From 33c592e981f93f207651b8353a8cbc3d09440353 Mon Sep 17 00:00:00 2001 From: Andrew Kelley Date: Fri, 18 Aug 2017 17:20:03 -0400 Subject: [PATCH] make udivmod generic and add tests --- CMakeLists.txt | 2 + std/special/compiler_rt/index.zig | 532 +- std/special/compiler_rt/udivmod.zig | 193 + std/special/compiler_rt/udivmoddi4.zig | 9 + std/special/compiler_rt/udivmoddi4_test.zig | 20610 ++++++++++++++++++ std/special/compiler_rt/udivmodti4.zig | 192 +- 6 files changed, 20969 insertions(+), 569 deletions(-) create mode 100644 std/special/compiler_rt/udivmod.zig create mode 100644 std/special/compiler_rt/udivmoddi4.zig create mode 100644 std/special/compiler_rt/udivmoddi4_test.zig diff --git a/CMakeLists.txt b/CMakeLists.txt index 70af668b3d..f8c862e3de 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -325,6 +325,8 @@ install(FILES "${CMAKE_SOURCE_DIR}/std/special/compiler_rt/fixunstfsi.zig" DESTI install(FILES "${CMAKE_SOURCE_DIR}/std/special/compiler_rt/fixunstfti.zig" DESTINATION "${ZIG_STD_DEST}/special/compiler_rt") install(FILES "${CMAKE_SOURCE_DIR}/std/special/compiler_rt/index.zig" DESTINATION "${ZIG_STD_DEST}/special/compiler_rt") install(FILES "${CMAKE_SOURCE_DIR}/std/special/compiler_rt/udivti3.zig" DESTINATION "${ZIG_STD_DEST}/special/compiler_rt") +install(FILES "${CMAKE_SOURCE_DIR}/std/special/compiler_rt/udivmod.zig" DESTINATION "${ZIG_STD_DEST}/special/compiler_rt") +install(FILES "${CMAKE_SOURCE_DIR}/std/special/compiler_rt/udivmoddi4.zig" DESTINATION "${ZIG_STD_DEST}/special/compiler_rt") install(FILES "${CMAKE_SOURCE_DIR}/std/special/compiler_rt/udivmodti4.zig" DESTINATION "${ZIG_STD_DEST}/special/compiler_rt") install(FILES "${CMAKE_SOURCE_DIR}/std/special/compiler_rt/umodti3.zig" DESTINATION "${ZIG_STD_DEST}/special/compiler_rt") install(FILES "${CMAKE_SOURCE_DIR}/std/special/test_runner.zig" DESTINATION "${ZIG_STD_DEST}/special") diff --git a/std/special/compiler_rt/index.zig b/std/special/compiler_rt/index.zig index e44268a754..236b07423c 100644 --- a/std/special/compiler_rt/index.zig +++ b/std/special/compiler_rt/index.zig @@ -1,4 +1,3 @@ -// Find all the exported functions. comptime { _ = @import("comparetf2.zig"); _ = @import("fixunsdfdi.zig"); @@ -10,223 +9,26 @@ comptime { _ = @import("fixunstfdi.zig"); _ = @import("fixunstfsi.zig"); _ = @import("fixunstfti.zig"); - _ = @import("udivti3.zig"); + _ = @import("udivmoddi4.zig"); _ = @import("udivmodti4.zig"); + _ = @import("udivti3.zig"); _ = @import("umodti3.zig"); } const builtin = @import("builtin"); const is_test = builtin.is_test; -const du_int = u64; -const di_int = i64; -const si_int = c_int; -const su_int = c_uint; +const __udivmoddi4 = @import("udivmoddi4.zig").__udivmoddi4; -const udwords = [2]su_int; -const low = if (builtin.is_big_endian) 1 else 0; -const high = 1 - low; - -export fn __udivdi3(a: du_int, b: du_int) -> du_int { +export fn __udivdi3(a: u64, b: u64) -> u64 { @setDebugSafety(this, is_test); return __udivmoddi4(a, b, null); } -fn du_int_to_udwords(x: du_int) -> udwords { - @setDebugSafety(this, is_test); - return *@ptrCast(&udwords, &x); -} - -export fn __udivmoddi4(a: du_int, b: du_int, maybe_rem: ?&du_int) -> du_int { +export fn __umoddi3(a: u64, b: u64) -> u64 { @setDebugSafety(this, is_test); - const n_uword_bits = su_int.bit_count; - const n_udword_bits = du_int.bit_count; - var n = du_int_to_udwords(a); - var d = du_int_to_udwords(b); - var q: udwords = undefined; - var r: udwords = undefined; - var sr: c_uint = undefined; - // special cases, X is unknown, K != 0 - if (n[high] == 0) { - if (d[high] == 0) { - // 0 X - // --- - // 0 X - if (maybe_rem) |rem| { - *rem = n[low] % d[low]; - } - return n[low] / d[low]; - } - // 0 X - // --- - // K X - if (maybe_rem) |rem| { - *rem = n[low]; - } - return 0; - } - // n[high] != 0 - if (d[low] == 0) { - if (d[high] == 0) { - // K X - // --- - // 0 0 - if (maybe_rem) |rem| { - *rem = n[high] % d[low]; - } - return n[high] / d[low]; - } - // d[high] != 0 - if (n[low] == 0) { - // K 0 - // --- - // K 0 - if (maybe_rem) |rem| { - r[high] = n[high] % d[high]; - r[low] = 0; - *rem = *@ptrCast(&du_int, &r[0]); - } - return n[high] / d[high]; - } - // K K - // --- - // K 0 - // if d is a power of 2 - if ((d[high] & (d[high] - 1)) == 0) { - if (maybe_rem) |rem| { - r[low] = n[low]; - r[high] = n[high] & (d[high] - 1); - *rem = *@ptrCast(&du_int, &r[0]); - } - return n[high] >> @ctz(d[high]); - } - // K K - // --- - // K 0 - sr = @clz(su_int(d[high])) - @clz(su_int(n[high])); - // 0 <= sr <= n_uword_bits - 2 or sr large - if (sr > n_uword_bits - 2) { - if (maybe_rem) |rem| { - *rem = *@ptrCast(&du_int, &n[0]); - } - return 0; - } - sr += 1; - // 1 <= sr <= n_uword_bits - 1 - // q.all = n.all << (n_udword_bits - sr); - q[low] = 0; - q[high] = n[low] << (n_uword_bits - sr); - // r.all = n.all >> sr; - r[high] = n[high] >> sr; - r[low] = (n[high] << (n_uword_bits - sr)) | (n[low] >> sr); - } else { - // d[low] != 0 - if (d[high] == 0) { - // K X - // --- - // 0 K - // if d is a power of 2 - if ((d[low] & (d[low] - 1)) == 0) { - if (maybe_rem) |rem| { - *rem = n[low] & (d[low] - 1); - } - if (d[low] == 1) { - return *@ptrCast(&du_int, &n[0]); - } - sr = @ctz(d[low]); - q[high] = n[high] >> sr; - q[low] = (n[high] << (n_uword_bits - sr)) | (n[low] >> sr); - return *@ptrCast(&du_int, &q[0]); - } - // K X - // --- - // 0 K - sr = 1 + n_uword_bits + c_uint(@clz(su_int(d[low]))) - c_uint(@clz(su_int(n[high]))); - // 2 <= sr <= n_udword_bits - 1 - // q.all = n.all << (n_udword_bits - sr); - // r.all = n.all >> sr; - if (sr == n_uword_bits) { - q[low] = 0; - q[high] = n[low]; - r[high] = 0; - r[low] = n[high]; - } else if (sr < n_uword_bits) { - // 2 <= sr <= n_uword_bits - 1 - q[low] = 0; - q[high] = n[low] << (n_uword_bits - sr); - r[high] = n[high] >> sr; - r[low] = (n[high] << (n_uword_bits - sr)) | (n[low] >> sr); - } else { - // n_uword_bits + 1 <= sr <= n_udword_bits - 1 - q[low] = n[low] << (n_udword_bits - sr); - q[high] = (n[high] << (n_udword_bits - sr)) | - (n[low] >> (sr - n_uword_bits)); - r[high] = 0; - r[low] = n[high] >> (sr - n_uword_bits); - } - } else { - // K X - // --- - // K K - sr = @bitCast(c_uint, c_int(@clz(su_int(d[high]))) - c_int(@clz(su_int(n[high])))); - // 0 <= sr <= n_uword_bits - 1 or sr large - if (sr > n_uword_bits - 1) { - if (maybe_rem) |rem| { - *rem = *@ptrCast(&du_int, &n[0]); - } - return 0; - } - sr += 1; - // 1 <= sr <= n_uword_bits - // q.all = n.all << (n_udword_bits - sr); - q[low] = 0; - if (sr == n_uword_bits) { - q[high] = n[low]; - r[high] = 0; - r[low] = n[high]; - } else { - q[high] = n[low] << (n_uword_bits - sr); - r[high] = n[high] >> sr; - r[low] = (n[high] << (n_uword_bits - sr)) | (n[low] >> sr); - } - } - } - // Not a special case - // q and r are initialized with: - // q.all = n.all << (n_udword_bits - sr); - // r.all = n.all >> sr; - // 1 <= sr <= n_udword_bits - 1 - var carry: su_int = 0; - while (sr > 0) { - // r:q = ((r:q) << 1) | carry - r[high] = (r[high] << 