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Commit 15040c11 authored by Russ Cox's avatar Russ Cox
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cmd/dist: copy needed packages from standard library during bootstrap 

This allows use of newer math/big (and later debug/pe)
without maintaining a vendored copy somewhere in cmd.

Use for math/big, deleting cmd/compile/internal/big.

Change-Id: I2bffa7a9ef115015be29fafdb02acc3e7a665d11
Reviewed-on: https://go-review.googlesource.com/31010Reviewed-by: default avatarMinux Ma <minux@golang.org>
Reviewed-by: default avatarIan Lance Taylor <iant@golang.org>
parent f444b48f
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Showing with 80 additions and 15478 deletions
src/cmd/compile/fmt_test.go
View file @ 15040c11
......@@ -506,9 +506,7 @@ func formatReplace(in string, f func(i int, s string) string) string {
// blacklistedPackages is the set of packages which can
// be ignored.
var blacklistedPackages = map[string]bool{
"cmd/compile/internal/big": true,
}
var blacklistedPackages = map[string]bool{}
// blacklistedFunctions is the set of functions which may have
// format-like arguments but which don't do any formatting and
......@@ -537,7 +535,7 @@ func init() {
// To print out a new table, run: go test -run Formats -v.
var knownFormats = map[string]string{
"*bytes.Buffer %s": "",
"*cmd/compile/internal/big.Int %#x": "",
"*math/big.Int %#x": "",
"*cmd/compile/internal/gc.Bits %v": "",
"*cmd/compile/internal/gc.Field %p": "",
"*cmd/compile/internal/gc.Field %v": "",
......
src/cmd/compile/internal/big/accuracy_string.go deleted 100644 → 0
View file @ f444b48f
// generated by stringer -type=Accuracy; DO NOT EDIT
package big
import "fmt"
const _Accuracy_name = "BelowExactAbove"
var _Accuracy_index = [...]uint8{0, 5, 10, 15}
func (i Accuracy) String() string {
i -= -1
if i < 0 || i+1 >= Accuracy(len(_Accuracy_index)) {
return fmt.Sprintf("Accuracy(%d)", i+-1)
}
return _Accuracy_name[_Accuracy_index[i]:_Accuracy_index[i+1]]
}
src/cmd/compile/internal/big/arith.go deleted 100644 → 0
View file @ f444b48f
// 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.
// This file provides Go implementations of elementary multi-precision
// arithmetic operations on word vectors. Needed for platforms without
// assembly implementations of these routines.
package big
// A Word represents a single digit of a multi-precision unsigned integer.
type Word uintptr
const (
// Compute the size _S of a Word in bytes.
_m = ^Word(0)
_logS = _m>>8&1 + _m>>16&1 + _m>>32&1
_S = 1 << _logS
_W = _S << 3 // word size in bits
_B = 1 << _W // digit base
_M = _B - 1 // digit mask
_W2 = _W / 2 // half word size in bits
_B2 = 1 << _W2 // half digit base
_M2 = _B2 - 1 // half digit mask
)
// ----------------------------------------------------------------------------
// Elementary operations on words
//
// These operations are used by the vector operations below.
// z1<<_W + z0 = x+y+c, with c == 0 or 1
func addWW_g(x, y, c Word) (z1, z0 Word) {
yc := y + c
z0 = x + yc
if z0 < x || yc < y {
z1 = 1
}
return
}
// z1<<_W + z0 = x-y-c, with c == 0 or 1
func subWW_g(x, y, c Word) (z1, z0 Word) {
yc := y + c
z0 = x - yc
if z0 > x || yc < y {
z1 = 1
}
return
}
// z1<<_W + z0 = x*y
// Adapted from Warren, Hacker's Delight, p. 132.
func mulWW_g(x, y Word) (z1, z0 Word) {
x0 := x & _M2
x1 := x >> _W2
y0 := y & _M2
y1 := y >> _W2
w0 := x0 * y0
t := x1*y0 + w0>>_W2
w1 := t & _M2
w2 := t >> _W2
w1 += x0 * y1
z1 = x1*y1 + w2 + w1>>_W2
z0 = x * y
return
}
// z1<<_W + z0 = x*y + c
func mulAddWWW_g(x, y, c Word) (z1, z0 Word) {
z1, zz0 := mulWW_g(x, y)
if z0 = zz0 + c; z0 < zz0 {
z1++
}
return
}
// Length of x in bits.
func bitLen_g(x Word) (n int) {
for ; x >= 0x8000; x >>= 16 {
n += 16
}
if x >= 0x80 {
x >>= 8
n += 8
}
if x >= 0x8 {
x >>= 4
n += 4
}
if x >= 0x2 {
x >>= 2
n += 2
}
if x >= 0x1 {
n++
}
return
}
// log2 computes the integer binary logarithm of x.
// The result is the integer n for which 2^n <= x < 2^(n+1).
// If x == 0, the result is -1.
func log2(x Word) int {
return bitLen(x) - 1
}
// nlz returns the number of leading zeros in x.
func nlz(x Word) uint {
return uint(_W - bitLen(x))
}
// nlz64 returns the number of leading zeros in x.
func nlz64(x uint64) uint {
switch _W {
case 32:
w := x >> 32
if w == 0 {
return 32 + nlz(Word(x))
}
return nlz(Word(w))
case 64:
return nlz(Word(x))
}
panic("unreachable")
}
// q = (u1<<_W + u0 - r)/y
// Adapted from Warren, Hacker's Delight, p. 152.
func divWW_g(u1, u0, v Word) (q, r Word) {
if u1 >= v {
return 1<<_W - 1, 1<<_W - 1
}
s := nlz(v)
v <<= s
vn1 := v >> _W2
vn0 := v & _M2
un32 := u1<<s | u0>>(_W-s)
un10 := u0 << s
un1 := un10 >> _W2
un0 := un10 & _M2
q1 := un32 / vn1
rhat := un32 - q1*vn1
for q1 >= _B2 || q1*vn0 > _B2*rhat+un1 {
q1--
rhat += vn1
if rhat >= _B2 {
break
}
}
un21 := un32*_B2 + un1 - q1*v
q0 := un21 / vn1
rhat = un21 - q0*vn1
for q0 >= _B2 || q0*vn0 > _B2*rhat+un0 {
q0--
rhat += vn1
if rhat >= _B2 {
break
}
}
return q1*_B2 + q0, (un21*_B2 + un0 - q0*v) >> s
}
// Keep for performance debugging.
// Using addWW_g is likely slower.
const use_addWW_g = false
// The resulting carry c is either 0 or 1.
func addVV_g(z, x, y []Word) (c Word) {
if use_addWW_g {
for i := range z {
c, z[i] = addWW_g(x[i], y[i], c)
}
return
}
for i, xi := range x[:len(z)] {
yi := y[i]
zi := xi + yi + c
z[i] = zi
// see "Hacker's Delight", section 2-12 (overflow detection)
c = (xi&yi | (xi|yi)&^zi) >> (_W - 1)
}
return
}
// The resulting carry c is either 0 or 1.
func subVV_g(z, x, y []Word) (c Word) {
if use_addWW_g {
for i := range z {
c, z[i] = subWW_g(x[i], y[i], c)
}
return
}
for i, xi := range x[:len(z)] {
yi := y[i]
zi := xi - yi - c
z[i] = zi
// see "Hacker's Delight", section 2-12 (overflow detection)
c = (yi&^xi | (yi|^xi)&zi) >> (_W - 1)
}
return
}
// The resulting carry c is either 0 or 1.
