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Merge pull request #23573 from samy-00007/bigint-shift-fix

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std.math.big.int: fix a bug in `llshl` and update test syntax
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Alex Rønne Petersen 2025-04-16 18:28:25 +02:00 • committed by GitHub
commit 1a2ceb36c8
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2 changed files with 760 additions and 448 deletions
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lib/std/math/big/int.zig
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@ -17,8 +17,6 @@ const Endian = std.builtin.Endian;
const Signedness = std.builtin.Signedness;
const native_endian = builtin.cpu.arch.endian();
const debug_safety = false;
/// Returns the number of limbs needed to store `scalar`, which must be a
/// primitive integer value.
/// Note: A comptime-known upper bound of this value that may be used
@ -92,8 +90,6 @@ pub fn calcTwosCompLimbCount(bit_count: usize) usize {
/// a + b * c + *carry, sets carry to the overflow bits
pub fn addMulLimbWithCarry(a: Limb, b: Limb, c: Limb, carry: *Limb) Limb {
@setRuntimeSafety(debug_safety);
// ov1[0] = a + *carry
const ov1 = @addWithOverflow(a, carry.*);
@ -213,7 +209,7 @@ pub const Mutable = struct {
for (self.limbs[0..self.len]) |limb| {
std.debug.print("{x} ", .{limb});
}
std.debug.print("capacity={} positive={}\n", .{ self.limbs.len, self.positive });
std.debug.print("len={} capacity={} positive={}\n", .{ self.len, self.limbs.len, self.positive });
}
/// Clones an Mutable and returns a new Mutable with the same value. The new Mutable is a deep copy and
@ -1107,8 +1103,8 @@ pub const Mutable = struct {
/// Asserts there is enough memory to fit the result. The upper bound Limb count is
/// `a.limbs.len + (shift / (@sizeOf(Limb) * 8))`.
pub fn shiftLeft(r: *Mutable, a: Const, shift: usize) void {
llshl(r.limbs, a.limbs, shift);
r.normalize(a.limbs.len + (shift / limb_bits) + 1);
const new_len = llshl(r.limbs, a.limbs, shift);
r.normalize(new_len);
r.positive = a.positive;
}
@ -1176,8 +1172,8 @@ pub const Mutable = struct {
// This shift should not be able to overflow, so invoke llshl and normalize manually
// to avoid the extra required limb.
llshl(r.limbs, a.limbs, shift);
r.normalize(a.limbs.len + (shift / limb_bits));
const new_len = llshl(r.limbs, a.limbs, shift);
r.normalize(new_len);
r.positive = a.positive;
}
@ -1185,7 +1181,7 @@ pub const Mutable = struct {
/// r and a may alias.
///
/// Asserts there is enough memory to fit the result. The upper bound Limb count is
/// `a.limbs.len - (shift / (@sizeOf(Limb) * 8))`.
/// `a.limbs.len - (shift / (@bitSizeOf(Limb)))`.
pub fn shiftRight(r: *Mutable, a: Const, shift: usize) void {
const full_limbs_shifted_out = shift / limb_bits;
const remaining_bits_shifted_out = shift % limb_bits;
@ -1213,9 +1209,9 @@ pub const Mutable = struct {
break :nonzero a.limbs[full_limbs_shifted_out] << not_covered != 0;
};
llshr(r.limbs, a.limbs, shift);
const new_len = llshr(r.limbs, a.limbs, shift);
r.len = a.limbs.len - full_limbs_shifted_out;
r.len = new_len;
r.positive = a.positive;
if (nonzero_negative_shiftout) r.addScalar(r.toConst(), -1);
r.normalize(r.len);
@ -1974,7 +1970,7 @@ pub const Const = struct {
for (self.limbs[0..self.limbs.len]) |limb| {
std.debug.print("{x} ", .{limb});
}
std.debug.print("positive={}\n", .{self.positive});
std.debug.print("len={} positive={}\n", .{ self.len, self.positive });
}
pub fn abs(self: Const) Const {
@ -2676,7 +2672,7 @@ pub const Managed = struct {
for (self.limbs[0..self.len()]) |limb| {
std.debug.print("{x} ", .{limb});
}
std.debug.print("capacity={} positive={}\n", .{ self.limbs.len, self.isPositive() });
std.debug.print("len={} capacity={} positive={}\n", .{ self.len(), self.limbs.len, self.isPositive() });
}
/// Negate the sign.
