Files
Nim/compiler/int128.nim

782 lines
30 KiB
Nim

## This module is for compiler internal use only. For reliable error
## messages and range checks, the compiler needs a data type that can
## hold all from ``low(BiggestInt)`` to ``high(BiggestUInt)``, This
## type is for that purpose.
from math import trunc
type
Int128* = object
udata: array[4,uint32]
template sdata(arg: Int128, idx: int): int32 =
# udata and sdata was supposed to be in a union, but unions are
# handled incorrectly in the VM.
cast[ptr int32](arg.udata[idx].unsafeAddr)[]
# encoding least significant int first (like LittleEndian)
const
Zero* = Int128(udata: [0'u32,0,0,0])
One* = Int128(udata: [1'u32,0,0,0])
Ten* = Int128(udata: [10'u32,0,0,0])
Min = Int128(udata: [0'u32,0,0,0x80000000'u32])
Max = Int128(udata: [high(uint32),high(uint32),high(uint32),uint32(high(int32))])
NegOne* = Int128(udata: [0xffffffff'u32,0xffffffff'u32,0xffffffff'u32,0xffffffff'u32])
template low*(t: typedesc[Int128]): Int128 = Min
template high*(t: typedesc[Int128]): Int128 = Max
proc `$`*(a: Int128): string
proc toInt128*[T: SomeInteger | bool](arg: T): Int128 =
when T is bool: result.sdata(0) = int32(arg)
elif T is SomeUnsignedInt:
when sizeof(arg) <= 4:
result.udata[0] = uint32(arg)
else:
result.udata[0] = uint32(arg and T(0xffffffff))
result.udata[1] = uint32(arg shr 32)
elif sizeof(arg) <= 4:
result.sdata(0) = int32(arg)
if arg < 0: # sign extend
result.sdata(1) = -1
result.sdata(2) = -1
result.sdata(3) = -1
else:
let tmp = int64(arg)
result.udata[0] = uint32(tmp and 0xffffffff)
result.sdata(1) = int32(tmp shr 32)
if arg < 0: # sign extend
result.sdata(2) = -1
result.sdata(3) = -1
template isNegative(arg: Int128): bool =
arg.sdata(3) < 0
template isNegative(arg: int32): bool =
arg < 0
proc bitconcat(a,b: uint32): uint64 =
(uint64(a) shl 32) or uint64(b)
proc bitsplit(a: uint64): (uint32,uint32) =
(cast[uint32](a shr 32), cast[uint32](a))
proc toInt64*(arg: Int128): int64 =
if isNegative(arg):
assert(arg.sdata(3) == -1, "out of range")
assert(arg.sdata(2) == -1, "out of range")
else:
assert(arg.sdata(3) == 0, "out of range")
assert(arg.sdata(2) == 0, "out of range")
cast[int64](bitconcat(arg.udata[1], arg.udata[0]))
proc toInt64Checked*(arg: Int128; onError: int64): int64 =
if isNegative(arg):
if arg.sdata(3) != -1 or arg.sdata(2) != -1:
return onError
else:
if arg.sdata(3) != 0 or arg.sdata(2) != 0:
return onError
return cast[int64](bitconcat(arg.udata[1], arg.udata[0]))
proc toInt32*(arg: Int128): int32 =
if isNegative(arg):
assert(arg.sdata(3) == -1, "out of range")
assert(arg.sdata(2) == -1, "out of range")
assert(arg.sdata(1) == -1, "out of range")
else:
assert(arg.sdata(3) == 0, "out of range")
assert(arg.sdata(2) == 0, "out of range")
assert(arg.sdata(1) == 0, "out of range")
arg.sdata(0)
proc toInt16*(arg: Int128): int16 =
if isNegative(arg):
assert(arg.sdata(3) == -1, "out of range")
assert(arg.sdata(2) == -1, "out of range")
assert(arg.sdata(1) == -1, "out of range")
else:
assert(arg.sdata(3) == 0, "out of range")
assert(arg.sdata(2) == 0, "out of range")
assert(arg.sdata(1) == 0, "out of range")
int16(arg.sdata(0))
proc toInt8*(arg: Int128): int8 =
if isNegative(arg):
assert(arg.sdata(3) == -1, "out of range")
assert(arg.sdata(2) == -1, "out of range")
assert(arg.sdata(1) == -1, "out of range")
else:
assert(arg.sdata(3) == 0, "out of range")
assert(arg.sdata(2) == 0, "out of range")
assert(arg.sdata(1) == 0, "out of range")
int8(arg.sdata(0))
proc toInt*(arg: Int128): int =
when sizeof(int) == 4:
cast[int](toInt32(arg))
else:
cast[int](toInt64(arg))
proc toUInt64*(arg: Int128): uint64 =
assert(arg.udata[3] == 0)
assert(arg.udata[2] == 0)
bitconcat(arg.udata[1], arg.udata[0])
proc toUInt32*(arg: Int128): uint32 =
assert(arg.udata[3] == 0)
assert(arg.udata[2] == 0)
assert(arg.udata[1] == 0)
arg.udata[0]
proc toUInt16*(arg: Int128): uint16 =
assert(arg.udata[3] == 0)
assert(arg.udata[2] == 0)
assert(arg.udata[1] == 0)
uint16(arg.udata[0])
proc toUInt8*(arg: Int128): uint8 =
assert(arg.udata[3] == 0)
assert(arg.udata[2] == 0)
assert(arg.udata[1] == 0)
uint8(arg.udata[0])
proc toUInt*(arg: Int128): uint =
when sizeof(int) == 4:
cast[uint](toInt32(arg))
else:
cast[uint](toInt64(arg))