func addVW_g(z, x []Word, y Word) (c Word) {
if use_addWW_g {
c = y
for i := range z {
c, z[i] = addWW_g(x[i], c, 0)
}
return
}
c = y
for i, xi := range x[:len(z)] {
zi := xi + c
z[i] = zi
c = xi &^ zi >> (_W - 1)
}
return
}
func subVW_g(z, x []Word, y Word) (c Word) {
if use_addWW_g {
c = y
for i := range z {
c, z[i] = subWW_g(x[i], c, 0)
}
return
}
c = y
for i, xi := range x[:len(z)] {
zi := xi - c
z[i] = zi
c = (zi &^ xi) >> (_W - 1)
}
return
}
func shlVU_g(z, x []Word, s uint) (c Word) {
if n := len(z); n > 0 {
ŝ := _W - s
w1 := x[n-1]
c = w1 >> ŝ
for i := n - 1; i > 0; i-- {
w := w1
w1 = x[i-1]
z[i] = w<<s | w1>>ŝ
}
z[0] = w1 << s
}
return
}
func shrVU_g(z, x []Word, s uint) (c Word) {
if n := len(z); n > 0 {
ŝ := _W - s
w1 := x[0]
c = w1 << ŝ
for i := 0; i < n-1; i++ {
w := w1
w1 = x[i+1]
z[i] = w>>s | w1<<ŝ
}
z[n-1] = w1 >> s
}
return
}
func mulAddVWW_g(z, x []Word, y, r Word) (c Word) {
c = r
for i := range z {
c, z[i] = mulAddWWW_g(x[i], y, c)
}
return
}
// TODO(gri) Remove use of addWW_g here and then we can remove addWW_g and subWW_g.
func addMulVVW_g(z, x []Word, y Word) (c Word) {
for i := range z {
z1, z0 := mulAddWWW_g(x[i], y, z[i])
c, z[i] = addWW_g(z0, c, 0)
c += z1
}
return
}
func divWVW_g(z []Word, xn Word, x []Word, y Word) (r Word) {
r = xn
for i := len(z) - 1; i >= 0; i-- {
z[i], r = divWW_g(r, x[i], y)
}
return
}
src/cmd/compile/internal/big/arith_decl.go deleted 100644 → 0
View file @ f444b48f
// Copyright 2015 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.
package big
func mulWW(x, y Word) (z1, z0 Word) {
return mulWW_g(x, y)
}
func divWW(x1, x0, y Word) (q, r Word) {
return divWW_g(x1, x0, y)
}
func addVV(z, x, y []Word) (c Word) {
return addVV_g(z, x, y)
}
func subVV(z, x, y []Word) (c Word) {
return subVV_g(z, x, y)
}
func addVW(z, x []Word, y Word) (c Word) {
return addVW_g(z, x, y)
}
func subVW(z, x []Word, y Word) (c Word) {
return subVW_g(z, x, y)
}
func shlVU(z, x []Word, s uint) (c Word) {
return shlVU_g(z, x, s)
}
func shrVU(z, x []Word, s uint) (c Word) {
return shrVU_g(z, x, s)
}
func mulAddVWW(z, x []Word, y, r Word) (c Word) {
return mulAddVWW_g(z, x, y, r)
}
func addMulVVW(z, x []Word, y Word) (c Word) {
return addMulVVW_g(z, x, y)
}
func divWVW(z []Word, xn Word, x []Word, y Word) (r Word) {
return divWVW_g(z, xn, x, y)
}
func bitLen(x Word) (n int) {
return bitLen_g(x)
}
src/cmd/compile/internal/big/arith_test.go deleted 100644 → 0
View file @ f444b48f
This diff is collapsed.
src/cmd/compile/internal/big/bits_test.go deleted 100644 → 0
View file @ f444b48f
// Copyright 2015 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.
// This file implements the Bits type used for testing Float operations
// via an independent (albeit slower) representations for floating-point
// numbers.
package big
import (
"fmt"
"sort"
"testing"
)
// A Bits value b represents a finite floating-point number x of the form
//
// x = 2**b[0] + 2**b[1] + ... 2**b[len(b)-1]
//
// The order of slice elements is not significant. Negative elements may be
// used to form fractions. A Bits value is normalized if each b[i] occurs at
// most once. For instance Bits{0, 0, 1} is not normalized but represents the
// same floating-point number as Bits{2}, which is normalized. The zero (nil)
// value of Bits is a ready to use Bits value and represents the value 0.
type Bits []int
func (x Bits) add(y Bits) Bits {
return append(x, y...)
}
func (x Bits) mul(y Bits) Bits {
var p Bits
for _, x := range x {
for _, y := range y {
p = append(p, x+y)
}
}
return p
}
func TestMulBits(t *testing.T) {
for _, test := range []struct {
x, y, want Bits
}{
{nil, nil, nil},
{Bits{}, Bits{}, nil},
{Bits{0}, Bits{0}, Bits{0}},
{Bits{0}, Bits{1}, Bits{1}},
{Bits{1}, Bits{1, 2, 3}, Bits{2, 3, 4}},
{Bits{-1}, Bits{1}, Bits{0}},
{Bits{-10, -1, 0, 1, 10}, Bits{1, 2, 3}, Bits{-9, -8, -7, 0, 1, 2, 1, 2, 3, 2, 3, 4, 11, 12, 13}},
} {
got := fmt.Sprintf("%v", test.x.mul(test.y))
want := fmt.Sprintf("%v", test.want)
if got != want {
t.Errorf("%v * %v = %s; want %s", test.x, test.y, got, want)
}
}
}
// norm returns the normalized bits for x: It removes multiple equal entries
// by treating them as an addition (e.g., Bits{5, 5} => Bits{6}), and it sorts
// the result list for reproducible results.
func (x Bits) norm() Bits {
m := make(map[int]bool)
for _, b := range x {
for m[b] {
m[b] = false
b++
}
m[b] = true
}
var z Bits
for b, set := range m {
if set {
z = append(z, b)
}
}
sort.Ints([]int(z))
return z
}
func TestNormBits(t *testing.T) {
for _, test := range []struct {
x, want Bits
}{
{nil, nil},
{Bits{}, Bits{}},
{Bits{0}, Bits{0}},
{Bits{0, 0}, Bits{1}},
{Bits{3, 1, 1}, Bits{2, 3}},
{Bits{10, 9, 8, 7, 6, 6}, Bits{11}},
} {
got := fmt.Sprintf("%v", test.x.norm())
want := fmt.Sprintf("%v", test.want)
if got != want {
t.Errorf("normBits(%v) = %s; want %s", test.x, got, want)
}
}
}
// round returns the Float value corresponding to x after rounding x
// to prec bits according to mode.
func (x Bits) round(prec uint, mode RoundingMode) *Float {
x = x.norm()
// determine range
var min, max int
for i, b := range x {
if i == 0 || b < min {
min = b
}
if i == 0 || b > max {
max = b
}
}
prec0 := uint(max + 1 - min)
if prec >= prec0 {
return x.Float()
}
// prec < prec0
// determine bit 0, rounding, and sticky bit, and result bits z
var bit0, rbit, sbit uint
var z Bits
r := max - int(prec)
for _, b := range x {
switch {
case b == r:
rbit = 1
case b < r:
sbit = 1
default:
// b > r
if b == r+1 {
bit0 = 1
}
z = append(z, b)
}
}
// round
f := z.Float() // rounded to zero
if mode == ToNearestAway {
panic("not yet implemented")
}
if mode == ToNearestEven && rbit == 1 && (sbit == 1 || sbit == 0 && bit0 != 0) || mode == AwayFromZero {
// round away from zero
f.SetMode(ToZero).SetPrec(prec)
f.Add(f, Bits{int(r) + 1}.Float())
}
return f
}
// Float returns the *Float z of the smallest possible precision such that
// z = sum(2**bits[i]), with i = range bits. If multiple bits[i] are equal,
// they are added: Bits{0, 1, 0}.Float() == 2**0 + 2**1 + 2**0 = 4.
func (bits Bits) Float() *Float {
// handle 0
if len(bits) == 0 {
return new(Float)
}
// len(bits) > 0
// determine lsb exponent
var min int
for i, b := range bits {
if i == 0 || b < min {
min = b
}
}
// create bit pattern
x := NewInt(0)
for _, b := range bits {
badj := b - min
// propagate carry if necessary
for x.Bit(badj) != 0 {
x.SetBit(x, badj, 0)
badj++
}
x.SetBit(x, badj, 1)
}
// create corresponding float
z := new(Float).SetInt(x) // normalized
if e := int64(z.exp) + int64(min); MinExp <= e && e <= MaxExp {
z.exp = int32(e)
} else {
// this should never happen for our test cases
panic("exponent out of range")
}
return z
}
func TestFromBits(t *testing.T) {
for _, test := range []struct {
bits Bits
want string
}{
// all different bit numbers
{nil, "0"},
{Bits{0}, "0x.8p+1"},
{Bits{1}, "0x.8p+2"},
{Bits{-1}, "0x.8p+0"},
{Bits{63}, "0x.8p+64"},
{Bits{33, -30}, "0x.8000000000000001p+34"},
{Bits{255, 0}, "0x.8000000000000000000000000000000000000000000000000000000000000001p+256"},
// multiple equal bit numbers
{Bits{0, 0}, "0x.8p+2"},
{Bits{0, 0, 0, 0}, "0x.8p+3"},
{Bits{0, 1, 0}, "0x.8p+3"},
{append(Bits{2, 1, 0} /* 7 */, Bits{3, 1} /* 10 */ ...), "0x.88p+5" /* 17 */},
} {
f := test.bits.Float()
if got := f.Text('p', 0); got != test.want {
t.Errorf("setBits(%v) = %s; want %s", test.bits, got, test.want)
}
}
}
src/cmd/compile/internal/big/calibrate_test.go deleted 100644 → 0
View file @ f444b48f
// 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.
