mirror of
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Make NewFromFloat respect the precision of the input (#100)
* Make NewFromFloat respect the precision of the input Restores the previous behaviour where input converted from float is truncated at the precision of the float. The precision is depending on the actual value. Simply making it 15 digits would make it faster, but would in some cases lose some precision. So the code from the stdlib that does this calculation (very well) has been included. Lots of good articles here: https://www.exploringbinary.com/decimal-precision-of-binary-floating-point-numbers/ Performance is around the same as the previous string roundtrip since it basically does the same, but allocations are a bit less. `BenchmarkNewFromStringFloat` is the old method, `BenchmarkNewFromFloat` is the new. ``` BenchmarkNewFromFloatWithExponent-8 10000000 260 ns/op 174 B/op 4 allocs/op BenchmarkNewFromFloat-8 2000000 744 ns/op 90 B/op 2 allocs/op BenchmarkNewFromStringFloat-8 2000000 822 ns/op 258 B/op 6 allocs/op ``` * Update Sin/Tan/Cos tests.
This commit is contained in:
Klaus Post
Victor Quinn
parent
7e43aed1c9
commit
cd690d0c9e
4 changed files with 797 additions and 48 deletions
414
decimal-go.go
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414
decimal-go.go
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@ -0,0 +1,414 @@
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// Copyright 2009 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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// Multiprecision decimal numbers.
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// For floating-point formatting only; not general purpose.
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// Only operations are assign and (binary) left/right shift.
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// Can do binary floating point in multiprecision decimal precisely
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// because 2 divides 10; cannot do decimal floating point
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// in multiprecision binary precisely.
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package decimal
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type decimal struct {
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d [800]byte // digits, big-endian representation
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nd int // number of digits used
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dp int // decimal point
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neg bool // negative flag
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trunc bool // discarded nonzero digits beyond d[:nd]
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}
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func (a *decimal) String() string {
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n := 10 + a.nd
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if a.dp > 0 {
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n += a.dp
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}
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if a.dp < 0 {
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n += -a.dp
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}
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buf := make([]byte, n)
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w := 0
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switch {
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case a.nd == 0:
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return "0"
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case a.dp <= 0:
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// zeros fill space between decimal point and digits
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buf[w] = '0'
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w++
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buf[w] = '.'
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w++
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w += digitZero(buf[w : w+-a.dp])
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w += copy(buf[w:], a.d[0:a.nd])
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case a.dp < a.nd:
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// decimal point in middle of digits
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w += copy(buf[w:], a.d[0:a.dp])
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buf[w] = '.'
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w++
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w += copy(buf[w:], a.d[a.dp:a.nd])
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default:
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// zeros fill space between digits and decimal point
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w += copy(buf[w:], a.d[0:a.nd])
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w += digitZero(buf[w : w+a.dp-a.nd])
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}
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return string(buf[0:w])
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}
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func digitZero(dst []byte) int {
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for i := range dst {
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dst[i] = '0'
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}
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return len(dst)
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}
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// trim trailing zeros from number.
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// (They are meaningless; the decimal point is tracked
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// independent of the number of digits.)
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func trim(a *decimal) {
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for a.nd > 0 && a.d[a.nd-1] == '0' {
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a.nd--
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}
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if a.nd == 0 {
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a.dp = 0
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}
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}
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// Assign v to a.
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func (a *decimal) Assign(v uint64) {
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var buf [24]byte
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// Write reversed decimal in buf.
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n := 0
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for v > 0 {
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v1 := v / 10
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v -= 10 * v1
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buf[n] = byte(v + '0')
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n++
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v = v1
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}
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// Reverse again to produce forward decimal in a.d.
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a.nd = 0
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for n--; n >= 0; n-- {
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a.d[a.nd] = buf[n]
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a.nd++
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}
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a.dp = a.nd
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trim(a)
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}
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// Maximum shift that we can do in one pass without overflow.
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// A uint has 32 or 64 bits, and we have to be able to accommodate 9<<k.
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const uintSize = 32 << (^uint(0) >> 63)
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const maxShift = uintSize - 4
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// Binary shift right (/ 2) by k bits. k <= maxShift to avoid overflow.
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func rightShift(a *decimal, k uint) {
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r := 0 // read pointer
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w := 0 // write pointer
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// Pick up enough leading digits to cover first shift.
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var n uint
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for ; n>>k == 0; r++ {
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if r >= a.nd {
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if n == 0 {
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// a == 0; shouldn't get here, but handle anyway.
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a.nd = 0
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return
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}
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for n>>k == 0 {
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n = n * 10
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r++
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}
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break
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}
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c := uint(a.d[r])
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n = n*10 + c - '0'
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}
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a.dp -= r - 1
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var mask uint = (1 << k) - 1
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// Pick up a digit, put down a digit.
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for ; r < a.nd; r++ {
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c := uint(a.d[r])
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dig := n >> k
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n &= mask
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a.d[w] = byte(dig + '0')
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w++
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n = n*10 + c - '0'
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}
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// Put down extra digits.
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for n > 0 {
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dig := n >> k
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n &= mask
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if w < len(a.d) {
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a.d[w] = byte(dig + '0')
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w++
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} else if dig > 0 {
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a.trunc = true
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}
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n = n * 10
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}
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a.nd = w
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trim(a)
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}
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// Cheat sheet for left shift: table indexed by shift count giving
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// number of new digits that will be introduced by that shift.
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//
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// For example, leftcheats[4] = {2, "625"}. That means that
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// if we are shifting by 4 (multiplying by 16), it will add 2 digits
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// when the string prefix is "625" through "999", and one fewer digit
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// if the string prefix is "000" through "624".
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//
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// Credit for this trick goes to Ken.
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type leftCheat struct {
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delta int // number of new digits
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cutoff string // minus one digit if original < a.
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}
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var leftcheats = []leftCheat{
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// Leading digits of 1/2^i = 5^i.
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// 5^23 is not an exact 64-bit floating point number,
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// so have to use bc for the math.
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// Go up to 60 to be large enough for 32bit and 64bit platforms.