proc castToInt64*(arg: Int128): int64 =
## Conversion to int64 without range check.
cast[int64](bitconcat(arg.udata[1], arg.udata[0]))
proc castToUInt64*(arg: Int128): uint64 =
## Conversion to uint64 without range check.
cast[uint64](bitconcat(arg.udata[1], arg.udata[0]))
proc addToHex(result: var string; arg: uint32) =
for i in 0..<8:
let idx = (arg shr ((7-i) * 4)) and 0xf
result.add "0123456789abcdef"[idx]
proc addToHex*(result: var string; arg: Int128) =
var i = 3
while i >= 0:
result.addToHex(arg.udata[i])
i -= 1
proc toHex*(arg: Int128): string =
result.addToHex(arg)
proc inc*(a: var Int128, y: uint32 = 1) =
let input = a
a.udata[0] += y
if unlikely(a.udata[0] < y):
a.udata[1].inc
if unlikely(a.udata[1] == 0):
a.udata[2].inc
if unlikely(a.udata[2] == 0):
a.udata[3].inc
doAssert(a.sdata(3) != low(int32), "overflow")
proc cmp*(a,b: Int128): int =
let tmp1 = cmp(a.sdata(3), b.sdata(3))
if tmp1 != 0: return tmp1
let tmp2 = cmp(a.udata[2], b.udata[2])
if tmp2 != 0: return tmp2
let tmp3 = cmp(a.udata[1], b.udata[1])
if tmp3 != 0: return tmp3
let tmp4 = cmp(a.udata[0], b.udata[0])
return tmp4
proc `<`*(a,b: Int128): bool =
cmp(a,b) < 0
proc `<=`*(a,b: Int128): bool =
cmp(a,b) <= 0
proc `==`*(a,b: Int128): bool =
if a.udata[0] != b.udata[0]: return false
if a.udata[1] != b.udata[1]: return false
if a.udata[2] != b.udata[2]: return false
if a.udata[3] != b.udata[3]: return false
return true
proc inplaceBitnot(a: var Int128) =
a.udata[0] = not a.udata[0]
a.udata[1] = not a.udata[1]
a.udata[2] = not a.udata[2]
a.udata[3] = not a.udata[3]
proc bitnot*(a: Int128): Int128 =
result.udata[0] = not a.udata[0]
result.udata[1] = not a.udata[1]
result.udata[2] = not a.udata[2]
result.udata[3] = not a.udata[3]
proc bitand*(a,b: Int128): Int128 =
result.udata[0] = a.udata[0] and b.udata[0]
result.udata[1] = a.udata[1] and b.udata[1]
result.udata[2] = a.udata[2] and b.udata[2]
result.udata[3] = a.udata[3] and b.udata[3]
proc bitor*(a,b: Int128): Int128 =
result.udata[0] = a.udata[0] or b.udata[0]
result.udata[1] = a.udata[1] or b.udata[1]
result.udata[2] = a.udata[2] or b.udata[2]
result.udata[3] = a.udata[3] or b.udata[3]
proc bitxor*(a,b: Int128): Int128 =
result.udata[0] = a.udata[0] xor b.udata[0]
result.udata[1] = a.udata[1] xor b.udata[1]
result.udata[2] = a.udata[2] xor b.udata[2]
result.udata[3] = a.udata[3] xor b.udata[3]
proc `shr`*(a: Int128, b: int): Int128 =
let b = b and 127
if b < 32:
result.sdata(3) = a.sdata(3) shr b
result.udata[2] = cast[uint32](bitconcat(a.udata[3], a.udata[2]) shr b)
result.udata[1] = cast[uint32](bitconcat(a.udata[2], a.udata[1]) shr b)
result.udata[0] = cast[uint32](bitconcat(a.udata[1], a.udata[0]) shr b)
elif b < 64:
if isNegative(a):
result.sdata(3) = -1
result.sdata(2) = a.sdata(3) shr (b and 31)
result.udata[1] = cast[uint32](bitconcat(a.udata[3], a.udata[2]) shr (b and 31))
result.udata[0] = cast[uint32](bitconcat(a.udata[2], a.udata[1]) shr (b and 31))
elif b < 96:
if isNegative(a):
result.sdata(3) = -1
result.sdata(2) = -1
result.sdata(1) = a.sdata(3) shr (b and 31)
result.udata[0] = cast[uint32](bitconcat(a.udata[3], a.udata[2]) shr (b and 31))
else: # b < 128
if isNegative(a):
result.sdata(3) = -1
result.sdata(2) = -1
result.sdata(1) = -1
result.sdata(0) = a.sdata(3) shr (b and 31)
proc `shl`*(a: Int128, b: int): Int128 =
let b = b and 127
if b < 32:
result.udata[0] = a.udata[0] shl b
result.udata[1] = cast[uint32]((bitconcat(a.udata[1], a.udata[0]) shl b) shr 32)
result.udata[2] = cast[uint32]((bitconcat(a.udata[2], a.udata[1]) shl b) shr 32)
result.udata[3] = cast[uint32]((bitconcat(a.udata[3], a.udata[2]) shl b) shr 32)