1) | (r[low] >> (n_uword_bits - 1)); - r[low] = (r[low] << 1) | (q[high] >> (n_uword_bits - 1)); - q[high] = (q[high] << 1) | (q[low] >> (n_uword_bits - 1)); - q[low] = (q[low] << 1) | carry; - // carry = 0; - // if (r.all >= d.all) - // { - // r.all -= d.all; - // carry = 1; - // } - const s: di_int = (di_int)(*@ptrCast(&du_int, &d[0]) -% *@ptrCast(&du_int, &r[0]) -% 1) >> (n_udword_bits - 1); - carry = su_int(s & 1); - *@ptrCast(&du_int, &r[0]) -= *@ptrCast(&du_int, &d[0]) & @bitCast(u64, s); - - sr -= 1; - } - *@ptrCast(&du_int, &q[0]) = (*@ptrCast(&du_int, &q[0]) << 1) | u64(carry); - if (maybe_rem) |rem| { - *rem = *@ptrCast(&du_int, &r[0]); - } - return *@ptrCast(&du_int, &q[0]); -} - -export fn __umoddi3(a: du_int, b: du_int) -> du_int { - @setDebugSafety(this, is_test); - - var r: du_int = undefined; + var r: u64 = undefined; _ = __udivmoddi4(a, b, &r); return r; } @@ -275,11 +77,11 @@ export nakedcc fn __aeabi_uidivmod() { @setGlobalLinkage(__aeabi_uidivmod, builtin.GlobalLinkage.Internal); } -export fn __udivmodsi4(a: su_int, b: su_int, rem: &su_int) -> su_int { +export fn __udivmodsi4(a: u32, b: u32, rem: &u32) -> u32 { @setDebugSafety(this, is_test); const d = __udivsi3(a, b); - *rem = su_int(si_int(a) -% (si_int(d) * si_int(b))); + *rem = u32(i32(a) -% (i32(d) * i32(b))); return d; } @@ -287,16 +89,16 @@ export fn __udivmodsi4(a: su_int, b: su_int, rem: &su_int) -> su_int { // TODO make this an alias instead of an extra function call // https://github.com/andrewrk/zig/issues/256 -export fn __aeabi_uidiv(n: su_int, d: su_int) -> su_int { +export fn __aeabi_uidiv(n: u32, d: u32) -> u32 { @setDebugSafety(this, is_test); return __udivsi3(n, d); } -export fn __udivsi3(n: su_int, d: su_int) -> su_int { +export fn __udivsi3(n: u32, d: u32) -> u32 { @setDebugSafety(this, is_test); - const n_uword_bits: c_uint = su_int.bit_count; + const n_uword_bits: c_uint = u32.bit_count; // special cases if (d == 0) return 0; // ?! @@ -311,9 +113,9 @@ export fn __udivsi3(n: su_int, d: su_int) -> su_int { sr += 1; // 1 <= sr <= n_uword_bits - 1 // Not a special case - var q: su_int = n << (n_uword_bits - sr); - var r: su_int = n >> sr; - var carry: su_int = 0; + var q: u32 = n << (n_uword_bits - sr); + var r: u32 = n >> sr; + var carry: u32 = 0; while (sr > 0) : (sr -= 1) { // r:q = ((r:q) << 1) | carry r = (r << 1) | (q >> (n_uword_bits - 1)); @@ -324,9 +126,9 @@ export fn __udivsi3(n: su_int, d: su_int) -> su_int { // r.all -= d.all; // carry = 1; // } - const s = si_int(d -% r -% 1) >> si_int(n_uword_bits - 1); - carry = su_int(s & 1); - r -= d & @bitCast(su_int, s); + const s = i32(d -% r -% 1) >> i32(n_uword_bits - 1); + carry = u32(s & 1); + r -= d & @bitCast(u32, s); } q = (q << 1) | carry; return q; @@ -340,173 +142,145 @@ test "test_umoddi3" { test_one_umoddi3(0xFFFFFFFFFFFFFFFF, 2, 0x1); } -fn test_one_umoddi3(a: du_int, b: du_int, expected_r: du_int) { +fn test_one_umoddi3(a: u64, b: u64, expected_r: u64) { const r = __umoddi3(a, b); assert(r == expected_r); } -test "test_udivmoddi4" { - const cases = [][4]du_int { - []du_int{0x0000000000000000, 0x0000000000000001, 0x0000000000000000, 0x0000000000000000}, - []du_int{0x0000000080000000, 0x0000000100000001, 0x0000000000000000, 0x0000000080000000}, - []du_int{0x7FFFFFFF00000001, 0x0000000000000001, 0x7FFFFFFF00000001, 0x0000000000000000}, - []du_int{0x7FFFFFFF7FFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x0000000000000000, 0x7FFFFFFF7FFFFFFF}, - []du_int{0x8000000000000002, 0xFFFFFFFFFFFFFFFE, 0x0000000000000000, 0x8000000000000002}, - []du_int{0x80000000FFFFFFFD, 0xFFFFFFFFFFFFFFFD, 0x0000000000000000, 0x80000000FFFFFFFD}, - []du_int{0xFFFFFFFD00000010, 0xFFFFFFFF80000000, 0x0000000000000000, 0xFFFFFFFD00000010}, - []du_int{0xFFFFFFFDFFFFFFFF, 0xFFFFFFFF7FFFFFFF, 0x0000000000000000, 0xFFFFFFFDFFFFFFFF}, - []du_int{0xFFFFFFFE0747AE14, 0xFFFFFFFF0747AE14, 0x0000000000000000, 0xFFFFFFFE0747AE14}, - []du_int{0xFFFFFFFF00000001, 0xFFFFFFFF078644FA, 0x0000000000000000, 0xFFFFFFFF00000001}, - []du_int{0xFFFFFFFF80000000, 0xFFFFFFFF00000010, 0x0000000000000001, 0x000000007FFFFFF0}, - []du_int{0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x0000000000000001, 0x0000000000000000}, - }; - - for (cases) |case| { - test_one_udivmoddi4(case[0], case[1], case[2], case[3]); - } -} - -fn test_one_udivmoddi4(a: du_int, b: du_int, expected_q: du_int, expected_r: du_int) { - var r: du_int = undefined; - const q = __udivmoddi4(a, b, &r); - assert(q == expected_q); - assert(r == expected_r); -} - test "test_udivsi3" { - const cases = [][3]su_int { - []su_int{0x00000000, 0x00000001, 0x00000000}, - []su_int{0x00000000, 0x00000002, 0x00000000}, - []su_int{0x00000000, 0x00000003, 0x00000000}, - []su_int{0x00000000, 0x00000010, 0x00000000}, - []su_int{0x00000000, 0x078644FA, 0x00000000}, - []su_int{0x00000000, 0x0747AE14, 0x00000000}, - []su_int{0x00000000, 0x7FFFFFFF, 0x00000000}, - []su_int{0x00000000, 0x80000000, 0x00000000}, - []su_int{0x00000000, 0xFFFFFFFD, 0x00000000}, - []su_int{0x00000000, 0xFFFFFFFE, 0x00000000}, - []su_int{0x00000000, 0xFFFFFFFF, 0x00000000}, - []su_int{0x00000001, 0x00000001, 0x00000001}, - []su_int{0x00000001, 0x00000002, 0x00000000}, - []su_int{0x00000001, 0x00000003, 0x00000000}, - []su_int{0x00000001, 0x00000010, 0x00000000}, - []su_int{0x00000001, 0x078644FA, 0x00000000}, - []su_int{0x00000001, 0x0747AE14, 0x00000000}, - []su_int{0x00000001, 0x7FFFFFFF, 0x00000000}, - []su_int{0x00000001, 0x80000000, 0x00000000}, - []su_int{0x00000001, 0xFFFFFFFD, 0x00000000}, - []su_int{0x00000001, 0xFFFFFFFE, 0x00000000}, - []su_int{0x00000001, 0xFFFFFFFF, 0x00000000}, - []su_int{0x00000002, 0x00000001, 0x00000002}, - []su_int{0x00000002, 0x00000002, 0x00000001}, - []su_int{0x00000002, 0x00000003, 0x00000000}, - []su_int{0x00000002, 0x00000010, 0x00000000}, - []su_int{0x00000002, 0x078644FA, 0x00000000}, - []su_int{0x00000002, 0x0747AE14, 0x00000000}, - []su_int{0x00000002, 0x7FFFFFFF, 0x00000000}, - []su_int{0x00000002, 0x80000000, 0x00000000}, - []su_int{0x00000002, 0xFFFFFFFD, 0x00000000}, - []su_int{0x00000002, 0xFFFFFFFE, 0x00000000}, - []su_int{0x00000002, 0xFFFFFFFF, 0x00000000}, - []su_int{0x00000003, 0x00000001, 0x00000003}, - []su_int{0x00000003, 0x00000002, 0x00000001}, - []su_int{0x00000003, 0x00000003, 0x00000001}, - []su_int{0x00000003, 0x00000010, 0x00000000}, - []su_int{0x00000003, 0x078644FA, 0x00000000}, - []su_int{0x00000003, 0x0747AE14, 0x00000000}, - []su_int{0x00000003, 0x7FFFFFFF, 0x00000000}, - []su_int{0x00000003, 0x80000000, 0x00000000}, - []su_int{0x00000003, 0xFFFFFFFD, 0x00000000}, - []su_int{0x00000003, 0xFFFFFFFE, 0x00000000}, - []su_int{0x00000003, 0xFFFFFFFF, 0x00000000}, - []su_int{0x00000010, 0x00000001, 0x00000010}, - []su_int{0x00000010, 0x00000002, 0x00000008}, - []su_int{0x00000010, 0x00000003, 0x00000005}, - []su_int{0x00000010, 0x00000010, 0x00000001}, - []su_int{0x00000010, 0x078644FA, 0x00000000}, - []su_int{0x00000010, 0x0747AE14, 