@ -3277,9 +3273,10 @@ const AccOp = enum {
///
/// The result is computed modulo `r.len`. When `r.len >= a.len + b.len`, no overflow occurs.
fn llmulacc(comptime op: AccOp, opt_allocator: ?Allocator, r: []Limb, a: []const Limb, b: []const Limb) void {
@setRuntimeSafety(debug_safety);
assert(r.len >= a.len);
assert(r.len >= b.len);
assert(!slicesOverlap(r, a));
assert(!slicesOverlap(r, b));
// Order greatest first.
var x = a;
@ -3316,9 +3313,10 @@ fn llmulaccKaratsuba(
a: []const Limb,
b: []const Limb,
) error{OutOfMemory}!void {
@setRuntimeSafety(debug_safety);
assert(r.len >= a.len);
assert(a.len >= b.len);
assert(!slicesOverlap(r, a));
assert(!slicesOverlap(r, b));
// Classical karatsuba algorithm:
// a = a1 * B + a0
@ -3479,7 +3477,6 @@ fn llmulaccKaratsuba(
/// r = r (op) a.
/// The result is computed modulo `r.len`.
fn llaccum(comptime op: AccOp, r: []Limb, a: []const Limb) void {
@setRuntimeSafety(debug_safety);
if (op == .sub) {
_ = llsubcarry(r, r, a);
return;
@ -3508,7 +3505,6 @@ fn llaccum(comptime op: AccOp, r: []Limb, a: []const Limb) void {
/// Returns -1, 0, 1 if |a| < |b|, |a| == |b| or |a| > |b| respectively for limbs.
pub fn llcmp(a: []const Limb, b: []const Limb) i8 {
@setRuntimeSafety(debug_safety);
const a_len = llnormalize(a);
const b_len = llnormalize(b);
if (a_len < b_len) {
@ -3537,7 +3533,6 @@ pub fn llcmp(a: []const Limb, b: []const Limb) i8 {
/// r = r (op) y * xi
/// The result is computed modulo `r.len`. When `r.len >= a.len + b.len`, no overflow occurs.
fn llmulaccLong(comptime op: AccOp, r: []Limb, a: []const Limb, b: []const Limb) void {
@setRuntimeSafety(debug_safety);
assert(r.len >= a.len);
assert(a.len >= b.len);
@ -3551,7 +3546,6 @@ fn llmulaccLong(comptime op: AccOp, r: []Limb, a: []const Limb, b: []const Limb)
/// The result is computed modulo `r.len`.
/// Returns whether the operation overflowed.
fn llmulLimb(comptime op: AccOp, acc: []Limb, y: []const Limb, xi: Limb) bool {
@setRuntimeSafety(debug_safety);
if (xi == 0) {
return false;
}
@ -3598,7 +3592,6 @@ fn llmulLimb(comptime op: AccOp, acc: []Limb, y: []const Limb, xi: Limb) bool {
/// returns the min length the limb could be.
fn llnormalize(a: []const Limb) usize {
@setRuntimeSafety(debug_safety);
var j = a.len;
while (j > 0) : (j -= 1) {
if (a[j - 1] != 0) {
@ -3612,7 +3605,6 @@ fn llnormalize(a: []const Limb) usize {
/// Knuth 4.3.1, Algorithm S.
fn llsubcarry(r: []Limb, a: []const Limb, b: []const Limb) Limb {
@setRuntimeSafety(debug_safety);
assert(a.len != 0 and b.len != 0);
assert(a.len >= b.len);
assert(r.len >= a.len);
@ -3638,14 +3630,12 @@ fn llsubcarry(r: []Limb, a: []const Limb, b: []const Limb) Limb {
}
fn llsub(r: []Limb, a: []const Limb, b: []const Limb) void {
@setRuntimeSafety(debug_safety);
assert(a.len > b.len or (a.len == b.len and a[a.len - 1] >= b[b.len - 1]));
assert(llsubcarry(r, a, b) == 0);
}
/// Knuth 4.3.1, Algorithm A.
fn lladdcarry(r: []Limb, a: []const Limb, b: []const Limb) Limb {
@setRuntimeSafety(debug_safety);
assert(a.len != 0 and b.len != 0);
assert(a.len >= b.len);
assert(r.len >= a.len);
@ -3671,14 +3661,12 @@ fn lladdcarry(r: []Limb, a: []const Limb, b: []const Limb) Limb {
}
fn lladd(r: []Limb, a: []const Limb, b: []const Limb) void {
@setRuntimeSafety(debug_safety);
assert(r.len >= a.len + 1);
r[a.len] = lladdcarry(r, a, b);
}
/// Knuth 4.3.1, Exercise 16.
