src/lib/strconv/decimal.go - go - Git at Google

 // 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 {
 	// TODO(rsc): Can make d[] a bit smaller and add
 	// truncated bool;
 	d [2000] byte;	// digits
 	nd int;	// number of digits used
 	dp int;	// decimal point
 };
 func (a *decimal) String() string;
 func (a *decimal) Assign(v uint64);
 func (a *decimal) Shift(k int) *decimal;
 func (a *decimal) Round(nd int) *decimal;
 func (a *decimal) RoundUp(nd int) *decimal;
 func (a *decimal) RoundDown(nd int) *decimal;
 func (a *decimal) RoundedInteger() uint64;


 func copy(dst []byte, src []byte) int;
 func digitZero(dst []byte) int;

 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:w+a.nd], a.d[0:a.nd]);

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

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

 func copy(dst []byte, src []byte) int {
 	for i := 0; i < len(dst); i++ {
 		dst[i] = src[i];
 	}
 	return len(dst);
 }

 func digitZero(dst []byte) int {
 	for i := 0; i < len(dst); i++ {
 		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 [50]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);
 }

 func newDecimal(i uint64) *decimal {
 	a := new(decimal);
 	a.Assign(i);
 	return a;
 }

 // Maximum shift that we can do in one pass without overflow.
 // Signed int has 31 bits, and we have to be able to accomodate 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;
 		a.d[w] = byte(dig+'0');
 		w++;
 		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)
 	}'
 	 */
 	leftCheat{ 0, "" },
 	leftCheat{ 1, "5" },	// * 2
 	leftCheat{ 1, "25" },	// * 4
 	leftCheat{ 1, "125" },	// * 8
 	leftCheat{ 2, "625" },	// * 16
 	leftCheat{ 2, "3125" },	// * 32
 	leftCheat{ 2, "15625" },	// * 64
 	leftCheat{ 3, "78125" },	// * 128
 	leftCheat{ 3, "390625" },	// * 256
 	leftCheat{ 3, "1953125" },	// * 512
 	leftCheat{ 4, "9765625" },	// * 1024
 	leftCheat{ 4, "48828125" },	// * 2048
 	leftCheat{ 4, "244140625" },	// * 4096
 	leftCheat{ 4, "1220703125" },	// * 8192
 	leftCheat{ 5, "6103515625" },	// * 16384
 	leftCheat{ 5, "30517578125" },	// * 32768
 	leftCheat{ 5, "152587890625" },	// * 65536
 	leftCheat{ 6, "762939453125" },	// * 131072
 	leftCheat{ 6, "3814697265625" },	// * 262144
 	leftCheat{ 6, "19073486328125" },	// * 524288
 	leftCheat{ 7, "95367431640625" },	// * 1048576
 	leftCheat{ 7, "476837158203125" },	// * 2097152
 	leftCheat{ 7, "2384185791015625" },	// * 4194304
 	leftCheat{ 7, "11920928955078125" },	// * 8388608
 	leftCheat{ 8, "59604644775390625" },	// * 16777216
 	leftCheat{ 8, "298023223876953125" },	// * 33554432
 	leftCheat{ 8, "1490116119384765625" },	// * 67108864
 	leftCheat{ 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--;
 		a.d[w] = byte(rem+'0');
 		n = quo;
 	}

 	// Put down extra digits.
 	for n > 0 {
 		quo := n/10;
 		rem := n - 10*quo;
 		w--;
 		a.d[w] = byte(rem+'0');
 		n = quo;
 	}

 	if w != 0 {
 		// TODO: Remove - has no business panicking.
 		panicln("strconv: bad leftShift", w);
 	}
 	a.nd += delta;
 	a.dp += delta;
 	trim(a);
 }

 // Binary shift left (k > 0) or right (k < 0).
 // Returns receiver for convenience.
 func (a *decimal) Shift(k int) *decimal {
 	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));
 	}
 	return a;
 }

 // 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
 		return (a.d[nd-1] - '0') % 2 != 0;
 	}
 	// not halfway - digit tells all
 	return a.d[nd] >= '5';
 }

 // Round a to nd digits (or fewer).
 // Returns receiver for convenience.
 func (a *decimal) Round(nd int) *decimal {
 	if nd <= 0 || nd >= a.nd {
 		return a;
 	}
 	if(shouldRoundUp(a, nd)) {
 		return a.RoundUp(nd);
 	}
 	return a.RoundDown(nd);
 }