elif b < 64:
result.udata[0] = 0
result.udata[1] = a.udata[0] shl (b and 31)
result.udata[2] = cast[uint32]((bitconcat(a.udata[1], a.udata[0]) shl (b and 31)) shr 32)
result.udata[3] = cast[uint32]((bitconcat(a.udata[2], a.udata[1]) shl (b and 31)) shr 32)
elif b < 96:
result.udata[0] = 0
result.udata[1] = 0
result.udata[2] = a.udata[0] shl (b and 31)
result.udata[3] = cast[uint32]((bitconcat(a.udata[1], a.udata[0]) shl (b and 31)) shr 32)
else:
result.udata[0] = 0
result.udata[1] = 0
result.udata[2] = 0
result.udata[3] = a.udata[0] shl (b and 31)
proc `+`*(a,b: Int128): Int128 =
let tmp0 = uint64(a.udata[0]) + uint64(b.udata[0])
result.udata[0] = cast[uint32](tmp0)
let tmp1 = uint64(a.udata[1]) + uint64(b.udata[1]) + (tmp0 shr 32)
result.udata[1] = cast[uint32](tmp1)
let tmp2 = uint64(a.udata[2]) + uint64(b.udata[2]) + (tmp1 shr 32)
result.udata[2] = cast[uint32](tmp2)
let tmp3 = uint64(a.udata[3]) + uint64(b.udata[3]) + (tmp2 shr 32)
result.udata[3] = cast[uint32](tmp3)
proc `+=`*(a: var Int128, b: Int128) =
a = a + b
proc `-`*(a: Int128): Int128 =
result = bitnot(a)
result.inc
proc `-`*(a,b: Int128): Int128 =
a + (-b)
proc `-=`*(a: var Int128, b: Int128) =
a = a - b
proc abs*(a: Int128): Int128 =
if isNegative(a):
-a
else:
a
proc abs(a: int32): int =
if a < 0: -a else: a
proc `*`(a: Int128, b: uint32): Int128 =
let tmp0 = uint64(a.udata[0]) * uint64(b)
let tmp1 = uint64(a.udata[1]) * uint64(b)
let tmp2 = uint64(a.udata[2]) * uint64(b)
let tmp3 = uint64(a.udata[3]) * uint64(b)
if unlikely(tmp3 > uint64(high(int32))):
assert(false, "overflow")
result.udata[0] = cast[uint32](tmp0)
result.udata[1] = cast[uint32](tmp1) + cast[uint32](tmp0 shr 32)
result.udata[2] = cast[uint32](tmp2) + cast[uint32](tmp1 shr 32)
result.udata[3] = cast[uint32](tmp3) + cast[uint32](tmp2 shr 32)
proc `*`*(a: Int128, b: int32): Int128 =
result = a * cast[uint32](abs(b))
if b < 0:
result = -result
proc `*=`*(a: var Int128, b: int32): Int128 =
result = result * b
proc makeInt128(high,low: uint64): Int128 =
result.udata[0] = cast[uint32](low)
result.udata[1] = cast[uint32](low shr 32)
result.udata[2] = cast[uint32](high)
result.udata[3] = cast[uint32](high shr 32)
proc high64(a: Int128): uint64 =
bitconcat(a.udata[3], a.udata[2])
proc low64(a: Int128): uint64 =
bitconcat(a.udata[1], a.udata[0])
proc `*`*(lhs,rhs: Int128): Int128 =
let
a = cast[uint64](lhs.udata[0])
b = cast[uint64](lhs.udata[1])
c = cast[uint64](lhs.udata[2])
d = cast[uint64](lhs.udata[3])
e = cast[uint64](rhs.udata[0])
f = cast[uint64](rhs.udata[1])
g = cast[uint64](rhs.udata[2])
h = cast[uint64](rhs.udata[3])
let a32 = cast[uint64](lhs.udata[1])
let a00 = cast[uint64](lhs.udata[0])
let b32 = cast[uint64](rhs.udata[1])
let b00 = cast[uint64](rhs.udata[0])
result = makeInt128(high64(lhs) * low64(rhs) + low64(lhs) * high64(rhs) + a32 * b32, a00 * b00)
result = result + toInt128(a32 * b00) shl 32
result = result + toInt128(a00 * b32) shl 32
proc `*=`*(a: var Int128, b: Int128) =
a = a * b
import bitops
proc fastLog2*(a: Int128): int =
if a.udata[3] != 0:
return 96 + fastLog2(a.udata[3])
if a.udata[2] != 0:
return 64 + fastLog2(a.udata[2])
if a.udata[1] != 0:
return 32 + fastLog2(a.udata[1])
if a.udata[0] != 0:
return fastLog2(a.udata[0])
proc divMod*(dividend, divisor: Int128): tuple[quotient, remainder: Int128] =
assert(divisor != Zero)
let isNegativeA = isNegative(dividend)
let isNegativeB = isNegative(divisor)
var dividend = abs(dividend)
let divisor = abs(divisor)
if divisor > dividend:
result.quotient = Zero
if isNegativeA:
result.remainder = -dividend
