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rounding.go
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package decimal128
import "fmt"
// Ceil returns the least integer value greater than or equal to d.
//
// Ceil is equivalent to:
//
// d.Ceil(0)
func Ceil(d Decimal) Decimal {
return d.Ceil(0)
}
// Floor returns the greatest integer value less than or equal to d.
//
// Floor is equivalent to:
//
// d.Floor(0)
func Floor(d Decimal) Decimal {
return d.Floor(0)
}
// Round returns the nearest integer, rounding half away from zero.
//
// Round is equivalent to:
//
// d.Round(0, decimal128.ToNearestAway)
func Round(d Decimal) Decimal {
return d.Round(0, ToNearestAway)
}
// Trunc returns the integer value of d.
//
// Trunc is equivalent to:
//
// d.Round(0, decimal128.ToZero)
func Trunc(d Decimal) Decimal {
return d.Round(0, ToZero)
}
// Ceil returns the least Decimal value greater than or equal to d that has no
// digits after the specified number of decimal places.
//
// The value of dp affects how many digits after the decimal point the Decimal
// would have if it were printed in decimal notation (for example, by the '%f'
// verb in Format). It can be zero to return an integer, and can also be
// negative to round off digits before the decimal point.
//
// NaN and infinity values are left untouched.
func (d Decimal) Ceil(dp int) Decimal {
if d.isSpecial() {
return d
}
sig, exp := d.decompose()
if sig[0]|sig[1] == 0 {
return zero(d.Signbit())
}
dp = dp*-1 + exponentBias
iexp := int(exp)
if iexp >= dp {
return d
}
if iexp < dp-maxDigits {
if d.Signbit() {
return zero(d.Signbit())
}
return compose(false, uint128{1, 0}, int16(dp))
}
var trunc int8
for iexp < dp {
var rem uint64
sig, rem = sig.div10()
if rem != 0 {
trunc = 1
}
if sig[0]|sig[1] == 0 {
iexp = dp
break
}
iexp++
}
neg := d.Signbit()
exp = int16(iexp)
if !neg {
for trunc != 0 {
sig = sig.add64(1)
trunc = 0
if sig[1] > 0x0002_7fff_ffff_ffff {
var rem uint64
sig, rem = sig.div10()
if rem != 0 {
trunc = 1
}
exp++
}
}
}
if exp > maxBiasedExponent {
return inf(neg)
}
return compose(neg, sig, exp)
}
// Floor returns the greatest Decimal value less than or equal to d that has no
// digits after the specified number of decimal places.
//
// The value of dp affects how many digits after the decimal point the Decimal
// would have if it were printed in decimal notation (for example, by the '%f'
// verb in Format). It can be zero to return an integer, and can also be
// negative to round off digits before the decimal point.
//
// NaN and infinity values are left untouched.
func (d Decimal) Floor(dp int) Decimal {
if d.isSpecial() {
return d
}
sig, exp := d.decompose()
if sig[0]|sig[1] == 0 {
return zero(d.Signbit())
}
dp = dp*-1 + exponentBias
iexp := int(exp)
if iexp >= dp {
return d
}
if iexp < dp-maxDigits {
if !d.Signbit() {
return zero(d.Signbit())
}
return compose(true, uint128{1, 0}, int16(dp))
}
var trunc int8
for iexp < dp {
var rem uint64
sig, rem = sig.div10()
if rem != 0 {
trunc = 1
}
if sig[0]|sig[1] == 0 {
iexp = dp
break
}
iexp++
}
neg := d.Signbit()
exp = int16(iexp)
if neg {
for trunc != 0 {
sig = sig.add64(1)
trunc = 0
if sig[1] > 0x0002_7fff_ffff_ffff {
var rem uint64
sig, rem = sig.div10()
if rem != 0 {
trunc = 1
}
exp++
}
}
}
if exp > maxBiasedExponent {
return inf(neg)
}
return compose(neg, sig, exp)
}
// Round rounds (or quantises) a Decimal value to the specified number of
// decimal places using the rounding mode provided.
//
// The value of dp affects how many digits after the decimal point the Decimal
// would have if it were printed in decimal notation (for example, by the '%f'
// verb in Format). It can be zero to round off all digits after the decimal
// point and return an integer, and can also be negative to round off digits
// before the decimal point.
//
// NaN and infinity values are left untouched.
func (d Decimal) Round(dp int, mode RoundingMode) Decimal {
if d.isSpecial() {
return d
}
sig, exp := d.decompose()
if sig[0]|sig[1] == 0 {
return zero(d.Signbit())
}
dp = dp*-1 + exponentBias
iexp := int(exp)
if iexp >= dp {
return d
}
if iexp < dp-maxDigits {
return zero(d.Signbit())
}
var trunc int8
var digit uint64
for iexp < dp {
if digit != 0 {
trunc = 1
}
sig, digit = sig.div10()
if sig[0]|sig[1]|digit == 0 {
return zero(d.Signbit())
}
iexp++
}
neg := d.Signbit()
sig, exp = mode.round(false, neg, sig, int16(iexp), trunc, digit)
if exp > maxBiasedExponent {
return inf(neg)
}
return compose(neg, sig, exp)
}
// RoundingMode determines how a Decimal value is rounded when the result of an
// operation is greater than the format can hold.