fn lldiv1(quo: []Limb, rem: *Limb, a: []const Limb, b: Limb) void {
@setRuntimeSafety(debug_safety);
assert(a.len > 1 or a[0] >= b);
assert(quo.len >= a.len);
@ -3704,7 +3692,6 @@ fn lldiv1(quo: []Limb, rem: *Limb, a: []const Limb, b: Limb) void {
}
fn lldiv0p5(quo: []Limb, rem: *Limb, a: []const Limb, b: HalfLimb) void {
@setRuntimeSafety(debug_safety);
assert(a.len > 1 or a[0] >= b);
assert(quo.len >= a.len);
@ -3727,69 +3714,114 @@ fn lldiv0p5(quo: []Limb, rem: *Limb, a: []const Limb, b: HalfLimb) void {
}
}
fn llshl(r: []Limb, a: []const Limb, shift: usize) void {
@setRuntimeSafety(debug_safety);
assert(a.len >= 1);
/// Performs r = a << shift and returns the amount of limbs affected
///
/// if a and r overlaps, then r.ptr >= a.ptr is asserted
/// r must have the capacity to store a << shift
fn llshl(r: []Limb, a: []const Limb, shift: usize) usize {
std.debug.assert(a.len >= 1);
if (slicesOverlap(a, r))
std.debug.assert(@intFromPtr(r.ptr) >= @intFromPtr(a.ptr));
const interior_limb_shift = @as(Log2Limb, @truncate(shift));
if (shift == 0) {
if (a.ptr != r.ptr)
std.mem.copyBackwards(Limb, r[0..a.len], a);
return a.len;
}
if (shift >= limb_bits) {
const limb_shift = shift / limb_bits;
const affected = llshl(r[limb_shift..], a, shift % limb_bits);
@memset(r[0..limb_shift], 0);
return limb_shift + affected;
}
// shift is guaranteed to be < limb_bits
const bit_shift: Log2Limb = @truncate(shift);
const opposite_bit_shift: Log2Limb = @truncate(limb_bits - bit_shift);
// We only need the extra limb if the shift of the last element overflows.
// This is useful for the implementation of `shiftLeftSat`.
if (a[a.len - 1] << interior_limb_shift >> interior_limb_shift != a[a.len - 1]) {
assert(r.len >= a.len + (shift / limb_bits) + 1);
const overflows = a[a.len - 1] >> opposite_bit_shift != 0;
if (overflows) {
std.debug.assert(r.len >= a.len + 1);
} else {
assert(r.len >= a.len + (shift / limb_bits));
std.debug.assert(r.len >= a.len);
}
const limb_shift = shift / limb_bits + 1;
var carry: Limb = 0;
var i: usize = 0;
while (i < a.len) : (i += 1) {
const src_i = a.len - i - 1;
const dst_i = src_i + limb_shift;
const src_digit = a[src_i];
r[dst_i] = carry | @call(.always_inline, math.shr, .{
Limb,
src_digit,
limb_bits - @as(Limb, @intCast(interior_limb_shift)),
});
carry = (src_digit << interior_limb_shift);
var i: usize = a.len;
if (overflows) {
// r is asserted to be large enough above
r[a.len] = a[a.len - 1] >> opposite_bit_shift;
}
while (i > 1) {
i -= 1;
r[i] = (a[i - 1] >> opposite_bit_shift) | (a[i] << bit_shift);
}
r[0] = a[0] << bit_shift;
r[limb_shift - 1] = carry;
@memset(r[0 .. limb_shift - 1], 0);
return a.len + @intFromBool(overflows);
}
fn llshr(r: []Limb, a: []const Limb, shift: usize) void {
@setRuntimeSafety(debug_safety);
assert(a.len >= 1);
assert(r.len >= a.len - (shift / limb_bits));
/// Performs r = a >> shift and returns the amount of limbs affected
///
/// if a and r overlaps, then r.ptr <= a.ptr is asserted
/// r must have the capacity to store a >> shift
///
/// See tests below for examples of behaviour
fn llshr(r: []Limb, a: []const Limb, shift: usize) usize {
if (slicesOverlap(a, r))