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

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

 	// 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 a;
 		}
 	}

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

 // 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;
 }
	// 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 {
	// TODO(rsc): Can make d[] a bit smaller and add
	// truncated bool;
	d [2000] byte; // digits
	nd int; // number of digits used
	dp int; // decimal point
	};
	func (a *decimal) String() string;
	func (a *decimal) Assign(v uint64);
	func (a decimal) Shift(k int) decimal;
	func (a decimal) Round(nd int) decimal;
	func (a decimal) RoundUp(nd int) decimal;
	func (a decimal) RoundDown(nd int) decimal;
	func (a *decimal) RoundedInteger() uint64;


	func copy(dst []byte, src []byte) int;
	func digitZero(dst []byte) int;

	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:w+a.nd], a.d[0:a.nd]);

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

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

	func copy(dst []byte, src []byte) int {
	for i := 0; i < len(dst); i++ {
	dst[i] = src[i];
	}
	return len(dst);
	}

	func digitZero(dst []byte) int {
	for i := 0; i < len(dst); i++ {
	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 [50]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);
	}

	func newDecimal(i uint64) *decimal {
	a := new(decimal);
	a.Assign(i);
	return a;
	}

	// Maximum shift that we can do in one pass without overflow.
	// Signed int has 31 bits, and we have to be able to accomodate 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;
	a.d[w] = byte(dig+'0');
	w++;
	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(log2NR+1), $0, 2*NR)
	}'
	*/
	leftCheat{ 0, "" },
	leftCheat{ 1, "5" }, // * 2
	leftCheat{ 1, "25" }, // * 4
	leftCheat{ 1, "125" }, // * 8
	leftCheat{ 2, "625" }, // * 16
	leftCheat{ 2, "3125" }, // * 32
	leftCheat{ 2, "15625" }, // * 64
	leftCheat{ 3, "78125" }, // * 128
	leftCheat{ 3, "390625" }, // * 256
	leftCheat{ 3, "1953125" }, // * 512
	leftCheat{ 4, "9765625" }, // * 1024
	leftCheat{ 4, "48828125" }, // * 2048
	leftCheat{ 4, "244140625" }, // * 4096
	leftCheat{ 4, "1220703125" }, // * 8192
	leftCheat{ 5, "6103515625" }, // * 16384
	leftCheat{ 5, "30517578125" }, // * 32768
	leftCheat{ 5, "152587890625" }, // * 65536
	leftCheat{ 6, "762939453125" }, // * 131072
	leftCheat{ 6, "3814697265625" }, // * 262144
	leftCheat{ 6, "19073486328125" }, // * 524288
	leftCheat{ 7, "95367431640625" }, // * 1048576
	leftCheat{ 7, "476837158203125" }, // * 2097152
	leftCheat{ 7, "2384185791015625" }, // * 4194304
	leftCheat{ 7, "11920928955078125" }, // * 8388608
	leftCheat{ 8, "59604644775390625" }, // * 16777216
	leftCheat{ 8, "298023223876953125" }, // * 33554432
	leftCheat{ 8, "1490116119384765625" }, // * 67108864
	leftCheat{ 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--;
	a.d[w] = byte(rem+'0');
	n = quo;
	}

	// Put down extra digits.
	for n > 0 {
	quo := n/10;
	rem := n - 10*quo;
	w--;
	a.d[w] = byte(rem+'0');
	n = quo;
	}

	if w != 0 {
	// TODO: Remove - has no business panicking.
	panicln("strconv: bad leftShift", w);
	}
	a.nd += delta;
	a.dp += delta;
	trim(a);
	}

	// Binary shift left (k > 0) or right (k < 0).
	// Returns receiver for convenience.
	func (a decimal) Shift(k int) decimal {
	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));
	}
	return a;
	}

	// 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
	return (a.d[nd-1] - '0') % 2 != 0;
	}
	// not halfway - digit tells all
	return a.d[nd] >= '5';
	}

	// Round a to nd digits (or fewer).
	// Returns receiver for convenience.
	func (a decimal) Round(nd int) decimal {
	if nd <= 0 \|\| nd >= a.nd {
	return a;
	}
	if(shouldRoundUp(a, nd)) {
	return a.RoundUp(nd);
	}
	return a.RoundDown(nd);
	}

	// Round a down to nd digits (or fewer).
	// Returns receiver for convenience.
	func (a decimal) RoundDown(nd int) decimal {
	if nd <= 0 \|\| nd >= a.nd {
	return a;
	}
	a.nd = nd;
	trim(a);
	return a;
	}

	// Round a up to nd digits (or fewer).
	// Returns receiver for convenience.
	func (a decimal) RoundUp(nd int) decimal {
	if nd <= 0 \|\| nd >= a.nd {
	return a;
	}

	// 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 a;
	}
	}

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

	// 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;
	}