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Merge pull request #12 from raverkamp/master

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replaced divsion code
This commit is contained in:
Victor Quinn 2017-01-30 10:08:29 -05:00 committed by GitHub
commit ea75adedfe
2 changed files with 334 additions and 13 deletions
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83
decimal.go
View file

@ -281,18 +281,81 @@ func (d Decimal) Mul(d2 Decimal) Decimal {
// Div returns d / d2. If it doesn't divide exactly, the result will have
// DivisionPrecision digits after the decimal point.
func (d Decimal) Div(d2 Decimal) Decimal {
// NOTE(vadim): division is hard, use Rat to do it
ratNum := d.Rat()
ratDenom := d2.Rat()
return d.DivRound(d2, int32(DivisionPrecision))
}
quoRat := big.NewRat(0, 1).Quo(ratNum, ratDenom)
// HACK(vadim): converting from Rat to Decimal inefficiently for now
ret, err := NewFromString(quoRat.FloatString(DivisionPrecision))
if err != nil {
panic(err) // this should never happen
// QuoRem does divsion with remainder
// d.QuoRem(d2,precision) returns quotient q and remainder r such that
// d = d2 * q + r, q an integer multiple of 10^(-precision)
// 0 <= r < abs(d2) * 10 ^(-precision) if d>=0
// 0 >= r > -abs(d2) * 10 ^(-precision) if d<0
// Note that precision<0 is allowed as input.
func (d Decimal) QuoRem(d2 Decimal, precision int32) (Decimal, Decimal) {
d.ensureInitialized()
d2.ensureInitialized()
if d2.value.Sign() == 0 {
panic("decimal division by 0")
}
scale := -precision
e := int64(d.exp - d2.exp - scale)
if e > math.MaxInt32 || e < math.MinInt32 {
panic("overflow in decimal QuoRem")
}
var aa, bb, expo big.Int
var scalerest int32
// d = a 10^ea
// d2 = b 10^eb
if e < 0 {
aa = *d.value
expo.SetInt64(-e)
bb.Exp(tenInt, &expo, nil)
bb.Mul(d2.value, &bb)
scalerest = d.exp
// now aa = a
// bb = b 10^(scale + eb - ea)
} else {
expo.SetInt64(e)
aa.Exp(tenInt, &expo, nil)
aa.Mul(d.value, &aa)
bb = *d2.value
scalerest = scale + d2.exp
// now aa = a ^ (ea - eb - scale)
// bb = b
}
var q, r big.Int
q.QuoRem(&aa, &bb, &r)
dq := Decimal{value: &q, exp: scale}
dr := Decimal{value: &r, exp: scalerest}
return dq, dr
}
// DivRound divides and rounds to a given precision
// i.e. to an integer multiple of 10^(-precision)
// for a positive quotient digit 5 is rounded up, away from 0
// if the quotient is negative then digit 5 is rounded down, away from 0
// Note that precision<0 is allowed as input.
func (d Decimal) DivRound(d2 Decimal, precision int32) Decimal {
// QuoRem already checks initialization
q, r := d.QuoRem(d2, precision)
// the actual rounding decision is based on comparing r*10^precision and d2/2
// instead compare 2 r 10 ^precision and d2
var rv2 big.Int
rv2.Abs(r.value)
rv2.Lsh(&rv2, 1)
// now rv2 = abs(r.value) * 2
r2 := Decimal{value: &rv2, exp: r.exp + precision}
// r2 is now 2 * r * 10 ^ precision
var c = r2.Cmp(d2.Abs())
if c < 0 {
return q
} else {
if d.value.Sign()*d2.value.Sign() < 0 {
return q.Sub(New(1, -precision))
} else {
return q.Add(New(1, -precision))
}
}
return ret
}
// Mod returns d % d2.