std.debug.assert(@intFromPtr(r.ptr) <= @intFromPtr(a.ptr));
const limb_shift = shift / limb_bits;
const interior_limb_shift = @as(Log2Limb, @truncate(shift));
if (a.len == 0) return 0;
if (shift == 0) {
std.debug.assert(r.len >= a.len);
if (a.ptr != r.ptr)
std.mem.copyForwards(Limb, r[0..a.len], a);
return a.len;
}
if (shift >= limb_bits) {
if (shift / limb_bits >= a.len) {
r[0] = 0;
return 1;
}
return llshr(r, a[shift / limb_bits ..], shift % limb_bits);
}
// shift is guaranteed to be < limb_bits
const bit_shift: Log2Limb = @truncate(shift);
const opposite_bit_shift: Log2Limb = @truncate(limb_bits - bit_shift);
// special case, where there is a risk to set r to 0
if (a.len == 1) {
r[0] = a[0] >> bit_shift;
return 1;
}
if (a.len == 0) {
r[0] = 0;
return 1;
}
// if the most significant limb becomes 0 after the shift
const shrink = a[a.len - 1] >> bit_shift == 0;
std.debug.assert(r.len >= a.len - @intFromBool(!shrink));
var i: usize = 0;
while (i < a.len - limb_shift) : (i += 1) {
const dst_i = i;
const src_i = dst_i + limb_shift;
const src_digit = a[src_i];
const src_digit_next = if (src_i + 1 < a.len) a[src_i + 1] else 0;
const carry = @call(.always_inline, math.shl, .{
Limb,
src_digit_next,
limb_bits - @as(Limb, @intCast(interior_limb_shift)),
});
r[dst_i] = carry | (src_digit >> interior_limb_shift);
while (i < a.len - 1) : (i += 1) {
r[i] = (a[i] >> bit_shift) | (a[i + 1] << opposite_bit_shift);
}
if (!shrink)
r[i] = a[i] >> bit_shift;
return a.len - @intFromBool(shrink);
}
// r = ~r
fn llnot(r: []Limb) void {
@setRuntimeSafety(debug_safety);
for (r) |*elem| {
elem.* = ~elem.*;
}
@ -3802,7 +3834,6 @@ fn llnot(r: []Limb) void {
// When b is positive, r requires at least `a.len` limbs of storage.
// When b is negative, r requires at least `b.len` limbs of storage.
fn llsignedor(r: []Limb, a: []const Limb, a_positive: bool, b: []const Limb, b_positive: bool) bool {
@setRuntimeSafety(debug_safety);
assert(r.len >= a.len);
assert(a.len >= b.len);
@ -3933,7 +3964,6 @@ fn llsignedor(r: []Limb, a: []const Limb, a_positive: bool, b: []const Limb, b_p
// 2. when b is negative but a is positive, r requires at least `a.len` limbs of storage,
// 3. when both a and b are negative, r requires at least `a.len + 1` limbs of storage.
fn llsignedand(r: []Limb, a: []const Limb, a_positive: bool, b: []const Limb, b_positive: bool) bool {
@setRuntimeSafety(debug_safety);
assert(a.len != 0 and b.len != 0);
assert(a.len >= b.len);
assert(r.len >= if (b_positive) b.len else if (a_positive) a.len else a.len + 1);
@ -4043,7 +4073,6 @@ fn llsignedand(r: []Limb, a: []const Limb, a_positive: bool, b: []const Limb, b_
// If the sign of a and b is equal, then r requires at least `@max(a.len, b.len)` limbs are required.
// Otherwise, r requires at least `@max(a.len, b.len) + 1` limbs.
fn llsignedxor(r: []Limb, a: []const Limb, a_positive: bool, b: []const Limb, b_positive: bool) bool {
@setRuntimeSafety(debug_safety);
assert(a.len != 0 and b.len != 0);
assert(r.len >= a.len);
assert(a.len >= b.len);
@ -4102,10 +4131,9 @@ fn llsignedxor(r: []Limb, a: []const Limb, a_positive: bool, b: []const Limb, b_
/// r MUST NOT alias x.