type RoundingMode uint8
const (
ToNearestEven RoundingMode = iota // == IEEE 754 roundTiesToEven
ToNearestAway // == IEEE 754 roundTiesToAway
ToZero // == IEEE 754 roundTowardZero
AwayFromZero // no IEEE 754 equivalent
ToNegativeInf // == IEEE 754 roundTowardNegative
ToPositiveInf // == IEEE 754 roundTowardPositive
)
// String returns a string representation of the rounding mode.
func (rm RoundingMode) String() string {
switch rm {
case ToNearestEven:
return "ToNearestEven"
case ToNearestAway:
return "ToNearestAway"
case ToZero:
return "ToZero"
case AwayFromZero:
return "AwayFromZero"
case ToNegativeInf:
return "ToNegativeInf"
case ToPositiveInf:
return "ToPositiveInf"
default:
return fmt.Sprintf("RoundingMode(%d)", uint8(rm))
}
}
func (rm RoundingMode) reduce256(neg bool, sig256 uint256, exp int16, trunc int8) (uint128, int16) {
for sig256[3] > 0 {
var rem uint64
sig256, rem = sig256.div1e19()
exp += 19
if rem != 0 {
trunc = 1
}
}
sig192 := uint192{sig256[0], sig256[1], sig256[2]}
if sig192[2] > 10000 {
var rem uint64
sig192, rem = sig192.div1e8()
exp += 8
if rem != 0 {
trunc = 1
}
}
for sig192[2] > 0 {
var rem uint64
sig192, rem = sig192.div10000()
exp += 4
if rem != 0 {
trunc = 1
}
}
sig := uint128{sig192[0], sig192[1]}
var digit uint64
if sig[1] > 0x09c4_0000_0000_0000 {
var rem uint64
sig, rem = sig.div10000()
exp += 4
if rem != 0 {
digit = rem / 1000
if rem%1000 != 0 {
trunc = 1
}
}
} else if sig[1] > 0x00fa_0000_0000_0000 {
var rem uint64
sig, rem = sig.div1000()
exp += 3
if rem != 0 {
digit = rem / 100
if rem%100 != 0 {
trunc = 1
}
}
} else if sig[1] > 0x0019_0000_0000_0000 {
var rem uint64
sig, rem = sig.div100()
exp += 2
if rem != 0 {
digit = rem / 10
if rem%10 != 0 {
trunc = 1
}
}
}
for sig[1] > 0x0002_7fff_ffff_ffff {
if digit != 0 {
trunc = 1
}
sig, digit = sig.div10()
exp++
}
for exp < minBiasedExponent {
if digit != 0 {
trunc = 1
}
sig, digit = sig.div10()
if sig[0]|sig[1]|digit == 0 {
trunc = 0
digit = 0
exp = 0
break
}
exp++
}
for exp > maxBiasedExponent && sig[1] < 0x0002_7fff_ffff_ffff {
tmp := sig.mul64(10)
if tmp[1] <= 0x0002_7fff_ffff_ffff {
sig = tmp
exp--
} else {
break
}
}
return rm.round(true, neg, sig, exp, trunc, digit)
}
func (rm RoundingMode) reduce192(neg bool, sig192 uint192, exp int16, trunc int8) (uint128, int16) {
if sig192[2] > 10000 {
var rem uint64
sig192, rem = sig192.div1e8()
exp += 8
if rem != 0 {
trunc = 1
}
}
for sig192[2] > 0 {
var rem uint64
sig192, rem = sig192.div10000()
exp += 4
if rem != 0 {
trunc = 1
}
}
sig := uint128{sig192[0], sig192[1]}
var digit uint64
if sig[1] > 0x09c4_0000_0000_0000 {
var rem uint64
sig, rem = sig.div10000()
exp += 4
if rem != 0 {
digit = rem / 1000
if rem%1000 != 0 {
trunc = 1
}
}
} else if sig[1] > 0x00fa_0000_0000_0000 {
var rem uint64
sig, rem = sig.div1000()
exp += 3
if rem != 0 {
digit = rem / 100
if rem%100 != 0 {
trunc = 1
}
}
} else if sig[1] > 0x0019_0000_0000_0000 {
var rem uint64
sig, rem = sig.div100()
exp += 2
if rem != 0 {
digit = rem / 10
if rem%10 != 0 {
trunc = 1
}
}
}
for sig[1] > 0x0002_7fff_ffff_ffff {
if digit != 0 {
trunc = 1
}
sig, digit = sig.div10()
exp++
}
for exp < minBiasedExponent {
if digit != 0 {
trunc = 1
}
sig, digit = sig.div10()
if sig[0]|sig[1]|digit == 0 {
trunc = 0
digit = 0
exp = 0
break
}
exp++
}
for exp > maxBiasedExponent && sig[1] < 0x0002_7fff_ffff_ffff {
tmp := sig.mul64(10)
if tmp[1] <= 0x0002_7fff_ffff_ffff {
sig = tmp
