2014-04-11 Marc Glisse <marc.glisse@inria.fr>

[official-gcc.git] / libgo / go / strconv / decimal.go

// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

// Multiprecision decimal numbers.
// For floating-point formatting only; not general purpose.
// Only operations are assign and (binary) left/right shift.
// Can do binary floating point in multiprecision decimal precisely
// because 2 divides 10; cannot do decimal floating point
// in multiprecision binary precisely.

package strconv

type decimal struct {
        d     [800]byte // digits
        nd    int       // number of digits used
        dp    int       // decimal point
        neg   bool
        trunc bool // discarded nonzero digits beyond d[:nd]
}

func (a *decimal) String() string {
        n := 10 + a.nd
        if a.dp > 0 {
                n += a.dp
        }
        if a.dp < 0 {
                n += -a.dp
        }

        buf := make([]byte, n)
        w := 0
        switch {
        case a.nd == 0:
                return "0"

        case a.dp <= 0:
                // zeros fill space between decimal point and digits
                buf[w] = '0'
                w++
                buf[w] = '.'
                w++
                w += digitZero(buf[w : w+-a.dp])
                w += copy(buf[w:], a.d[0:a.nd])

        case a.dp < a.nd:
                // decimal point in middle of digits
                w += copy(buf[w:], a.d[0:a.dp])
                buf[w] = '.'
                w++
                w += copy(buf[w:], a.d[a.dp:a.nd])

        default:
                // zeros fill space between digits and decimal point
                w += copy(buf[w:], a.d[0:a.nd])
                w += digitZero(buf[w : w+a.dp-a.nd])
        }
        return string(buf[0:w])
}

func digitZero(dst []byte) int {
        for i := range dst {
                dst[i] = '0'
        }
        return len(dst)
}

// trim trailing zeros from number.
// (They are meaningless; the decimal point is tracked
// independent of the number of digits.)
func trim(a *decimal) {
        for a.nd > 0 && a.d[a.nd-1] == '0' {
                a.nd--
        }
        if a.nd == 0 {
                a.dp = 0
        }
}

// Assign v to a.
func (a *decimal) Assign(v uint64) {
        var buf [24]byte

        // Write reversed decimal in buf.
        n := 0
        for v > 0 {
                v1 := v / 10
                v -= 10 * v1
                buf[n] = byte(v + '0')
                n++
                v = v1
        }

        // Reverse again to produce forward decimal in a.d.
        a.nd = 0
        for n--; n >= 0; n-- {
                a.d[a.nd] = buf[n]
                a.nd++
        }
        a.dp = a.nd
        trim(a)
}

// Maximum shift that we can do in one pass without overflow.
// Signed int has 31 bits, and we have to be able to accommodate 9<<k.
const maxShift = 27

// Binary shift right (* 2) by k bits.  k <= maxShift to avoid overflow.
func rightShift(a *decimal, k uint) {
        r := 0 // read pointer
        w := 0 // write pointer

        // Pick up enough leading digits to cover first shift.
        n := 0
        for ; n>>k == 0; r++ {
                if r >= a.nd {
                        if n == 0 {
                                // a == 0; shouldn't get here, but handle anyway.
                                a.nd = 0
                                return
                        }
                        for n>>k == 0 {
                                n = n * 10
                                r++
                        }
                        break
                }
                c := int(a.d[r])
                n = n*10 + c - '0'
        }
        a.dp -= r - 1

        // Pick up a digit, put down a digit.
        for ; r < a.nd; r++ {
                c := int(a.d[r])
                dig := n >> k
                n -= dig << k
                a.d[w] = byte(dig + '0')
                w++
                n = n*10 + c - '0'
        }

        // Put down extra digits.
        for n > 0 {
                dig := n >> k
                n -= dig << k
                if w < len(a.d) {
                        a.d[w] = byte(dig + '0')
                        w++
                } else if dig > 0 {
                        a.trunc = true
                }
                n = n * 10
        }

        a.nd = w
        trim(a)
}

// Cheat sheet for left shift: table indexed by shift count giving
// number of new digits that will be introduced by that shift.
//
// For example, leftcheats[4] = {2, "625"}.  That means that
// if we are shifting by 4 (multiplying by 16), it will add 2 digits
// when the string prefix is "625" through "999", and one fewer digit
// if the string prefix is "000" through "624".
//
// Credit for this trick goes to Ken.

type leftCheat struct {
        delta  int    // number of new digits
        cutoff string //   minus one digit if original < a.
}