fn llsquareBasecase(r: []Limb, x: []const Limb) void {
@setRuntimeSafety(debug_safety);
const x_norm = x;
assert(r.len >= 2 * x_norm.len + 1);
assert(!slicesOverlap(r, x));
// Compute the square of a N-limb bigint with only (N^2 + N)/2
// multiplications by exploiting the symmetry of the coefficients around the
@ -4129,7 +4157,7 @@ fn llsquareBasecase(r: []Limb, x: []const Limb) void {
}
// Each product appears twice, multiply by 2
llshl(r, r[0 .. 2 * x_norm.len], 1);
_ = llshl(r, r[0 .. 2 * x_norm.len], 1);
for (x_norm, 0..) |v, i| {
// Compute and add the squares
@ -4201,6 +4229,290 @@ fn fixedIntFromSignedDoubleLimb(A: SignedDoubleLimb, storage: []Limb) Mutable {
};
}
fn slicesOverlap(a: []const Limb, b: []const Limb) bool {
// there is no overlap if a.ptr + a.len <= b.ptr or b.ptr + b.len <= a.ptr
return @intFromPtr(a.ptr + a.len) > @intFromPtr(b.ptr) and @intFromPtr(b.ptr + b.len) > @intFromPtr(a.ptr);
}
test {
_ = @import("int_test.zig");
}
const testing_allocator = std.testing.allocator;
test "llshl shift by whole number of limb" {
const padding = std.math.maxInt(Limb);
var r: [10]Limb = @splat(padding);
const A: Limb = @truncate(0xCCCCCCCCCCCCCCCCCCCCCCC);
const B: Limb = @truncate(0x22222222222222222222222);
const data = [2]Limb{ A, B };
for (0..9) |i| {
@memset(&r, padding);
const len = llshl(&r, &data, i * @bitSizeOf(Limb));
try std.testing.expectEqual(i + 2, len);
try std.testing.expectEqualSlices(Limb, &data, r[i .. i + 2]);
for (r[0..i]) |x|
try std.testing.expectEqual(0, x);
for (r[i + 2 ..]) |x|
try std.testing.expectEqual(padding, x);
}
}
test llshl {
if (limb_bits != 64) return error.SkipZigTest;
// 1 << 63
const left_one = 0x8000000000000000;
const maxint: Limb = 0xFFFFFFFFFFFFFFFF;
// zig fmt: off
try testOneShiftCase(.llshl, .{0, &.{0}, &.{0}});
try testOneShiftCase(.llshl, .{0, &.{1}, &.{1}});
try testOneShiftCase(.llshl, .{0, &.{125484842448}, &.{125484842448}});
try testOneShiftCase(.llshl, .{0, &.{0xdeadbeef}, &.{0xdeadbeef}});
try testOneShiftCase(.llshl, .{0, &.{maxint}, &.{maxint}});
try testOneShiftCase(.llshl, .{0, &.{left_one}, &.{left_one}});
try testOneShiftCase(.llshl, .{0, &.{0, 1}, &.{0, 1}});
try testOneShiftCase(.llshl, .{0, &.{1, 2}, &.{1, 2}});
try testOneShiftCase(.llshl, .{0, &.{left_one, 1}, &.{left_one, 1}});
try testOneShiftCase(.llshl, .{1, &.{0}, &.{0}});
try testOneShiftCase(.llshl, .{1, &.{2}, &.{1}});
try testOneShiftCase(.llshl, .{1, &.{250969684896}, &.{125484842448}});
try testOneShiftCase(.llshl, .{1, &.{0x1bd5b7dde}, &.{0xdeadbeef}});
try testOneShiftCase(.llshl, .{1, &.{0xfffffffffffffffe, 1}, &.{maxint}});
try testOneShiftCase(.llshl, .{1, &.{0, 1}, &.{left_one}});
try testOneShiftCase(.llshl, .{1, &.{0, 2}, &.{0, 1}});
try testOneShiftCase(.llshl, .{1, &.{2, 4}, &.{1, 2}});
try testOneShiftCase(.llshl, .{1, &.{0, 3}, &.{left_one, 1}});
try testOneShiftCase(.llshl, .{5, &.{32}, &.{1}});
try testOneShiftCase(.llshl, .{5, &.{4015514958336}, &.{125484842448}});
try testOneShiftCase(.llshl, .{5, &.{0x1bd5b7dde0}, &.{0xdeadbeef}});
try testOneShiftCase(.llshl, .{5, &.{0xffffffffffffffe0, 0x1f}, &.{maxint}});
try testOneShiftCase(.llshl, .{5, &.{0, 16}, &.{left_one}});
try testOneShiftCase(.llshl, .{5, &.{0, 32}, &.{0, 1}});
try testOneShiftCase(.llshl, .{5, &.{32, 64}, &.{1, 2}});