// This file prints execution times for the Mul benchmark
// given different Karatsuba thresholds. The result may be
// used to manually fine-tune the threshold constant. The
// results are somewhat fragile; use repeated runs to get
// a clear picture.
// Usage: go test -run=TestCalibrate -calibrate
package big
import (
"flag"
"fmt"
"testing"
"time"
)
var calibrate = flag.Bool("calibrate", false, "run calibration test")
func karatsubaLoad(b *testing.B) {
BenchmarkMul(b)
}
// measureKaratsuba returns the time to run a Karatsuba-relevant benchmark
// given Karatsuba threshold th.
func measureKaratsuba(th int) time.Duration {
th, karatsubaThreshold = karatsubaThreshold, th
res := testing.Benchmark(karatsubaLoad)
karatsubaThreshold = th
return time.Duration(res.NsPerOp())
}
func computeThresholds() {
fmt.Printf("Multiplication times for varying Karatsuba thresholds\n")
fmt.Printf("(run repeatedly for good results)\n")
// determine Tk, the work load execution time using basic multiplication
Tb := measureKaratsuba(1e9) // th == 1e9 => Karatsuba multiplication disabled
fmt.Printf("Tb = %10s\n", Tb)
// thresholds
th := 4
th1 := -1
th2 := -1
var deltaOld time.Duration
for count := -1; count != 0 && th < 128; count-- {
// determine Tk, the work load execution time using Karatsuba multiplication
Tk := measureKaratsuba(th)
// improvement over Tb
delta := (Tb - Tk) * 100 / Tb
fmt.Printf("th = %3d Tk = %10s %4d%%", th, Tk, delta)
// determine break-even point
if Tk < Tb && th1 < 0 {
th1 = th
fmt.Print(" break-even point")
}
// determine diminishing return
if 0 < delta && delta < deltaOld && th2 < 0 {
th2 = th
fmt.Print(" diminishing return")
}
deltaOld = delta
fmt.Println()
// trigger counter
if th1 >= 0 && th2 >= 0 && count < 0 {
count = 10 // this many extra measurements after we got both thresholds
}
th++
}
}
func TestCalibrate(t *testing.T) {
if *calibrate {
computeThresholds()
}
}
src/cmd/compile/internal/big/decimal.go deleted 100644 → 0
View file @ f444b48f
// Copyright 2015 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.
// This file implements multi-precision decimal numbers.
// The implementation is for float to decimal conversion only;
// not general purpose use.
// The only operations are precise conversion from binary to
// decimal and rounding.
//
// The key observation and some code (shr) is borrowed from
// strconv/decimal.go: conversion of binary fractional values can be done
// precisely in multi-precision decimal because 2 divides 10 (required for
// >> of mantissa); but conversion of decimal floating-point values cannot
// be done precisely in binary representation.
//
// In contrast to strconv/decimal.go, only right shift is implemented in
// decimal format - left shift can be done precisely in binary format.
package big
// A decimal represents an unsigned floating-point number in decimal representation.
// The value of a non-zero decimal d is d.mant * 10**d.exp with 0.5 <= d.mant < 1,
// with the most-significant mantissa digit at index 0. For the zero decimal, the
// mantissa length and exponent are 0.
// The zero value for decimal represents a ready-to-use 0.0.
type decimal struct {
mant []byte // mantissa ASCII digits, big-endian
exp int // exponent
}
// at returns the i'th mantissa digit, starting with the most significant digit at 0.
func (d *decimal) at(i int) byte {
if 0 <= i && i < len(d.mant) {
return d.mant[i]
}
return '0'
}
// Maximum shift amount that can be done in one pass without overflow.
// A Word has _W bits and (1<<maxShift - 1)*10 + 9 must fit into Word.
const maxShift = _W - 4
// TODO(gri) Since we know the desired decimal precision when converting
// a floating-point number, we may be able to limit the number of decimal
// digits that need to be computed by init by providing an additional
// precision argument and keeping track of when a number was truncated early
// (equivalent of "sticky bit" in binary rounding).
// TODO(gri) Along the same lines, enforce some limit to shift magnitudes
// to avoid "infinitely" long running conversions (until we run out of space).
// Init initializes x to the decimal representation of m << shift (for
// shift >= 0), or m >> -shift (for shift < 0).
func (x *decimal) init(m nat, shift int) {
// special case 0
if len(m) == 0 {
x.mant = x.mant[:0]
x.exp = 0
return
}
// Optimization: If we need to shift right, first remove any trailing
// zero bits from m to reduce shift amount that needs to be done in
// decimal format (since that is likely slower).
if shift < 0 {
ntz := m.trailingZeroBits()
s := uint(-shift)
if s >= ntz {
s = ntz // shift at most ntz bits
}
m = nat(nil).shr(m, s)
shift += int(s)
}
// Do any shift left in binary representation.
if shift > 0 {
m = nat(nil).shl(m, uint(shift))
shift = 0
}
// Convert mantissa into decimal representation.
s := m.utoa(10)
n := len(s)
x.exp = n
// Trim trailing zeros; instead the exponent is tracking
// the decimal point independent of the number of digits.
for n > 0 && s[n-1] == '0' {
n--
}
x.mant = append(x.mant[:0], s[:n]...)
// Do any (remaining) shift right in decimal representation.
if shift < 0 {
for shift < -maxShift {
shr(x, maxShift)
shift += maxShift
}
shr(x, uint(-shift))
}
}
// shr implements x >> s, for s <= maxShift.
func shr(x *decimal, s uint) {
// Division by 1<<s using shift-and-subtract algorithm.
// pick up enough leading digits to cover first shift
r := 0 // read index
var n Word
for n>>s == 0 && r < len(x.mant) {
ch := Word(x.mant[r])
r++
n = n*10 + ch - '0'
}
if n == 0 {
// x == 0; shouldn't get here, but handle anyway
x.mant = x.mant[:0]
return
}
for n>>s == 0 {
r++
n *= 10
}
x.exp += 1 - r
// read a digit, write a digit
w := 0 // write index
for r < len(x.mant) {
ch := Word(x.mant[r])
r++
d := n >> s
n -= d << s
x.mant[w] = byte(d + '0')
w++
n = n*10 + ch - '0'
}
// write extra digits that still fit
for n > 0 && w < len(x.mant) {
d := n >> s
n -= d << s
x.mant[w] = byte(d + '0')
w++
n = n * 10
}
x.mant = x.mant[:w] // the number may be shorter (e.g. 1024 >> 10)
// append additional digits that didn't fit
for n > 0 {
d := n >> s
n -= d << s
x.mant = append(x.mant, byte(d+'0'))
n = n * 10
}
trim(x)
}
func (x *decimal) String() string {
if len(x.mant) == 0 {
return "0"
}
var buf []byte
switch {
case x.exp <= 0:
// 0.00ddd
buf = append(buf, "0."...)
buf = appendZeros(buf, -x.exp)
buf = append(buf, x.mant...)
case /* 0 < */ x.exp < len(x.mant):
// dd.ddd
buf = append(buf, x.mant[:x.exp]...)
buf = append(buf, '.')
buf = append(buf, x.mant[x.exp:]...)
default: // len(x.mant) <= x.exp
// ddd00
buf = append(buf, x.mant...)
buf = appendZeros(buf, x.exp-len(x.mant))
}
return string(buf)
}
// appendZeros appends n 0 digits to buf and returns buf.
func appendZeros(buf []byte, n int) []byte {
for ; n > 0; n-- {
buf = append(buf, '0')
}
return buf
}
// shouldRoundUp reports if x should be rounded up
// if shortened to n digits. n must be a valid index
// for x.mant.
func shouldRoundUp(x *decimal, n int) bool {
if x.mant[n] == '5' && n+1 == len(x.mant) {
// exactly halfway - round to even
return n > 0 && (x.mant[n-1]-'0')&1 != 0
}
// not halfway - digit tells all (x.mant has no trailing zeros)
return x.mant[n] >= '5'
}
// round sets x to (at most) n mantissa digits by rounding it
// to the nearest even value with n (or fever) mantissa digits.