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/*
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seq 60 | sed 's/^/5^/' | bc |
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awk 'BEGIN{ print "\t{ 0, \"\" }," }
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{
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log2 = log(2)/log(10)
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printf("\t{ %d, \"%s\" },\t// * %d\n",
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int(log2*NR+1), $0, 2**NR)
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}'
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*/
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{0, ""},
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{1, "5"}, // * 2
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{1, "25"}, // * 4
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{1, "125"}, // * 8
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{2, "625"}, // * 16
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{2, "3125"}, // * 32
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{2, "15625"}, // * 64
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{3, "78125"}, // * 128
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{3, "390625"}, // * 256
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{3, "1953125"}, // * 512
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{4, "9765625"}, // * 1024
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{4, "48828125"}, // * 2048
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{4, "244140625"}, // * 4096
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{4, "1220703125"}, // * 8192
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{5, "6103515625"}, // * 16384
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{5, "30517578125"}, // * 32768
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{5, "152587890625"}, // * 65536
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{6, "762939453125"}, // * 131072
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{6, "3814697265625"}, // * 262144
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{6, "19073486328125"}, // * 524288
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{7, "95367431640625"}, // * 1048576
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{7, "476837158203125"}, // * 2097152
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{7, "2384185791015625"}, // * 4194304
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{7, "11920928955078125"}, // * 8388608
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{8, "59604644775390625"}, // * 16777216
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{8, "298023223876953125"}, // * 33554432
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{8, "1490116119384765625"}, // * 67108864
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{9, "7450580596923828125"}, // * 134217728
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{9, "37252902984619140625"}, // * 268435456
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{9, "186264514923095703125"}, // * 536870912
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{10, "931322574615478515625"}, // * 1073741824
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{10, "4656612873077392578125"}, // * 2147483648
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{10, "23283064365386962890625"}, // * 4294967296
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{10, "116415321826934814453125"}, // * 8589934592
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{11, "582076609134674072265625"}, // * 17179869184
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{11, "2910383045673370361328125"}, // * 34359738368
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{11, "14551915228366851806640625"}, // * 68719476736
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{12, "72759576141834259033203125"}, // * 137438953472
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{12, "363797880709171295166015625"}, // * 274877906944
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{12, "1818989403545856475830078125"}, // * 549755813888
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{13, "9094947017729282379150390625"}, // * 1099511627776
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{13, "45474735088646411895751953125"}, // * 2199023255552
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{13, "227373675443232059478759765625"}, // * 4398046511104
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{13, "1136868377216160297393798828125"}, // * 8796093022208
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{14, "5684341886080801486968994140625"}, // * 17592186044416
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{14, "28421709430404007434844970703125"}, // * 35184372088832
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{14, "142108547152020037174224853515625"}, // * 70368744177664
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{15, "710542735760100185871124267578125"}, // * 140737488355328
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{15, "3552713678800500929355621337890625"}, // * 281474976710656
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{15, "17763568394002504646778106689453125"}, // * 562949953421312
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{16, "88817841970012523233890533447265625"}, // * 1125899906842624
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{16, "444089209850062616169452667236328125"}, // * 2251799813685248
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{16, "2220446049250313080847263336181640625"}, // * 4503599627370496
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{16, "11102230246251565404236316680908203125"}, // * 9007199254740992
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{17, "55511151231257827021181583404541015625"}, // * 18014398509481984
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{17, "277555756156289135105907917022705078125"}, // * 36028797018963968
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{17, "1387778780781445675529539585113525390625"}, // * 72057594037927936
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{18, "6938893903907228377647697925567626953125"}, // * 144115188075855872
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{18, "34694469519536141888238489627838134765625"}, // * 288230376151711744
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{18, "173472347597680709441192448139190673828125"}, // * 576460752303423488
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{19, "867361737988403547205962240695953369140625"}, // * 1152921504606846976
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}
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// Is the leading prefix of b lexicographically less than s?
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func prefixIsLessThan(b []byte, s string) bool {
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for i := 0; i < len(s); i++ {
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if i >= len(b) {
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return true
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}
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if b[i] != s[i] {
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return b[i] < s[i]
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}
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}
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return false
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}
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// Binary shift left (* 2) by k bits. k <= maxShift to avoid overflow.
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func leftShift(a *decimal, k uint) {
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delta := leftcheats[k].delta
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if prefixIsLessThan(a.d[0:a.nd], leftcheats[k].cutoff) {
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delta--
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}
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r := a.nd // read index
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w := a.nd + delta // write index
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// Pick up a digit, put down a digit.
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var n uint
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for r--; r >= 0; r-- {
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n += (uint(a.d[r]) - '0') << k
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quo := n / 10
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rem := n - 10*quo
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w--
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if w < len(a.d) {
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a.d[w] = byte(rem + '0')
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} else if rem != 0 {
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a.trunc = true
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}
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n = quo
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}
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// Put down extra digits.
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for n > 0 {
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quo := n / 10
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rem := n - 10*quo
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w--
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if w < len(a.d) {
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a.d[w] = byte(rem + '0')
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} else if rem != 0 {
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a.trunc = true
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}
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n = quo
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}
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a.nd += delta
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if a.nd >= len(a.d) {
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a.nd = len(a.d)
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}
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a.dp += delta
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trim(a)
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}
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// Binary shift left (k > 0) or right (k < 0).
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func (a *decimal) Shift(k int) {
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switch {
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case a.nd == 0:
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// nothing to do: a == 0
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case k > 0:
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for k > maxShift {
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leftShift(a, maxShift)
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k -= maxShift
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}
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leftShift(a, uint(k))
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case k < 0:
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for k < -maxShift {
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rightShift(a, maxShift)
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k += maxShift
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}
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rightShift(a, uint(-k))
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}
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}
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// If we chop a at nd digits, should we round up?
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func shouldRoundUp(a *decimal, nd int) bool {
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if nd < 0 || nd >= a.nd {
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return false
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}
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if a.d[nd] == '5' && nd+1 == a.nd { // exactly halfway - round to even
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// if we truncated, a little higher than what's recorded - always round up
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if a.trunc {
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return true
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}
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return nd > 0 && (a.d[nd-1]-'0')%2 != 0
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}
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// not halfway - digit tells all
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return a.d[nd] >= '5'
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}
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// Round a to nd digits (or fewer).
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// If nd is zero, it means we're rounding
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// just to the left of the digits, as in
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// 0.09 -> 0.1.
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func (a *decimal) Round(nd int) {
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if nd < 0 || nd >= a.nd {
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return
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}
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if shouldRoundUp(a, nd) {
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a.RoundUp(nd)
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} else {
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a.RoundDown(nd)
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}
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}
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// Round a down to nd digits (or fewer).
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func (a *decimal) RoundDown(nd int) {
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if nd < 0 || nd >= a.nd {
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return
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}
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a.nd = nd
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trim(a)
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}
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// Round a up to nd digits (or fewer).
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func (a *decimal) RoundUp(nd int) {
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if nd < 0 || nd >= a.nd {
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return
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}
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// round up
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for i := nd - 1; i >= 0; i-- {
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c := a.d[i]
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if c < '9' { // can stop after this digit
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a.d[i]++
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a.nd = i + 1
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return
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}
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}
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// Number is all 9s.
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// Change to single 1 with adjusted decimal point.
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a.d[0] = '1'
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a.nd = 1
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a.dp++
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}
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// Extract integer part, rounded appropriately.
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// No guarantees about overflow.
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func (a *decimal) RoundedInteger() uint64 {
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if a.dp > 20 {
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return 0xFFFFFFFFFFFFFFFF
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}
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var i int
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n := uint64(0)
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for i = 0; i < a.dp && i < a.nd; i++ {
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n = n*10 + uint64(a.d[i]-'0')
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}
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for ; i < a.dp; i++ {
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n *= 10
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}
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if shouldRoundUp(a, a.dp) {
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n++
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}
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return n
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}
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81
decimal.go
81
decimal.go
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@ -171,17 +171,84 @@ func RequireFromString(value string) Decimal {
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// NewFromFloat converts a float64 to Decimal.
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//
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// Example:
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// The converted number will contain the number of significant digits that can be
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// represented in a float with reliable roundtrip.
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// This is typically 15 digits, but may be more in some cases.
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// See https://www.exploringbinary.com/decimal-precision-of-binary-floating-point-numbers/ for more information.
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//
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// NewFromFloat(123.45678901234567).String() // output: "123.4567890123456"
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// NewFromFloat(.00000000000000001).String() // output: "0.00000000000000001"
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//
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// NOTE: some float64 numbers can take up about 300 bytes of memory in decimal representation.