else:
result.remainder = dividend
return
if divisor == dividend:
if isNegativeA xor isNegativeB:
result.quotient = NegOne
else:
result.quotient = One
result.remainder = Zero
return
var denominator = divisor
var quotient = Zero
# Left aligns the MSB of the denominator and the dividend.
let shift = fastLog2(dividend) - fastLog2(denominator)
denominator = denominator shl shift
# Uses shift-subtract algorithm to divide dividend by denominator. The
# remainder will be left in dividend.
for i in 0..shift:
quotient = quotient shl 1
if dividend >= denominator:
dividend = dividend - denominator
quotient = bitor(quotient, One)
denominator = denominator shr 1
if isNegativeA xor isNegativeB:
result.quotient = -quotient
else:
result.quotient = quotient
if isNegativeA:
result.remainder = -dividend
else:
result.remainder = dividend
proc `div`*(a,b: Int128): Int128 =
let (a,b) = divMod(a,b)
return a
proc `mod`*(a,b: Int128): Int128 =
let (a,b) = divMod(a,b)
return b
proc addInt128*(result: var string; value: Int128) =
let initialSize = result.len
if value == Zero:
result.add "0"
elif value == low(Int128):
result.add "-170141183460469231731687303715884105728"
else:
let isNegative = isNegative(value)
var value = abs(value)
while value > Zero:
let (quot, rem) = divMod(value, Ten)
result.add "0123456789"[rem.toInt64]
value = quot
if isNegative:
result.add '-'
var i = initialSize
var j = high(result)
while i < j:
swap(result[i], result[j])
i += 1
j -= 1
proc `$`*(a: Int128): string =
result.addInt128(a)
proc parseDecimalInt128*(arg: string, pos: int = 0): Int128 =
assert(pos < arg.len)
assert(arg[pos] in {'-','0'..'9'})
var isNegative = false
var pos = pos
if arg[pos] == '-':
isNegative = true
pos += 1
result = Zero
while pos < arg.len and arg[pos] in '0'..'9':
result = result * Ten
result.inc(uint32(arg[pos]) - uint32('0'))
pos += 1
if isNegative:
result = -result
# fluff
proc `<`*(a: Int128, b: BiggestInt): bool =
cmp(a,toInt128(b)) < 0
proc `<`*(a: BiggestInt, b: Int128): bool =
cmp(toInt128(a), b) < 0
proc `<=`*(a: Int128, b: BiggestInt): bool =
cmp(a,toInt128(b)) <= 0
proc `<=`*(a: BiggestInt, b: Int128): bool =
cmp(toInt128(a), b) <= 0
proc `==`*(a: Int128, b: BiggestInt): bool =
a == toInt128(b)
proc `==`*(a: BiggestInt, b: Int128): bool =
toInt128(a) == b
proc `-`*(a: BiggestInt, b: Int128): Int128 =
toInt128(a) - b
proc `-`*(a: Int128, b: BiggestInt): Int128 =
a - toInt128(b)
proc `+`*(a: BiggestInt, b: Int128): Int128 =
toInt128(a) + b
proc `+`*(a: Int128, b: BiggestInt): Int128 =
a + toInt128(b)
proc toFloat64*(arg: Int128): float64 =
let isNegative = isNegative(arg)
let arg = abs(arg)
let a = float64(bitconcat(arg.udata[1], arg.udata[0]))
let b = float64(bitconcat(arg.udata[3], arg.udata[2]))
result = a + 18446744073709551616'f64 * b # a + 2^64 * b
if isNegative:
result = -result
proc ldexp(x: float64, exp: cint): float64 {.importc: "ldexp", header: "<math.h>".}
template bitor(a,b,c: Int128): Int128 = bitor(bitor(a,b), c)
proc toInt128*(arg: float64): Int128 =
let isNegative = arg < 0
let v0 = ldexp(abs(arg), -100)
let w0 = uint64(trunc(v0))
let v1 = ldexp(v0 - float64(w0), 50)
let w1 = uint64(trunc(v1))
let v2 = ldexp(v1 - float64(w1), 50)
let w2 = uint64(trunc(v2))
let res = bitor(toInt128(w0) shl 100, toInt128(w1) shl 50, toInt128(w2))
if isNegative:
return -res
else:
return res
proc maskUInt64*(arg: Int128): Int128 {.noinit, inline.} =
result.udata[0] = arg.udata[0]
result.udata[1] = arg.udata[1]
result.udata[2] = 0
result.udata[3] = 0
proc maskUInt32*(arg: Int128): Int128 {.noinit, inline.} =
result.udata[0] = arg.udata[0]
