mirror of
https://github.com/autc04/Retro68.git
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782 lines
20 KiB
D
782 lines
20 KiB
D
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/**********************************************
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* This module implements integral arithmetic primitives that check
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* for out-of-range results.
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*
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* Integral arithmetic operators operate on fixed width types.
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* Results that are not representable in those fixed widths are silently
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* truncated to fit.
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* This module offers integral arithmetic primitives that produce the
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* same results, but set an 'overflow' flag when such truncation occurs.
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* The setting is sticky, meaning that numerous operations can be cascaded
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* and then the flag need only be checked at the end.
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* Whether the operation is signed or unsigned is indicated by an 's' or 'u'
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* suffix, respectively. While this could be achieved without such suffixes by
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* using overloading on the signedness of the types, the suffix makes it clear
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* which is happening without needing to examine the types.
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*
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* While the generic versions of these functions are computationally expensive
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* relative to the cost of the operation itself, compiler implementations are free
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* to recognize them and generate equivalent and faster code.
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*
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* References: $(LINK2 http://blog.regehr.org/archives/1139, Fast Integer Overflow Checks)
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* Copyright: Copyright (c) Walter Bright 2014.
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* License: $(LINK2 http://www.boost.org/LICENSE_1_0.txt, Boost License 1.0)
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* Authors: Walter Bright
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* Source: $(DRUNTIMESRC core/_checkedint.d)
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*/
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module core.checkedint;
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nothrow:
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@safe:
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@nogc:
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pure:
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/*******************************
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* Add two signed integers, checking for overflow.
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*
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* The overflow is sticky, meaning a sequence of operations can
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* be done and overflow need only be checked at the end.
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* Params:
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* x = left operand
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* y = right operand
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* overflow = set if an overflow occurs, is not affected otherwise
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* Returns:
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* the sum
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*/
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pragma(inline, true)
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int adds(int x, int y, ref bool overflow)
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{
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long r = cast(long)x + cast(long)y;
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if (r < int.min || r > int.max)
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overflow = true;
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return cast(int)r;
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}
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unittest
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{
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bool overflow;
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assert(adds(2, 3, overflow) == 5);
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assert(!overflow);
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assert(adds(1, int.max - 1, overflow) == int.max);
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assert(!overflow);
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assert(adds(int.min + 1, -1, overflow) == int.min);
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assert(!overflow);
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assert(adds(int.max, 1, overflow) == int.min);
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assert(overflow);
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overflow = false;
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assert(adds(int.min, -1, overflow) == int.max);
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assert(overflow);
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assert(adds(0, 0, overflow) == 0);
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assert(overflow); // sticky
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}
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/// ditto
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pragma(inline, true)
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long adds(long x, long y, ref bool overflow)
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{
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long r = cast(ulong)x + cast(ulong)y;
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if (x < 0 && y < 0 && r >= 0 ||
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x >= 0 && y >= 0 && r < 0)
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overflow = true;
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return r;
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}
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unittest
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{
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bool overflow;
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assert(adds(2L, 3L, overflow) == 5);
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assert(!overflow);
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assert(adds(1L, long.max - 1, overflow) == long.max);
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assert(!overflow);
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assert(adds(long.min + 1, -1, overflow) == long.min);
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assert(!overflow);
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assert(adds(long.max, 1, overflow) == long.min);
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assert(overflow);
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overflow = false;
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assert(adds(long.min, -1, overflow) == long.max);
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assert(overflow);
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assert(adds(0L, 0L, overflow) == 0);
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assert(overflow); // sticky
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}
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static if (is(cent))
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{
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/// ditto
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pragma(inline, true)
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cent adds(cent x, cent y, ref bool overflow)
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{
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cent r = cast(ucent)x + cast(ucent)y;
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if (x < 0 && y < 0 && r >= 0 ||
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x >= 0 && y >= 0 && r < 0)
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overflow = true;
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return r;
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}
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unittest
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{
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bool overflow;
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assert(adds(cast(cent)2L, 3L, overflow) == 5);
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assert(!overflow);
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assert(adds(1L, cent.max - 1, overflow) == cent.max);
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assert(!overflow);
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assert(adds(cent.min + 1, -1, overflow) == cent.min);
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assert(!overflow);
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assert(adds(cent.max, 1, overflow) == cent.min);
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assert(overflow);
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overflow = false;
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assert(adds(cent.min, -1, overflow) == cent.max);
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assert(overflow);
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assert(adds(cast(cent)0L, 0L, overflow) == 0);
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assert(overflow); // sticky
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}
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}
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/*******************************
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* Add two unsigned integers, checking for overflow (aka carry).