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// Consider using NewFromFloatWithExponent if space is more important than precision.
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// For slightly faster conversion, use NewFromFloatWithExponent where you can specify the precision in absolute terms.
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//
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// NOTE: this will panic on NaN, +/-inf
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func NewFromFloat(value float64) Decimal {
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return NewFromFloatWithExponent(value, math.MinInt32)
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if value == 0 {
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return New(0, 0)
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}
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return newFromFloat(value, math.Float64bits(value), &float64info)
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}
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// NewFromFloat converts a float32 to Decimal.
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//
|
||||
// The converted number will contain the number of significant digits that can be
|
||||
// represented in a float with reliable roundtrip.
|
||||
// This is typically 6-8 digits depending on the input.
|
||||
// See https://www.exploringbinary.com/decimal-precision-of-binary-floating-point-numbers/ for more information.
|
||||
//
|
||||
// For slightly faster conversion, use NewFromFloatWithExponent where you can specify the precision in absolute terms.
|
||||
//
|
||||
// NOTE: this will panic on NaN, +/-inf
|
||||
func NewFromFloat32(value float32) Decimal {
|
||||
if value == 0 {
|
||||
return New(0, 0)
|
||||
}
|
||||
// XOR is workaround for https://github.com/golang/go/issues/26285
|
||||
a := math.Float32bits(value) ^ 0x80808080
|
||||
return newFromFloat(float64(value), uint64(a)^0x80808080, &float32info)
|
||||
}
|
||||
|
||||
func newFromFloat(val float64, bits uint64, flt *floatInfo) Decimal {
|
||||
if math.IsNaN(val) || math.IsInf(val, 0) {
|
||||
panic(fmt.Sprintf("Cannot create a Decimal from %v", val))
|
||||
}
|
||||
exp := int(bits>>flt.mantbits) & (1<<flt.expbits - 1)
|
||||
mant := bits & (uint64(1)<<flt.mantbits - 1)
|
||||
|
||||
switch exp {
|
||||
case 0:
|
||||
// denormalized
|
||||
exp++
|
||||
|
||||
default:
|
||||
// add implicit top bit
|
||||
mant |= uint64(1) << flt.mantbits
|
||||
}
|
||||
exp += flt.bias
|
||||
|
||||
var d decimal
|
||||
d.Assign(mant)
|
||||
d.Shift(exp - int(flt.mantbits))
|
||||
d.neg = bits>>(flt.expbits+flt.mantbits) != 0
|
||||
|
||||
roundShortest(&d, mant, exp, flt)
|
||||
// If less than 19 digits, we can do calculation in an int64.
|
||||
if d.nd < 19 {
|
||||
tmp := int64(0)
|
||||
m := int64(1)
|
||||
for i := d.nd - 1; i >= 0; i-- {
|
||||
tmp += m * int64(d.d[i]-'0')
|
||||
m *= 10
|
||||
}
|
||||
if d.neg {
|
||||
tmp *= -1
|
||||
}
|
||||
return Decimal{value: big.NewInt(tmp), exp: int32(d.dp) - int32(d.nd)}
|
||||
}
|
||||
dValue := new(big.Int)
|
||||
dValue, ok := dValue.SetString(string(d.d[:d.nd]), 10)
|
||||
if ok {
|
||||
return Decimal{value: dValue, exp: int32(d.dp) - int32(d.nd)}
|
||||
}
|
||||
|
||||
return NewFromFloatWithExponent(val, int32(d.dp)-int32(d.nd))
|
||||
}
|
||||
|
||||
// NewFromFloatWithExponent converts a float64 to Decimal, with an arbitrary
|
||||
|
|
|
|||
224
decimal_test.go
224
decimal_test.go
|
|
@ -4,13 +4,16 @@ import (
|
|||
"database/sql/driver"
|
||||
"encoding/json"
|
||||
"encoding/xml"
|
||||
"fmt"
|
||||
"math"
|
||||
"math/big"
|
||||
"math/rand"
|
||||
"reflect"
|
||||
"sort"
|
||||
"strconv"
|
||||
"strings"
|
||||
"testing"
|
||||
"testing/quick"
|
||||
"time"
|
||||
)
|
||||
|
||||
|
|
@ -42,9 +45,19 @@ var testTable = []*testEnt{
|
|||
{.1000000000000003, "0.1000000000000003", "", "0.1000000000000003000000000000001234123412"},
|
||||
{.1000000000000005, "0.1000000000000005", "", "0.1000000000000005000000000000000006441234"},
|
||||
{.1000000000000008, "0.1000000000000008", "", "0.100000000000000800000000000000000009999999999999999999999999999"},
|
||||
{1e25, "10000000000000000000000000", "", "10000000000000000000000000.00000000000000000098798978"},
|
||||
{math.MaxInt64, strconv.FormatInt(math.MaxInt64, 10), "", strconv.FormatInt(math.MaxInt64, 10)},
|
||||
{1.29067116156722e-309, "0", "", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001290671161567218558822290567835270536800098852722416870074139002112543896676308448335063375297788379444685193974290737962187240854947838776604607190387984577130572928111657710645015086812756013489109884753559084166516937690932698276436869274093950997935137476803610007959500457935217950764794724766740819156974617155861568214427828145972181876775307023388139991104942469299524961281641158436752347582767153796914843896176260096039358494077706152272661453132497761307744086665088096215425146090058519888494342944692629602847826300550628670375451325582843627504604013541465361435761965354140678551369499812124085312128659002910905639984075064968459581691226705666561364681985266583563078466180095375402399087817404368974165082030458595596655868575908243656158447265625000000000000000000000000000000000000004440000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"},
|
||||
{1e25, "10000000000000000000000000", "", ""},
|
||||
{1.5e14, "150000000000000", "", ""},
|
||||
{1.5e15, "1500000000000000", "", ""},
|
||||
{1.5e16, "15000000000000000", "", ""},
|
||||
{1.0001e25, "10001000000000000000000000", "", ""},
|
||||
{1.0001000000000000033e25, "10001000000000000000000000", "", ""},
|
||||
{2e25, "20000000000000000000000000", "", ""},
|
||||
{4e25, "40000000000000000000000000", "", ""},
|
||||
{8e25, "80000000000000000000000000", "", ""},
|
||||
{1e250, "10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "", ""},
|
||||
{2e250, "20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "", ""},
|
||||
{math.MaxInt64, strconv.FormatFloat(float64(math.MaxInt64), 'f', -1, 64), "", strconv.FormatInt(math.MaxInt64, 10)},
|
||||
{1.29067116156722e-309, "0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000129067116156722", "", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001290671161567218558822290567835270536800098852722416870074139002112543896676308448335063375297788379444685193974290737962187240854947838776604607190387984577130572928111657710645015086812756013489109884753559084166516937690932698276436869274093950997935137476803610007959500457935217950764794724766740819156974617155861568214427828145972181876775307023388139991104942469299524961281641158436752347582767153796914843896176260096039358494077706152272661453132497761307744086665088096215425146090058519888494342944692629602847826300550628670375451325582843627504604013541465361435761965354140678551369499812124085312128659002910905639984075064968459581691226705666561364681985266583563078466180095375402399087817404368974165082030458595596655868575908243656158447265625000000000000000000000000000000000000004440000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"},
|
||||
}
|
||||
|
||||
var testTableScientificNotation = map[string]string{
|
||||
|
|
@ -89,11 +102,11 @@ func init() {
|
|||
|
||||
func TestNewFromFloat(t *testing.T) {
|
||||