result.udata[1] = 0
result.udata[2] = 0
result.udata[3] = 0
proc maskUInt16*(arg: Int128): Int128 {.noinit, inline.} =
result.udata[0] = arg.udata[0] and 0xffff
result.udata[1] = 0
result.udata[2] = 0
result.udata[3] = 0
proc maskUInt8*(arg: Int128): Int128 {.noinit, inline.} =
result.udata[0] = arg.udata[0] and 0xff
result.udata[1] = 0
result.udata[2] = 0
result.udata[3] = 0
proc maskBytes*(arg: Int128, numbytes: int): Int128 {.noinit.} =
case numbytes
of 1:
return maskUInt8(arg)
of 2:
return maskUInt16(arg)
of 4:
return maskUInt32(arg)
of 8:
return maskUInt64(arg)
else:
assert(false, "masking only implemented for 1, 2, 4 and 8 bytes")
when isMainModule:
let (a,b) = divMod(Ten,Ten)
doAssert $One == "1"
doAssert $Ten == "10"
doAssert $Zero == "0"
let c = parseDecimalInt128("12345678989876543210123456789")
doAssert $c == "12345678989876543210123456789"
var d : array[39, Int128]
d[0] = parseDecimalInt128("1")
d[1] = parseDecimalInt128("10")
d[2] = parseDecimalInt128("100")
d[3] = parseDecimalInt128("1000")
d[4] = parseDecimalInt128("10000")
d[5] = parseDecimalInt128("100000")
d[6] = parseDecimalInt128("1000000")
d[7] = parseDecimalInt128("10000000")
d[8] = parseDecimalInt128("100000000")
d[9] = parseDecimalInt128("1000000000")
d[10] = parseDecimalInt128("10000000000")
d[11] = parseDecimalInt128("100000000000")
d[12] = parseDecimalInt128("1000000000000")
d[13] = parseDecimalInt128("10000000000000")
d[14] = parseDecimalInt128("100000000000000")
d[15] = parseDecimalInt128("1000000000000000")
d[16] = parseDecimalInt128("10000000000000000")
d[17] = parseDecimalInt128("100000000000000000")
d[18] = parseDecimalInt128("1000000000000000000")
d[19] = parseDecimalInt128("10000000000000000000")
d[20] = parseDecimalInt128("100000000000000000000")
d[21] = parseDecimalInt128("1000000000000000000000")
d[22] = parseDecimalInt128("10000000000000000000000")
d[23] = parseDecimalInt128("100000000000000000000000")
d[24] = parseDecimalInt128("1000000000000000000000000")
d[25] = parseDecimalInt128("10000000000000000000000000")
d[26] = parseDecimalInt128("100000000000000000000000000")
d[27] = parseDecimalInt128("1000000000000000000000000000")
d[28] = parseDecimalInt128("10000000000000000000000000000")
d[29] = parseDecimalInt128("100000000000000000000000000000")
d[30] = parseDecimalInt128("1000000000000000000000000000000")
d[31] = parseDecimalInt128("10000000000000000000000000000000")
d[32] = parseDecimalInt128("100000000000000000000000000000000")
d[33] = parseDecimalInt128("1000000000000000000000000000000000")
d[34] = parseDecimalInt128("10000000000000000000000000000000000")
d[35] = parseDecimalInt128("100000000000000000000000000000000000")
d[36] = parseDecimalInt128("1000000000000000000000000000000000000")
d[37] = parseDecimalInt128("10000000000000000000000000000000000000")
d[38] = parseDecimalInt128("100000000000000000000000000000000000000")
for i in 0..<d.len:
for j in 0..<d.len:
doAssert(cmp(d[i], d[j]) == cmp(i,j))
if i + j < d.len:
doAssert d[i] * d[j] == d[i+j]
if i - j >= 0:
doAssert d[i] div d[j] == d[i-j]
var sum: Int128
for it in d:
sum += it
doAssert $sum == "111111111111111111111111111111111111111"
for it in d.mitems:
it = -it
for i in 0..<d.len:
for j in 0..<d.len:
doAssert(cmp(d[i], d[j]) == -cmp(i,j))
if i + j < d.len:
doAssert d[i] * d[j] == -d[i+j]
if i - j >= 0:
doAssert d[i] div d[j] == -d[i-j]
doAssert $high(Int128) == "170141183460469231731687303715884105727"
doAssert $low(Int128) == "-170141183460469231731687303715884105728"
var ma = 100'i64
var mb = 13
doAssert toInt128(ma) * toInt128(0) == toInt128(0)
