]);
w1.clear();
w2.clear();
formattedWrite(w1, fmt, BigInt(-10));
//formattedWrite(w2, fmt, -10);
//assert(w1.data == w2.data);
assert(w1.data == entry[2]);
w1.clear();
//w2.clear();
}
}
@safe unittest
{
import std.array;
import std.format.write : formattedWrite;
immutable string[][] table = [
/* fmt, +10 -10 */
["%X", "A", "-A"],
["%+X", "A", "-A"],
["%-X", "A", "-A"],
["%+-X", "A", "-A"],
["%4X", " A", " -A"],
["%+4X", " A", " -A"],
["%-4X", "A ", "-A "],
["%+-4X", "A ", "-A "],
["%04X", "000A", "-00A"],
["%+04X", "000A", "-00A"],
["%-04X", "A ", "-A "],
["%+-04X", "A ", "-A "],
["% 04X", "000A", "-00A"],
["%+ 04X", "000A", "-00A"],
["%- 04X", "A ", "-A "],
["%+- 04X", "A ", "-A "],
];
auto w1 = appender!(char[])();
auto w2 = appender!(char[])();
foreach (entry; table)
{
immutable fmt = entry[0];
formattedWrite(w1, fmt, BigInt(10));
formattedWrite(w2, fmt, 10);
assert(w1.data == w2.data); // Equal only positive BigInt
assert(w1.data == entry[1]);
w1.clear();
w2.clear();
formattedWrite(w1, fmt, BigInt(-10));
//formattedWrite(w2, fmt, -10);
//assert(w1.data == w2.data);
assert(w1.data == entry[2]);
w1.clear();
//w2.clear();
}
}
// https://issues.dlang.org/show_bug.cgi?id=6448
@safe unittest
{
import std.array;
import std.format.write : formattedWrite;
auto w1 = appender!string();
auto w2 = appender!string();
int x = 100;
formattedWrite(w1, "%010d", x);
BigInt bx = x;
formattedWrite(w2, "%010d", bx);
assert(w1.data == w2.data);
// https://issues.dlang.org/show_bug.cgi?id=8011
BigInt y = -3;
++y;
assert(y.toLong() == -2);
y = 1;
--y;
assert(y.toLong() == 0);
--y;
assert(y.toLong() == -1);
--y;
assert(y.toLong() == -2);
}
@safe unittest
{
import std.math.algebraic : abs;
auto r = abs(BigInt(-1000)); // https://issues.dlang.org/show_bug.cgi?id=6486
assert(r == 1000);
auto r2 = abs(const(BigInt)(-500)); // https://issues.dlang.org/show_bug.cgi?id=11188
assert(r2 == 500);
auto r3 = abs(immutable(BigInt)(-733)); // https://issues.dlang.org/show_bug.cgi?id=11188
assert(r3 == 733);
// opCast!bool
BigInt one = 1, zero;
assert(one && !zero);
}
// https://issues.dlang.org/show_bug.cgi?id=6850
@safe unittest
{
pure long pureTest() {
BigInt a = 1;
BigInt b = 1336;
a += b;
return a.toLong();
}
assert(pureTest() == 1337);
}
// https://issues.dlang.org/show_bug.cgi?id=8435
// https://issues.dlang.org/show_bug.cgi?id=10118
@safe unittest
{
auto i = BigInt(100);
auto j = BigInt(100);
// Two separate BigInt instances representing same value should have same
// hash.
assert(typeid(i).getHash(&i) == typeid(j).getHash(&j));
assert(typeid(i).compare(&i, &j) == 0);
// BigInt AA keys should behave consistently.