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*
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* The overflow is sticky, meaning a sequence of operations can
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* be done and overflow need only be checked at the end.
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* Params:
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* x = left operand
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* y = right operand
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* overflow = set if an overflow occurs, is not affected otherwise
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* Returns:
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* the sum
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*/
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pragma(inline, true)
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uint addu(uint x, uint y, ref bool overflow)
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{
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immutable uint r = x + y;
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if (r < x || r < y)
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overflow = true;
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return r;
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}
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unittest
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{
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bool overflow;
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assert(addu(2, 3, overflow) == 5);
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assert(!overflow);
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assert(addu(1, uint.max - 1, overflow) == uint.max);
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assert(!overflow);
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assert(addu(uint.min, -1, overflow) == uint.max);
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assert(!overflow);
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assert(addu(uint.max, 1, overflow) == uint.min);
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assert(overflow);
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overflow = false;
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assert(addu(uint.min + 1, -1, overflow) == uint.min);
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assert(overflow);
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assert(addu(0, 0, overflow) == 0);
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assert(overflow); // sticky
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}
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/// ditto
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pragma(inline, true)
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ulong addu(ulong x, ulong y, ref bool overflow)
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{
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immutable ulong r = x + y;
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if (r < x || r < y)
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overflow = true;
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return r;
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}
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unittest
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{
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bool overflow;
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assert(addu(2L, 3L, overflow) == 5);
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assert(!overflow);
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assert(addu(1, ulong.max - 1, overflow) == ulong.max);
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assert(!overflow);
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assert(addu(ulong.min, -1L, overflow) == ulong.max);
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assert(!overflow);
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assert(addu(ulong.max, 1, overflow) == ulong.min);
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assert(overflow);
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overflow = false;
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assert(addu(ulong.min + 1, -1L, overflow) == ulong.min);
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assert(overflow);
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assert(addu(0L, 0L, overflow) == 0);
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assert(overflow); // sticky
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}
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static if (is(ucent))
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{
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/// ditto
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pragma(inline, true)
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ucent addu(ucent x, ucent y, ref bool overflow)
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{
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immutable ucent r = x + y;
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if (r < x || r < y)
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overflow = true;
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return r;
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}
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unittest
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{
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bool overflow;
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assert(addu(cast(ucent)2L, 3L, overflow) == 5);
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assert(!overflow);
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assert(addu(1, ucent.max - 1, overflow) == ucent.max);
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assert(!overflow);
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assert(addu(ucent.min, -1L, overflow) == ucent.max);
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assert(!overflow);
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assert(addu(ucent.max, 1, overflow) == ucent.min);
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assert(overflow);
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overflow = false;
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assert(addu(ucent.min + 1, -1L, overflow) == ucent.min);
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assert(overflow);
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assert(addu(cast(ucent)0L, 0L, overflow) == 0);
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assert(overflow); // sticky
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}
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}
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/*******************************
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* Subtract two signed integers, checking for overflow.
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*
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* The overflow is sticky, meaning a sequence of operations can
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* be done and overflow need only be checked at the end.