doAssert toInt128(-ma) * toInt128(0) == toInt128(0)
# sign correctness
doAssert divMod(toInt128( ma),toInt128( mb)) == (toInt128( ma div mb), toInt128( ma mod mb))
doAssert divMod(toInt128(-ma),toInt128( mb)) == (toInt128(-ma div mb), toInt128(-ma mod mb))
doAssert divMod(toInt128( ma),toInt128(-mb)) == (toInt128( ma div -mb), toInt128( ma mod -mb))
doAssert divMod(toInt128(-ma),toInt128(-mb)) == (toInt128(-ma div -mb), toInt128(-ma mod -mb))
doAssert divMod(toInt128( mb),toInt128( mb)) == (toInt128( mb div mb), toInt128( mb mod mb))
doAssert divMod(toInt128(-mb),toInt128( mb)) == (toInt128(-mb div mb), toInt128(-mb mod mb))
doAssert divMod(toInt128( mb),toInt128(-mb)) == (toInt128( mb div -mb), toInt128( mb mod -mb))
doAssert divMod(toInt128(-mb),toInt128(-mb)) == (toInt128(-mb div -mb), toInt128(-mb mod -mb))
doAssert divMod(toInt128( mb),toInt128( ma)) == (toInt128( mb div ma), toInt128( mb mod ma))
doAssert divMod(toInt128(-mb),toInt128( ma)) == (toInt128(-mb div ma), toInt128(-mb mod ma))
doAssert divMod(toInt128( mb),toInt128(-ma)) == (toInt128( mb div -ma), toInt128( mb mod -ma))
doAssert divMod(toInt128(-mb),toInt128(-ma)) == (toInt128(-mb div -ma), toInt128(-mb mod -ma))
let e = parseDecimalInt128("70997106675279150998592376708984375")
let strArray = [
# toHex(e shr 0), toHex(e shr 1), toHex(e shr 2), toHex(e shr 3)
"000dac6d782d266a37300c32591eee37", "0006d636bc1693351b9806192c8f771b", "00036b1b5e0b499a8dcc030c9647bb8d", "0001b58daf05a4cd46e601864b23ddc6",
"0000dac6d782d266a37300c32591eee3", "00006d636bc1693351b9806192c8f771", "000036b1b5e0b499a8dcc030c9647bb8", "00001b58daf05a4cd46e601864b23ddc",
"00000dac6d782d266a37300c32591eee", "000006d636bc1693351b9806192c8f77", "0000036b1b5e0b499a8dcc030c9647bb", "000001b58daf05a4cd46e601864b23dd",
"000000dac6d782d266a37300c32591ee", "0000006d636bc1693351b9806192c8f7", "00000036b1b5e0b499a8dcc030c9647b", "0000001b58daf05a4cd46e601864b23d",
"0000000dac6d782d266a37300c32591e", "00000006d636bc1693351b9806192c8f", "000000036b1b5e0b499a8dcc030c9647", "00000001b58daf05a4cd46e601864b23",
"00000000dac6d782d266a37300c32591", "000000006d636bc1693351b9806192c8", "0000000036b1b5e0b499a8dcc030c964", "000000001b58daf05a4cd46e601864b2",
"000000000dac6d782d266a37300c3259", "0000000006d636bc1693351b9806192c", "00000000036b1b5e0b499a8dcc030c96", "0000000001b58daf05a4cd46e601864b",
"0000000000dac6d782d266a37300c325", "00000000006d636bc1693351b9806192", "000000000036b1b5e0b499a8dcc030c9", "00000000001b58daf05a4cd46e601864",
"00000000000dac6d782d266a37300c32", "000000000006d636bc1693351b980619", "0000000000036b1b5e0b499a8dcc030c", "000000000001b58daf05a4cd46e60186",
"000000000000dac6d782d266a37300c3", "0000000000006d636bc1693351b98061", "00000000000036b1b5e0b499a8dcc030", "0000000000001b58daf05a4cd46e6018",
"0000000000000dac6d782d266a37300c", "00000000000006d636bc1693351b9806", "000000000000036b1b5e0b499a8dcc03", "00000000000001b58daf05a4cd46e601",
"00000000000000dac6d782d266a37300", "000000000000006d636bc1693351b980", "0000000000000036b1b5e0b499a8dcc0", "000000000000001b58daf05a4cd46e60",
"000000000000000dac6d782d266a3730", "0000000000000006d636bc1693351b98", "00000000000000036b1b5e0b499a8dcc", "0000000000000001b58daf05a4cd46e6",
"0000000000000000dac6d782d266a373", "00000000000000006d636bc1693351b9", "000000000000000036b1b5e0b499a8dc", "00000000000000001b58daf05a4cd46e",
"00000000000000000dac6d782d266a37", "000000000000000006d636bc1693351b", "0000000000000000036b1b5e0b499a8d", "000000000000000001b58daf05a4cd46",
"000000000000000000dac6d782d266a3", "0000000000000000006d636bc1693351", "00000000000000000036b1b5e0b499a8", "0000000000000000001b58daf05a4cd4",