for _, x := range testTable {
|
||||
s := x.exact
|
||||
s := x.short
|
||||
d := NewFromFloat(x.float)
|
||||
if d.String() != s {
|
||||
t.Errorf("expected %s, got %s (%s, %d)",
|
||||
s, d.String(),
|
||||
t.Errorf("expected %s, got %s (float: %v) (%s, %d)",
|
||||
s, d.String(), x.float,
|
||||
d.value.String(), d.exp)
|
||||
}
|
||||
}
|
||||
|
|
@ -112,6 +125,121 @@ func TestNewFromFloat(t *testing.T) {
|
|||
}
|
||||
}
|
||||
|
||||
func TestNewFromFloatRandom(t *testing.T) {
|
||||
n := 0
|
||||
rng := rand.New(rand.NewSource(0xdead1337))
|
||||
for {
|
||||
n++
|
||||
if n == 10 {
|
||||
break
|
||||
}
|
||||
in := (rng.Float64() - 0.5) * math.MaxFloat64 * 2
|
||||
want, err := NewFromString(strconv.FormatFloat(in, 'f', -1, 64))
|
||||
if err != nil {
|
||||
t.Error(err)
|
||||
continue
|
||||
}
|
||||
got := NewFromFloat(in)
|
||||
if !want.Equal(got) {
|
||||
t.Errorf("in: %v, expected %s (%s, %d), got %s (%s, %d) ",
|
||||
in, want.String(), want.value.String(), want.exp,
|
||||
got.String(), got.value.String(), got.exp)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestNewFromFloatQuick(t *testing.T) {
|
||||
err := quick.Check(func(f float64) bool {
|
||||
want, werr := NewFromString(strconv.FormatFloat(f, 'f', -1, 64))
|
||||
if werr != nil {
|
||||
return true
|
||||
}
|
||||
got := NewFromFloat(f)
|
||||
return got.Equal(want)
|
||||
}, &quick.Config{})
|
||||
if err != nil {
|
||||
t.Error(err)
|
||||
}
|
||||
}
|
||||
|
||||
func TestNewFromFloat32Random(t *testing.T) {
|
||||
n := 0
|
||||
rng := rand.New(rand.NewSource(0xdead1337))
|
||||
for {
|
||||
n++
|
||||
if n == 10 {
|
||||
break
|
||||
}
|
||||
in := float32((rng.Float64() - 0.5) * math.MaxFloat32 * 2)
|
||||
want, err := NewFromString(strconv.FormatFloat(float64(in), 'f', -1, 32))
|
||||
if err != nil {
|
||||
t.Error(err)
|
||||
continue
|
||||
}
|
||||
got := NewFromFloat32(in)
|
||||
if !want.Equal(got) {
|
||||
t.Errorf("in: %v, expected %s (%s, %d), got %s (%s, %d) ",
|
||||
in, want.String(), want.value.String(), want.exp,
|
||||
got.String(), got.value.String(), got.exp)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestNewFromFloat32Quick(t *testing.T) {
|
||||
err := quick.Check(func(f float32) bool {
|
||||
want, werr := NewFromString(strconv.FormatFloat(float64(f), 'f', -1, 32))
|
||||
if werr != nil {
|
||||
return true
|
||||
}
|
||||
got := NewFromFloat32(f)
|
||||
return got.Equal(want)
|
||||
}, &quick.Config{})
|
||||
if err != nil {
|
||||
t.Error(err)
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkNewFromFloatWithExponent(b *testing.B) {
|
||||
rng := rand.New(rand.NewSource(0xdead1337))
|
||||
in := make([]float64, b.N)
|
||||
for i := range in {
|
||||
in[i] = rng.NormFloat64() * 10e20
|
||||
}
|
||||
b.ReportAllocs()
|
||||
b.StartTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
in := rng.NormFloat64() * 10e20
|
||||
_ = NewFromFloatWithExponent(in, math.MinInt32)
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkNewFromFloat(b *testing.B) {
|
||||
rng := rand.New(rand.NewSource(0xdead1337))
|
||||
in := make([]float64, b.N)
|
||||
for i := range in {
|
||||
in[i] = rng.NormFloat64() * 10e20
|
||||
}
|
||||
b.ReportAllocs()
|
||||
b.StartTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
_ = NewFromFloat(in[i])
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkNewFromStringFloat(b *testing.B) {
|
||||
rng := rand.New(rand.NewSource(0xdead1337))
|
||||
in := make([]float64, b.N)
|
||||
for i := range in {
|
||||
in[i] = rng.NormFloat64() * 10e20
|
||||
}
|
||||
b.ReportAllocs()
|
||||
b.StartTimer()
|
||||
for i := 0; i < b.N; i++ {
|
||||
in := strconv.FormatFloat(in[i], 'f', -1, 64)
|
||||
_, _ = NewFromString(in)
|
||||
}
|
||||
}
|
||||
|
||||
func TestNewFromString(t *testing.T) {
|
||||
for _, x := range testTable {
|
||||
s := x.short
|
||||
|
|
@ -151,6 +279,9 @@ func TestNewFromString(t *testing.T) {
|
|||
|
||||
func TestFloat64(t *testing.T) {
|
||||
for _, x := range testTable {
|
||||
if x.inexact == "" || x.inexact == "-" {
|
||||
continue
|
||||
}
|
||||
s := x.exact
|
||||
d, err := NewFromString(s)
|
||||
if err != nil {
|
||||
|
|
@ -2301,15 +2432,15 @@ func TestAtan(t *testing.T) {
|
|||
"11000020.2407442310156021090304691671842603586882014729198302312846062338790031898128063403419218957424",
|
||||
}
|
||||
sols := []string{
|
||||
"-1.2407643882205801102743706275310603586882014729198302312846062338790031898128063403419218957424163818359375",
|
||||
"-0.78539816339744833061616997868383017934410073645991511564230311693950159490640317017096094787120819091796875",
|
||||
"-1.24076438822058001027437062753106",
|
||||
"-0.78539816339744833061616997868383",
|
||||
"-0.24497866312686415",
|
||||
"0.0",
|
||||
"0.318747560420644443",
|
||||
"0.78539816339744833061616997868383017934410073645991511564230311693950159490640317017096094787120819091796875",
|
||||
"1.3734007669450159012323399573676603586882014729198302312846062338790031898128063403419218957424163818359375",
|
||||
"1.4711276743037346312323399573676603586882014729198302312846062338790031898128063403419218957424163818359375",
|
||||
"1.5707962358859730612325945023537403586882014729198302312846062338790031898128063403419218957424163818359375",
|
||||
"0.78539816339744833061616997868383",
|
||||
"1.37340076694501580123233995736766",
|
||||
"1.47112767430373453123233995736766",
|
||||
"1.57079623588597296123259450235374",
|
||||
}
|
||||
for i, inp := range inps {
|
||||
d, err := NewFromString(inp)
|
||||
|
|
@ -2340,16 +2471,15 @@ func TestSin(t *testing.T) {
|
|||
"10",
|
||||
"11000020.2407442310156021090304691671842603586882014729198302312846062338790031898128063403419218957424",
|
||||
}
|
||||
sols := []string{
|
||||
"-0.220571862520030093613839729898389234591448264443828979962999436149729548845614563657783710150808249493659603883785557750857064742068654401611592366453156979425089038732558977915147138610177101332138819745624841999009731533470874398791630404814623756725761484209848526893621903868344844362592350061614721709283168025028307789990557501123216276655612701350632840149744527732872833304632776220881820168763715880072271900752263175824768749676997835634284780882959485313122780499486873741058283218325040301421620652217699025347852371634749059985101913743575566482455108757945784327770283152556778940395109157571785095552777237471737930299497127855782791647416409676751196562400230573256919649166116220548146722732673811940013822174052471575484241086300786209457059067702404625074214637302180559257156598478224357461349695824437855046828206155188482292930722180491096361781653423287753045189099820938975700063357767823639345982521057442719437079960883170296730778877529726323641962581167118741985973085143794261349309399843621404104514700512532703761239968546841161640494797236796414402075947283426422877298624337798757146020442229118476349906575010431352541089067121029579490866064323880357132858662072455977109093817967157613567800944577216024589669093782841129397681562208313003621389103425798339230823330581188201904296875",
|
||||