try testOneShiftCase(.llshl, .{5, &.{0, 48}, &.{left_one, 1}});
try testOneShiftCase(.llshl, .{64, &.{0, 1}, &.{1}});
try testOneShiftCase(.llshl, .{64, &.{0, 125484842448}, &.{125484842448}});
try testOneShiftCase(.llshl, .{64, &.{0, 0xdeadbeef}, &.{0xdeadbeef}});
try testOneShiftCase(.llshl, .{64, &.{0, maxint}, &.{maxint}});
try testOneShiftCase(.llshl, .{64, &.{0, left_one}, &.{left_one}});
try testOneShiftCase(.llshl, .{64, &.{0, 0, 1}, &.{0, 1}});
try testOneShiftCase(.llshl, .{64, &.{0, 1, 2}, &.{1, 2}});
try testOneShiftCase(.llshl, .{64, &.{0, left_one, 1}, &.{left_one, 1}});
try testOneShiftCase(.llshl, .{35, &.{0x800000000}, &.{1}});
try testOneShiftCase(.llshl, .{35, &.{13534986488655118336, 233}, &.{125484842448}});
try testOneShiftCase(.llshl, .{35, &.{0xf56df77800000000, 6}, &.{0xdeadbeef}});
try testOneShiftCase(.llshl, .{35, &.{0xfffffff800000000, 0x7ffffffff}, &.{maxint}});
try testOneShiftCase(.llshl, .{35, &.{0, 17179869184}, &.{left_one}});
try testOneShiftCase(.llshl, .{35, &.{0, 0x800000000}, &.{0, 1}});
try testOneShiftCase(.llshl, .{35, &.{0x800000000, 0x1000000000}, &.{1, 2}});
try testOneShiftCase(.llshl, .{35, &.{0, 0xc00000000}, &.{left_one, 1}});
try testOneShiftCase(.llshl, .{70, &.{0, 64}, &.{1}});
try testOneShiftCase(.llshl, .{70, &.{0, 8031029916672}, &.{125484842448}});
try testOneShiftCase(.llshl, .{70, &.{0, 0x37ab6fbbc0}, &.{0xdeadbeef}});
try testOneShiftCase(.llshl, .{70, &.{0, 0xffffffffffffffc0, 63}, &.{maxint}});
try testOneShiftCase(.llshl, .{70, &.{0, 0, 32}, &.{left_one}});
try testOneShiftCase(.llshl, .{70, &.{0, 0, 64}, &.{0, 1}});
try testOneShiftCase(.llshl, .{70, &.{0, 64, 128}, &.{1, 2}});
try testOneShiftCase(.llshl, .{70, &.{0, 0, 0x60}, &.{left_one, 1}});
// zig fmt: on
}
test "llshl shift 0" {
const n = @bitSizeOf(Limb);
if (n <= 20) return error.SkipZigTest;
// zig fmt: off
try testOneShiftCase(.llshl, .{0, &.{0}, &.{0}});
try testOneShiftCase(.llshl, .{1, &.{0}, &.{0}});
try testOneShiftCase(.llshl, .{5, &.{0}, &.{0}});
try testOneShiftCase(.llshl, .{13, &.{0}, &.{0}});
try testOneShiftCase(.llshl, .{20, &.{0}, &.{0}});
try testOneShiftCase(.llshl, .{0, &.{0, 0}, &.{0, 0}});
try testOneShiftCase(.llshl, .{2, &.{0, 0}, &.{0, 0}});
try testOneShiftCase(.llshl, .{7, &.{0, 0}, &.{0, 0}});
try testOneShiftCase(.llshl, .{11, &.{0, 0}, &.{0, 0}});
try testOneShiftCase(.llshl, .{19, &.{0, 0}, &.{0, 0}});
try testOneShiftCase(.llshl, .{0, &.{0}, &.{0}});
try testOneShiftCase(.llshl, .{n, &.{0, 0}, &.{0}});
try testOneShiftCase(.llshl, .{2*n, &.{0, 0, 0}, &.{0}});
try testOneShiftCase(.llshl, .{3*n, &.{0, 0, 0, 0}, &.{0}});
try testOneShiftCase(.llshl, .{4*n, &.{0, 0, 0, 0, 0}, &.{0}});
try testOneShiftCase(.llshl, .{0, &.{0, 0}, &.{0, 0}});
try testOneShiftCase(.llshl, .{n, &.{0, 0, 0}, &.{0, 0}});
try testOneShiftCase(.llshl, .{2*n, &.{0, 0, 0, 0}, &.{0, 0}});
try testOneShiftCase(.llshl, .{3*n, &.{0, 0, 0, 0, 0}, &.{0, 0}});
try testOneShiftCase(.llshl, .{4*n, &.{0, 0, 0, 0, 0, 0}, &.{0, 0}});
// zig fmt: on
}
test "llshr shift 0" {
const n = @bitSizeOf(Limb);
// zig fmt: off
try testOneShiftCase(.llshr, .{0, &.{0}, &.{0}});
try testOneShiftCase(.llshr, .{1, &.{0}, &.{0}});
try testOneShiftCase(.llshr, .{5, &.{0}, &.{0}});
try testOneShiftCase(.llshr, .{13, &.{0}, &.{0}});
try testOneShiftCase(.llshr, .{20, &.{0}, &.{0}});