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* Params:
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* x = left operand
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* y = right operand
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* overflow = set if an overflow occurs, is not affected otherwise
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* Returns:
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* the difference
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*/
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pragma(inline, true)
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int subs(int x, int y, ref bool overflow)
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{
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immutable long r = cast(long)x - cast(long)y;
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if (r < int.min || r > int.max)
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overflow = true;
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return cast(int)r;
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}
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unittest
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{
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bool overflow;
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assert(subs(2, -3, overflow) == 5);
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assert(!overflow);
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assert(subs(1, -int.max + 1, overflow) == int.max);
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assert(!overflow);
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assert(subs(int.min + 1, 1, overflow) == int.min);
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assert(!overflow);
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assert(subs(int.max, -1, overflow) == int.min);
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assert(overflow);
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overflow = false;
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assert(subs(int.min, 1, overflow) == int.max);
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assert(overflow);
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assert(subs(0, 0, overflow) == 0);
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assert(overflow); // sticky
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}
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/// ditto
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pragma(inline, true)
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long subs(long x, long y, ref bool overflow)
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{
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immutable long r = cast(ulong)x - cast(ulong)y;
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if (x < 0 && y >= 0 && r >= 0 ||
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x >= 0 && y < 0 && (r < 0 || y == long.min))
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overflow = true;
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return r;
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}
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unittest
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{
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bool overflow;
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assert(subs(2L, -3L, overflow) == 5);
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assert(!overflow);
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assert(subs(1L, -long.max + 1, overflow) == long.max);
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assert(!overflow);
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assert(subs(long.min + 1, 1, overflow) == long.min);
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assert(!overflow);
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assert(subs(-1L, long.min, overflow) == long.max);
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assert(!overflow);
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assert(subs(long.max, -1, overflow) == long.min);
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assert(overflow);
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overflow = false;
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assert(subs(long.min, 1, overflow) == long.max);
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assert(overflow);
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assert(subs(0L, 0L, overflow) == 0);
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assert(overflow); // sticky
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}
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static if (is(cent))
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{
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/// ditto
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pragma(inline, true)
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cent subs(cent x, cent y, ref bool overflow)
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{
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immutable cent r = cast(ucent)x - cast(ucent)y;
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if (x < 0 && y >= 0 && r >= 0 ||
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x >= 0 && y < 0 && (r < 0 || y == long.min))
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overflow = true;
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return r;
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}
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unittest
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{
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bool overflow;
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assert(subs(cast(cent)2L, -3L, overflow) == 5);
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assert(!overflow);
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assert(subs(1L, -cent.max + 1, overflow) == cent.max);
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assert(!overflow);
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assert(subs(cent.min + 1, 1, overflow) == cent.min);
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assert(!overflow);
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assert(subs(-1L, cent.min, overflow) == cent.max);
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assert(!overflow);
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assert(subs(cent.max, -1, overflow) == cent.min);
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assert(overflow);
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overflow = false;
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assert(subs(cent.min, 1, overflow) == cent.max);
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assert(overflow);
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assert(subs(cast(cent)0L, 0L, overflow) == 0);
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assert(overflow); // sticky
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}
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}
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/*******************************
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* Subtract two unsigned integers, checking for overflow (aka borrow).
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*
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* The overflow is sticky, meaning a sequence of operations can
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* be done and overflow need only be checked at the end.
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* Params:
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* x = left operand
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* y = right operand
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* overflow = set if an overflow occurs, is not affected otherwise
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* Returns:
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* the difference
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*/
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pragma(inline, true)
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uint subu(uint x, uint y, ref bool overflow)
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{
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if (x < y)
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overflow = true;
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return x - y;
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}
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unittest
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{
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bool overflow;
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assert(subu(3, 2, overflow) == 1);
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assert(!overflow);
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assert(subu(uint.max, 1, overflow) == uint.max - 1);
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assert(!overflow);
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assert(subu(1, 1, overflow) == uint.min);
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assert(!overflow);
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assert(subu(0, 1, overflow) == uint.max);
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assert(overflow);
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overflow = false;
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assert(subu(uint.max - 1, uint.max, overflow) == uint.max);
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assert(overflow);
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assert(subu(0, 0, overflow) == 0);
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assert(overflow); // sticky
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}
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/// ditto
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pragma(inline, true)
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ulong subu(ulong x, ulong y, ref bool overflow)
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{
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if (x < y)
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overflow = true;
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return x - y;
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}
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unittest
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{
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bool overflow;
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assert(subu(3UL, 2UL, overflow) == 1);
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assert(!overflow);
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assert(subu(ulong.max, 1, overflow) == ulong.max - 1);
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assert(!overflow);
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assert(subu(1UL, 1UL, overflow) == ulong.min);
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assert(!overflow);
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assert(subu(0UL, 1UL, overflow) == ulong.max);
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assert(overflow);
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overflow = false;
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assert(subu(ulong.max - 1, ulong.max, overflow) == ulong.max);
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assert(overflow);
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assert(subu(0UL, 0UL, overflow) == 0);
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assert(overflow); // sticky
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}
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static if (is(ucent))
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{
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/// ditto
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pragma(inline, true)
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ucent subu(ucent x, ucent y, ref bool overflow)
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{
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if (x < y)
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overflow = true;
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return x - y;
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}
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unittest
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{
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bool overflow;
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assert(subu(cast(ucent)3UL, 2UL, overflow) == 1);
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assert(!overflow);
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assert(subu(ucent.max, 1, overflow) == ucent.max - 1);
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assert(!overflow);
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assert(subu(1UL, 1UL, overflow) == ucent.min);
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assert(!overflow);
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assert(subu(cast(ucent)0UL, 1UL, overflow) == ucent.max);
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assert(overflow);
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overflow = false;
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assert(subu(ucent.max - 1, ucent.max, overflow) == ucent.max);
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assert(overflow);
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assert(subu(cast(ucent)0UL, 0UL, overflow) == 0);
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assert(overflow); // sticky
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}
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}
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/***********************************************
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* Negate an integer.