0x00000000}, - []su_int{0x00000010, 0x7FFFFFFF, 0x00000000}, - []su_int{0x00000010, 0x80000000, 0x00000000}, - []su_int{0x00000010, 0xFFFFFFFD, 0x00000000}, - []su_int{0x00000010, 0xFFFFFFFE, 0x00000000}, - []su_int{0x00000010, 0xFFFFFFFF, 0x00000000}, - []su_int{0x078644FA, 0x00000001, 0x078644FA}, - []su_int{0x078644FA, 0x00000002, 0x03C3227D}, - []su_int{0x078644FA, 0x00000003, 0x028216FE}, - []su_int{0x078644FA, 0x00000010, 0x0078644F}, - []su_int{0x078644FA, 0x078644FA, 0x00000001}, - []su_int{0x078644FA, 0x0747AE14, 0x00000001}, - []su_int{0x078644FA, 0x7FFFFFFF, 0x00000000}, - []su_int{0x078644FA, 0x80000000, 0x00000000}, - []su_int{0x078644FA, 0xFFFFFFFD, 0x00000000}, - []su_int{0x078644FA, 0xFFFFFFFE, 0x00000000}, - []su_int{0x078644FA, 0xFFFFFFFF, 0x00000000}, - []su_int{0x0747AE14, 0x00000001, 0x0747AE14}, - []su_int{0x0747AE14, 0x00000002, 0x03A3D70A}, - []su_int{0x0747AE14, 0x00000003, 0x026D3A06}, - []su_int{0x0747AE14, 0x00000010, 0x00747AE1}, - []su_int{0x0747AE14, 0x078644FA, 0x00000000}, - []su_int{0x0747AE14, 0x0747AE14, 0x00000001}, - []su_int{0x0747AE14, 0x7FFFFFFF, 0x00000000}, - []su_int{0x0747AE14, 0x80000000, 0x00000000}, - []su_int{0x0747AE14, 0xFFFFFFFD, 0x00000000}, - []su_int{0x0747AE14, 0xFFFFFFFE, 0x00000000}, - []su_int{0x0747AE14, 0xFFFFFFFF, 0x00000000}, - []su_int{0x7FFFFFFF, 0x00000001, 0x7FFFFFFF}, - []su_int{0x7FFFFFFF, 0x00000002, 0x3FFFFFFF}, - []su_int{0x7FFFFFFF, 0x00000003, 0x2AAAAAAA}, - []su_int{0x7FFFFFFF, 0x00000010, 0x07FFFFFF}, - []su_int{0x7FFFFFFF, 0x078644FA, 0x00000011}, - []su_int{0x7FFFFFFF, 0x0747AE14, 0x00000011}, - []su_int{0x7FFFFFFF, 0x7FFFFFFF, 0x00000001}, - []su_int{0x7FFFFFFF, 0x80000000, 0x00000000}, - []su_int{0x7FFFFFFF, 0xFFFFFFFD, 0x00000000}, - []su_int{0x7FFFFFFF, 0xFFFFFFFE, 0x00000000}, - []su_int{0x7FFFFFFF, 0xFFFFFFFF, 0x00000000}, - []su_int{0x80000000, 0x00000001, 0x80000000}, - []su_int{0x80000000, 0x00000002, 0x40000000}, - []su_int{0x80000000, 0x00000003, 0x2AAAAAAA}, - []su_int{0x80000000, 0x00000010, 0x08000000}, - []su_int{0x80000000, 0x078644FA, 0x00000011}, - []su_int{0x80000000, 0x0747AE14, 0x00000011}, - []su_int{0x80000000, 0x7FFFFFFF, 0x00000001}, - []su_int{0x80000000, 0x80000000, 0x00000001}, - []su_int{0x80000000, 0xFFFFFFFD, 0x00000000}, - []su_int{0x80000000, 0xFFFFFFFE, 0x00000000}, - []su_int{0x80000000, 0xFFFFFFFF, 0x00000000}, - []su_int{0xFFFFFFFD, 0x00000001, 0xFFFFFFFD}, - []su_int{0xFFFFFFFD, 0x00000002, 0x7FFFFFFE}, - []su_int{0xFFFFFFFD, 0x00000003, 0x55555554}, - []su_int{0xFFFFFFFD, 0x00000010, 0x0FFFFFFF}, - []su_int{0xFFFFFFFD, 0x078644FA, 0x00000022}, - []su_int{0xFFFFFFFD, 0x0747AE14, 0x00000023}, - []su_int{0xFFFFFFFD, 0x7FFFFFFF, 0x00000001}, - []su_int{0xFFFFFFFD, 0x80000000, 0x00000001}, - []su_int{0xFFFFFFFD, 0xFFFFFFFD, 0x00000001}, - []su_int{0xFFFFFFFD, 0xFFFFFFFE, 0x00000000}, - []su_int{0xFFFFFFFD, 0xFFFFFFFF, 0x00000000}, - []su_int{0xFFFFFFFE, 0x00000001, 0xFFFFFFFE}, - []su_int{0xFFFFFFFE, 0x00000002, 0x7FFFFFFF}, - []su_int{0xFFFFFFFE, 0x00000003, 0x55555554}, - []su_int{0xFFFFFFFE, 0x00000010, 0x0FFFFFFF}, - []su_int{0xFFFFFFFE, 0x078644FA, 0x00000022}, - []su_int{0xFFFFFFFE, 0x0747AE14, 0x00000023}, - []su_int{0xFFFFFFFE, 0x7FFFFFFF, 0x00000002}, - []su_int{0xFFFFFFFE, 0x80000000, 0x00000001}, - []su_int{0xFFFFFFFE, 0xFFFFFFFD, 0x00000001}, - []su_int{0xFFFFFFFE, 0xFFFFFFFE, 0x00000001}, - []su_int{0xFFFFFFFE, 0xFFFFFFFF, 0x00000000}, - []su_int{0xFFFFFFFF, 0x00000001, 0xFFFFFFFF}, - []su_int{0xFFFFFFFF, 0x00000002, 0x7FFFFFFF}, - []su_int{0xFFFFFFFF, 0x00000003, 0x55555555}, - []su_int{0xFFFFFFFF, 0x00000010, 0x0FFFFFFF}, - []su_int{0xFFFFFFFF, 0x078644FA, 0x00000022}, - []su_int{0xFFFFFFFF, 0x0747AE14, 0x00000023}, - []su_int{0xFFFFFFFF, 0x7FFFFFFF, 0x00000002}, - []su_int{0xFFFFFFFF, 0x80000000, 0x00000001}, - []su_int{0xFFFFFFFF, 0xFFFFFFFD, 0x00000001}, - []su_int{0xFFFFFFFF, 0xFFFFFFFE, 0x00000001}, - []su_int{0xFFFFFFFF, 0xFFFFFFFF, 0x00000001}, + const cases = [][3]u32 { + []u32{0x00000000, 0x00000001, 0x00000000}, + []u32{0x00000000, 0x00000002, 0x00000000}, + []u32{0x00000000, 0x00000003, 0x00000000}, + []u32{0x00000000, 0x00000010, 0x00000000}, + []u32{0x00000000, 0x078644FA, 0x00000000}, + []u32{0x00000000, 0x0747AE14, 0x00000000}, + []u32{0x00000000, 0x7FFFFFFF, 0x00000000}, + []u32{0x00000000, 0x80000000, 0x00000000}, + []u32{0x00000000, 0xFFFFFFFD, 0x00000000}, + []u32{0x00000000, 0xFFFFFFFE, 0x00000000}, + []u32{0x00000000, 0xFFFFFFFF, 0x00000000}, + []u32{0x00000001, 0x00000001, 0x00000001}, + []u32{0x00000001, 0x00000002, 0x00000000}, + []u32{0x00000001, 0x00000003, 0x00000000}, + []u32{0x00000001, 0x00000010, 0x00000000}, + []u32{0x00000001, 0x078644FA, 0x00000000}, + []u32{0x00000001, 0x0747AE14, 0x00000000}, + []u32{0x00000001, 0x7FFFFFFF, 0x00000000}, + []u32{0x00000001, 0x80000000, 0x00000000}, + []u32{0x00000001, 0xFFFFFFFD, 0x00000000}, + []u32{0x00000001, 0xFFFFFFFE, 0x00000000}, + []u32{0x00000001, 0xFFFFFFFF, 0x00000000}, + []u32{0x00000002, 0x00000001, 0x00000002}, + []u32{0x00000002, 0x00000002, 0x00000001}, + []u32{0x00000002, 0x00000003, 0x00000000}, + []u32{0x00000002, 0x00000010, 0x00000000}, + []u32{0x00000002, 0x078644FA, 0x00000000}, + []u32{0x00000002, 0x0747AE14, 0x00000000}, + []u32{0x00000002, 0x7FFFFFFF, 0x00000000}, + []u32{0x00000002, 0x80000000, 0x00000000}, + []u32{0x00000002, 0xFFFFFFFD, 0x00000000}, + []u32{0x00000002, 0xFFFFFFFE, 0x00000000}, + []u32{0x00000002, 0xFFFFFFFF, 0x00000000}, + []u32{0x00000003, 0x00000001, 0x00000003}, + []u32{0x00000003, 0x00000002, 0x00000001}, + []u32{0x00000003, 0x00000003, 0x00000001}, + []u32{0x00000003, 0x00000010, 0x00000000}, + []u32{0x00000003, 0x078644FA, 0x00000000}, + []u32{0x00000003, 0x0747AE14, 0x00000000}, + []u32{0x00000003, 0x7FFFFFFF, 0x00000000}, + []u32{0x00000003, 0x80000000, 0x00000000}, + []u32{0x00000003, 0xFFFFFFFD, 0x00000000}, + []u32{0x00000003, 0xFFFFFFFE, 0x00000000}, + []u32{0x00000003, 0xFFFFFFFF, 0x00000000}, + []u32{0x00000010, 0x00000001, 0x00000010}, + []u32{0x00000010, 0x00000002, 0x00000008}, + []u32{0x00000010, 0x00000003, 0x00000005}, + []u32{0x00000010, 0x00000010, 0x00000001}, + []u32{0x00000010, 0x078644FA, 0x00000000}, + []u32{0x00000010, 0x0747AE14, 0x00000000}, + []u32{0x00000010, 0x7FFFFFFF, 0x00000000}, + []u32{0x00000010, 0x80000000, 0x00000000}, + []u32{0x00000010, 0xFFFFFFFD, 0x00000000}, + []u32{0x00000010, 0xFFFFFFFE, 0x00000000}, + []u32{0x00000010, 0xFFFFFFFF, 0x00000000}, + []u32{0x078644FA, 0x00000001, 0x078644FA}, + []u32{0x078644FA, 0x00000002, 0x03C3227D}, + []u32{0x078644FA, 0x00000003, 0x028216FE}, + []u32{0x078644FA, 0x00000010, 0x0078644F}, + []u32{0x078644FA, 0x078644FA, 0x00000001}, + []u32{0x078644FA, 0x0747AE14, 0x00000001}, + []u32{0x078644FA, 0x7FFFFFFF, 0x00000000}, + []u32{0x078644FA, 0x80000000, 0x00000000}, + []u32{0x078644FA, 0xFFFFFFFD, 0x00000000}, + []u32{0x078644FA, 0xFFFFFFFE, 0x00000000}, + []u32{0x078644FA, 0xFFFFFFFF, 0x00000000}, + []u32{0x0747AE14, 0x00000001, 0x0747AE14}, + []u32{0x0747AE14, 