var leftcheats = []leftCheat{
        // Leading digits of 1/2^i = 5^i.
        // 5^23 is not an exact 64-bit floating point number,
        // so have to use bc for the math.
        /*
                seq 27 | sed 's/^/5^/' | bc |
                awk 'BEGIN{ print "\tleftCheat{ 0, \"\" }," }
                {
                        log2 = log(2)/log(10)
                        printf("\tleftCheat{ %d, \"%s\" },\t// * %d\n",
                                int(log2*NR+1), $0, 2**NR)
                }'
        */
        {0, ""},
        {1, "5"},                   // * 2
        {1, "25"},                  // * 4
        {1, "125"},                 // * 8
        {2, "625"},                 // * 16
        {2, "3125"},                // * 32
        {2, "15625"},               // * 64
        {3, "78125"},               // * 128
        {3, "390625"},              // * 256
        {3, "1953125"},             // * 512
        {4, "9765625"},             // * 1024
        {4, "48828125"},            // * 2048
        {4, "244140625"},           // * 4096
        {4, "1220703125"},          // * 8192
        {5, "6103515625"},          // * 16384
        {5, "30517578125"},         // * 32768
        {5, "152587890625"},        // * 65536
        {6, "762939453125"},        // * 131072
        {6, "3814697265625"},       // * 262144
        {6, "19073486328125"},      // * 524288
        {7, "95367431640625"},      // * 1048576
        {7, "476837158203125"},     // * 2097152
        {7, "2384185791015625"},    // * 4194304
        {7, "11920928955078125"},   // * 8388608
        {8, "59604644775390625"},   // * 16777216
        {8, "298023223876953125"},  // * 33554432
        {8, "1490116119384765625"}, // * 67108864
        {9, "7450580596923828125"}, // * 134217728
}

// Is the leading prefix of b lexicographically less than s?
func prefixIsLessThan(b []byte, s string) bool {
        for i := 0; i < len(s); i++ {
                if i >= len(b) {
                        return true
                }
                if b[i] != s[i] {
                        return b[i] < s[i]
                }
        }
        return false
}

// Binary shift left (/ 2) by k bits.  k <= maxShift to avoid overflow.
func leftShift(a *decimal, k uint) {
        delta := leftcheats[k].delta
        if prefixIsLessThan(a.d[0:a.nd], leftcheats[k].cutoff) {
                delta--
        }

        r := a.nd         // read index
        w := a.nd + delta // write index
        n := 0

        // Pick up a digit, put down a digit.
        for r--; r >= 0; r-- {
                n += (int(a.d[r]) - '0') << k
                quo := n / 10
                rem := n - 10*quo
                w--
                if w < len(a.d) {
                        a.d[w] = byte(rem + '0')
                } else if rem != 0 {
                        a.trunc = true
                }
                n = quo
        }

        // Put down extra digits.
        for n > 0 {
                quo := n / 10
                rem := n - 10*quo
                w--
                if w < len(a.d) {
                        a.d[w] = byte(rem + '0')
                } else if rem != 0 {
                        a.trunc = true
                }
                n = quo
        }

        a.nd += delta
        if a.nd >= len(a.d) {
                a.nd = len(a.d)
        }
        a.dp += delta
        trim(a)
}

// Binary shift left (k > 0) or right (k < 0).
func (a *decimal) Shift(k int) {
        switch {
        case a.nd == 0:
                // nothing to do: a == 0
        case k > 0:
                for k > maxShift {
                        leftShift(a, maxShift)
                        k -= maxShift
                }
                leftShift(a, uint(k))
        case k < 0:
                for k < -maxShift {
                        rightShift(a, maxShift)
                        k += maxShift
                }
                rightShift(a, uint(-k))
        }
}

// If we chop a at nd digits, should we round up?
func shouldRoundUp(a *decimal, nd int) bool {
        if nd < 0 || nd >= a.nd {
                return false
        }
        if a.d[nd] == '5' && nd+1 == a.nd { // exactly halfway - round to even
                // if we truncated, a little higher than what's recorded - always round up
                if a.trunc {
                        return true
                }
                return nd > 0 && (a.d[nd-1]-'0')%2 != 0
        }
        // not halfway - digit tells all
        return a.d[nd] >= '5'
}

// Round a to nd digits (or fewer).
// If nd is zero, it means we're rounding
// just to the left of the digits, as in
// 0.09 -> 0.1.
func (a *decimal) Round(nd int) {
        if nd < 0 || nd >= a.nd {
                return
        }
        if shouldRoundUp(a, nd) {
                a.RoundUp(nd)
        } else {
                a.RoundDown(nd)
        }
}

// Round a down to nd digits (or fewer).
func (a *decimal) RoundDown(nd int) {
        if nd < 0 || nd >= a.nd {
                return
        }
        a.nd = nd
        trim(a)
}

// Round a up to nd digits (or fewer).
func (a *decimal) RoundUp(nd int) {
        if nd < 0 || nd >= a.nd {
                return
        }

        // round up
        for i := nd - 1; i >= 0; i-- {
                c := a.d[i]
                if c < '9' { // can stop after this digit
                        a.d[i]++
                        a.nd = i + 1
                        return
                }
        }

        // Number is all 9s.
        // Change to single 1 with adjusted decimal point.
        a.d[0] = '1'
        a.nd = 1
        a.dp++
}

// Extract integer part, rounded appropriately.
// No guarantees about overflow.
func (a *decimal) RoundedInteger() uint64 {
        if a.dp > 20 {
                return 0xFFFFFFFFFFFFFFFF
        }
        var i int
        n := uint64(0)
        for i = 0; i < a.dp && i < a.nd; i++ {
                n = n*10 + uint64(a.d[i]-'0')
        }
        for ; i < a.dp; i++ {
                n *= 10
        }
        if shouldRoundUp(a, a.dp) {
                n++
        }
        return n
}