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*
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* Params:
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* x = operand
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* overflow = set if x cannot be negated, is not affected otherwise
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* Returns:
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* the negation of x
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*/
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pragma(inline, true)
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int negs(int x, ref bool overflow)
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{
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if (x == int.min)
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overflow = true;
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return -x;
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}
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unittest
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{
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bool overflow;
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assert(negs(0, overflow) == -0);
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assert(!overflow);
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assert(negs(1234, overflow) == -1234);
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assert(!overflow);
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assert(negs(-5678, overflow) == 5678);
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assert(!overflow);
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assert(negs(int.min, overflow) == -int.min);
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assert(overflow);
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assert(negs(0, overflow) == -0);
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assert(overflow); // sticky
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}
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/// ditto
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pragma(inline, true)
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long negs(long x, ref bool overflow)
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{
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if (x == long.min)
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overflow = true;
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return -x;
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}
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unittest
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{
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bool overflow;
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assert(negs(0L, overflow) == -0);
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assert(!overflow);
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assert(negs(1234L, overflow) == -1234);
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assert(!overflow);
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assert(negs(-5678L, overflow) == 5678);
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assert(!overflow);
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assert(negs(long.min, overflow) == -long.min);
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assert(overflow);
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assert(negs(0L, overflow) == -0);
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assert(overflow); // sticky
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}
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static if (is(cent))
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{
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/// ditto
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pragma(inline, true)
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cent negs(cent x, ref bool overflow)
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{
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if (x == cent.min)
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overflow = true;
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return -x;
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}
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unittest
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{
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bool overflow;
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assert(negs(cast(cent)0L, overflow) == -0);
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assert(!overflow);
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assert(negs(cast(cent)1234L, overflow) == -1234);
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assert(!overflow);
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assert(negs(cast(cent)-5678L, overflow) == 5678);
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assert(!overflow);
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assert(negs(cent.min, overflow) == -cent.min);
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assert(overflow);
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assert(negs(cast(cent)0L, overflow) == -0);
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assert(overflow); // sticky
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}
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}
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/*******************************
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* Multiply two signed integers, checking for overflow.
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*
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* The overflow is sticky, meaning a sequence of operations can
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* be done and overflow need only be checked at the end.