"-0.84147098480789650683573384227719871264659725213827912307678945963233888758666252541652307542471941569920950873234694687123276222626964952320957348347806244448304658355378064371162688704108432893734339281119107889886243608606771440333499496399246182550579552307436056577989755048676139388257574972355638331020916986327112812449023235994235220681962126402627149122741398037411569225585167209440887381294958909446263040889436515610243685011381400045762457675558838333095494482138227725013381292722259213324814381642325470123171162316406069142833674558352099403808484142312206036567122374357983536120130367436871049536150555321227634134943262101222587962853023526365048081446005272233936756658798560188088496199440605960018665932771208203273875932636591008594752836095901878899636892331191188133444513639520743904232369072391326448163751628578886099960312207261234582748222511007033947148867295201489673608530271710726980420265749989442268185776660104680951516862727780322815011940555693819786827407000470928166813302681223319136916385379500478197064927760223020342764479386095349145229773585152310192696649682836151684354735282894320955021997802761069713870309184654536840910246184967655772931790056052366745119986847633246318705770507591911530119455091063686301656648189606417807689546576464738456252196397075290117772324937902655849801056962584258183367906235526162380299193832940968379238027598232552151102936477400362491607666015625",
|
||||
"-0.247403959254522929719728461264852108650160857317149198152655832001777826134603088803487480618059635162353515625",
|
||||
"0.0",
|
||||
"0.324043028394868345912501559420824735488967340443112210114701957327566252120565337691004970110952854156494140625",
|
||||
"0.84147098480789650683573384227719871264659725213827912307678945963233888758666252541652307542471941569920950873234694687123276222626964952320957348347806244448304658355378064371162688704108432893734339281119107889886243608606771440333499496399246182550579552307436056577989755048676139388257574972355638331020916986327112812449023235994235220681962126402627149122741398037411569225585167209440887381294958909446263040889436515610243685011381400045762457675558838333095494482138227725013381292722259213324814381642325470123171162316406069142833674558352099403808484142312206036567122374357983536120130367436871049536150555321227634134943262101222587962853023526365048081446005272233936756658798560188088496199440605960018665932771208203273875932636591008594752836095901878899636892331191188133444513639520743904232369072391326448163751628578886099960312207261234582748222511007033947148867295201489673608530271710726980420265749989442268185776660104680951516862727780322815011940555693819786827407000470928166813302681223319136916385379500478197064927760223020342764479386095349145229773585152310192696649682836151684354735282894320955021997802761069713870309184654536840910246184967655772931790056052366745119986847633246318705770507591911530119455091063686301656648189606417807689546576464738456252196397075290117772324937902655849801056962584258183367906235526162380299193832940968379238027598232552151102936477400362491607666015625",
|
||||
"-0.95892427466313846886683534084169138601699178595056142681129038893400410281163045903621198874295374290149806823897075576057724999482959874362888984630786877750800707948164478439888413437709227541296453939066231042449153560817956529124771991719434464325257307490209688817348630841990228088502580219431623697760216390920129365244393334429239217501291865772417470981461975427863913628459487634361457463896191397206119089801538318057594728767278995563353925328463456560840888895608182514323808823801838724482524462741712473496938668730262585034295941891365544300178534659369917661430555201335114597830077556398746790054730682231578093617522006106659977088453875512527401574137870617360741477467052899927465250688663724908651769559466919777914497651416655110015287957761809374118954830175592272643086681859204507636705728518901196924686915642366269243409467335313632803457424138328976320449572075303129501941586734619627126950347146441488301272523732890971103193432131967093584975094064352688636321088866275878367912478080039614015674090467373532503838989934725811696669260106530065305130564789502177378344025691707116401561519233199329283661803416619394138904068356512359009119169667571681552281997620458915816124425995894145459910451225779660911316891499301549117918834162954131295015995478902576153796243561887919093281708146016725119431774666779045011119428333353937254827947830587875729623490751729608660980375134386122226715087890625",
|
||||
"-0.544021110889369814404798546234261521735237410341301440744913863554325413910729487222404754912397132389280869582562649416317020824255899391102716253549602359933406667420857908751554064982667505778980864397665237869392769251295144996601379178780771501957858736340861984904014191524939793604688756271913886434778180316203812548425041682948461830667971245994025528380063656691687013885731759172341309655658172703937945366976128597657101230629806658897303549468649147494313422814604383947907342285887634159176609268080528703630505118954169027929142559898709956536517735787676487117591429732597764129997800544321069045676840705169697409709450991200259966568075515292000715246707423119024660809599616729869855242609248565503156233847151639381625642548896051440565640966333400046266460293523862957282305141303657282623793830073310394349418290939283661501995774676808852008306303431767521000117474347792119119745767325061425517820206720145795639782171641765977980488850129569363740173287329545019826050789666603219553652178298235868990551128361160456166647394642535572127727629420370720856130359966967599668830582910424823037763854828905673063487188976311335956440851988180468345725600705105113853947651574770698730911647817190648000646872041955859376392859382055300138695355787127336060458870914402496055117808282375335693359375",
|
||||
"-0.564291758073920672156060501108780948637502927903402695682970758082173347334144085493099932047342878232107294208163423635351694839181128599190761981992082190183414367145761958978263205360050276797203465120166463337285861568628620441149869080262018002460551105733370384496691552603807079787064355499979892738941692390909198368605275928720995456124329350110140031040327865030504338978174244479702663590952255309812151905391076362043165507118546398673253957125454990703254702293833362635280840010399956637688760201442320428708562854314419339362472820724298986435162931641340060501848890585327411159080467227885852591584159465243368331681937734746160681439404005233844642476786199607795910618003577395193096223575912506207477927572401934790710176468073033112942732454695154492720511230782735184156027155137618173659003878927697237751139877779082916148874086491265428313018347132700490228131397266369640661232003084568637049642401980172435548737268283623715380443755530399410106957744899992161330205161097513785489406292271887390739430612193060474304401657511461250218562733033893187306639264886516827894130028111468708805823753758224864450015655567869605537758979198887215555526950741196023433812962018677695204317878927956155283357420412564940844662156159296973147878187706628631717213628871121500196750275790691375732421875",
|
||||
sols := []string{"-0.22057186252002995641471297726318877448242875710373383657841216606788849153474483300147427943530288911869356126149550184271061369789963810497434594683859566879253561990821788142048867910104964466745284318577343435957806286762494529983369776697504436326725441516925396488258485248699247367113416543705253919473126183478178486954138205996912770183192357029798618739277146694040778731661407420114923656224752540889120768",