int[BigInt] aa;
aa[BigInt(123)] = 123;
assert(BigInt(123) in aa);
aa[BigInt(123)] = 321;
assert(aa[BigInt(123)] == 321);
auto keys = aa.byKey;
assert(keys.front == BigInt(123));
keys.popFront();
assert(keys.empty);
}
// https://issues.dlang.org/show_bug.cgi?id=11148
@safe unittest
{
void foo(BigInt) {}
const BigInt cbi = 3;
immutable BigInt ibi = 3;
foo(cbi);
foo(ibi);
import std.conv : to;
import std.meta : AliasSeq;
static foreach (T1; AliasSeq!(BigInt, const(BigInt), immutable(BigInt)))
{
static foreach (T2; AliasSeq!(BigInt, const(BigInt), immutable(BigInt)))
{{
T1 t1 = 2;
T2 t2 = t1;
T2 t2_1 = to!T2(t1);
T2 t2_2 = cast(T2) t1;
assert(t2 == t1);
assert(t2 == 2);
assert(t2_1 == t1);
assert(t2_1 == 2);
assert(t2_2 == t1);
assert(t2_2 == 2);
}}
}
BigInt n = 2;
n *= 2;
assert(n == 4);
}
// https://issues.dlang.org/show_bug.cgi?id=8167
@safe unittest
{
BigInt a = BigInt(3);
BigInt b = BigInt(a);
assert(b == 3);
}
// https://issues.dlang.org/show_bug.cgi?id=9061
@safe unittest
{
long l1 = 0x12345678_90ABCDEF;
long l2 = 0xFEDCBA09_87654321;
long l3 = l1 | l2;
long l4 = l1 & l2;
long l5 = l1 ^ l2;
BigInt b1 = l1;
BigInt b2 = l2;
BigInt b3 = b1 | b2;
BigInt b4 = b1 & b2;
BigInt b5 = b1 ^ b2;
assert(l3 == b3);
assert(l4 == b4);
assert(l5 == b5);
}
// https://issues.dlang.org/show_bug.cgi?id=11600
@safe unittest
{
import std.conv;
import std.exception : assertThrown;
// Original bug report
assertThrown!ConvException(to!BigInt("avadakedavra"));
// Digit string lookalikes that are actually invalid
assertThrown!ConvException(to!BigInt("0123hellothere"));
assertThrown!ConvException(to!BigInt("-hihomarylowe"));
assertThrown!ConvException(to!BigInt("__reallynow__"));
assertThrown!ConvException(to!BigInt("-123four"));
}
// https://issues.dlang.org/show_bug.cgi?id=11583
@safe unittest
{
BigInt x = 0;
assert((x > 0) == false);
}
// https://issues.dlang.org/show_bug.cgi?id=13391
@safe unittest
{
BigInt x1 = "123456789";
BigInt x2 = "123456789123456789";
BigInt x3 = "123456789123456789123456789";
import std.meta : AliasSeq;
static foreach (T; AliasSeq!(byte, ubyte, short, ushort, int, uint, long, ulong))
{
assert((x1 * T.max) / T.max == x1);
assert((x2 * T.max) / T.max == x2);
assert((x3 * T.max) / T.max == x3);
}
assert(x1 / -123456789 == -1);
assert(x1 / 123456789U == 1);
assert(x1 / -123456789L == -1);
assert(x1 / 123456789UL == 1);
assert(x2 / -123456789123456789L == -1);
assert(x2 / 123456789123456789UL == 1);
assert(x1 / uint.max == 0);
assert(x1 / ulong.max == 0);
assert(x2 / ulong.max == 0);
x1 /= 123456789UL;
assert(x1 == 1);
x2 /= 123456789123456789UL;
assert(x2 == 1);
}
// https://issues.dlang.org/show_bug.cgi?id=13963
@safe unittest
{
BigInt x = 1;
import std.meta : AliasSeq;
static foreach (Int; AliasSeq!(byte, ubyte, short, ushort, int))
{
assert(is(typeof(x % Int(1)) == int));
}
assert(is(typeof(x % 1U) == long));
assert(is(typeof(x % 1L) == long));
assert(is(typeof(x % 1UL) == BigInt));
auto x0 = BigInt(uint.max - 1);
auto x1 = BigInt(8);
assert(x1 / x == x1);
auto x2 = -BigInt(long.min) + 1;
// uint
assert( x0 % uint.max == x0 % BigInt(uint.max));
assert(-x0 % uint.max == -x0 % BigInt(uint.max));
assert( x0 % uint.max == long(uint.max - 1));
assert(-x0 % uint.max == -long(uint.max - 1));
// long
assert(x1 % 2L == 0L);
assert(-x1 % 2L == 0L);
assert(x1 % 3L == 2L);
assert(x1 % -3L == 2L);
assert(-x1 % 3L == -2L);
assert(-x1 % -3L == -2L);
assert(x1 % 11L == 8L);
assert(x1 % -11L == 8L);
assert(-x1 % 11L == -8L);
assert(-x1 % -11L == -8L);
// ulong
assert(x1 % 2UL == BigInt(0));
assert(-x1 % 2UL == BigInt(0));
assert(x1 % 3UL == BigInt(2));
assert(-x1 % 3UL == -BigInt(2));
assert(x1 % 11UL == BigInt(8));
assert(-x1 % 11UL == -BigInt(8));
assert(x2 % ulong.max == x2);
assert(-x2 % ulong.max == -x2);
}
// https://issues.dlang.org/show_bug.cgi?id=14124
@safe unittest
{
auto x = BigInt(-3);
x %= 3;
assert(!x.isNegative);
assert(x.isZero);
x = BigInt(-3);
x %= cast(ushort) 3;
assert(!x.isNegative);
assert(x.isZero);
x = BigInt(-3);
x %= 3L;
assert(!x.isNegative);
assert(x.isZero);
x = BigInt(3);
x %= -3;
assert(!x.isNegative);
assert(x.isZero);
}
// https://issues.dlang.org/show_bug.cgi?id=15678
@safe unittest
{
import std.exception : assertThrown;
assertThrown!ConvException(BigInt(""));
assertThrown!ConvException(BigInt("0x1234BARF"));
assertThrown!ConvException(BigInt("1234PUKE"));
}
// https://issues.dlang.org/show_bug.cgi?id=6447
@safe unittest
{
import std.algorithm.comparison : equal;
import std.range : iota;
auto s = BigInt(1_000_000_000_000);
auto e = BigInt(1_000_000_000_003);
auto r = iota(s, e);
assert(r.equal([
BigInt(1_000_000_000_000),
BigInt(1_000_000_000_001),
BigInt(1_000_000_000_002)
]));
}
// https://issues.dlang.org/show_bug.cgi?id=17330
@safe unittest
{
auto b = immutable BigInt("123");
assert(b == 123);
}
// https://issues.dlang.org/show_bug.cgi?id=14767
@safe pure unittest
{
static immutable a = BigInt("340282366920938463463374607431768211455");
assert(a == BigInt("340282366920938463463374607431768211455"));
BigInt plusTwo(in BigInt n)
{
return n + 2;
}
enum BigInt test1 = BigInt(123);
enum BigInt test2 = plusTwo(test1);
assert(test2 == 125);
}
/**
* Finds the quotient and remainder for the given dividend and divisor in one operation.