0x00000002, 0x03A3D70A}, + []u32{0x0747AE14, 0x00000003, 0x026D3A06}, + []u32{0x0747AE14, 0x00000010, 0x00747AE1}, + []u32{0x0747AE14, 0x078644FA, 0x00000000}, + []u32{0x0747AE14, 0x0747AE14, 0x00000001}, + []u32{0x0747AE14, 0x7FFFFFFF, 0x00000000}, + []u32{0x0747AE14, 0x80000000, 0x00000000}, + []u32{0x0747AE14, 0xFFFFFFFD, 0x00000000}, + []u32{0x0747AE14, 0xFFFFFFFE, 0x00000000}, + []u32{0x0747AE14, 0xFFFFFFFF, 0x00000000}, + []u32{0x7FFFFFFF, 0x00000001, 0x7FFFFFFF}, + []u32{0x7FFFFFFF, 0x00000002, 0x3FFFFFFF}, + []u32{0x7FFFFFFF, 0x00000003, 0x2AAAAAAA}, + []u32{0x7FFFFFFF, 0x00000010, 0x07FFFFFF}, + []u32{0x7FFFFFFF, 0x078644FA, 0x00000011}, + []u32{0x7FFFFFFF, 0x0747AE14, 0x00000011}, + []u32{0x7FFFFFFF, 0x7FFFFFFF, 0x00000001}, + []u32{0x7FFFFFFF, 0x80000000, 0x00000000}, + []u32{0x7FFFFFFF, 0xFFFFFFFD, 0x00000000}, + []u32{0x7FFFFFFF, 0xFFFFFFFE, 0x00000000}, + []u32{0x7FFFFFFF, 0xFFFFFFFF, 0x00000000}, + []u32{0x80000000, 0x00000001, 0x80000000}, + []u32{0x80000000, 0x00000002, 0x40000000}, + []u32{0x80000000, 0x00000003, 0x2AAAAAAA}, + []u32{0x80000000, 0x00000010, 0x08000000}, + []u32{0x80000000, 0x078644FA, 0x00000011}, + []u32{0x80000000, 0x0747AE14, 0x00000011}, + []u32{0x80000000, 0x7FFFFFFF, 0x00000001}, + []u32{0x80000000, 0x80000000, 0x00000001}, + []u32{0x80000000, 0xFFFFFFFD, 0x00000000}, + []u32{0x80000000, 0xFFFFFFFE, 0x00000000}, + []u32{0x80000000, 0xFFFFFFFF, 0x00000000}, + []u32{0xFFFFFFFD, 0x00000001, 0xFFFFFFFD}, + []u32{0xFFFFFFFD, 0x00000002, 0x7FFFFFFE}, + []u32{0xFFFFFFFD, 0x00000003, 0x55555554}, + []u32{0xFFFFFFFD, 0x00000010, 0x0FFFFFFF}, + []u32{0xFFFFFFFD, 0x078644FA, 0x00000022}, + []u32{0xFFFFFFFD, 0x0747AE14, 0x00000023}, + []u32{0xFFFFFFFD, 0x7FFFFFFF, 0x00000001}, + []u32{0xFFFFFFFD, 0x80000000, 0x00000001}, + []u32{0xFFFFFFFD, 0xFFFFFFFD, 0x00000001}, + []u32{0xFFFFFFFD, 0xFFFFFFFE, 0x00000000}, + []u32{0xFFFFFFFD, 0xFFFFFFFF, 0x00000000}, + []u32{0xFFFFFFFE, 0x00000001, 0xFFFFFFFE}, + []u32{0xFFFFFFFE, 0x00000002, 0x7FFFFFFF}, + []u32{0xFFFFFFFE, 0x00000003, 0x55555554}, + []u32{0xFFFFFFFE, 0x00000010, 0x0FFFFFFF}, + []u32{0xFFFFFFFE, 0x078644FA, 0x00000022}, + []u32{0xFFFFFFFE, 0x0747AE14, 0x00000023}, + []u32{0xFFFFFFFE, 0x7FFFFFFF, 0x00000002}, + []u32{0xFFFFFFFE, 0x80000000, 0x00000001}, + []u32{0xFFFFFFFE, 0xFFFFFFFD, 0x00000001}, + []u32{0xFFFFFFFE, 0xFFFFFFFE, 0x00000001}, + []u32{0xFFFFFFFE, 0xFFFFFFFF, 0x00000000}, + []u32{0xFFFFFFFF, 0x00000001, 0xFFFFFFFF}, + []u32{0xFFFFFFFF, 0x00000002, 0x7FFFFFFF}, + []u32{0xFFFFFFFF, 0x00000003, 0x55555555}, + []u32{0xFFFFFFFF, 0x00000010, 0x0FFFFFFF}, + []u32{0xFFFFFFFF, 0x078644FA, 0x00000022}, + []u32{0xFFFFFFFF, 0x0747AE14, 0x00000023}, + []u32{0xFFFFFFFF, 0x7FFFFFFF, 0x00000002}, + []u32{0xFFFFFFFF, 0x80000000, 0x00000001}, + []u32{0xFFFFFFFF, 0xFFFFFFFD, 0x00000001}, + []u32{0xFFFFFFFF, 0xFFFFFFFE, 0x00000001}, + []u32{0xFFFFFFFF, 0xFFFFFFFF, 0x00000001}, }; for (cases) |case| { @@ -514,8 +288,8 @@ test "test_udivsi3" { } } -fn test_one_udivsi3(a: su_int, b: su_int, expected_q: su_int) { - const q: su_int = __udivsi3(a, b); +fn test_one_udivsi3(a: u32, b: u32, expected_q: u32) { + const q: u32 = __udivsi3(a, b); assert(q == expected_q); } diff --git a/std/special/compiler_rt/udivmod.zig b/std/special/compiler_rt/udivmod.zig new file mode 100644 index 0000000000..3eea4bd5f2 --- /dev/null +++ b/std/special/compiler_rt/udivmod.zig @@ -0,0 +1,193 @@ +const builtin = @import("builtin"); +const is_test = builtin.is_test; + +const low = if (builtin.is_big_endian) 1 else 0; +const high = 1 - low; + +pub fn udivmod(comptime DoubleInt: type, a: DoubleInt, b: DoubleInt, maybe_rem: ?&DoubleInt) -> DoubleInt { + @setDebugSafety(this, is_test); + + const SingleInt = @IntType(false, @divExact(DoubleInt.bit_count, 2)); + const SignedDoubleInt = @IntType(true, DoubleInt.bit_count); + + const n = *@ptrCast(&[2]SingleInt, &a); // TODO issue #421 + const d = *@ptrCast(&[2]SingleInt, &b); // TODO issue #421 + var q: [2]SingleInt = undefined; + var r: [2]SingleInt = undefined; + var sr: c_uint = undefined; + // special cases, X is unknown, K != 0 + if (n[high] == 0) { + if (d[high] == 0) { + // 0 X + // --- + // 0 X + if (maybe_rem) |rem| { + *rem = n[low] % d[low]; + } + return n[low] / d[low]; + } + // 0 X + // --- + // K X + if (maybe_rem) |rem| { + *rem = n[low]; + } + return 0; + } + // n[high] != 0 + if (d[low] == 0) { + if (d[high] == 0) { + // K X + // --- + // 0 0 + if (maybe_rem) |rem| { + *rem = n[high] % d[low]; + } + return n[high] / d[low]; + } + // d[high] != 0 + if (n[low] == 0) { + // K 0 + // --- + // K 0 + if (maybe_rem) |rem| { + r[high] = n[high] % d[high]; + r[low] = 0; + *rem = *@ptrCast(&DoubleInt, &r[0]); // TODO issue #421 + } + return n[high] / d[high]; + } + // K K + // --- + // K 0 + if ((d[high] & (d[high] - 1)) == 0) { + // d is a power of 2 + if (maybe_rem) |rem| { + r[low] = n[low]; + r[high] = n[high] & (d[high] - 1); + *rem = *@ptrCast(&DoubleInt, &r[0]); // TODO issue #421 + } + return n[high] >> @ctz(d[high]); + } + // K K + // --- + // K 0 + sr = @bitCast(c_uint, c_int(@clz(d[high])) - c_int(@clz(n[high]))); + // 0 <= sr <= SingleInt.bit_count - 2 or sr large + if (sr > SingleInt.bit_count - 2) { + if (maybe_rem) |rem| { + *rem = a; + } + return 0; + } + sr += 1; + // 1 <= sr <= SingleInt.bit_count - 1 + // q.all = a << (DoubleInt.bit_count - sr); + q[low] = 0; + q[high] = n[low] << (SingleInt.bit_count - sr); + // r.all = a >> sr; + r[high] = n[high] >> sr; + r[low] = (n[high] << (SingleInt.bit_count - sr)) | (n[low] >> sr); + } else { + // d[low] != 0 + if (d[high] == 0) { + // K X + // --- + // 0 K + if ((d[low] & (d[low] - 1)) == 0) { + // d is a power of 2 + if (maybe_rem) |rem| { + *rem = n[low] & (d[low] - 1); + } + if (d[low] == 1) { + return a; + } + sr = @ctz(d[low]); + q[high] = n[high] >> sr; + q[low] = (n[high] << (SingleInt.bit_count - sr)) | (n[low] >> sr); + return *@ptrCast(&DoubleInt, &q[0]); // TODO issue #421 + } + // K X + // --- + // 0 K + sr = 1 + SingleInt.bit_count + c_uint(@clz(d[low])) - c_uint(@clz(n[high])); + // 2 <= sr <= DoubleInt.bit_count - 1 + // q.all = a << (DoubleInt.bit_count - sr); + // r.all = a >> sr; + if (sr == SingleInt.bit_count) { + q[low] = 0; + q[high] = n[low]; + r[high] = 0; + r[low] = n[high]; + } else if (sr < SingleInt.bit_count) { + // 2 <= sr <= SingleInt.bit_count - 1 + q[low] = 0; + q[high] = n[low] << (SingleInt.bit_count - sr); + r[high] = n[high] >> sr; + r[low] = (n[high] << (SingleInt.bit_count - sr)) | (n[low] >> sr); + } else { + // SingleInt.bit_count + 1 <= sr <= DoubleInt.bit_count - 1 + q[low] = n[low] << (DoubleInt.bit_count - sr); + q[high] = (n[high] << (DoubleInt.bit_count - sr)) | (n[low] >> (sr - SingleInt.bit_count)); + r[high] = 0; + r[low] = n[high] >> (sr - SingleInt.bit_count); + } + } else { + // K X + // --- + // K K + sr = @bitCast(c_uint, c_int(@clz(d[high])) - c_int(@clz(n[high]))); + // 0 <= sr <= SingleInt.bit_count - 1 or sr large + if (sr > SingleInt.bit_count - 1) { + if (maybe_rem) |rem| { + *rem = a; + } + return 0; + } + sr += 1; + // 1 <= sr <= SingleInt.bit_count + // q.all = a << (DoubleInt.bit_count - sr); + // r.all = a >> sr; + q[low] = 0; + if (sr == SingleInt.bit_count) { + q[high] = n[low]; + r[high] = 0; + r[low] = n[high]; + } else { + r[high] = n[high] >> sr; + r[low] = (n[high] << (SingleInt.bit_count - sr)) | (n[low] >> sr); + q[high] = n[low] << (SingleInt.bit_count - sr); + } + } + } + // Not a special case + // q and r are initialized with: + // q.all = a << (DoubleInt.bit_count - sr); + // r.all = a >> sr; + // 1 <= sr <= DoubleInt.bit_count - 1 + var carry: u32 = 0; + var r_all: DoubleInt = undefined; + while (sr > 0) : (sr -= 1) { + // r:q = ((r:q) << 1) | carry + r[high] = (r[high] << 1) | (r[low] >> (SingleInt.bit_count - 1)); + r[low] = (r[low] << 1) | (q[high] >> (SingleInt.bit_count - 1)); + q[high] = (q[high] << 1) | (q[low] >> (SingleInt.bit_count - 1)); + q[low] = (q[low] << 1) | carry; + // carry = 0; + // if (r.all >= b) + // { + // r.all -= b; + // carry = 1; + // } + r_all = *@ptrCast(&DoubleInt, &r[0]); // TODO issue #421 + const s: SignedDoubleInt = SignedDoubleInt(b -% r_all -% 1) >> (DoubleInt.bit_count - 1); + carry = u32(s & 1); + r_all -= b & @bitCast(DoubleInt, s); + r = *@ptrCast(&[2]SingleInt, &r_all); // TODO issue #421 + } + const q_all = ((*@ptrCast(&DoubleInt, &q[0])) << 1) | carry; // TODO issue #421 + if (maybe_rem) |rem| { + *rem = r_all; + } + return q_all; +} diff --git a/std/special/compiler_rt/udivmoddi4.zig b/std/special/compiler_rt/udivmoddi4.zig new file mode 100644 index 0000000000..23ed5420cb --- /dev/null +++ b/std/special/compiler_rt/udivmoddi4.zig @@ -0,0 +1,9 @@ +const udivmod = @import("udivmod.zig").udivmod; + +export fn __udivmoddi4(a: u64, b: u64, maybe_rem: ?&u64) -> u64 { + return udivmod(u64, a, b, maybe_rem); +} + +test "import udivmoddi4" { + _ = @import("udivmoddi4_test.zig"); +} diff --git a/std/special/compiler_rt/udivmoddi4_test.zig b/std/special/compiler_rt/udivmoddi4_test.zig new file mode 100644 index 0000000000..3cc5359a51 --- /dev/null +++ b/std/special/compiler_rt/udivmoddi4_test.zig @@ -0,0 +1,20610 @@ +const __udivmoddi4 = @import("udivmoddi4.zig").__udivmoddi4; +const assert = @import("std").debug.assert; + +fn test__udivmoddi4(a: u64, b: u64, expected_q: u64, expected_r: u64) { + var r: u64 = undefined; + const q = __udivmoddi4(a, b, &r); + assert(q == expected_q); + assert(r == expected_r); +} + +test "udivmoddi4" { + for (cases) |case| { + test__udivmoddi4(case[0], case[1], case[2], case[3]); + } +} + +const cases = [][4]u64{ + []u64{0x0000000000000000, 0x0000000000000001, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000000000002, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000000000003, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000000000010, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000000078644FA, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x000000000747AE14, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x000000007FFFFFFF, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000080000000, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000000FFFFFFFD, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000000FFFFFFFE, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000000FFFFFFFF, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000100000000, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000100000001, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000100000002, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000100000003, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000100000010, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000001078644FA, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x000000010747AE14, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x000000017FFFFFFF, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000180000000, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000001FFFFFFFD, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000001FFFFFFFE, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000001FFFFFFFF, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000200000000, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000200000001, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000200000002, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000200000003, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000200000010, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000002078644FA, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x000000020747AE14, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x000000027FFFFFFF, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000280000000, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000002FFFFFFFD, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000002FFFFFFFE, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000002FFFFFFFF, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000300000000, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000300000001, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000300000002, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000300000003, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000300000010, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000003078644FA, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x000000030747AE14, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x000000037FFFFFFF, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000000380000000, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000003FFFFFFFD, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000003FFFFFFFE, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000003FFFFFFFF, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000001000000000, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000001000000001, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000001000000002, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000001000000003, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000001000000010, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000010078644FA, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x000000100747AE14, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x000000107FFFFFFF, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x0000001080000000, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000010FFFFFFFD, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000010FFFFFFFE, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x00000010FFFFFFFF, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x078644FA00000000, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x078644FA00000001, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x078644FA00000002, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x078644FA00000003, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x078644FA00000010, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x078644FA078644FA, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x078644FA0747AE14, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x078644FA7FFFFFFF, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x078644FA80000000, 