264
decimal_test.go
View file

@ -4,6 +4,7 @@ import (
"encoding/json"
"encoding/xml"
"math"
"math/big"
"sort"
"strconv"
"strings"
@ -643,7 +644,7 @@ func TestDecimal_Div(t *testing.T) {
Inp{"-4612301402398.4753343454", "23.5"}: "-196268144782.9138440146978723",
}
for inp, expected := range inputs {
for inp, expectedStr := range inputs {
num, err := NewFromString(inp.a)
if err != nil {
t.FailNow()
@ -653,10 +654,15 @@ func TestDecimal_Div(t *testing.T) {
t.FailNow()
}
got := num.Div(denom)
if got.String() != expected {
t.Errorf("expected %s when dividing %v by %v, got %v",
expected, _ := NewFromString(expectedStr)
if !got.Equals(expected) {
t.Errorf("expected %v when dividing %v by %v, got %v",
expected, num, denom, got)
}
got2 := num.DivRound(denom, int32(DivisionPrecision))
if !got2.Equals(expected) {
t.Errorf("expected %v on DivRound (%v,%v), got %v", expected, num, denom, got2)
}
}
type Inp2 struct {
@ -696,6 +702,258 @@ func TestDecimal_Div(t *testing.T) {
}
}
func TestDecimal_QuoRem(t *testing.T) {
type Inp4 struct {
d string
d2 string
exp int32
q string
r string
}
cases := []Inp4{
Inp4{"10", "1", 0, "10", "0"},
Inp4{"1", "10", 0, "0", "1"},
Inp4{"1", "4", 2, "0.25", "0"},
Inp4{"1", "8", 2, "0.12", "0.04"},
Inp4{"10", "3", 1, "3.3", "0.1"},
Inp4{"100", "3", 1, "33.3", "0.1"},
Inp4{"1000", "10", -3, "0", "1000"},
Inp4{"1e-3", "2e-5", 0, "50", "0"},
Inp4{"1e-3", "2e-3", 1, "0.5", "0"},
Inp4{"4e-3", "0.8", 4, "5e-3", "0"},
Inp4{"4.1e-3", "0.8", 3, "5e-3", "1e-4"},
Inp4{"-4", "-3", 0, "1", "-1"},
Inp4{"-4", "3", 0, "-1", "-1"},
}
for _, inp4 := range cases {
d, _ := NewFromString(inp4.d)
d2, _ := NewFromString(inp4.d2)
prec := inp4.exp
q, r := d.QuoRem(d2, prec)
expectedQ, _ := NewFromString(inp4.q)
expectedR, _ := NewFromString(inp4.r)
if !q.Equals(expectedQ) || !r.Equals(expectedR) {
t.Errorf("bad QuoRem division %s , %s , %d got %v, %v expected %s , %s",
inp4.d, inp4.d2, prec, q, r, inp4.q, inp4.r)
}
if !d.Equals(d2.Mul(q).Add(r)) {
t.Errorf("not fitting: d=%v, d2= %v, prec=%d, q=%v, r=%v",
d, d2, prec, q, r)
}
if !q.Equals(q.Truncate(prec)) {
t.Errorf("quotient wrong precision: d=%v, d2= %v, prec=%d, q=%v, r=%v",
d, d2, prec, q, r)
}
if r.Abs().Cmp(d2.Abs().Mul(New(1, -prec))) >= 0 {
t.Errorf("remainder too large: d=%v, d2= %v, prec=%d, q=%v, r=%v",
d, d2, prec, q, r)
}
if r.value.Sign()*d.value.Sign() < 0 {
t.Errorf("signum of divisor and rest do not match: d=%v, d2= %v, prec=%d, q=%v, r=%v",
d, d2, prec, q, r)
}
}
}
type DivTestCase struct {
d Decimal
d2 Decimal
prec int32
}
func createDivTestCases() []DivTestCase {
res := make([]DivTestCase, 0)
var n int32 = 5
a := []int{1, 2, 3, 6, 7, 10, 100, 14, 5, 400, 0, 1000000, 1000000 + 1, 1000000 - 1}
for s := -1; s < 2; s = s + 2 { // 2
for s2 := -1; s2 < 2; s2 = s2 + 2 { // 2
for e1 := -n; e1 <= n; e1++ { // 2n+1
for e2 := -n; e2 <= n; e2++ { // 2n+1
var prec int32
for prec = -n; prec <= n; prec++ { // 2n+1
for _, v1 := range a { // 11
for _, v2 := range a { // 11, even if 0 is skipped
sign1 := New(int64(s), 0)
sign2 := New(int64(s2), 0)
d := sign1.Mul(New(int64(v1), int32(e1)))
d2 := sign2.Mul(New(int64(v2), int32(e2)))
res = append(res, DivTestCase{d, d2, prec})
}
}
}
}
}
}
}
return res
}
func TestDecimal_QuoRem2(t *testing.T) {
for _, tc := range createDivTestCases() {
d := tc.d
if sign(tc.d2) == 0 {
continue
}
d2 := tc.d2
prec := tc.prec
q, r := d.QuoRem(d2, prec)
// rule 1: d = d2*q +r
if !d.Equals(d2.Mul(q).Add(r)) {
t.Errorf("not fitting, d=%v, d2=%v, prec=%d, q=%v, r=%v",
d, d2, prec, q, r)
}
// rule 2: q is integral multiple of 10^(-prec)
if !q.Equals(q.Truncate(prec)) {
t.Errorf("quotient wrong precision, d=%v, d2=%v, prec=%d, q=%v, r=%v",
d, d2, prec, q, r)
}
// rule 3: abs(r)<abs(d) * 10^(-prec)
if r.Abs().Cmp(d2.Abs().Mul(New(1, -prec))) >= 0 {
t.Errorf("remainder too large, d=%v, d2=%v, prec=%d, q=%v, r=%v",
d, d2, prec, q, r)
}
// rule 4: r and d have the same sign
if r.value.Sign()*d.value.Sign() < 0 {
t.Errorf("signum of divisor and rest do not match, "+
"d=%v, d2=%v, prec=%d, q=%v, r=%v",
d, d2, prec, q, r)
}
}
}
// this is the old Div method from decimal
// Div returns d / d2. If it doesn't divide exactly, the result will have
// DivisionPrecision digits after the decimal point.