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* Params:
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* x = left operand
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* y = right operand
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* overflow = set if an overflow occurs, is not affected otherwise
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* Returns:
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* the product
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*/
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pragma(inline, true)
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int muls(int x, int y, ref bool overflow)
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{
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long r = cast(long)x * cast(long)y;
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if (r < int.min || r > int.max)
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|
overflow = true;
|
|
return cast(int)r;
|
|
}
|
|
|
|
unittest
|
|
{
|
|
bool overflow;
|
|
assert(muls(2, 3, overflow) == 6);
|
|
assert(!overflow);
|
|
assert(muls(-200, 300, overflow) == -60_000);
|
|
assert(!overflow);
|
|
assert(muls(1, int.max, overflow) == int.max);
|
|
assert(!overflow);
|
|
assert(muls(int.min, 1, overflow) == int.min);
|
|
assert(!overflow);
|
|
assert(muls(int.max, 2, overflow) == (int.max * 2));
|
|
assert(overflow);
|
|
overflow = false;
|
|
assert(muls(int.min, -1, overflow) == int.min);
|
|
assert(overflow);
|
|
assert(muls(0, 0, overflow) == 0);
|
|
assert(overflow); // sticky
|
|
}
|
|
|
|
/// ditto
|
|
pragma(inline, true)
|
|
long muls(long x, long y, ref bool overflow)
|
|
{
|
|
immutable long r = cast(ulong)x * cast(ulong)y;
|
|
enum not0or1 = ~1L;
|
|
if ((x & not0or1) && ((r == y)? r : (r / x) != y))
|
|
overflow = true;
|
|
return r;
|
|
}
|
|
|
|
unittest
|
|
{
|
|
bool overflow;
|
|
assert(muls(2L, 3L, overflow) == 6);
|
|
assert(!overflow);
|
|
assert(muls(-200L, 300L, overflow) == -60_000);
|
|
assert(!overflow);
|
|
assert(muls(1, long.max, overflow) == long.max);
|
|
assert(!overflow);
|
|
assert(muls(long.min, 1L, overflow) == long.min);
|
|
assert(!overflow);
|
|
assert(muls(long.max, 2L, overflow) == (long.max * 2));
|
|
assert(overflow);
|
|
overflow = false;
|
|
assert(muls(-1L, long.min, overflow) == long.min);
|
|
assert(overflow);
|
|
overflow = false;
|
|
assert(muls(long.min, -1L, overflow) == long.min);
|
|
assert(overflow);
|
|
assert(muls(0L, 0L, overflow) == 0);
|
|
assert(overflow); // sticky
|
|
}
|
|
|
|
static if (is(cent))
|
|
{
|
|
/// ditto
|
|
pragma(inline, true)
|
|
cent muls(cent x, cent y, ref bool overflow)
|
|
{
|
|
immutable cent r = cast(ucent)x * cast(ucent)y;
|
|
enum not0or1 = ~1L;
|
|
if ((x & not0or1) && ((r == y)? r : (r / x) != y))
|
|
overflow = true;
|
|
return r;
|
|
}
|
|
|
|
unittest
|
|
{
|
|
bool overflow;
|
|
assert(muls(cast(cent)2L, 3L, overflow) == 6);
|
|
assert(!overflow);
|
|
assert(muls(cast(cent)-200L, 300L, overflow) == -60_000);
|
|
assert(!overflow);
|
|
assert(muls(1, cent.max, overflow) == cent.max);
|
|
assert(!overflow);
|
|
assert(muls(cent.min, 1L, overflow) == cent.min);
|
|
assert(!overflow);
|
|
assert(muls(cent.max, 2L, overflow) == (cent.max * 2));
|
|
assert(overflow);
|
|
overflow = false;
|
|
assert(muls(-1L, cent.min, overflow) == cent.min);
|
|
assert(overflow);
|
|
overflow = false;
|
|
assert(muls(cent.min, -1L, overflow) == cent.min);
|
|
assert(overflow);
|
|
assert(muls(cast(cent)0L, 0L, overflow) == 0);
|
|
assert(overflow); // sticky
|
|
}
|
|
}
|
|
|
|
|
|
/*******************************
|
|
* Multiply two unsigned integers, checking for overflow (aka carry).
|
|
*
|
|
* The overflow is sticky, meaning a sequence of operations can
|
|
* be done and overflow need only be checked at the end.