// If n < 0, x remains unchanged.
func (x *decimal) round(n int) {
if n < 0 || n >= len(x.mant) {
return // nothing to do
}
if shouldRoundUp(x, n) {
x.roundUp(n)
} else {
x.roundDown(n)
}
}
func (x *decimal) roundUp(n int) {
if n < 0 || n >= len(x.mant) {
return // nothing to do
}
// 0 <= n < len(x.mant)
// find first digit < '9'
for n > 0 && x.mant[n-1] >= '9' {
n--
}
if n == 0 {
// all digits are '9's => round up to '1' and update exponent
x.mant[0] = '1' // ok since len(x.mant) > n
x.mant = x.mant[:1]
x.exp++
return
}
// n > 0 && x.mant[n-1] < '9'
x.mant[n-1]++
x.mant = x.mant[:n]
// x already trimmed
}
func (x *decimal) roundDown(n int) {
if n < 0 || n >= len(x.mant) {
return // nothing to do
}
x.mant = x.mant[:n]
trim(x)
}
// trim cuts off any trailing zeros from x's mantissa;
// they are meaningless for the value of x.
func trim(x *decimal) {
i := len(x.mant)
for i > 0 && x.mant[i-1] == '0' {
i--
}
x.mant = x.mant[:i]
if i == 0 {
x.exp = 0
}
}
src/cmd/compile/internal/big/decimal_test.go deleted 100644 → 0
View file @ f444b48f
// Copyright 2015 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.
package big
import "testing"
func TestDecimalString(t *testing.T) {
for _, test := range []struct {
x decimal
want string
}{
{want: "0"},
{decimal{nil, 1000}, "0"}, // exponent of 0 is ignored
{decimal{[]byte("12345"), 0}, "0.12345"},
{decimal{[]byte("12345"), -3}, "0.00012345"},
{decimal{[]byte("12345"), +3}, "123.45"},
{decimal{[]byte("12345"), +10}, "1234500000"},
} {
if got := test.x.String(); got != test.want {
t.Errorf("%v == %s; want %s", test.x, got, test.want)
}
}
}
func TestDecimalInit(t *testing.T) {
for _, test := range []struct {
x Word
shift int
want string
}{
{0, 0, "0"},
{0, -100, "0"},
{0, 100, "0"},
{1, 0, "1"},
{1, 10, "1024"},
{1, 100, "1267650600228229401496703205376"},
{1, -100, "0.0000000000000000000000000000007888609052210118054117285652827862296732064351090230047702789306640625"},
{12345678, 8, "3160493568"},
{12345678, -8, "48225.3046875"},
{195312, 9, "99999744"},
{1953125, 9, "1000000000"},
} {
var d decimal
d.init(nat{test.x}.norm(), test.shift)
if got := d.String(); got != test.want {
t.Errorf("%d << %d == %s; want %s", test.x, test.shift, got, test.want)
}
}
}
func TestDecimalRounding(t *testing.T) {
for _, test := range []struct {
x uint64
n int
down, even, up string
}{
{0, 0, "0", "0", "0"},
{0, 1, "0", "0", "0"},
{1, 0, "0", "0", "10"},
{5, 0, "0", "0", "10"},
{9, 0, "0", "10", "10"},
{15, 1, "10", "20", "20"},
{45, 1, "40", "40", "50"},
{95, 1, "90", "100", "100"},
{12344999, 4, "12340000", "12340000", "12350000"},
{12345000, 4, "12340000", "12340000", "12350000"},
{12345001, 4, "12340000", "12350000", "12350000"},
{23454999, 4, "23450000", "23450000", "23460000"},
{23455000, 4, "23450000", "23460000", "23460000"},
{23455001, 4, "23450000", "23460000", "23460000"},
{99994999, 4, "99990000", "99990000", "100000000"},
{99995000, 4, "99990000", "100000000", "100000000"},
{99999999, 4, "99990000", "100000000", "100000000"},
{12994999, 4, "12990000", "12990000", "13000000"},
{12995000, 4, "12990000", "13000000", "13000000"},
{12999999, 4, "12990000", "13000000", "13000000"},
} {
x := nat(nil).setUint64(test.x)
var d decimal
d.init(x, 0)
d.roundDown(test.n)
if got := d.String(); got != test.down {
t.Errorf("roundDown(%d, %d) = %s; want %s", test.x, test.n, got, test.down)
}
d.init(x, 0)
d.round(test.n)
if got := d.String(); got != test.even {
t.Errorf("round(%d, %d) = %s; want %s", test.x, test.n, got, test.even)
}
d.init(x, 0)
d.roundUp(test.n)
if got := d.String(); got != test.up {
t.Errorf("roundUp(%d, %d) = %s; want %s", test.x, test.n, got, test.up)
}
}
}
var sink string
func BenchmarkDecimalConversion(b *testing.B) {
for i := 0; i < b.N; i++ {
for shift := -100; shift <= +100; shift++ {
var d decimal
d.init(natOne, shift)
sink = d.String()
}
}
}
src/cmd/compile/internal/big/doc.go deleted 100644 → 0
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// 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.
/*
Package big implements arbitrary-precision arithmetic (big numbers).
The following numeric types are supported:
Int signed integers
Rat rational numbers
Float floating-point numbers
The zero value for an Int, Rat, or Float correspond to 0. Thus, new
values can be declared in the usual ways and denote 0 without further
initialization:
var x Int // &x is an *Int of value 0
var r = &Rat{} // r is a *Rat of value 0
y := new(Float) // y is a *Float of value 0
Alternatively, new values can be allocated and initialized with factory
functions of the form:
func NewT(v V) *T
For instance, NewInt(x) returns an *Int set to the value of the int64
argument x, NewRat(a, b) returns a *Rat set to the fraction a/b where
a and b are int64 values, and NewFloat(f) returns a *Float initialized
to the float64 argument f. More flexibility is provided with explicit
setters, for instance:
var z1 Int
z1.SetUint64(123) // z1 := 123
z2 := new(Rat).SetFloat64(1.2) // z2 := 6/5
z3 := new(Float).SetInt(z1) // z3 := 123.0
Setters, numeric operations and predicates are represented as methods of
the form:
func (z *T) SetV(v V) *T // z = v
func (z *T) Unary(x *T) *T // z = unary x
func (z *T) Binary(x, y *T) *T // z = x binary y
func (x *T) Pred() P // p = pred(x)
with T one of Int, Rat, or Float. For unary and binary operations, the
result is the receiver (usually named z in that case; see below); if it
is one of the operands x or y it may be safely overwritten (and its memory
reused).
Arithmetic expressions are typically written as a sequence of individual
method calls, with each call corresponding to an operation. The receiver
denotes the result and the method arguments are the operation's operands.
For instance, given three *Int values a, b and c, the invocation
c.Add(a, b)
computes the sum a + b and stores the result in c, overwriting whatever
value was held in c before. Unless specified otherwise, operations permit
aliasing of parameters, so it is perfectly ok to write
sum.Add(sum, x)
to accumulate values x in a sum.
(By always passing in a result value via the receiver, memory use can be
much better controlled. Instead of having to allocate new memory for each
result, an operation can reuse the space allocated for the result value,
and overwrite that value with the new result in the process.)
Notational convention: Incoming method parameters (including the receiver)
are named consistently in the API to clarify their use. Incoming operands
are usually named x, y, a, b, and so on, but never z. A parameter specifying
the result is named z (typically the receiver).