|
||||
"-0.841470984807896544828551915928318375739843472469519282898610111931110319333748010828751784005573402229699531838022117989945539661588502120624574802425114599802714611508860519655182175315926637327774878594985045816542706701485174683683726979309922117859910272413672784175028365607893544855897795184024100973080880074046886009375162838756876336134083638363801171409953672944184918309063800980214873465660723218405962257950683415203634506166523593278",
|
||||
"-0.2474039592545229296662577977006816864013671875",
|
||||
"0",
|
||||
"0.3240430283948683457891331120415701894104386268737728",
|
||||
"0.841470984807896544828551915928318375739843472469519282898610111931110319333748010828751784005573402229699531838022117989945539661588502120624574802425114599802714611508860519655182175315926637327774878594985045816542706701485174683683726979309922117859910272413672784175028365607893544855897795184024100973080880074046886009375162838756876336134083638363801171409953672944184918309063800980214873465660723218405962257950683415203634506166523593278",
|
||||
"-0.958924274663138409032065951037351417114444405831206421994322505831797734568720303321152847999323782235893449831846516332891972309733806145798957570823292783131379570446989311599459252931842975162373777189193072018951049969744350662993214861042908755303566670204873618202680865638534865944483058650517380292320436016362659617294570185140789829574277032406195741535138712427510938542219940873171248862329526140744770994303733112530324791184417282382",
|
||||
"-0.54402111088937016772477554483765124109312606762621462357463994520238396180161585438877562935656067241573063207614488370477645194661241525080677431257416988398683714890165970942834453391033857378247849486306346743023618509617104937236345831462093934032592562972419977883837745736210439651143668255744843041350221801750331646628192115694352540293150183983357476391787825596543270240461102629075832777618592034309799936",
|
||||
"-0.564291758480422881634770440632390475980828840253516895637281099241819037882007239070203007530085741820184955492382572029153491807930868879341091067301689987699567034024159005627332722089169680203292567574310010066799858914647295684974242359142300929248173166551428537696685165964880390889406578530338963341989826231514301546476672476399906348023294571001061677668735117509440368611093448917120819545826797975989350435900286332895885871219875665471968941335407351099209738417818747252638912592184093301853338763294381446907254104878969784040526201729163408095795934201105630182851806342356035203279670146684553491616847294749721014579109870396804713831114709372638323643327823671187472335866664108658093206409882794958673673978956925250261545083579947618620746006004554405785185537391110314728988164693223775249484198058394348289545771967707968288542718255197272633789792059019367104377340604030147471453833808674013259696102003732963091159662478879760121731138091114134586544668859915547568540172541576138084166990547345181184322550297604278946942918844039406876827936831612756344331500301118652183156052728447906384772901595431751550607818380262138322673253023464533931883787069611052589166000316238423939491520880451263927981787175602294299295744",
|
||||
}
|
||||
for i, inp := range inps {
|
||||
d, err := NewFromString(inp)
|
||||
|
|
@ -2381,15 +2511,15 @@ func TestCos(t *testing.T) {
|
|||
"11000020.2407442310156021090304691671842603586882014729198302312846062338790031898128063403419218957424",
|
||||
}
|
||||
sols := []string{
|
||||
"-0.975370726167463436728505866323714237868918798735337852490354630275400590397256757982930518671177656988788392411709345759154371178337418085499048191038650091945778580197329516971729513331012900776507504230803826799226710606177535289143559059224362661001603838745169803182674368143452935332062804519861768577138064573259069358975042122485627388192604101700302462362798592115038066626006203292151971117547825788365029212778673068841445412348366566041687247190622871297208478844658065023427261675103854131453079888921085982507674462174796122088474426882259116347806427809304457623578281770915649130727943036401841073052876646614496797452163682420483896962238944883515469778180754205404941121141599952645904787654598990827384683885441411829970587806867632776521257761008506280475694989732289455150722563701599552835784792787892378475275568451704113581492707873602587027241507884412830033365653914549639245334821262039117311046735253960816076120011217151854994903031629514573221302055487026138480621515317251868170670711382669181677841187033304861609062981031260474272177938456322715827189878292157663041430578246790062347759217920400856872733420989333068628730367636465064551304273677450773043171019346261214827671284261815921602597267030573778706635242318228554033918329328451836597811660816887574069149657366695399451977163530476815743551656054860762997757628606444388219917589048259254358441694421344436705112457275390625",
|
||||
"0.5403023058681397185594704958555785318789737039530258806063132922287686731767103380722879951346341700301934154242672285869862285136280035256635149087722026456653060623287636554810379311566025776640284286043366692017812351065106848975433243878434601646053373656175870219143335780037780263780528022552589948882631781788387243759097393407418459341665025578959743680402679565710214589639277870162089735459876789876164945626397889278949094061300698882180972876375063478762441763141045691438279791675986386217937407677843979434037325100615614204173839676230023544297002103390623811623287987178412049715000660987495684907814359780765658960715423795658408220614069561530422742718922893554271137549412369147629593458239490366605797325139239944180051692566520667214675204069476110320173267646327440417945329562672924843423546460029298423629611979148079742086487910832189641973781754022003095306885302971446512196936121388134045074972570593581133444925052909080976768554628154520121141808489601642421723177702083881285314379847744230155051966361158007017591582046619808944751148550841102122653076944135728372456492657514171872121435155305860386442665726120257630353953444221670261220705805623292334551636518107895571396829211893470388375917284217734121333575035514871632238034279250742569584498765995392820238318876135963364504277706146240234375",
|
||||
"0.968912421710644784098953478920868172610959295777507211448260716808741793725813506998889579335809685289859771728515625",
|
||||
"1.0",
|
||||
"0.946042343528386971548655274719127421974169853736868957009626534392384054569270779300182994120405055582523345947265625",
|
||||
"0.5403023058681397185594704958555785318789737039530258806063132922287686731767103380722879951346341700301934154242672285869862285136280035256635149087722026456653060623287636554810379311566025776640284286043366692017812351065106848975433243878434601646053373656175870219143335780037780263780528022552589948882631781788387243759097393407418459341665025578959743680402679565710214589639277870162089735459876789876164945626397889278949094061300698882180972876375063478762441763141045691438279791675986386217937407677843979434037325100615614204173839676230023544297002103390623811623287987178412049715000660987495684907814359780765658960715423795658408220614069561530422742718922893554271137549412369147629593458239490366605797325139239944180051692566520667214675204069476110320173267646327440417945329562672924843423546460029298423629611979148079742086487910832189641973781754022003095306885302971446512196936121388134045074972570593581133444925052909080976768554628154520121141808489601642421723177702083881285314379847744230155051966361158007017591582046619808944751148550841102122653076944135728372456492657514171872121435155305860386442665726120257630353953444221670261220705805623292334551636518107895571396829211893470388375917284217734121333575035514871632238034279250742569584498765995392820238318876135963364504277706146240234375",