0x0000000000000000, 0x0000000000000000}, + []u64{0x0000000000000000, 0x078644FAFFFFFFFD, 0x0000000000000000, 0x0000000000000000}, + 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[]u64{0x0747AE140747AE14, 0x0000000000000010, 0x00747AE140747AE1, 0x0000000000000004}, + []u64{0x0747AE140747AE14, 0x00000000078644FA, 0x00000000F7AE911E, 0x00000000008DFEC8}, + []u64{0x0747AE140747AE14, 0x000000000747AE14, 0x0000000100000001, 0x0000000000000000}, + []u64{0x0747AE140747AE14, 0x000000007FFFFFFF, 0x000000000E8F5C28, 0x0000000015D70A3C}, + []u64{0x0747AE140747AE14, 0x0000000080000000, 0x000000000E8F5C28, 0x000000000747AE14}, + []u64{0x0747AE140747AE14, 0x00000000FFFFFFFD, 0x000000000747AE14, 0x000000001D1EB850}, + []u64{0x0747AE140747AE14, 0x00000000FFFFFFFE, 0x000000000747AE14, 0x0000000015D70A3C}, + []u64{0x0747AE140747AE14, 0x00000000FFFFFFFF, 0x000000000747AE14, 0x000000000E8F5C28}, + []u64{0x0747AE140747AE14, 0x0000000100000000, 0x000000000747AE14, 0x000000000747AE14}, + []u64{0x0747AE140747AE14, 0x0000000100000001, 0x000000000747AE14, 0x0000000000000000}, + []u64{0x0747AE140747AE14, 0x0000000100000002, 0x000000000747AE13, 0x00000000F8B851EE}, + []u64{0x0747AE140747AE14, 0x0000000100000003, 0x000000000747AE13, 0x00000000F170A3DB}, + []u64{0x0747AE140747AE14, 0x0000000100000010, 0x000000000747AE13, 0x0000000092CCCCE4}, + []u64{0x0747AE140747AE14, 0x00000001078644FA, 0x000000000712773F, 0x0000000013987E8E}, + []u64{0x0747AE140747AE14, 0x000000010747AE14, 0x00000000071425A5, 0x00000000D45B9730}, + []u64{0x0747AE140747AE14, 0x000000017FFFFFFF, 0x0000000004DA740D, 0x000000008C222221}, + []u64{0x0747AE140747AE14, 0x0000000180000000, 0x0000000004DA740D, 0x000000008747AE14}, + []u64{0x0747AE140747AE14, 0x00000001FFFFFFFD, 0x0000000003A3D70A, 0x0000000012333332}, + []u64{0x0747AE140747AE14, 0x00000001FFFFFFFE, 0x0000000003A3D70A, 0x000000000E8F5C28}, + []u64{0x0747AE140747AE14, 0x00000001FFFFFFFF, 0x0000000003A3D70A, 0x000000000AEB851E}, + []u64{0x0747AE140747AE14, 0x0000000200000000, 0x0000000003A3D70A, 0x000000000747AE14}, + []u64{0x0747AE140747AE14, 0x0000000200000001, 0x0000000003A3D70A, 0x0000000003A3D70A}, + []u64{0x0747AE140747AE14, 0x0000000200000002, 0x0000000003A3D70A, 0x0000000000000000}, + []u64{0x0747AE140747AE14, 0x0000000200000003, 0x0000000003A3D709, 0x00000001FC5C28F9}, + []u64{0x0747AE140747AE14, 0x0000000200000010, 0x0000000003A3D709, 0x00000001CD0A3D84}, + []u64{0x0747AE140747AE14, 0x00000002078644FA, 0x0000000003965801, 0x000000007F8F791A}, + []u64{0x0747AE140747AE14, 0x000000020747AE14, 0x000000000396C6B1, 0x00000001525CDA40}, + []u64{0x0747AE140747AE14, 0x000000027FFFFFFF, 0x0000000002E978D4, 0x000000020A3126E8}, + []u64{0x0747AE140747AE14, 0x0000000280000000, 0x0000000002E978D4, 0x000000020747AE14}, + []u64{0x0747AE140747AE14, 0x00000002FFFFFFFD, 0x00000000026D3A06, 0x000000020E8F5C26}, + []u64{0x0747AE140747AE14, 0x00000002FFFFFFFE, 0x00000000026D3A06, 0x000000020C222220}, + []u64{0x0747AE140747AE14, 0x00000002FFFFFFFF, 0x00000000026D3A06, 0x0000000209B4E81A}, + []u64{0x0747AE140747AE14, 0x0000000300000000, 0x00000000026D3A06, 0x000000020747AE14}, + []u64{0x0747AE140747AE14, 0x0000000300000001, 0x00000000026D3A06, 0x0000000204DA740E}, + []u64{0x0747AE140747AE14, 0x0000000300000002, 0x00000000026D3A06, 0x00000002026D3A08}, + []u64{0x0747AE140747AE14, 0x0000000300000003, 0x00000000026D3A06, 0x0000000200000002}, + []u64{0x0747AE140747AE14, 0x0000000300000010, 0x00000000026D3A06, 0x00000001E0740DB4}, + []u64{0x0747AE140747AE14, 0x00000003078644FA, 0x0000000002673301, 0x000000018B6D9B1A}, + []u64{0x0747AE140747AE14, 0x000000030747AE14, 0x00000000026764AB, 0x00000002F85A96B8}, + []u64{0x0747AE140747AE14, 0x000000037FFFFFFF, 0x0000000002147AE1, 0x00000000895C28F5}, + []u64{0x0747AE140747AE14, 0x0000000380000000, 0x0000000002147AE1, 0x000000008747AE14}, + []u64{0x0747AE140747AE14, 0x00000003FFFFFFFD, 0x0000000001D1EB85, 0x000000000CBD70A3}, + []u64{0x0747AE140747AE14, 0x00000003FFFFFFFE, 0x0000000001D1EB85, 0x000000000AEB851E}, + []u64{0x0747AE140747AE14, 0x00000003FFFFFFFF, 0x0000000001D1EB85, 0x0000000009199999}, + []u64{0x0747AE140747AE14, 0x0000001000000000, 0x0000000000747AE1, 0x000000040747AE14}, + []u64{0x0747AE140747AE14, 0x0000001000000001, 0x0000000000747AE1, 0x0000000406D33333}, + []u64{0x0747AE140747AE14, 0x0000001000000002, 0x0000000000747AE1, 0x00000004065EB852}, + []u64{0x0747AE140747AE14, 0x0000001000000003, 0x0000000000747AE1, 0x0000000405EA3D71}, + []u64{0x0747AE140747AE14, 0x0000001000000010, 0x0000000000747AE1, 0x0000000400000004}, + []u64{0x0747AE140747AE14, 0x00000010078644FA, 0x0000000000744433, 0x0000000B9BED8846}, + []u64{0x0747AE140747AE14, 0x000000100747AE14, 0x00000000007445F9, 0x0000000BBF93F8A0}, + []u64{0x0747AE140747AE14, 0x000000107FFFFFFF, 0x000000000070F347, 0x0000000087B8A15B}, + []u64{0x0747AE140747AE14, 0x0000001080000000, 0x000000000070F347, 0x000000008747AE14}, + []u64{0x0747AE140747AE14, 0x00000010FFFFFFFD, 0x00000000006DA0D4, 0x0000000008909090}, + []u64{0x0747AE140747AE14, 0x00000010FFFFFFFE, 0x00000000006DA0D4, 0x000000000822EFBC}, + []u64{0x0747AE140747AE14, 0x00000010FFFFFFFF, 0x00000000006DA0D4, 0x0000000007B54EE8}, + []u64{0x0747AE140747AE14, 0x078644FA00000000, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x078644FA00000001, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x078644FA00000002, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x078644FA00000003, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x078644FA00000010, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x078644FA078644FA, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x078644FA0747AE14, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x078644FA7FFFFFFF, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x078644FA80000000, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x078644FAFFFFFFFD, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x078644FAFFFFFFFE, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x078644FAFFFFFFFF, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x0747AE1400000000, 0x0000000000000001, 0x000000000747AE14}, + []u64{0x0747AE140747AE14, 0x0747AE1400000001, 0x0000000000000001, 0x000000000747AE13}, + []u64{0x0747AE140747AE14, 0x0747AE1400000002, 0x0000000000000001, 0x000000000747AE12}, + []u64{0x0747AE140747AE14, 0x0747AE1400000003, 0x0000000000000001, 0x000000000747AE11}, + []u64{0x0747AE140747AE14, 0x0747AE1400000010, 0x0000000000000001, 0x000000000747AE04}, + []u64{0x0747AE140747AE14, 0x0747AE14078644FA, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x0747AE140747AE14, 0x0000000000000001, 0x0000000000000000}, + []u64{0x0747AE140747AE14, 