For instance, the arguments for (*Int).Add are named x and y, and because
the receiver specifies the result destination, it is called z:
func (z *Int) Add(x, y *Int) *Int
Methods of this form typically return the incoming receiver as well, to
enable simple call chaining.
Methods which don't require a result value to be passed in (for instance,
Int.Sign), simply return the result. In this case, the receiver is typically
the first operand, named x:
func (x *Int) Sign() int
Various methods support conversions between strings and corresponding
numeric values, and vice versa: *Int, *Rat, and *Float values implement
the Stringer interface for a (default) string representation of the value,
but also provide SetString methods to initialize a value from a string in
a variety of supported formats (see the respective SetString documentation).
Finally, *Int, *Rat, and *Float satisfy the fmt package's Scanner interface
for scanning and (except for *Rat) the Formatter interface for formatted
printing.
*/
package big
src/cmd/compile/internal/big/example_rat_test.go deleted 100644 → 0
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// Copyright 2015 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.
package big_test
import (
"cmd/compile/internal/big"
"fmt"
)
// Use the classic continued fraction for e
// e = [1; 0, 1, 1, 2, 1, 1, ... 2n, 1, 1, ...]
// i.e., for the nth term, use
// 1 if n mod 3 != 1
// (n-1)/3 * 2 if n mod 3 == 1
func recur(n, lim int64) *big.Rat {
term := new(big.Rat)
if n%3 != 1 {
term.SetInt64(1)
} else {
term.SetInt64((n - 1) / 3 * 2)
}
if n > lim {
return term
}
// Directly initialize frac as the fractional
// inverse of the result of recur.
frac := new(big.Rat).Inv(recur(n+1, lim))
return term.Add(term, frac)
}
// This example demonstrates how to use big.Rat to compute the
// first 15 terms in the sequence of rational convergents for
// the constant e (base of natural logarithm).
func Example_eConvergents() {
for i := 1; i <= 15; i++ {
r := recur(0, int64(i))
// Print r both as a fraction and as a floating-point number.
// Since big.Rat implements fmt.Formatter, we can use %-13s to
// get a left-aligned string representation of the fraction.
fmt.Printf("%-13s = %s\n", r, r.FloatString(8))
}
// Output:
// 2/1 = 2.00000000
// 3/1 = 3.00000000
// 8/3 = 2.66666667
// 11/4 = 2.75000000
// 19/7 = 2.71428571
// 87/32 = 2.71875000
// 106/39 = 2.71794872
// 193/71 = 2.71830986
// 1264/465 = 2.71827957
// 1457/536 = 2.71828358
// 2721/1001 = 2.71828172
// 23225/8544 = 2.71828184
// 25946/9545 = 2.71828182
// 49171/18089 = 2.71828183
// 517656/190435 = 2.71828183
}
src/cmd/compile/internal/big/example_test.go deleted 100644 → 0
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// Copyright 2012 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.
package big_test
import (
"cmd/compile/internal/big"
"fmt"
"log"
"math"
)
func ExampleRat_SetString() {
r := new(big.Rat)
r.SetString("355/113")
fmt.Println(r.FloatString(3))
// Output: 3.142
}
func ExampleInt_SetString() {
i := new(big.Int)
i.SetString("644", 8) // octal
fmt.Println(i)
// Output: 420
}
func ExampleRat_Scan() {
// The Scan function is rarely used directly;
// the fmt package recognizes it as an implementation of fmt.Scanner.
r := new(big.Rat)
_, err := fmt.Sscan("1.5000", r)
if err != nil {
log.Println("error scanning value:", err)
} else {
fmt.Println(r)
}
// Output: 3/2
}
func ExampleInt_Scan() {
// The Scan function is rarely used directly;
// the fmt package recognizes it as an implementation of fmt.Scanner.
i := new(big.Int)
_, err := fmt.Sscan("18446744073709551617", i)
if err != nil {
log.Println("error scanning value:", err)
} else {
fmt.Println(i)
}
// Output: 18446744073709551617
}
// This example demonstrates how to use big.Int to compute the smallest
// Fibonacci number with 100 decimal digits and to test whether it is prime.
func Example_fibonacci() {
// Initialize two big ints with the first two numbers in the sequence.
a := big.NewInt(0)
b := big.NewInt(1)
// Initialize limit as 10^99, the smallest integer with 100 digits.
var limit big.Int
limit.Exp(big.NewInt(10), big.NewInt(99), nil)
// Loop while a is smaller than 1e100.
for a.Cmp(&limit) < 0 {
// Compute the next Fibonacci number, storing it in a.
a.Add(a, b)
// Swap a and b so that b is the next number in the sequence.
a, b = b, a
}
fmt.Println(a) // 100-digit Fibonacci number
// Test a for primality.
// (ProbablyPrimes' argument sets the number of Miller-Rabin
// rounds to be performed. 20 is a good value.)
fmt.Println(a.ProbablyPrime(20))
// Output:
// 1344719667586153181419716641724567886890850696275767987106294472017884974410332069524504824747437757
// false
}
// This example shows how to use big.Float to compute the square root of 2 with
// a precision of 200 bits, and how to print the result as a decimal number.
func Example_sqrt2() {
// We'll do computations with 200 bits of precision in the mantissa.
const prec = 200
// Compute the square root of 2 using Newton's Method. We start with
// an initial estimate for sqrt(2), and then iterate:
// x_{n+1} = 1/2 * ( x_n + (2.0 / x_n) )
// Since Newton's Method doubles the number of correct digits at each
// iteration, we need at least log_2(prec) steps.
steps := int(math.Log2(prec))
// Initialize values we need for the computation.
two := new(big.Float).SetPrec(prec).SetInt64(2)
half := new(big.Float).SetPrec(prec).SetFloat64(0.5)
// Use 1 as the initial estimate.
x := new(big.Float).SetPrec(prec).SetInt64(1)
// We use t as a temporary variable. There's no need to set its precision
// since big.Float values with unset (== 0) precision automatically assume
// the largest precision of the arguments when used as the result (receiver)
// of a big.Float operation.
t := new(big.Float)
// Iterate.
for i := 0; i <= steps; i++ {
t.Quo(two, x) // t = 2.0 / x_n
t.Add(x, t) // t = x_n + (2.0 / x_n)
x.Mul(half, t) // x_{n+1} = 0.5 * t
}
// We can use the usual fmt.Printf verbs since big.Float implements fmt.Formatter
fmt.Printf("sqrt(2) = %.50f\n", x)
// Print the error between 2 and x*x.
t.Mul(x, x) // t = x*x
fmt.Printf("error = %e\n", t.Sub(two, t))
// Output:
// sqrt(2) = 1.41421356237309504880168872420969807856967187537695
// error = 0.000000e+00
}
src/cmd/compile/internal/big/float.go deleted 100644 → 0
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src/cmd/compile/internal/big/float_test.go deleted 100644 → 0
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src/cmd/compile/internal/big/floatconv.go deleted 100644 → 0
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// Copyright 2015 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.
// This file implements string-to-Float conversion functions.
package big
import (
"fmt"
"io"
"strings"
)
// SetString sets z to the value of s and returns z and a boolean indicating
// success. s must be a floating-point number of the same format as accepted
// by Parse, with base argument 0.
func (z *Float) SetString(s string) (*Float, bool) {
if f, _, err := z.Parse(s, 0); err == nil {
return f, true
}
return nil, false
}
// scan is like Parse but reads the longest possible prefix representing a valid
// floating point number from an io.ByteScanner rather than a string. It serves
// as the implementation of Parse. It does not recognize ±Inf and does not expect
// EOF at the end.
func (z *Float) scan(r io.ByteScanner, base int) (f *Float, b int, err error) {
prec := z.prec
if prec == 0 {
prec = 64
}
// A reasonable value in case of an error.
z.form = zero
// sign
z.neg, err = scanSign(r)
if err != nil {
return
}
// mantissa
var fcount int // fractional digit count; valid if <= 0
z.mant, b, fcount, err = z.mant.scan(r, base, true)
if err != nil {
return
}
// exponent
var exp int64
var ebase int
exp, ebase, err = scanExponent(r, true)
if err != nil {
return
}
// special-case 0
if len(z.mant) == 0 {
z.prec = prec
z.acc = Exact
z.form = zero
f = z
return
}
// len(z.mant) > 0
// The mantissa may have a decimal point (fcount <= 0) and there
// may be a nonzero exponent exp. The decimal point amounts to a
// division by b**(-fcount). An exponent means multiplication by
// ebase**exp. Finally, mantissa normalization (shift left) requires
// a correcting multiplication by 2**(-shiftcount). Multiplications
// are commutative, so we can apply them in any order as long as there
// is no loss of precision. We only have powers of 2 and 10, and
// we split powers of 10 into the product of the same powers of
// 2 and 5. This reduces the size of the multiplication factor
// needed for base-10 exponents.