exp--
} else {
break
}
}
return rm.round(true, neg, sig, exp, trunc, digit)
}
func (rm RoundingMode) reduce128(neg bool, sig uint128, exp int16, trunc int8) (uint128, int16) {
var digit uint64
if sig[1] > 0x09c4_0000_0000_0000 {
var rem uint64
sig, rem = sig.div10000()
exp += 4
if rem != 0 {
digit = rem / 1000
if rem%1000 != 0 {
trunc = 1
}
}
} else if sig[1] > 0x00fa_0000_0000_0000 {
var rem uint64
sig, rem = sig.div1000()
exp += 3
if rem != 0 {
digit = rem / 100
if rem%100 != 0 {
trunc = 1
}
}
} else if sig[1] > 0x0019_0000_0000_0000 {
var rem uint64
sig, rem = sig.div100()
exp += 2
if rem != 0 {
digit = rem / 10
if rem%10 != 0 {
trunc = 1
}
}
}
for sig[1] > 0x0002_7fff_ffff_ffff {
if digit != 0 {
trunc = 1
}
sig, digit = sig.div10()
exp++
}
for exp < minBiasedExponent {
if digit != 0 {
trunc = 1
}
sig, digit = sig.div10()
if sig[0]|sig[1]|digit == 0 {
trunc = 0
digit = 0
exp = 0
break
}
exp++
}
for exp > maxBiasedExponent && sig[1] < 0x0002_7fff_ffff_ffff {
tmp := sig.mul64(10)
if tmp[1] <= 0x0002_7fff_ffff_ffff {
sig = tmp
exp--
} else {
break
}
}
return rm.round(true, neg, sig, exp, trunc, digit)
}
func (rm RoundingMode) reduce64(neg bool, sig64 uint64, exp int16) (uint128, int16) {
var trunc int8
var digit uint64
for exp < minBiasedExponent {
if digit != 0 {
trunc = 1
}
digit = sig64 % 10
sig64 = sig64 / 10
if sig64|digit == 0 {
trunc = 0
digit = 0
exp = 0
break
}
exp++
}
sig := uint128{sig64, 0}
for exp > maxBiasedExponent && sig[1] < 0x0002_7fff_ffff_ffff {
tmp := sig.mul64(10)
if tmp[1] <= 0x0002_7fff_ffff_ffff {
sig = tmp
exp--
} else {
break
}
}
return rm.round(true, neg, sig, exp, trunc, digit)
}
func (rm RoundingMode) round(shift, neg bool, sig uint128, exp int16, trunc int8, digit uint64) (uint128, int16) {
for {
var adjust int
switch rm {
case ToNearestEven:
if trunc == 1 {
if digit >= 5 {
adjust = 1
}
} else if trunc == -1 {
if digit > 5 {
adjust = 1
}
} else {
if digit > 5 {
adjust = 1
} else if digit == 5 {
if sig[0]%2 != 0 {
adjust = 1
}
}
}
case ToNearestAway:
if digit >= 5 {
adjust = 1
}
case ToZero:
if trunc == -1 && digit == 0 {
adjust = -1
}
case AwayFromZero:
if trunc == 1 || digit != 0 {
adjust = 1
}
case ToPositiveInf:
if neg {
if trunc == -1 && digit == 0 {
adjust = -1
}
} else if trunc == 1 || digit != 0 {
adjust = 1
}
case ToNegativeInf:
if neg {
if trunc == 1 || digit != 0 {
adjust = 1
}
} else if trunc == -1 && digit == 0 {
adjust = -1
}
}
if adjust != 0 {
var tsig uint128
if adjust == 1 {
if shift {
if sig[0]|sig[1] != 0 {
if exp >= minBiasedExponent+19 && sig[1] == 0 {
sig = sig.mul64(10_000_000_000_000_000_000)
exp -= 19
}
for exp > minBiasedExponent && sig[1] < 0x0002_7fff_ffff_ffff/10 {
sig = sig.mul64(10)
exp--
}
} else {
exp = minBiasedExponent
}
shift = false
}
tsig = sig.add64(1)
} else {
if shift {
if sig[0]|sig[1] != 0 {
if exp >= minBiasedExponent+19 && sig[1] == 0 {
sig = sig.mul64(10_000_000_000_000_000_000)
exp -= 19
}
for exp > minBiasedExponent && sig[1] <= 0x0002_7fff_ffff_ffff/10 {
sig = sig.mul64(10)
exp--
}
} else {
exp = minBiasedExponent
}
shift = false
}
tsig = sig.sub64(1)
}
if tsig[1] > 0x0002_7fff_ffff_ffff {
if digit != 0 {
trunc = 1
}
sig, digit = sig.div10()
exp++
continue
}
sig = tsig
}
return sig, exp
}
}
// DefaultRoundingMode is the rounding mode used by any methods where an
// alternate rounding mode isn't provided.
var DefaultRoundingMode RoundingMode = ToNearestEven