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math/big: implement precise Float to decimal conversion (core functionality)
Change-Id: Ic0153397922ded28a5cb362e86ecdfec42e92163 Reviewed-on: https://go-review.googlesource.com/3752 Reviewed-by: Alan Donovan <adonovan@google.com>
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src/math/big/decimal.go
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191
src/math/big/decimal.go
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// Copyright 2015 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// This file implements multi-precision decimal numbers.
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// The implementation is for float to decimal conversion only;
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// not general purpose use.
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// The only operations are precise conversion from binary to
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// decimal and rounding.
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//
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// The key observation and some code (shr) is borrowed from
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// strconv/decimal.go: conversion of binary fractional values can be done
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// precisely in multi-precision decimal because 2 divides 10 (required for
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// >> of mantissa); but conversion of decimal floating-point values cannot
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// be done precisely in binary representation.
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//
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// In contrast to strconv/decimal.go, only right shift is implemented in
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// decimal format - left shift can be done precisely in binary format.
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package big
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// A decimal represents a floating-point number in decimal representation.
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// The value of a decimal x is x.mant * 10 ** x.exp with 0.5 <= x.mant < 1,
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// with the most-significant mantissa digit at index 0.
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type decimal struct {
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mant []byte // mantissa ASCII digits, big-endian
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exp int // exponent, valid if len(mant) > 0
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}
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// Maximum shift amount that can be done in one pass without overflow.
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// A Word has _W bits and (1<<maxShift - 1)*10 + 9 must fit into Word.
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const maxShift = _W - 4
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// TODO(gri) Since we know the desired decimal precision when converting
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// a floating-point number, we may be able to limit the number of decimal
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// digits that need to be computed by init by providing an additional
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// precision argument and keeping track of when a number was truncated early
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// (equivalent of "sticky bit" in binary rounding).
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// Init initializes x to the decimal representation of m << shift (for
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// shift >= 0), or m >> -shift (for shift < 0).
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func (x *decimal) init(m nat, shift int) {
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// special case 0
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if len(m) == 0 {
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x.mant = x.mant[:0]
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return
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}
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// Optimization: If we need to shift right, first remove any trailing
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// zero bits from m to reduce shift amount that needs to be done in
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// decimal format (since that is likely slower).
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if shift < 0 {
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ntz := m.trailingZeroBits()
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s := uint(-shift)
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if s >= ntz {
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s = ntz // shift at most ntz bits
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}
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m = nat(nil).shr(m, s)
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shift += int(s)
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}
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// Do any shift left in binary representation.
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if shift > 0 {
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m = nat(nil).shl(m, uint(shift))
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shift = 0
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}
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// Convert mantissa into decimal representation.
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s := m.decimalString() // TODO(gri) avoid string conversion here
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n := len(s)
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x.exp = n
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// Trim trailing zeros; instead the exponent is tracking
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// the decimal point independent of the number of digits.
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for n > 0 && s[n-1] == 0 {
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n--
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}
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x.mant = make([]byte, n)
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copy(x.mant, s)
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// Do any (remaining) shift right in decimal representation.
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if shift < 0 {
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for shift < -maxShift {
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x.shr(maxShift)
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shift += maxShift
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}
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x.shr(uint(-shift))
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}
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}
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// Possibly optimization: The current implementation of nat.string takes
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// a charset argument. When a right shift is needed, we could provide
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// "\x00\x01...\x09" instead of "012..9" (as in nat.decimalString) and
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// avoid the repeated +'0' and -'0' operations in decimal.shr (and do a
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// single +'0' pass at the end).
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// shr implements x >> s, for s <= maxShift.
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func (x *decimal) shr(s uint) {
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// Division by 1<<s using shift-and-subtract algorithm.