// normalize mantissa and determine initial exponent contributions
exp2 := int64(len(z.mant))*_W - fnorm(z.mant)
exp5 := int64(0)
// determine binary or decimal exponent contribution of decimal point
if fcount < 0 {
// The mantissa has a "decimal" point ddd.dddd; and
// -fcount is the number of digits to the right of '.'.
// Adjust relevant exponent accordingly.
d := int64(fcount)
switch b {
case 10:
exp5 = d
fallthrough // 10**e == 5**e * 2**e
case 2:
exp2 += d
case 16:
exp2 += d * 4 // hexadecimal digits are 4 bits each
default:
panic("unexpected mantissa base")
}
// fcount consumed - not needed anymore
}
// take actual exponent into account
switch ebase {
case 10:
exp5 += exp
fallthrough
case 2:
exp2 += exp
default:
panic("unexpected exponent base")
}
// exp consumed - not needed anymore
// apply 2**exp2
if MinExp <= exp2 && exp2 <= MaxExp {
z.prec = prec
z.form = finite
z.exp = int32(exp2)
f = z
} else {
err = fmt.Errorf("exponent overflow")
return
}
if exp5 == 0 {
// no decimal exponent contribution
z.round(0)
return
}
// exp5 != 0
// apply 5**exp5
p := new(Float).SetPrec(z.Prec() + 64) // use more bits for p -- TODO(gri) what is the right number?
if exp5 < 0 {
z.Quo(z, p.pow5(uint64(-exp5)))
} else {
z.Mul(z, p.pow5(uint64(exp5)))
}
return
}
// These powers of 5 fit into a uint64.
//
// for p, q := uint64(0), uint64(1); p < q; p, q = q, q*5 {
// fmt.Println(q)
// }
//
var pow5tab = [...]uint64{
1,
5,
25,
125,
625,
3125,
15625,
78125,
390625,
1953125,
9765625,
48828125,
244140625,
1220703125,
6103515625,
30517578125,
152587890625,
762939453125,
3814697265625,
19073486328125,
95367431640625,
476837158203125,
2384185791015625,
11920928955078125,
59604644775390625,
298023223876953125,
1490116119384765625,
7450580596923828125,
}
// pow5 sets z to 5**n and returns z.
// n must not be negative.
func (z *Float) pow5(n uint64) *Float {
const m = uint64(len(pow5tab) - 1)
if n <= m {
return z.SetUint64(pow5tab[n])
}
// n > m
z.SetUint64(pow5tab[m])
n -= m
// use more bits for f than for z
// TODO(gri) what is the right number?
f := new(Float).SetPrec(z.Prec() + 64).SetUint64(5)
for n > 0 {
if n&1 != 0 {
z.Mul(z, f)
}
f.Mul(f, f)
n >>= 1
}
return z
}
// Parse parses s which must contain a text representation of a floating-
// point number with a mantissa in the given conversion base (the exponent
// is always a decimal number), or a string representing an infinite value.
//
// It sets z to the (possibly rounded) value of the corresponding floating-
// point value, and returns z, the actual base b, and an error err, if any.
// If z's precision is 0, it is changed to 64 before rounding takes effect.
// The number must be of the form:
//
// number = [ sign ] [ prefix ] mantissa [ exponent ] | infinity .
// sign = "+" | "-" .
// prefix = "0" ( "x" | "X" | "b" | "B" ) .
// mantissa = digits | digits "." [ digits ] | "." digits .
// exponent = ( "E" | "e" | "p" ) [ sign ] digits .
// digits = digit { digit } .
// digit = "0" ... "9" | "a" ... "z" | "A" ... "Z" .
// infinity = [ sign ] ( "inf" | "Inf" ) .
//
// The base argument must be 0, 2, 10, or 16. Providing an invalid base
// argument will lead to a run-time panic.
//
// For base 0, the number prefix determines the actual base: A prefix of
// "0x" or "0X" selects base 16, and a "0b" or "0B" prefix selects
// base 2; otherwise, the actual base is 10 and no prefix is accepted.
// The octal prefix "0" is not supported (a leading "0" is simply
// considered a "0").
//
// A "p" exponent indicates a binary (rather then decimal) exponent;
// for instance "0x1.fffffffffffffp1023" (using base 0) represents the
// maximum float64 value. For hexadecimal mantissae, the exponent must
// be binary, if present (an "e" or "E" exponent indicator cannot be
// distinguished from a mantissa digit).
//
// The returned *Float f is nil and the value of z is valid but not
// defined if an error is reported.
//
func (z *Float) Parse(s string, base int) (f *Float, b int, err error) {
// scan doesn't handle ±Inf
if len(s) == 3 && (s == "Inf" || s == "inf") {
f = z.SetInf(false)
return
}
if len(s) == 4 && (s[0] == '+' || s[0] == '-') && (s[1:] == "Inf" || s[1:] == "inf") {
f = z.SetInf(s[0] == '-')
return
}
r := strings.NewReader(s)
if f, b, err = z.scan(r, base); err != nil {
return
}
// entire string must have been consumed
if ch, err2 := r.ReadByte(); err2 == nil {
err = fmt.Errorf("expected end of string, found %q", ch)
} else if err2 != io.EOF {
err = err2
}
return
}
// ParseFloat is like f.Parse(s, base) with f set to the given precision
// and rounding mode.
func ParseFloat(s string, base int, prec uint, mode RoundingMode) (f *Float, b int, err error) {
return new(Float).SetPrec(prec).SetMode(mode).Parse(s, base)
}
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// Copyright 2015 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.
package big_test
import (
"cmd/compile/internal/big"
"fmt"
"math"
)
func ExampleFloat_Add() {
// Operate on numbers of different precision.
var x, y, z big.Float
x.SetInt64(1000) // x is automatically set to 64bit precision
y.SetFloat64(2.718281828) // y is automatically set to 53bit precision
z.SetPrec(32)
z.Add(&x, &y)
fmt.Printf("x = %.10g (%s, prec = %d, acc = %s)\n", &x, x.Text('p', 0), x.Prec(), x.Acc())
fmt.Printf("y = %.10g (%s, prec = %d, acc = %s)\n", &y, y.Text('p', 0), y.Prec(), y.Acc())
fmt.Printf("z = %.10g (%s, prec = %d, acc = %s)\n", &z, z.Text('p', 0), z.Prec(), z.Acc())
// Output:
// x = 1000 (0x.fap+10, prec = 64, acc = Exact)
// y = 2.718281828 (0x.adf85458248cd8p+2, prec = 53, acc = Exact)
// z = 1002.718282 (0x.faadf854p+10, prec = 32, acc = Below)
}
func ExampleFloat_shift() {
// Implement Float "shift" by modifying the (binary) exponents directly.