try testOneShiftCase(.llshr, .{0, &.{0, 0}, &.{0, 0}});
try testOneShiftCase(.llshr, .{2, &.{0}, &.{0, 0}});
try testOneShiftCase(.llshr, .{7, &.{0}, &.{0, 0}});
try testOneShiftCase(.llshr, .{11, &.{0}, &.{0, 0}});
try testOneShiftCase(.llshr, .{19, &.{0}, &.{0, 0}});
try testOneShiftCase(.llshr, .{n, &.{0}, &.{0}});
try testOneShiftCase(.llshr, .{2*n, &.{0}, &.{0}});
try testOneShiftCase(.llshr, .{3*n, &.{0}, &.{0}});
try testOneShiftCase(.llshr, .{4*n, &.{0}, &.{0}});
try testOneShiftCase(.llshr, .{n, &.{0}, &.{0, 0}});
try testOneShiftCase(.llshr, .{2*n, &.{0}, &.{0, 0}});
try testOneShiftCase(.llshr, .{3*n, &.{0}, &.{0, 0}});
try testOneShiftCase(.llshr, .{4*n, &.{0}, &.{0, 0}});
try testOneShiftCase(.llshr, .{1, &.{}, &.{}});
try testOneShiftCase(.llshr, .{2, &.{}, &.{}});
try testOneShiftCase(.llshr, .{64, &.{}, &.{}});
// zig fmt: on
}
test "llshr to 0" {
const n = @bitSizeOf(Limb);
if (n != 64 and n != 32) return error.SkipZigTest;
// zig fmt: off
try testOneShiftCase(.llshr, .{1, &.{0}, &.{0}});
try testOneShiftCase(.llshr, .{1, &.{0}, &.{1}});
try testOneShiftCase(.llshr, .{5, &.{0}, &.{1}});
try testOneShiftCase(.llshr, .{65, &.{0}, &.{0, 1}});
try testOneShiftCase(.llshr, .{193, &.{0}, &.{0, 0, std.math.maxInt(Limb)}});
try testOneShiftCase(.llshr, .{193, &.{0}, &.{std.math.maxInt(Limb), 1, std.math.maxInt(Limb)}});
try testOneShiftCase(.llshr, .{193, &.{0}, &.{0xdeadbeef, 0xabcdefab, 0x1234}});
// zig fmt: on
}
test "llshr single" {
if (limb_bits != 64) return error.SkipZigTest;
// 1 << 63
const left_one = 0x8000000000000000;
const maxint: Limb = 0xFFFFFFFFFFFFFFFF;
// zig fmt: off
try testOneShiftCase(.llshr, .{0, &.{0}, &.{0}});
try testOneShiftCase(.llshr, .{0, &.{1}, &.{1}});
try testOneShiftCase(.llshr, .{0, &.{125484842448}, &.{125484842448}});
try testOneShiftCase(.llshr, .{0, &.{0xdeadbeef}, &.{0xdeadbeef}});
try testOneShiftCase(.llshr, .{0, &.{maxint}, &.{maxint}});
try testOneShiftCase(.llshr, .{0, &.{left_one}, &.{left_one}});
try testOneShiftCase(.llshr, .{1, &.{0}, &.{0}});
try testOneShiftCase(.llshr, .{1, &.{1}, &.{2}});
try testOneShiftCase(.llshr, .{1, &.{62742421224}, &.{125484842448}});
try testOneShiftCase(.llshr, .{1, &.{62742421223}, &.{125484842447}});
try testOneShiftCase(.llshr, .{1, &.{0x6f56df77}, &.{0xdeadbeef}});
try testOneShiftCase(.llshr, .{1, &.{0x7fffffffffffffff}, &.{maxint}});
try testOneShiftCase(.llshr, .{1, &.{0x4000000000000000}, &.{left_one}});
try testOneShiftCase(.llshr, .{8, &.{1}, &.{256}});
try testOneShiftCase(.llshr, .{8, &.{490175165}, &.{125484842448}});
try testOneShiftCase(.llshr, .{8, &.{0xdeadbe}, &.{0xdeadbeef}});
try testOneShiftCase(.llshr, .{8, &.{0xffffffffffffff}, &.{maxint}});
try testOneShiftCase(.llshr, .{8, &.{0x80000000000000}, &.{left_one}});
// zig fmt: on
}
test llshr {
if (limb_bits != 64) return error.SkipZigTest;
// 1 << 63
const left_one = 0x8000000000000000;
const maxint: Limb = 0xFFFFFFFFFFFFFFFF;
// zig fmt: off
try testOneShiftCase(.llshr, .{0, &.{0, 0}, &.{0, 0}});
try testOneShiftCase(.llshr, .{0, &.{0, 1}, &.{0, 1}});
try testOneShiftCase(.llshr, .{0, &.{15, 1}, &.{15, 1}});
try testOneShiftCase(.llshr, .{0, &.{987656565, 123456789456}, &.{987656565, 123456789456}});
try testOneShiftCase(.llshr, .{0, &.{0xfeebdaed, 0xdeadbeef}, &.{0xfeebdaed, 0xdeadbeef}});