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// pick up enough leading digits to cover first shift
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r := 0 // read index
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var n Word
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for n>>s == 0 && r < len(x.mant) {
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ch := Word(x.mant[r])
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r++
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n = n*10 + ch - '0'
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}
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if n == 0 {
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// x == 0; shouldn't get here, but handle anyway
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x.mant = x.mant[:0]
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return
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}
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for n>>s == 0 {
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r++
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n *= 10
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}
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x.exp += 1 - r
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// read a digit, write a digit
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w := 0 // write index
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for r < len(x.mant) {
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ch := Word(x.mant[r])
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r++
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d := n >> s
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n -= d << s
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x.mant[w] = byte(d + '0')
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w++
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n = n*10 + ch - '0'
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}
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// write extra digits that still fit
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for n > 0 && w < len(x.mant) {
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d := n >> s
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n -= d << s
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x.mant[w] = byte(d + '0')
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w++
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n = n * 10
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}
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x.mant = x.mant[:w] // the number may be shorter (e.g. 1024 >> 10)
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// append additional digits that didn't fit
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for n > 0 {
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d := n >> s
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n -= d << s
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x.mant = append(x.mant, byte(d+'0'))
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n = n * 10
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}
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// remove trailing zeros
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w = len(x.mant)
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for w > 0 && x.mant[w-1] == '0' {
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w--
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}
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x.mant = x.mant[:w]
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}
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func (x *decimal) String() string {
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if len(x.mant) == 0 {
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return "0"
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}
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var buf []byte
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switch {
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case x.exp <= 0:
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// 0.00ddd
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buf = append(buf, "0."...)
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buf = appendZeros(buf, -x.exp)
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buf = append(buf, x.mant...)
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case /* 0 < */ x.exp < len(x.mant):
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// dd.ddd
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buf = append(buf, x.mant[:x.exp]...)
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buf = append(buf, '.')
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buf = append(buf, x.mant[x.exp:]...)
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default: // len(x.mant) <= x.exp
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// ddd00
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buf = append(buf, x.mant...)
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buf = appendZeros(buf, x.exp-len(x.mant))
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}
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return string(buf)
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}
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// appendZeros appends n 0 digits to buf and returns buf.
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func appendZeros(buf []byte, n int) []byte {
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for ; n > 0; n-- {
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buf = append(buf, '0')
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}
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return buf
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}
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51
src/math/big/decimal_test.go
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51
src/math/big/decimal_test.go
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@ -0,0 +1,51 @@
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// Copyright 2015 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package big
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import "testing"
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func TestDecimalString(t *testing.T) {
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for _, test := range []struct {
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x decimal
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want string
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}{
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{want: "0"},
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{decimal{nil, 1000}, "0"}, // exponent of 0 is ignored
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{decimal{[]byte("12345"), 0}, "0.12345"},
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{decimal{[]byte("12345"), -3}, "0.00012345"},
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{decimal{[]byte("12345"), +3}, "123.45"},
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{decimal{[]byte("12345"), +10}, "1234500000"},
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} {
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if got := test.x.String(); got != test.want {
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t.Errorf("%v == %s; want %s", test.x, got, test.want)
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}
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}
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}
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func TestDecimalInit(t *testing.T) {
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for _, test := range []struct {
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x Word
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shift int
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want string
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}{
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{0, 0, "0"},
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{0, -100, "0"},
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{0, 100, "0"},
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{1, 0, "1"},
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{1, 10, "1024"},
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{1, 100, "1267650600228229401496703205376"},
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{1, -100, "0.0000000000000000000000000000007888609052210118054117285652827862296732064351090230047702789306640625"},
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{12345678, 8, "3160493568"},
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{12345678, -8, "48225.3046875"},
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{195312, 9, "99999744"},
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{1953125, 9, "1000000000"},
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} {
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var d decimal
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d.init(nat{test.x}.norm(), test.shift)
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if got := d.String(); got != test.want {
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t.Errorf("%d << %d == %s; want %s", test.x, test.shift, got, test.want)
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}
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}
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}
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