for s := -5; s <= 5; s++ {
x := big.NewFloat(0.5)
x.SetMantExp(x, x.MantExp(nil)+s) // shift x by s
fmt.Println(x)
}
// Output:
// 0.015625
// 0.03125
// 0.0625
// 0.125
// 0.25
// 0.5
// 1
// 2
// 4
// 8
// 16
}
func ExampleFloat_Cmp() {
inf := math.Inf(1)
zero := 0.0
operands := []float64{-inf, -1.2, -zero, 0, +1.2, +inf}
fmt.Println(" x y cmp")
fmt.Println("---------------")
for _, x64 := range operands {
x := big.NewFloat(x64)
for _, y64 := range operands {
y := big.NewFloat(y64)
fmt.Printf("%4g %4g %3d\n", x, y, x.Cmp(y))
}
fmt.Println()
}
// Output:
// x y cmp
// ---------------
// -Inf -Inf 0
// -Inf -1.2 -1
// -Inf -0 -1
// -Inf 0 -1
// -Inf 1.2 -1
// -Inf +Inf -1
//
// -1.2 -Inf 1
// -1.2 -1.2 0
// -1.2 -0 -1
// -1.2 0 -1
// -1.2 1.2 -1
// -1.2 +Inf -1
//
// -0 -Inf 1
// -0 -1.2 1
// -0 -0 0
// -0 0 0
// -0 1.2 -1
// -0 +Inf -1
//
// 0 -Inf 1
// 0 -1.2 1
// 0 -0 0
// 0 0 0
// 0 1.2 -1
// 0 +Inf -1
//
// 1.2 -Inf 1
// 1.2 -1.2 1
// 1.2 -0 1
// 1.2 0 1
// 1.2 1.2 0
// 1.2 +Inf -1
//
// +Inf -Inf 1
// +Inf -1.2 1
// +Inf -0 1
// +Inf 0 1
// +Inf 1.2 1
// +Inf +Inf 0
}
func ExampleRoundingMode() {
operands := []float64{2.6, 2.5, 2.1, -2.1, -2.5, -2.6}
fmt.Print(" x")
for mode := big.ToNearestEven; mode <= big.ToPositiveInf; mode++ {
fmt.Printf(" %s", mode)
}
fmt.Println()
for _, f64 := range operands {
fmt.Printf("%4g", f64)
for mode := big.ToNearestEven; mode <= big.ToPositiveInf; mode++ {
// sample operands above require 2 bits to represent mantissa
// set binary precision to 2 to round them to integer values
f := new(big.Float).SetPrec(2).SetMode(mode).SetFloat64(f64)
fmt.Printf(" %*g", len(mode.String()), f)
}
fmt.Println()
}
// Output:
// x ToNearestEven ToNearestAway ToZero AwayFromZero ToNegativeInf ToPositiveInf
// 2.6 3 3 2 3 2 3
// 2.5 2 3 2 3 2 3
// 2.1 2 2 2 3 2 3
// -2.1 -2 -2 -2 -3 -3 -2
// -2.5 -2 -3 -2 -3 -3 -2
// -2.6 -3 -3 -2 -3 -3 -2
}
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// Copyright 2015 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.
// This file implements encoding/decoding of Floats.
package big
import (
"encoding/binary"
"fmt"
)
// Gob codec version. Permits backward-compatible changes to the encoding.
const floatGobVersion byte = 1
// GobEncode implements the gob.GobEncoder interface.
// The Float value and all its attributes (precision,
// rounding mode, accuracy) are marshalled.
func (x *Float) GobEncode() ([]byte, error) {
if x == nil {
return nil, nil
}
// determine max. space (bytes) required for encoding
sz := 1 + 1 + 4 // version + mode|acc|form|neg (3+2+2+1bit) + prec
n := 0 // number of mantissa words
if x.form == finite {
// add space for mantissa and exponent
n = int((x.prec + (_W - 1)) / _W) // required mantissa length in words for given precision
// actual mantissa slice could be shorter (trailing 0's) or longer (unused bits):
// - if shorter, only encode the words present
// - if longer, cut off unused words when encoding in bytes
// (in practice, this should never happen since rounding
// takes care of it, but be safe and do it always)
if len(x.mant) < n {
n = len(x.mant)
}
// len(x.mant) >= n
sz += 4 + n*_S // exp + mant
}
buf := make([]byte, sz)
buf[0] = floatGobVersion
b := byte(x.mode&7)<<5 | byte((x.acc+1)&3)<<3 | byte(x.form&3)<<1
if x.neg {
b |= 1
}
buf[1] = b
binary.BigEndian.PutUint32(buf[2:], x.prec)
if x.form == finite {
binary.BigEndian.PutUint32(buf[6:], uint32(x.exp))
x.mant[len(x.mant)-n:].bytes(buf[10:]) // cut off unused trailing words
}
return buf, nil
}
// GobDecode implements the gob.GobDecoder interface.
// The result is rounded per the precision and rounding mode of
// z unless z's precision is 0, in which case z is set exactly
// to the decoded value.
func (z *Float) GobDecode(buf []byte) error {
if len(buf) == 0 {
// Other side sent a nil or default value.
*z = Float{}
return nil
}
if buf[0] != floatGobVersion {
return fmt.Errorf("Float.GobDecode: encoding version %d not supported", buf[0])
}
oldPrec := z.prec
oldMode := z.mode
b := buf[1]
z.mode = RoundingMode((b >> 5) & 7)
z.acc = Accuracy((b>>3)&3) - 1
z.form = form((b >> 1) & 3)
z.neg = b&1 != 0
z.prec = binary.BigEndian.Uint32(buf[2:])
if z.form == finite {
z.exp = int32(binary.BigEndian.Uint32(buf[6:]))
z.mant = z.mant.setBytes(buf[10:])
}
if oldPrec != 0 {
z.mode = oldMode
z.SetPrec(uint(oldPrec))
}
return nil
}
// MarshalText implements the encoding.TextMarshaler interface.
// Only the Float value is marshaled (in full precision), other
// attributes such as precision or accuracy are ignored.
func (x *Float) MarshalText() (text []byte, err error) {
if x == nil {
return []byte("<nil>"), nil
}
var buf []byte
return x.Append(buf, 'g', -1), nil
}
// UnmarshalText implements the encoding.TextUnmarshaler interface.
// The result is rounded per the precision and rounding mode of z.
// If z's precision is 0, it is changed to 64 before rounding takes
// effect.
func (z *Float) UnmarshalText(text []byte) error {
// TODO(gri): get rid of the []byte/string conversion
_, _, err := z.Parse(string(text), 0)
if err != nil {
err = fmt.Errorf("math/big: cannot unmarshal %q into a *big.Float (%v)", text, err)
}
return err
}
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// Copyright 2015 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.
package big
import (
"bytes"
"encoding/gob"
"encoding/json"
"io"
"testing"
)
var floatVals = []string{
"0",
"1",
"0.1",
"2.71828",
"1234567890",
"3.14e1234",
"3.14e-1234",
"0.738957395793475734757349579759957975985497e100",
"0.73895739579347546656564656573475734957975995797598589749859834759476745986795497e100",
"inf",
"Inf",
}
func TestFloatGobEncoding(t *testing.T) {
var medium bytes.Buffer
enc := gob.NewEncoder(&medium)
dec := gob.NewDecoder(&medium)
for _, test := range floatVals {
for _, sign := range []string{"", "+", "-"} {
for _, prec := range []uint{0, 1, 2, 10, 53, 64, 100, 1000} {
for _, mode := range []RoundingMode{ToNearestEven, ToNearestAway, ToZero, AwayFromZero, ToNegativeInf, ToPositiveInf} {
medium.Reset() // empty buffer for each test case (in case of failures)
x := sign + test
var tx Float
_, _, err := tx.SetPrec(prec).SetMode(mode).Parse(x, 0)
if err != nil {
t.Errorf("parsing of %s (%dbits, %v) failed (invalid test case): %v", x, prec, mode, err)
continue
}
// If tx was set to prec == 0, tx.Parse(x, 0) assumes precision 64. Correct it.