func (d Decimal) DivOld(d2 Decimal, prec int) Decimal {
// NOTE(vadim): division is hard, use Rat to do it
ratNum := d.Rat()
ratDenom := d2.Rat()
quoRat := big.NewRat(0, 1).Quo(ratNum, ratDenom)
// HACK(vadim): converting from Rat to Decimal inefficiently for now
ret, err := NewFromString(quoRat.FloatString(prec))
if err != nil {
panic(err) // this should never happen
}
return ret
}
func Benchmark_DivideOriginal(b *testing.B) {
tcs := createDivTestCases()
b.ResetTimer()
for i := 0; i < b.N; i++ {
for _, tc := range tcs {
d := tc.d
if sign(tc.d2) == 0 {
continue
}
d2 := tc.d2
prec := tc.prec
a := d.DivOld(d2, int(prec))
if sign(a) > 2 {
panic("dummy panic")
}
}
}
}
func Benchmark_DivideNew(b *testing.B) {
tcs := createDivTestCases()
b.ResetTimer()
for i := 0; i < b.N; i++ {
for _, tc := range tcs {
d := tc.d
if sign(tc.d2) == 0 {
continue
}
d2 := tc.d2
prec := tc.prec
a := d.DivRound(d2, prec)
if sign(a) > 2 {
panic("dummy panic")
}
}
}
}
func sign(d Decimal) int {
return d.value.Sign()
}
// rules for rounded divide, rounded to integer
// rounded_divide(d,d2) = q
// sign q * sign (d/d2) >= 0
// for d and d2 >0 :
// q is already rounded
// q = d/d2 + r , with r > -0.5 and r <= 0.5
// thus q-d/d2 = r, with r > -0.5 and r <= 0.5
// and d2 q -d = r d2 with r d2 > -d2/2 and r d2 <= d2/2
// and 2 (d2 q -d) = x with x > -d2 and x <= d2
// if we factor in precision then x > -d2 * 10^(-precision) and x <= d2 * 10(-precision)
func TestDecimal_DivRound(t *testing.T) {
cases := []struct {
d string
d2 string
prec int32
result string
}{
{"2", "2", 0, "1"},
{"1", "2", 0, "1"},
{"-1", "2", 0, "-1"},
{"-1", "-2", 0, "1"},
{"1", "-2", 0, "-1"},
{"1", "-20", 1, "-0.1"},
{"1", "-20", 2, "-0.05"},
{"1", "20.0000000000000000001", 1, "0"},
{"1", "19.9999999999999999999", 1, "0.1"},
}
for _, s := range cases {
d, _ := NewFromString(s.d)
d2, _ := NewFromString(s.d2)
result, _ := NewFromString(s.result)
prec := s.prec
q := d.DivRound(d2, prec)
if sign(q)*sign(d)*sign(d2) < 0 {
t.Errorf("sign of quotient wrong, got: %v/%v is about %v", d, d2, q)
}
x := q.Mul(d2).Abs().Sub(d.Abs()).Mul(New(2, 0))
if x.Cmp(d2.Abs().Mul(New(1, -prec))) > 0 {
t.Errorf("wrong rounding, got: %v/%v prec=%d is about %v", d, d2, prec, q)
}
if x.Cmp(d2.Abs().Mul(New(-1, -prec))) <= 0 {
t.Errorf("wrong rounding, got: %v/%v prec=%d is about %v", d, d2, prec, q)
}
if !q.Equals(result) {
t.Errorf("rounded division wrong %s / %s scale %d = %s, got %v", s.d, s.d2, prec, s.result, q)
}
}
}
func TestDecimal_DivRound2(t *testing.T) {
for _, tc := range createDivTestCases() {
d := tc.d
if sign(tc.d2) == 0 {
continue
}
d2 := tc.d2
prec := tc.prec
q := d.DivRound(d2, prec)
if sign(q)*sign(d)*sign(d2) < 0 {
t.Errorf("sign of quotient wrong, got: %v/%v is about %v", d, d2, q)
}
x := q.Mul(d2).Abs().Sub(d.Abs()).Mul(New(2, 0))
if x.Cmp(d2.Abs().Mul(New(1, -prec))) > 0 {
t.Errorf("wrong rounding, got: %v/%v prec=%d is about %v", d, d2, prec, q)
}
if x.Cmp(d2.Abs().Mul(New(-1, -prec))) <= 0 {
t.Errorf("wrong rounding, got: %v/%v prec=%d is about %v", d, d2, prec, q)
}
}
}
func TestDecimal_Mod(t *testing.T) {
type Inp struct {
a string