"0000000000000000000dac6d782d266a", "00000000000000000006d636bc169335", "000000000000000000036b1b5e0b499a", "00000000000000000001b58daf05a4cd",
"00000000000000000000dac6d782d266", "000000000000000000006d636bc16933", "0000000000000000000036b1b5e0b499", "000000000000000000001b58daf05a4c",
"000000000000000000000dac6d782d26", "0000000000000000000006d636bc1693", "00000000000000000000036b1b5e0b49", "0000000000000000000001b58daf05a4",
"0000000000000000000000dac6d782d2", "00000000000000000000006d636bc169", "000000000000000000000036b1b5e0b4", "00000000000000000000001b58daf05a",
"00000000000000000000000dac6d782d", "000000000000000000000006d636bc16", "0000000000000000000000036b1b5e0b", "000000000000000000000001b58daf05",
"000000000000000000000000dac6d782", "0000000000000000000000006d636bc1", "00000000000000000000000036b1b5e0", "0000000000000000000000001b58daf0",
"0000000000000000000000000dac6d78", "00000000000000000000000006d636bc", "000000000000000000000000036b1b5e", "00000000000000000000000001b58daf",
"00000000000000000000000000dac6d7", "000000000000000000000000006d636b", "0000000000000000000000000036b1b5", "000000000000000000000000001b58da",
"000000000000000000000000000dac6d", "0000000000000000000000000006d636", "00000000000000000000000000036b1b", "0000000000000000000000000001b58d",
"0000000000000000000000000000dac6", "00000000000000000000000000006d63", "000000000000000000000000000036b1", "00000000000000000000000000001b58",
"00000000000000000000000000000dac", "000000000000000000000000000006d6", "0000000000000000000000000000036b", "000000000000000000000000000001b5",
"000000000000000000000000000000da", "0000000000000000000000000000006d", "00000000000000000000000000000036", "0000000000000000000000000000001b",
"0000000000000000000000000000000d", "00000000000000000000000000000006", "00000000000000000000000000000003", "00000000000000000000000000000001",
"00000000000000000000000000000000", "00000000000000000000000000000000", "00000000000000000000000000000000", "00000000000000000000000000000000",
"00000000000000000000000000000000", "00000000000000000000000000000000", "00000000000000000000000000000000", "00000000000000000000000000000000",
"00000000000000000000000000000000", "00000000000000000000000000000000", "00000000000000000000000000000000", "00000000000000000000000000000000",
]
for i in 0 ..< 128:
let str1 = toHex(e shr i)
let str2 = strArray[i]
doAssert str1 == str2
let strArray2 = [
"000dac6d782d266a37300c32591eee37", "001b58daf05a4cd46e601864b23ddc6e", "0036b1b5e0b499a8dcc030c9647bb8dc", "006d636bc1693351b9806192c8f771b8",
"00dac6d782d266a37300c32591eee370", "01b58daf05a4cd46e601864b23ddc6e0", "036b1b5e0b499a8dcc030c9647bb8dc0", "06d636bc1693351b9806192c8f771b80",
"0dac6d782d266a37300c32591eee3700", "1b58daf05a4cd46e601864b23ddc6e00", "36b1b5e0b499a8dcc030c9647bb8dc00", "6d636bc1693351b9806192c8f771b800",
"dac6d782d266a37300c32591eee37000", "b58daf05a4cd46e601864b23ddc6e000", "6b1b5e0b499a8dcc030c9647bb8dc000", "d636bc1693351b9806192c8f771b8000",
"ac6d782d266a37300c32591eee370000", "58daf05a4cd46e601864b23ddc6e0000", "b1b5e0b499a8dcc030c9647bb8dc0000", "636bc1693351b9806192c8f771b80000",
"c6d782d266a37300c32591eee3700000", "8daf05a4cd46e601864b23ddc6e00000", "1b5e0b499a8dcc030c9647bb8dc00000", "36bc1693351b9806192c8f771b800000",
"6d782d266a37300c32591eee37000000", "daf05a4cd46e601864b23ddc6e000000", "b5e0b499a8dcc030c9647bb8dc000000", "6bc1693351b9806192c8f771b8000000",
"d782d266a37300c32591eee370000000", "af05a4cd46e601864b23ddc6e0000000", "5e0b499a8dcc030c9647bb8dc0000000", "bc1693351b9806192c8f771b80000000",