try testOneShiftCase(.llshr, .{0, &.{1, maxint}, &.{1, maxint}});
try testOneShiftCase(.llshr, .{0, &.{0, left_one}, &.{0, left_one}});
try testOneShiftCase(.llshr, .{1, &.{0}, &.{0, 0}});
try testOneShiftCase(.llshr, .{1, &.{left_one}, &.{0, 1}});
try testOneShiftCase(.llshr, .{1, &.{0x8000000000000007}, &.{15, 1}});
try testOneShiftCase(.llshr, .{1, &.{493828282, 61728394728}, &.{987656565, 123456789456}});
try testOneShiftCase(.llshr, .{1, &.{0x800000007f75ed76, 0x6f56df77}, &.{0xfeebdaed, 0xdeadbeef}});
try testOneShiftCase(.llshr, .{1, &.{left_one, 0x7fffffffffffffff}, &.{1, maxint}});
try testOneShiftCase(.llshr, .{1, &.{0, 0x4000000000000000}, &.{0, left_one}});
try testOneShiftCase(.llshr, .{64, &.{0}, &.{0, 0}});
try testOneShiftCase(.llshr, .{64, &.{1}, &.{0, 1}});
try testOneShiftCase(.llshr, .{64, &.{1}, &.{15, 1}});
try testOneShiftCase(.llshr, .{64, &.{123456789456}, &.{987656565, 123456789456}});
try testOneShiftCase(.llshr, .{64, &.{0xdeadbeef}, &.{0xfeebdaed, 0xdeadbeef}});
try testOneShiftCase(.llshr, .{64, &.{maxint}, &.{1, maxint}});
try testOneShiftCase(.llshr, .{64, &.{left_one}, &.{0, left_one}});
try testOneShiftCase(.llshr, .{72, &.{0}, &.{0, 0}});
try testOneShiftCase(.llshr, .{72, &.{0}, &.{0, 1}});
try testOneShiftCase(.llshr, .{72, &.{0}, &.{15, 1}});
try testOneShiftCase(.llshr, .{72, &.{482253083}, &.{987656565, 123456789456}});
try testOneShiftCase(.llshr, .{72, &.{0xdeadbe}, &.{0xfeebdaed, 0xdeadbeef}});
try testOneShiftCase(.llshr, .{72, &.{0xffffffffffffff}, &.{1, maxint}});
try testOneShiftCase(.llshr, .{72, &.{0x80000000000000}, &.{0, left_one}});
// zig fmt: on
}
const Case = struct { usize, []const Limb, []const Limb };
fn testOneShiftCase(comptime function: enum { llshr, llshl }, case: Case) !void {
const func = if (function == .llshl) llshl else llshr;
const shift_direction = if (function == .llshl) -1 else 1;
try testOneShiftCaseNoAliasing(func, case);
try testOneShiftCaseAliasing(func, case, shift_direction);
}
fn testOneShiftCaseNoAliasing(func: fn ([]Limb, []const Limb, usize) usize, case: Case) !void {
const padding = std.math.maxInt(Limb);
var r: [20]Limb = @splat(padding);
const shift = case[0];
const expected = case[1];
const data = case[2];
std.debug.assert(expected.len <= 20);
const len = func(&r, data, shift);
try std.testing.expectEqual(expected.len, len);
try std.testing.expectEqualSlices(Limb, expected, r[0..len]);
try std.testing.expect(mem.allEqual(Limb, r[len..], padding));
}
fn testOneShiftCaseAliasing(func: fn ([]Limb, []const Limb, usize) usize, case: Case, shift_direction: isize) !void {
const padding = std.math.maxInt(Limb);
var r: [60]Limb = @splat(padding);
const base = 20;
assert(shift_direction == 1 or shift_direction == -1);
for (0..10) |limb_shift| {
const shift = case[0];
const expected = case[1];
const data = case[2];
std.debug.assert(expected.len <= 20);
@memset(&r, padding);
const final_limb_base: usize = @intCast(base + shift_direction * @as(isize, @intCast(limb_shift)));
const written_data = r[final_limb_base..][0..data.len];
@memcpy(written_data, data);
const len = func(r[base..], written_data, shift);
try std.testing.expectEqual(expected.len, len);
try std.testing.expectEqualSlices(Limb, expected, r[base .. base + len]);
}
}

742
lib/std/math/big/int_test.zig
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