0x0747AE147FFFFFFF, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x0747AE1480000000, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x0747AE14FFFFFFFD, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x0747AE14FFFFFFFE, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x0747AE14FFFFFFFF, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x7FFFFFFF00000000, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x7FFFFFFF00000001, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x7FFFFFFF00000002, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x7FFFFFFF00000003, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x7FFFFFFF00000010, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x7FFFFFFF078644FA, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x7FFFFFFF0747AE14, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x7FFFFFFF7FFFFFFF, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x7FFFFFFF80000000, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x7FFFFFFFFFFFFFFD, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x7FFFFFFFFFFFFFFE, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x7FFFFFFFFFFFFFFF, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x8000000000000000, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x8000000000000001, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x8000000000000002, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x8000000000000003, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x8000000000000010, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x80000000078644FA, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x800000000747AE14, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x800000007FFFFFFF, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x8000000080000000, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x80000000FFFFFFFD, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x80000000FFFFFFFE, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0x80000000FFFFFFFF, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFD00000000, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFD00000001, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFD00000002, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFD00000003, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFD00000010, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFD078644FA, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFD0747AE14, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFD7FFFFFFF, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFD80000000, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFDFFFFFFFD, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFDFFFFFFFE, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFDFFFFFFFF, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFE00000000, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFE00000001, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFE00000002, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFE00000003, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFE00000010, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFE078644FA, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFE0747AE14, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFE7FFFFFFF, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFE80000000, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFEFFFFFFFD, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFEFFFFFFFE, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFEFFFFFFFF, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFF00000000, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFF00000001, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFF00000002, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFF00000003, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFF00000010, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFF078644FA, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFF0747AE14, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFF7FFFFFFF, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFF80000000, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFFFFFFFFFD, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFFFFFFFFFE, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE140747AE14, 0xFFFFFFFFFFFFFFFF, 0x0000000000000000, 0x0747AE140747AE14}, + []u64{0x0747AE147FFFFFFF, 0x0000000000000001, 0x0747AE147FFFFFFF, 0x0000000000000000}, + []u64{0x0747AE147FFFFFFF, 0x0000000000000002, 0x03A3D70A3FFFFFFF, 0x0000000000000001}, + []u64{0x0747AE147FFFFFFF, 0x0000000000000003, 0x026D3A06D5555555, 0x0000000000000000}, + []u64{0x0747AE147FFFFFFF, 0x0000000000000010, 0x00747AE147FFFFFF, 0x000000000000000F}, + []u64{0x0747AE147FFFFFFF, 0x00000000078644FA, 0x00000000F7AE912E, 0x0000000000E20113}, + []u64{0x0747AE147FFFFFFF, 0x000000000747AE14, 0x0000000100000011, 0x00000000043D70AB}, + []u64{0x0747AE147FFFFFFF, 0x000000007FFFFFFF, 0x000000000E8F5C29, 0x000000000E8F5C28}, + []u64{0x0747AE147FFFFFFF, 0x0000000080000000, 0x000000000E8F5C28, 0x000000007FFFFFFF}, + []u64{0x0747AE147FFFFFFF, 0x00000000FFFFFFFD, 0x000000000747AE14, 0x0000000095D70A3B}, + []u64{0x0747AE147FFFFFFF, 0x00000000FFFFFFFE, 0x000000000747AE14, 0x000000008E8F5C27}, + []u64{0x0747AE147FFFFFFF, 0x00000000FFFFFFFF, 0x000000000747AE14, 0x000000008747AE13}, + []u64{0x0747AE147FFFFFFF, 0x0000000100000000, 0x000000000747AE14, 0x000000007FFFFFFF}, + []u64{0x0747AE147FFFFFFF, 0x0000000100000001, 0x000000000747AE14, 0x0000000078B851EB}, + []u64{0x0747AE147FFFFFFF, 0x0000000100000002, 0x000000000747AE14, 0x000000007170A3D7}, + []u64{0x0747AE147FFFFFFF, 0x0000000100000003, 0x000000000747AE14, 0x000000006A28F5C3}, + []u64{0x0747AE147FFFFFFF, 0x0000000100000010, 0x000000000747AE14, 0x000000000B851EBF}, + []u64{0x0747AE147FFFFFFF, 0x00000001078644FA, 0x000000000712773F, 0x000000008C50D079}, + []u64{0x0747AE147FFFFFFF, 0x000000010747AE14, 0x00000000071425A6, 0x0000000045CC3B07}, + []u64{0x0747AE147FFFFFFF, 0x000000017FFFFFFF, 0x0000000004DA740D, 0x0000000104DA740C}, + []u64{0x0747AE147FFFFFFF, 0x0000000180000000, 0x0000000004DA740D, 0x00000000FFFFFFFF}, + []u64{0x0747AE147FFFFFFF, 0x00000001FFFFFFFD, 0x0000000003A3D70A, 0x000000008AEB851D}, + []u64{0x0747AE147FFFFFFF, 0x00000001FFFFFFFE, 0x0000000003A3D70A, 0x000000008747AE13}, + []u64{0x0747AE147FFFFFFF, 0x00000001FFFFFFFF, 0x0000000003A3D70A, 0x0000000083A3D709}, + []u64{0x0747AE147FFFFFFF, 0x0000000200000000, 0x0000000003A3D70A, 0x000000007FFFFFFF}, + []u64{0x0747AE147FFFFFFF, 0x0000000200000001, 0x0000000003A3D70A, 0x000000007C5C28F5}, + 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[]u64{0x0747AE14FFFFFFFE, 