|
||||
"0.2836621854632262640413454705014792126730041372592792257206146645426601396441260356011571632089582618925838153657699769828738164020634023542401271546832973668591965970780399287846132178786932147719489387057249755694634919271032742386467263343003762216059912285589934893404186137482489686474984451054771103493648603655340770275593072267521598532667125806036270513157359920795997662877180316554125323347714021810156977000099765637673158040510070215919734518464013962899531358902754977185164550708058199871247160015886870149163066556093196783440812874006182781633602366172183573725257608628866745555998550377960547686470245458626674802626292796549871502254193653242073557087898962773658255810053531370802115864997325060870572958692356612208396119690852149106422002310275167937817158288794799498840438933404405058238604063789542363766559068475105058515056790385539505205746157593694133334912162302627008416603294000615739181111749007688625782080015509782711717307370897514073199106746929535880890780214210719294387601483817437596151502942142722181977054762243644235893248214844557965863434535805464134779033144520828071538407409414463996182938827134980848798774952211899634360773590821173224015934994691863733763099257382589344052735164638723090648652823314675360473802118354232333173901927332659182734442282480813446454703807830810546875",
|
||||
"-0.839071529076452452453116298055375283024545196907005751226679269494945423257632785713674884440909521085910953206821682885350514489569383484553680293874464258013074629595233233440423524040185080138431677219644537006650333440982266180848432613265727672098505530500860099490052714852637696219860623419861733967504942346257426883650461547676693756422205686582533132927538864456011428540560137047577109540901355332714454892042154044099772961016405398585134639556422987015399944634792029504830682794892974110049771680445087591216461375304720930330852114906188605879368500242393092090599991056282929140339515922705640197683216586300345608814191348583643897583052496585038234458432300602598656172228800591628810870703061601079842675931288590090649649722933122710180797353905585641576282107791663819561479911160784057959370842865399560455463184561649904326467913053219927760200406450092385176263660350059186320075841952511620387666555291853410264149054381143798602019026379808898830628940629734269442061546806433026794983473131041596411391519359668360706593453379582689919628495055879290310156211842712529358591580000339115277557733264569390191184923563095676385834461753760385376605508361399123052214852866448517012467160704995276728328831739643710159503245565807479821789258404871375420699263398077037976545179716664243275062643380243567701961405078734621807138136709079831010972563517559541512724763379083015024662017822265625",
|
||||
"-0.825575442809343611824362325239811764094510857054278582264067433862269037693599066167126550050055810893236466513641579446123546053932400340779013543022627343780304207889697484852104716170210387967098979368968667582761587933736919053415297219989844530337025837550322738303417999408570541023209479831053490074672524731593393200211612747267787376420912055466715589243670137116181283653627378091767001266729750523670904813955028404725364549436654773973161631448021217524149606880882398338428340541423336476442278764927060929088442662022809429880029452211569992113848964950861453209500601571720208371076364637312918805739974730928391130012733244321591317884640789514132100142038718855057870855384682083191451172141637084656463668180074273357513986650562276924927490092054490207521493248546634803683905992004777812863248355102626794030220223795127136641375381651724046389855784239897808572076152799212203148992979849462537797025824681362178656342679605636982892165755312758468261428421302359039383473990693745647491195856344807310687765672840471336376933282820265780965117564858639226791165667469629053398278240657443123596015059287606479740468263567953594727359402416208210264162078048896806628308236533843407536450642386891796397818074083632855343175466156403711148552219179067451933509186842662133841059218230787130271284099320325244795528905606899665072032213644123281103167139222988313296269780039438046514987945556640625",
|
||||
"-0.975370726167463467746508538219884948528729295145689640359666742268127382748782064668565276308334226452812521220478854320025773591423493734486361306323829818426063430805234608660356853863442937297855742231573288105774823103008774355455799906250461848079705023428527473474556899228935370709945979509634251305018978306493011197513482210179171510947538040406781879762352211326273272515279567525396877609653501706919545667682725671944948392322552266752",
|
||||
"0.54030230586813965874561515067176071767603141150991567490927772778673118786033739102174242337864109186439207498973007363884202112942385976796862442063752663646870430360736682397798633852405003167527051283327366631405990604840629657123985368031838052877290142895506386796217551784101265975360960112885444847880134909594560331781699767647860744559228420471946006511861233129745921297270844542687374552066388998112901504",
|
||||
"0.968912421710644784099084544806854121387004852294921875",
|
||||
"1",
|
||||
"0.9460423435283869715490383692051286742343482760977712222",
|
||||
"0.54030230586813965874561515067176071767603141150991567490927772778673118786033739102174242337864109186439207498973007363884202112942385976796862442063752663646870430360736682397798633852405003167527051283327366631405990604840629657123985368031838052877290142895506386796217551784101265975360960112885444847880134909594560331781699767647860744559228420471946006511861233129745921297270844542687374552066388998112901504",
|
||||
"0.28366218546322646623291670213892426815646045792775066552057877370468842342090306560693620285882975471913545189522117672866861003904575909174769890684057564495184019705963607555427518763375472432216131070235796577209064861003009894615394882021220247535890708789312783718414424224334988974848162884228012265684775651099758365989567444515619764427493598258393280941942356912304265535918025036942025858493361644535438208",
|
||||
"-0.839071529076452222947082170022504835457755803801719612447629165523199043803440231769716865070163209041973184176293170330332317060558438085478980463542480791358920580076809381102480339018809694514100495572097422057215638383077242523713704127605770444906854175870243452753002238589530499630034663296166308443155999957196346563161387705205277189957388653461251461388391745795979375660087266037741360406956289962327970672363315696841378765492754546688",
|
||||