if prec == 0 {
tx.SetPrec(0)
}
if err := enc.Encode(&tx); err != nil {
t.Errorf("encoding of %v (%dbits, %v) failed: %v", &tx, prec, mode, err)
continue
}
var rx Float
if err := dec.Decode(&rx); err != nil {
t.Errorf("decoding of %v (%dbits, %v) failed: %v", &tx, prec, mode, err)
continue
}
if rx.Cmp(&tx) != 0 {
t.Errorf("transmission of %s failed: got %s want %s", x, rx.String(), tx.String())
continue
}
if rx.Prec() != prec {
t.Errorf("transmission of %s's prec failed: got %d want %d", x, rx.Prec(), prec)
}
if rx.Mode() != mode {
t.Errorf("transmission of %s's mode failed: got %s want %s", x, rx.Mode(), mode)
}
if rx.Acc() != tx.Acc() {
t.Errorf("transmission of %s's accuracy failed: got %s want %s", x, rx.Acc(), tx.Acc())
}
}
}
}
}
}
func TestFloatCorruptGob(t *testing.T) {
var buf bytes.Buffer
tx := NewFloat(4 / 3).SetPrec(1000).SetMode(ToPositiveInf)
if err := gob.NewEncoder(&buf).Encode(tx); err != nil {
t.Fatal(err)
}
b := buf.Bytes()
var rx Float
if err := gob.NewDecoder(bytes.NewReader(b)).Decode(&rx); err != nil {
t.Fatal(err)
}
if err := gob.NewDecoder(bytes.NewReader(b[:10])).Decode(&rx); err != io.ErrUnexpectedEOF {
t.Errorf("got %v want EOF", err)
}
b[1] = 0
if err := gob.NewDecoder(bytes.NewReader(b)).Decode(&rx); err == nil {
t.Fatal("got nil want version error")
}
}
func TestFloatJSONEncoding(t *testing.T) {
for _, test := range floatVals {
for _, sign := range []string{"", "+", "-"} {
for _, prec := range []uint{0, 1, 2, 10, 53, 64, 100, 1000} {
x := sign + test
var tx Float
_, _, err := tx.SetPrec(prec).Parse(x, 0)
if err != nil {
t.Errorf("parsing of %s (prec = %d) failed (invalid test case): %v", x, prec, err)
continue
}
b, err := json.Marshal(&tx)
if err != nil {
t.Errorf("marshaling of %v (prec = %d) failed: %v", &tx, prec, err)
continue
}
var rx Float
rx.SetPrec(prec)
if err := json.Unmarshal(b, &rx); err != nil {
t.Errorf("unmarshaling of %v (prec = %d) failed: %v", &tx, prec, err)
continue
}
if rx.Cmp(&tx) != 0 {
t.Errorf("JSON encoding of %v (prec = %d) failed: got %v want %v", &tx, prec, &rx, &tx)
}
}
}
}
}
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// Copyright 2012 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.
// This file implements a GCD benchmark.
// Usage: go test math/big -test.bench GCD
package big
import (
"math/rand"
"testing"
)
// randInt returns a pseudo-random Int in the range [1<<(size-1), (1<<size) - 1]
func randInt(r *rand.Rand, size uint) *Int {
n := new(Int).Lsh(intOne, size-1)
x := new(Int).Rand(r, n)
return x.Add(x, n) // make sure result > 1<<(size-1)
}
func runGCD(b *testing.B, aSize, bSize uint) {
b.Run("WithoutXY", func(b *testing.B) {
runGCDExt(b, aSize, bSize, false)
})
b.Run("WithXY", func(b *testing.B) {
runGCDExt(b, aSize, bSize, true)
})
}
func runGCDExt(b *testing.B, aSize, bSize uint, calcXY bool) {
b.StopTimer()
var r = rand.New(rand.NewSource(1234))
aa := randInt(r, aSize)
bb := randInt(r, bSize)
var x, y *Int
if calcXY {
x = new(Int)
y = new(Int)
}
b.StartTimer()
for i := 0; i < b.N; i++ {
new(Int).GCD(x, y, aa, bb)
}
}
func BenchmarkGCD10x10(b *testing.B) { runGCD(b, 10, 10) }
func BenchmarkGCD10x100(b *testing.B) { runGCD(b, 10, 100) }
func BenchmarkGCD10x1000(b *testing.B) { runGCD(b, 10, 1000) }
func BenchmarkGCD10x10000(b *testing.B) { runGCD(b, 10, 10000) }
func BenchmarkGCD10x100000(b *testing.B) { runGCD(b, 10, 100000) }
func BenchmarkGCD100x100(b *testing.B) { runGCD(b, 100, 100) }
func BenchmarkGCD100x1000(b *testing.B) { runGCD(b, 100, 1000) }
func BenchmarkGCD100x10000(b *testing.B) { runGCD(b, 100, 10000) }
func BenchmarkGCD100x100000(b *testing.B) { runGCD(b, 100, 100000) }
func BenchmarkGCD1000x1000(b *testing.B) { runGCD(b, 1000, 1000) }
func BenchmarkGCD1000x10000(b *testing.B) { runGCD(b, 1000, 10000) }
func BenchmarkGCD1000x100000(b *testing.B) { runGCD(b, 1000, 100000) }
func BenchmarkGCD10000x10000(b *testing.B) { runGCD(b, 10000, 10000) }
func BenchmarkGCD10000x100000(b *testing.B) { runGCD(b, 10000, 100000) }
func BenchmarkGCD100000x100000(b *testing.B) { runGCD(b, 100000, 100000) }
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// Copyright 2015 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.
// This file implements encoding/decoding of Ints.
package big
import "fmt"
// Gob codec version. Permits backward-compatible changes to the encoding.
const intGobVersion byte = 1
// GobEncode implements the gob.GobEncoder interface.
func (x *Int) GobEncode() ([]byte, error) {
if x == nil {
return nil, nil
}
buf := make([]byte, 1+len(x.abs)*_S) // extra byte for version and sign bit
i := x.abs.bytes(buf) - 1 // i >= 0
b := intGobVersion << 1 // make space for sign bit
if x.neg {
b |= 1
}
buf[i] = b
return buf[i:], nil
}
// GobDecode implements the gob.GobDecoder interface.
func (z *Int) GobDecode(buf []byte) error {
if len(buf) == 0 {
// Other side sent a nil or default value.
*z = Int{}
return nil
}
b := buf[0]
if b>>1 != intGobVersion {
return fmt.Errorf("Int.GobDecode: encoding version %d not supported", b>>1)
}
z.neg = b&1 != 0
z.abs = z.abs.setBytes(buf[1:])
return nil
}
// MarshalText implements the encoding.TextMarshaler interface.
func (x *Int) MarshalText() (text []byte, err error) {
if x == nil {
return []byte("<nil>"), nil
}
return x.abs.itoa(x.neg, 10), nil
}
// UnmarshalText implements the encoding.TextUnmarshaler interface.
func (z *Int) UnmarshalText(text []byte) error {
// TODO(gri): get rid of the []byte/string conversion
if _, ok := z.SetString(string(text), 0); !ok {
return fmt.Errorf("math/big: cannot unmarshal %q into a *big.Int", text)
}
return nil
}
// The JSON marshallers are only here for API backward compatibility
// (programs that explicitly look for these two methods). JSON works
// fine with the TextMarshaler only.
// MarshalJSON implements the json.Marshaler interface.
func (x *Int) MarshalJSON() ([]byte, error) {
return x.MarshalText()
}
// UnmarshalJSON implements the json.Unmarshaler interface.
func (z *Int) UnmarshalJSON(text []byte) error {
// Ignore null, like in the main JSON package.
if string(text) == "null" {
return nil
}
return z.UnmarshalText(text)
}
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// generated by stringer -type=RoundingMode; DO NOT EDIT
package big
import "fmt"
const _RoundingMode_name = "ToNearestEvenToNearestAwayToZeroAwayFromZeroToNegativeInfToPositiveInf"
var _RoundingMode_index = [...]uint8{0, 13, 26, 32, 44, 57, 70}
func (i RoundingMode) String() string {
if i+1 >= RoundingMode(len(_RoundingMode_index)) {
return fmt.Sprintf("RoundingMode(%d)", i)
}
return _RoundingMode_name[_RoundingMode_index[i]:_RoundingMode_index[i+1]]
}
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......@@ -132,7 +132,7 @@ package gc
import (
"bufio"
"bytes"
"cmd/compile/internal/big"
"math/big"
"encoding/binary"
"fmt"
"sort"
......
src/cmd/compile/internal/gc/bimport.go
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......@@ -10,7 +10,7 @@ package gc
import (
"bufio"
"cmd/compile/internal/big"
"math/big"
"encoding/binary"
"fmt"
"strconv"
......
src/cmd/compile/internal/gc/mpfloat.go
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......@@ -5,9 +5,9 @@
package gc
import (
"cmd/compile/internal/big"
"fmt"
"math"
"math/big"
)
// implements float arithmetic
......
src/cmd/compile/internal/gc/mpint.go
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