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Source file src/strconv/decimal.go

Documentation: strconv

  // 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, big-endian representation
  	nd    int       // number of digits used
  	dp    int       // decimal point
  	neg   bool      // negative flag
  	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.
  // A uint has 32 or 64 bits, and we have to be able to accommodate 9<<k.
  const uintSize = 32 << (^uint(0) >> 63)
  const maxShift = uintSize - 4
  
  // 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.
  	var n uint
  	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 := uint(a.d[r])
  		n = n*10 + c - '0'
  	}
  	a.dp -= r - 1
  
  	var mask uint = (1 << k) - 1
  
  	// Pick up a digit, put down a digit.
  	for ; r < a.nd; r++ {
  		c := uint(a.d[r])
  		dig := n >> k
  		n &= mask
  		a.d[w] = byte(dig + '0')
  		w++
  		n = n*10 + c - '0'
  	}
  
  	// Put down extra digits.
  	for n > 0 {
  		dig := n >> k
  		n &= mask
  		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.
  	// Go up to 60 to be large enough for 32bit and 64bit platforms.
  	/*
  		seq 60 | sed 's/^/5^/' | bc |
  		awk 'BEGIN{ print "\t{ 0, \"\" }," }
  		{
  			log2 = log(2)/log(10)
  			printf("\t{ %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
  	{9, "37252902984619140625"},                        // * 268435456
  	{9, "186264514923095703125"},                       // * 536870912
  	{10, "931322574615478515625"},                      // * 1073741824
  	{10, "4656612873077392578125"},                     // * 2147483648
  	{10, "23283064365386962890625"},                    // * 4294967296
  	{10, "116415321826934814453125"},                   // * 8589934592
  	{11, "582076609134674072265625"},                   // * 17179869184
  	{11, "2910383045673370361328125"},                  // * 34359738368
  	{11, "14551915228366851806640625"},                 // * 68719476736
  	{12, "72759576141834259033203125"},                 // * 137438953472
  	{12, "363797880709171295166015625"},                // * 274877906944
  	{12, "1818989403545856475830078125"},               // * 549755813888
  	{13, "9094947017729282379150390625"},               // * 1099511627776
  	{13, "45474735088646411895751953125"},              // * 2199023255552
  	{13, "227373675443232059478759765625"},             // * 4398046511104
  	{13, "1136868377216160297393798828125"},            // * 8796093022208
  	{14, "5684341886080801486968994140625"},            // * 17592186044416
  	{14, "28421709430404007434844970703125"},           // * 35184372088832
  	{14, "142108547152020037174224853515625"},          // * 70368744177664
  	{15, "710542735760100185871124267578125"},          // * 140737488355328
  	{15, "3552713678800500929355621337890625"},         // * 281474976710656
  	{15, "17763568394002504646778106689453125"},        // * 562949953421312
  	{16, "88817841970012523233890533447265625"},        // * 1125899906842624
  	{16, "444089209850062616169452667236328125"},       // * 2251799813685248
  	{16, "2220446049250313080847263336181640625"},      // * 4503599627370496
  	{16, "11102230246251565404236316680908203125"},     // * 9007199254740992
  	{17, "55511151231257827021181583404541015625"},     // * 18014398509481984
  	{17, "277555756156289135105907917022705078125"},    // * 36028797018963968
  	{17, "1387778780781445675529539585113525390625"},   // * 72057594037927936
  	{18, "6938893903907228377647697925567626953125"},   // * 144115188075855872
  	{18, "34694469519536141888238489627838134765625"},  // * 288230376151711744
  	{18, "173472347597680709441192448139190673828125"}, // * 576460752303423488
  	{19, "867361737988403547205962240695953369140625"}, // * 1152921504606846976
  }
  
  // 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
  
  	// Pick up a digit, put down a digit.
  	var n uint
  	for r--; r >= 0; r-- {
  		n += (uint(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
  }
  

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