"-0.82557544253149396284458404188071504476091346830440347376462206521981928020803354950315062147200396866217255527509254080721982393941347365824137698491042935894213870423296625749297033966815252917361266452901192457318047750698424190124169875103436588397415032138037063155981648677895645409699825582226442363080800781881653440538927704569142007751338851079530521979429507520541625303794665680584709171813053216867014700596866196844144286737568957809383224972108999354839705480223052622003994027222120126949093911643497423100187973906980635670000034664323357488815820848035808846624518774608931622703631130673844138378087837990739103263093532314835289302930152150130664948083902949999427848344301686172490282395687167681679607401220592559832932068966455384902377056623736013617949634746332323529256184776892339963173795176200590119077305668901887229709592836744082027738666294887303249770621722032438202753270710379312736193201366287952361100525126056993039858894987153270630277483613793395809214871734783742285495171911648254647287555645360520115341268930844095156502348405343740866836850201634640011708462641462047870611041595707018966032206807675586825362640000739202116391403514629284000986232673698892843586989003952425039512325844566790376383098534975022847888104706525937115931692008959513984157709954859352131323440787667052399474107219968",
|
||||
}
|
||||
for i, inp := range inps {
|
||||
d, err := NewFromString(inp)
|
||||
|
|
@ -2421,15 +2551,15 @@ func TestTan(t *testing.T) {
|
|||
"11000020.2407442310156021090304691671842603586882014729198302312846062338790031898128063403419218957424",
|
||||
}
|
||||
sols := []string{
|
||||
"0.226141565050579195128504091376587961550743024795950198353192839504353407742431869564825319685041904449462890625",
|
||||
"-1.5574077246549022",
|
||||
"0.2261415650505790298980791606748881031998682652",
|
||||
"-1.5574077246549025",
|
||||
"-0.255341921221036275",
|
||||
"0.0",
|
||||
"0.342524867530038963",
|
||||
"1.5574077246549022",
|
||||
"-3.3805150062465857",
|
||||
"0.648360827459086657992079596346674836000458368506527382600293171822426231687419573290753760375082492828369140625",
|
||||
"0.683513254892486971935899897806108130234891903543492515192842067427622421368508870073710248504975849182264766875",
|
||||
"1.5574077246549025",
|
||||
"-3.3805150062465829",
|
||||
"0.6483608274590872485524085572681343280321117494",
|
||||
"0.68351325561491170753499935023939368502774607234006019034769919811202010905597996164029250820702097041244539696",
|
||||
}
|
||||
for i, inp := range inps {
|
||||
d, err := NewFromString(inp)
|
||||
|
|
@ -2446,3 +2576,23 @@ func TestTan(t *testing.T) {
|
|||
}
|
||||
}
|
||||
}
|
||||
|
||||
func ExampleNewFromFloat32() {
|
||||
fmt.Println(NewFromFloat32(123.123123123123).String())
|
||||
fmt.Println(NewFromFloat32(.123123123123123).String())
|
||||
fmt.Println(NewFromFloat32(-1e13).String())
|
||||
// OUTPUT:
|
||||
//123.12312
|
||||
//0.123123124
|
||||
//-10000000000000
|
||||
}
|
||||
|
||||
func ExampleNewFromFloat() {
|
||||
fmt.Println(NewFromFloat(123.123123123123).String())
|
||||
fmt.Println(NewFromFloat(.123123123123123).String())
|
||||
fmt.Println(NewFromFloat(-1e13).String())
|
||||
// OUTPUT:
|
||||
//123.123123123123
|
||||
//0.123123123123123
|
||||
//-10000000000000
|
||||
}
|
||||
|
|
|
|||
118
rounding.go
Normal file
118
rounding.go
Normal file
|
|
@ -0,0 +1,118 @@
|
|||
// 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 decimal
|
||||
|
||||
type floatInfo struct {
|
||||
mantbits uint
|
||||
expbits uint
|
||||
bias int
|
||||
}
|
||||
|
||||
var float32info = floatInfo{23, 8, -127}
|
||||
var float64info = floatInfo{52, 11, -1023}
|
||||
|
||||
// roundShortest rounds d (= mant * 2^exp) to the shortest number of digits
|
||||
// that will let the original floating point value be precisely reconstructed.
|
||||
func roundShortest(d *decimal, mant uint64, exp int, flt *floatInfo) {
|
||||
// If mantissa is zero, the number is zero; stop now.
|
||||
if mant == 0 {
|
||||
d.nd = 0
|
||||
return
|
||||
}
|
||||
|
||||
// Compute upper and lower such that any decimal number
|
||||
// between upper and lower (possibly inclusive)
|
||||
// will round to the original floating point number.
|
||||
|
||||
// We may see at once that the number is already shortest.
|
||||
//
|
||||
// Suppose d is not denormal, so that 2^exp <= d < 10^dp.
|
||||
// The closest shorter number is at least 10^(dp-nd) away.
|
||||
// The lower/upper bounds computed below are at distance
|
||||
// at most 2^(exp-mantbits).
|
||||
//
|
||||
// So the number is already shortest if 10^(dp-nd) > 2^(exp-mantbits),
|
||||
// or equivalently log2(10)*(dp-nd) > exp-mantbits.
|
||||
// It is true if 332/100*(dp-nd) >= exp-mantbits (log2(10) > 3.32).
|
||||
minexp := flt.bias + 1 // minimum possible exponent
|
||||
if exp > minexp && 332*(d.dp-d.nd) >= 100*(exp-int(flt.mantbits)) {
|
||||
// The number is already shortest.
|
||||
return
|
||||
}
|
||||
|
||||
// d = mant << (exp - mantbits)
|
||||
// Next highest floating point number is mant+1 << exp-mantbits.
|
||||
// Our upper bound is halfway between, mant*2+1 << exp-mantbits-1.
|
||||
upper := new(decimal)
|
||||
upper.Assign(mant*2 + 1)
|
||||
upper.Shift(exp - int(flt.mantbits) - 1)
|
||||
|
||||
// d = mant << (exp - mantbits)
|
||||
// Next lowest floating point number is mant-1 << exp-mantbits,
|
||||
// unless mant-1 drops the significant bit and exp is not the minimum exp,
|
||||
// in which case the next lowest is mant*2-1 << exp-mantbits-1.
|
||||
// Either way, call it mantlo << explo-mantbits.
|
||||
// Our lower bound is halfway between, mantlo*2+1 << explo-mantbits-1.
|
||||
var mantlo uint64
|
||||
var explo int
|
||||
if mant > 1<<flt.mantbits || exp == minexp {
|
||||
mantlo = mant - 1
|
||||
explo = exp
|
||||
} else {
|
||||
mantlo = mant*2 - 1
|
||||
explo = exp - 1
|
||||
}
|
||||
lower := new(decimal)
|
||||
lower.Assign(mantlo*2 + 1)
|
||||
lower.Shift(explo - int(flt.mantbits) - 1)
|
||||
|
||||
// The upper and lower bounds are possible outputs only if
|
||||
// the original mantissa is even, so that IEEE round-to-even
|
||||
// would round to the original mantissa and not the neighbors.
|
||||
inclusive := mant%2 == 0
|
||||
|
||||
// Now we can figure out the minimum number of digits required.
|
||||
// Walk along until d has distinguished itself from upper and lower.
|
||||
for i := 0; i < d.nd; i++ {
|
||||
l := byte('0') // lower digit
|
||||
if i < lower.nd {
|
||||
l = lower.d[i]
|
||||
}
|
||||
m := d.d[i] // middle digit
|
||||
u := byte('0') // upper digit
|
||||
if i < upper.nd {
|
||||
u = upper.d[i]
|
||||
}
|
||||
|
||||
// Okay to round down (truncate) if lower has a different digit
|
||||
// or if lower is inclusive and is exactly the result of rounding
|
||||
// down (i.e., and we have reached the final digit of lower).
|
||||
okdown := l != m || inclusive && i+1 == lower.nd
|
||||
|
||||
// Okay to round up if upper has a different digit and either upper
|
||||
// is inclusive or upper is bigger than the result of rounding up.
|
||||
okup := m != u && (inclusive || m+1 < u || i+1 < upper.nd)
|
||||
|
||||
// If it's okay to do either, then round to the nearest one.
|
||||
// If it's okay to do only one, do it.
|
||||
switch {
|
||||
case okdown && okup:
|
||||
d.Round(i + 1)
|
||||
return
|
||||
case okdown:
|
||||
d.RoundDown(i + 1)
|
||||
return
|
||||
case okup:
|
||||
d.RoundUp(i + 1)
|
||||
return
|
||||
}
|
||||
}
|
||||
}
|
||||
Loading…
Reference in a new issue