"782d266a37300c32591eee3700000000", "f05a4cd46e601864b23ddc6e00000000", "e0b499a8dcc030c9647bb8dc00000000", "c1693351b9806192c8f771b800000000",
"82d266a37300c32591eee37000000000", "05a4cd46e601864b23ddc6e000000000", "0b499a8dcc030c9647bb8dc000000000", "1693351b9806192c8f771b8000000000",
"2d266a37300c32591eee370000000000", "5a4cd46e601864b23ddc6e0000000000", "b499a8dcc030c9647bb8dc0000000000", "693351b9806192c8f771b80000000000",
"d266a37300c32591eee3700000000000", "a4cd46e601864b23ddc6e00000000000", "499a8dcc030c9647bb8dc00000000000", "93351b9806192c8f771b800000000000",
"266a37300c32591eee37000000000000", "4cd46e601864b23ddc6e000000000000", "99a8dcc030c9647bb8dc000000000000", "3351b9806192c8f771b8000000000000",
"66a37300c32591eee370000000000000", "cd46e601864b23ddc6e0000000000000", "9a8dcc030c9647bb8dc0000000000000", "351b9806192c8f771b80000000000000",
"6a37300c32591eee3700000000000000", "d46e601864b23ddc6e00000000000000", "a8dcc030c9647bb8dc00000000000000", "51b9806192c8f771b800000000000000",
"a37300c32591eee37000000000000000", "46e601864b23ddc6e000000000000000", "8dcc030c9647bb8dc000000000000000", "1b9806192c8f771b8000000000000000",
"37300c32591eee370000000000000000", "6e601864b23ddc6e0000000000000000", "dcc030c9647bb8dc0000000000000000", "b9806192c8f771b80000000000000000",
"7300c32591eee3700000000000000000", "e601864b23ddc6e00000000000000000", "cc030c9647bb8dc00000000000000000", "9806192c8f771b800000000000000000",
"300c32591eee37000000000000000000", "601864b23ddc6e000000000000000000", "c030c9647bb8dc000000000000000000", "806192c8f771b8000000000000000000",
"00c32591eee370000000000000000000", "01864b23ddc6e0000000000000000000", "030c9647bb8dc0000000000000000000", "06192c8f771b80000000000000000000",
"0c32591eee3700000000000000000000", "1864b23ddc6e00000000000000000000", "30c9647bb8dc00000000000000000000", "6192c8f771b800000000000000000000",
"c32591eee37000000000000000000000", "864b23ddc6e000000000000000000000", "0c9647bb8dc000000000000000000000", "192c8f771b8000000000000000000000",
"32591eee370000000000000000000000", "64b23ddc6e0000000000000000000000", "c9647bb8dc0000000000000000000000", "92c8f771b80000000000000000000000",
"2591eee3700000000000000000000000", "4b23ddc6e00000000000000000000000", "9647bb8dc00000000000000000000000", "2c8f771b800000000000000000000000",
"591eee37000000000000000000000000", "b23ddc6e000000000000000000000000", "647bb8dc000000000000000000000000", "c8f771b8000000000000000000000000",
"91eee370000000000000000000000000", "23ddc6e0000000000000000000000000", "47bb8dc0000000000000000000000000", "8f771b80000000000000000000000000",
"1eee3700000000000000000000000000", "3ddc6e00000000000000000000000000", "7bb8dc00000000000000000000000000", "f771b800000000000000000000000000",
"eee37000000000000000000000000000", "ddc6e000000000000000000000000000", "bb8dc000000000000000000000000000", "771b8000000000000000000000000000",
"ee370000000000000000000000000000", "dc6e0000000000000000000000000000", "b8dc0000000000000000000000000000", "71b80000000000000000000000000000",
"e3700000000000000000000000000000", "c6e00000000000000000000000000000", "8dc00000000000000000000000000000", "1b800000000000000000000000000000",
"37000000000000000000000000000000", "6e000000000000000000000000000000", "dc000000000000000000000000000000", "b8000000000000000000000000000000",
"70000000000000000000000000000000", "e0000000000000000000000000000000", "c0000000000000000000000000000000", "80000000000000000000000000000000",
]
for i in 0 ..< 128:
let str1 = toHex(e shl i)
let str2 = strArray2[i]
doAssert str1 == str2