|
|
* Params:
|
|
* x = left operand
|
|
* y = right operand
|
|
* overflow = set if an overflow occurs, is not affected otherwise
|
|
* Returns:
|
|
* the product
|
|
*/
|
|
|
|
pragma(inline, true)
|
|
uint mulu(uint x, uint y, ref bool overflow)
|
|
{
|
|
immutable ulong r = ulong(x) * ulong(y);
|
|
if (r >> 32)
|
|
overflow = true;
|
|
return cast(uint) r;
|
|
}
|
|
|
|
unittest
|
|
{
|
|
void test(uint x, uint y, uint r, bool overflow) @nogc nothrow
|
|
{
|
|
bool o;
|
|
assert(mulu(x, y, o) == r);
|
|
assert(o == overflow);
|
|
}
|
|
test(2, 3, 6, false);
|
|
test(1, uint.max, uint.max, false);
|
|
test(0, 1, 0, false);
|
|
test(0, uint.max, 0, false);
|
|
test(uint.max, 2, 2 * uint.max, true);
|
|
test(1 << 16, 1U << 16, 0, true);
|
|
|
|
bool overflow = true;
|
|
assert(mulu(0, 0, overflow) == 0);
|
|
assert(overflow); // sticky
|
|
}
|
|
|
|
/// ditto
|
|
pragma(inline, true)
|
|
ulong mulu(ulong x, uint y, ref bool overflow)
|
|
{
|
|
ulong r = x * y;
|
|
if (x >> 32 &&
|
|
r / x != y)
|
|
overflow = true;
|
|
return r;
|
|
}
|
|
|
|
/// ditto
|
|
pragma(inline, true)
|
|
ulong mulu(ulong x, ulong y, ref bool overflow)
|
|
{
|
|
immutable ulong r = x * y;
|
|
if ((x | y) >> 32 &&
|
|
x &&
|
|
r / x != y)
|
|
overflow = true;
|
|
return r;
|
|
}
|
|
|
|
unittest
|
|
{
|
|
void test(T, U)(T x, U y, ulong r, bool overflow) @nogc nothrow
|
|
{
|
|
bool o;
|
|
assert(mulu(x, y, o) == r);
|
|
assert(o == overflow);
|
|
}
|
|
// One operand is zero
|
|
test(0, 3, 0, false);
|
|
test(0UL, 3, 0, false);
|
|
test(0UL, 3UL, 0, false);
|
|
test(3, 0, 0, false);
|
|
test(3UL, 0, 0, false);
|
|
test(3UL, 0UL, 0, false);
|
|
// Small numbers
|
|
test(2, 3, 6, false);
|
|
test(2UL, 3, 6, false);
|
|
test(2UL, 3UL, 6, false);
|
|
// At the 32/64 border
|
|
test(1, ulong(uint.max), uint.max, false);
|
|
test(1UL, ulong(uint.max), uint.max, false);
|
|
test(ulong(uint.max), 1, uint.max, false);
|
|
test(ulong(uint.max), 1UL, uint.max, false);
|
|
test(1, 1 + ulong(uint.max), 1 + ulong(uint.max), false);
|
|
test(1UL, 1 + ulong(uint.max), 1 + ulong(uint.max), false);
|
|
test(1 + ulong(uint.max), 1, 1 + ulong(uint.max), false);
|
|
test(1 + ulong(uint.max), 1UL, 1 + ulong(uint.max), false);
|
|
// At the limit
|
|
test(1, ulong.max, ulong.max, false);
|
|
test(1UL, ulong.max, ulong.max, false);
|
|
test(ulong.max, 1, ulong.max, false);
|
|
test(ulong.max, 1UL, ulong.max, false);
|
|
// Miscellaneous
|
|
test(0, 1, 0, false);
|
|
test(0, ulong.max, 0, false);
|
|
test(ulong.max, 2, 2 * ulong.max, true);
|
|
test(1UL << 32, 1UL << 32, 0, true);
|
|
// Must be sticky
|
|
bool overflow = true;
|
|
assert(mulu(0UL, 0UL, overflow) == 0);
|
|
assert(overflow); // sticky
|
|
}
|
|
|
|
static if (is(ucent))
|
|
{
|
|
/// ditto
|
|
pragma(inline, true)
|
|
ucent mulu(ucent x, ucent y, ref bool overflow)
|
|
{
|
|
immutable ucent r = x * y;
|
|
if (x && (r / x) != y)
|
|
overflow = true;
|
|
return r;
|
|
}
|
|
|
|
unittest
|
|
{
|
|
void test(ucent x, ucent y, ucent r, bool overflow) @nogc nothrow
|
|
{
|
|
bool o;
|
|
assert(mulu(x, y, o) == r);
|
|
assert(o == overflow);
|
|
}
|
|
test(2, 3, 6, false);
|
|
test(1, ucent.max, ucent.max, false);
|
|
test(0, 1, 0, false);
|
|
test(0, ucent.max, 0, false);
|
|
test(ucent.max, 2, 2 * ucent.max, true);
|
|
test(cast(ucent)1UL << 64, cast(ucent)1UL << 64, 0, true);
|
|
|
|
bool overflow = true;
|
|
assert(mulu(0UL, 0UL, overflow) == 0);
|
|
assert(overflow); // sticky
|
|
}
|
|
}
|