0xFFFFFFFE078644FA, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFE0747AE14, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFE7FFFFFFF, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFE80000000, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFEFFFFFFFD, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFEFFFFFFFE, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFEFFFFFFFF, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFF00000000, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFF00000001, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFF00000002, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFF00000003, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFF00000010, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFF078644FA, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFF0747AE14, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFF7FFFFFFF, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFF80000000, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFFFFFFFFFD, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFFFFFFFFFE, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFE, 0xFFFFFFFFFFFFFFFF, 0x0000000000000000, 0x0747AE14FFFFFFFE}, + []u64{0x0747AE14FFFFFFFF, 0x0000000000000001, 0x0747AE14FFFFFFFF, 0x0000000000000000}, + []u64{0x0747AE14FFFFFFFF, 0x0000000000000002, 0x03A3D70A7FFFFFFF, 0x0000000000000001}, + []u64{0x0747AE14FFFFFFFF, 0x0000000000000003, 0x026D3A06FFFFFFFF, 0x0000000000000002}, + 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[]u64{0xFFFFFFFFFFFFFFFF, 0xFFFFFFFF00000010, 0x0000000000000001, 0x00000000FFFFFFEF}, + []u64{0xFFFFFFFFFFFFFFFF, 0xFFFFFFFF078644FA, 0x0000000000000001, 0x00000000F879BB05}, + []u64{0xFFFFFFFFFFFFFFFF, 0xFFFFFFFF0747AE14, 0x0000000000000001, 0x00000000F8B851EB}, + []u64{0xFFFFFFFFFFFFFFFF, 0xFFFFFFFF7FFFFFFF, 0x0000000000000001, 0x0000000080000000}, + []u64{0xFFFFFFFFFFFFFFFF, 0xFFFFFFFF80000000, 0x0000000000000001, 0x000000007FFFFFFF}, + []u64{0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFD, 0x0000000000000001, 0x0000000000000002}, + []u64{0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFE, 0x0000000000000001, 0x0000000000000001}, + []u64{0xFFFFFFFFFFFFFFFF, 0xFFFFFFFFFFFFFFFF, 0x0000000000000001, 0x0000000000000000}, +}; diff --git a/std/special/compiler_rt/udivmodti4.zig b/std/special/compiler_rt/udivmodti4.zig index fbec0a2d6c..8048362bc5 100644 --- a/std/special/compiler_rt/udivmodti4.zig +++ b/std/special/compiler_rt/udivmodti4.zig @@ -1,195 +1,7 @@ -const builtin = @import("builtin"); -const is_test = builtin.is_test; - -const low = if (builtin.is_big_endian) 1 else 0; -const high = 1 - low; +const udivmod = @import("udivmod.zig").udivmod; export fn __udivmodti4(a: u128, b: u128, maybe_rem: ?&u128) -> u128 { - @setDebugSafety(this, is_test); - - const n_udword_bits = u64.bit_count; - const n_utword_bits = u128.bit_count; - const n = *@ptrCast(&[2]u64, &a); // TODO issue #421 - const d = *@ptrCast(&[2]u64, &b); // TODO issue #421 - var q: [2]u64 = undefined; - var r: [2]u64 = undefined; - var sr: c_uint = undefined; - // special cases, X is unknown, K != 0 - if (n[high] == 0) { - if (d[high] == 0) { - // 0 X - // --- - // 0 X - if (maybe_rem) |rem| { - *rem = n[low] % d[low]; - } - return n[low] / d[low]; - } - // 0 X - // --- - // K X - if (maybe_rem) |rem| { - *rem = n[low]; - } - return 0; - } - // n[high] != 0 - if (d[low] == 0) { - if (d[high] == 0) { - // K X - // --- - // 0 0 - if (maybe_rem) |rem| { - *rem = n[high] % d[low]; - } - return n[high] / d[low]; - } - // d[high] != 0 */ - if (n[low] == 0) { - // K 0 - // --- - // K 0 - if (maybe_rem) |rem| { - r[high] = n[high] % d[high]; - r[low] = 0; - *rem = *@ptrCast(&u128, &r[0]); // TODO issue #421 - } - return n[high] / d[high]; - } - // K K - // --- - // K 0 - if ((d[high] & (d[high] - 1)) == 0) { - // d is a power of 2 - if (maybe_rem) |rem| { - r[low] = n[low]; - r[high] = n[high] & (d[high] - 1); - *rem = *@ptrCast(&u128, &r[0]); // TODO issue #421 - } - return n[high] >> @ctz(d[high]); - } - // K K - // --- - // K 0 - sr = @bitCast(c_uint, c_int(@clz(d[high])) - c_int(@clz(n[high]))); - // 0 <= sr <= n_udword_bits - 2 or sr large - if (sr > n_udword_bits - 2) { - if (maybe_rem) |rem| { - *rem = a; - } - return 0; - } - sr += 1; - // 1 <= sr <= n_udword_bits - 1 - // q.all = a << (n_utword_bits - sr); - q[low] = 0; - q[high] = n[low] << (n_udword_bits - sr); - // r.all = a >> sr; - r[high] = n[high] >> sr; - r[low] = (n[high] << (n_udword_bits - sr)) | (n[low] >> sr); - } else { - // d[low] != 0 - if (d[high] == 0) { - // K X - // --- - // 0 K - if ((d[low] & (d[low] - 1)) == 0) { - // if d is a power of 2 - if (maybe_rem) |rem| { - *rem = n[low] & (d[low] - 1); - } - if (d[low] == 1) - return a; - sr = @ctz(d[low]); - q[high] = n[high] >> sr; - q[low] = (n[high] << (n_udword_bits - sr)) | (n[low] >> sr); - return *@ptrCast(&u128, &q[0]); // TODO issue #421 - } - // K X - // --- - // 0 K - sr = 1 + n_udword_bits + c_uint(@clz(d[low])) - - c_uint(@clz(n[high])); - // 2 <= sr <= n_utword_bits - 1 - // q.all = a << (n_utword_bits - sr); - // r.all = a >> sr; - if (sr == n_udword_bits) { - q[low] = 0; - q[high] = n[low]; - r[high] = 0; - r[low] = n[high]; - } else if (sr < n_udword_bits) { - // 2 <= sr <= n_udword_bits - 1 - q[low] = 0; - q[high] = n[low] << (n_udword_bits - sr); - r[high] = n[high] >> sr; - r[low] = (n[high] << (n_udword_bits - sr)) | (n[low] >> sr); - } else { - // n_udword_bits + 1 <= sr <= n_utword_bits - 1 - q[low] = n[low] << (n_utword_bits - sr); - q[high] = (n[high] << (n_utword_bits - sr)) | - (n[low] >> (sr - n_udword_bits)); - r[high] = 0; - r[low] = n[high] >> (sr - n_udword_bits); - } - } else { - // K X - // --- - // K K - sr = @bitCast(c_uint, c_int(@clz(d[high])) - c_int(@clz(n[high]))); - // 0 <= sr <= n_udword_bits - 1 or sr large - if (sr > n_udword_bits - 1) { - if (maybe_rem) |rem| { - *rem = a; - } - return 0; - } - sr += 1; - // 1 <= sr <= n_udword_bits - // q.all = a << (n_utword_bits - sr); - // r.all = a >> sr; - q[low] = 0; - if (sr == n_udword_bits) { - q[high] = n[low]; - r[high] = 0; - r[low] = n[high]; - } else { - r[high] = n[high] >> sr; - r[low] = (n[high] << (n_udword_bits - sr)) | (n[low] >> sr); - q[high] = n[low] << (n_udword_bits - sr); - } - } - } - // Not a special case - // q and r are initialized with: - // q.all = a << (n_utword_bits - sr); - // r.all = a >> sr; - // 1 <= sr <= n_utword_bits - 1 - var carry: u32 = 0; - var r_all: u128 = undefined; - while (sr > 0) : (sr -= 1) { - // r:q = ((r:q) << 1) | carry - r[high] = (r[high] << 1) | (r[low] >> (n_udword_bits - 1)); - r[low] = (r[low] << 1) | (q[high] >> (n_udword_bits - 1)); - q[high] = (q[high] << 1) | (q[low] >> (n_udword_bits - 1)); - q[low] = (q[low] << 1) | carry; - // carry = 0; - // if (r.all >= b) - // { - // r.all -= b; - // carry = 1; - // } - r_all = *@ptrCast(&u128, &r[0]); // TODO issue #421 - const s: i128 = i128(b -% r_all -% 1) >> (n_utword_bits - 1); - carry = u32(s & 1); - r_all -= b & @bitCast(u128, s); - r = *@ptrCast(&[2]u64, &r_all); // TODO issue #421 - } - const q_all = ((*@ptrCast(&u128, &q[0])) << 1) | carry; // TODO issue #421 - if (maybe_rem) |rem| { - *rem = r_all; - } - return q_all; + return udivmod(u128, a, b, maybe_rem); } test "import udivmodti4" {