*
* Params:
* dividend = the $(LREF BigInt) to divide
* divisor = the $(LREF BigInt) to divide the dividend by
* quotient = is set to the result of the division
* remainder = is set to the remainder of the division
*/
void divMod(const BigInt dividend, const BigInt divisor, out BigInt quotient, out BigInt remainder) pure nothrow @safe
{
BigUint q, r;
BigUint.divMod(dividend.data, divisor.data, q, r);
quotient.sign = dividend.sign != divisor.sign;
quotient.data = q;
remainder.sign = r.isZero() ? false : dividend.sign;
remainder.data = r;
}
///
@safe pure nothrow unittest
{
auto a = BigInt(123);
auto b = BigInt(25);
BigInt q, r;
divMod(a, b, q, r);
assert(q == 4);
assert(r == 23);
assert(q * b + r == a);
}
// https://issues.dlang.org/show_bug.cgi?id=18086
@safe pure nothrow unittest
{
BigInt q = 1;
BigInt r = 1;
BigInt c = 1024;
BigInt d = 100;
divMod(c, d, q, r);
assert(q == 10);
assert(r == 24);
assert((q * d + r) == c);
divMod(c, -d, q, r);
assert(q == -10);
assert(r == 24);
assert(q * -d + r == c);
divMod(-c, -d, q, r);
assert(q == 10);
assert(r == -24);
assert(q * -d + r == -c);
divMod(-c, d, q, r);
assert(q == -10);
assert(r == -24);
assert(q * d + r == -c);
}
// https://issues.dlang.org/show_bug.cgi?id=22771
@safe pure nothrow unittest
{
BigInt quotient, remainder;
divMod(BigInt(-50), BigInt(1), quotient, remainder);
assert(remainder == 0);
}
// https://issues.dlang.org/show_bug.cgi?id=19740
@safe unittest
{
BigInt a = BigInt(
"241127122100380210001001124020210001001100000200003101000062221012075223052000021042250111300200000000000" ~
"000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000");
BigInt b = BigInt(
"700200000000500418321000401140010110000022007221432000000141020011323301104104060202100200457210001600142" ~
"000001012245300100001110215200000000120000000000000000000000000000000000000000000000000000000000000000000" ~
"00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000");
BigInt c = a * b;
assert(c == BigInt(
"1688372108948068874722901180228375682334987075822938736581472847151834613694489486296103575639363261807341" ~
"3910091006778604956808730652275328822700182498926542563654351871390166691461743896850906716336187966456064" ~
"2702007176328110013356024000000000000000000000000000000000000000000000000000000000000000000000000000000000" ~
"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" ~
"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000"));
}
@safe unittest
{
auto n = BigInt("1234"d);
}
/**
Fast power modulus calculation for $(LREF BigInt) operands.
Params:
base = the $(LREF BigInt) is basic operands.
exponent = the $(LREF BigInt) is power exponent of base.
modulus = the $(LREF BigInt) is modules to be modular of base ^ exponent.
Returns:
The power modulus value of (base ^ exponent) % modulus.
*/
BigInt powmod(BigInt base, BigInt exponent, BigInt modulus) pure nothrow @safe
{
BigInt result = 1;
while (exponent)
{
if (exponent.data.peekUint(0) & 1)
{
result = (result * base) % modulus;
}
auto tmp = base % modulus;
base = (tmp * tmp) % modulus;
exponent >>= 1;
}
return result;
}
/// for powmod
@safe unittest
{
BigInt base = BigInt("123456789012345678901234567890");
BigInt exponent = BigInt("1234567890123456789012345678901234567");
BigInt modulus = BigInt("1234567");
BigInt result = powmod(base, exponent, modulus);
assert(result == 359079);
}