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Diffstat (limited to 'vendor/golang.org/x/text/internal/number/extfloat.go')
| -rw-r--r-- | vendor/golang.org/x/text/internal/number/extfloat.go | 671 |
1 files changed, 0 insertions, 671 deletions
diff --git a/vendor/golang.org/x/text/internal/number/extfloat.go b/vendor/golang.org/x/text/internal/number/extfloat.go deleted file mode 100644 index 97138e2b0..000000000 --- a/vendor/golang.org/x/text/internal/number/extfloat.go +++ /dev/null @@ -1,671 +0,0 @@ -// Copyright 2011 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. - -// TODO: use build tags once a low-level public API has been established in -// package strconv. - -package number - -// An extFloat represents an extended floating-point number, with more -// precision than a float64. It does not try to save bits: the -// number represented by the structure is mant*(2^exp), with a negative -// sign if neg is true. -type extFloat struct { - mant uint64 - exp int - neg bool -} - -// Powers of ten taken from double-conversion library. -// http://code.google.com/p/double-conversion/ -const ( - firstPowerOfTen = -348 - stepPowerOfTen = 8 -) - -var smallPowersOfTen = [...]extFloat{ - {1 << 63, -63, false}, // 1 - {0xa << 60, -60, false}, // 1e1 - {0x64 << 57, -57, false}, // 1e2 - {0x3e8 << 54, -54, false}, // 1e3 - {0x2710 << 50, -50, false}, // 1e4 - {0x186a0 << 47, -47, false}, // 1e5 - {0xf4240 << 44, -44, false}, // 1e6 - {0x989680 << 40, -40, false}, // 1e7 -} - -var powersOfTen = [...]extFloat{ - {0xfa8fd5a0081c0288, -1220, false}, // 10^-348 - {0xbaaee17fa23ebf76, -1193, false}, // 10^-340 - {0x8b16fb203055ac76, -1166, false}, // 10^-332 - {0xcf42894a5dce35ea, -1140, false}, // 10^-324 - {0x9a6bb0aa55653b2d, -1113, false}, // 10^-316 - {0xe61acf033d1a45df, -1087, false}, // 10^-308 - {0xab70fe17c79ac6ca, -1060, false}, // 10^-300 - {0xff77b1fcbebcdc4f, -1034, false}, // 10^-292 - {0xbe5691ef416bd60c, -1007, false}, // 10^-284 - {0x8dd01fad907ffc3c, -980, false}, // 10^-276 - {0xd3515c2831559a83, -954, false}, // 10^-268 - {0x9d71ac8fada6c9b5, -927, false}, // 10^-260 - {0xea9c227723ee8bcb, -901, false}, // 10^-252 - {0xaecc49914078536d, -874, false}, // 10^-244 - {0x823c12795db6ce57, -847, false}, // 10^-236 - {0xc21094364dfb5637, -821, false}, // 10^-228 - {0x9096ea6f3848984f, -794, false}, // 10^-220 - {0xd77485cb25823ac7, -768, false}, // 10^-212 - {0xa086cfcd97bf97f4, -741, false}, // 10^-204 - {0xef340a98172aace5, -715, false}, // 10^-196 - {0xb23867fb2a35b28e, -688, false}, // 10^-188 - {0x84c8d4dfd2c63f3b, -661, false}, // 10^-180 - {0xc5dd44271ad3cdba, -635, false}, // 10^-172 - {0x936b9fcebb25c996, -608, false}, // 10^-164 - {0xdbac6c247d62a584, -582, false}, // 10^-156 - {0xa3ab66580d5fdaf6, -555, false}, // 10^-148 - {0xf3e2f893dec3f126, -529, false}, // 10^-140 - {0xb5b5ada8aaff80b8, -502, false}, // 10^-132 - {0x87625f056c7c4a8b, -475, false}, // 10^-124 - {0xc9bcff6034c13053, -449, false}, // 10^-116 - {0x964e858c91ba2655, -422, false}, // 10^-108 - {0xdff9772470297ebd, -396, false}, // 10^-100 - {0xa6dfbd9fb8e5b88f, -369, false}, // 10^-92 - {0xf8a95fcf88747d94, -343, false}, // 10^-84 - {0xb94470938fa89bcf, -316, false}, // 10^-76 - {0x8a08f0f8bf0f156b, -289, false}, // 10^-68 - {0xcdb02555653131b6, -263, false}, // 10^-60 - {0x993fe2c6d07b7fac, -236, false}, // 10^-52 - {0xe45c10c42a2b3b06, -210, false}, // 10^-44 - {0xaa242499697392d3, -183, false}, // 10^-36 - {0xfd87b5f28300ca0e, -157, false}, // 10^-28 - {0xbce5086492111aeb, -130, false}, // 10^-20 - {0x8cbccc096f5088cc, -103, false}, // 10^-12 - {0xd1b71758e219652c, -77, false}, // 10^-4 - {0x9c40000000000000, -50, false}, // 10^4 - {0xe8d4a51000000000, -24, false}, // 10^12 - {0xad78ebc5ac620000, 3, false}, // 10^20 - {0x813f3978f8940984, 30, false}, // 10^28 - {0xc097ce7bc90715b3, 56, false}, // 10^36 - {0x8f7e32ce7bea5c70, 83, false}, // 10^44 - {0xd5d238a4abe98068, 109, false}, // 10^52 - {0x9f4f2726179a2245, 136, false}, // 10^60 - {0xed63a231d4c4fb27, 162, false}, // 10^68 - {0xb0de65388cc8ada8, 189, false}, // 10^76 - {0x83c7088e1aab65db, 216, false}, // 10^84 - {0xc45d1df942711d9a, 242, false}, // 10^92 - {0x924d692ca61be758, 269, false}, // 10^100 - {0xda01ee641a708dea, 295, false}, // 10^108 - {0xa26da3999aef774a, 322, false}, // 10^116 - {0xf209787bb47d6b85, 348, false}, // 10^124 - {0xb454e4a179dd1877, 375, false}, // 10^132 - {0x865b86925b9bc5c2, 402, false}, // 10^140 - {0xc83553c5c8965d3d, 428, false}, // 10^148 - {0x952ab45cfa97a0b3, 455, false}, // 10^156 - {0xde469fbd99a05fe3, 481, false}, // 10^164 - {0xa59bc234db398c25, 508, false}, // 10^172 - {0xf6c69a72a3989f5c, 534, false}, // 10^180 - {0xb7dcbf5354e9bece, 561, false}, // 10^188 - {0x88fcf317f22241e2, 588, false}, // 10^196 - {0xcc20ce9bd35c78a5, 614, false}, // 10^204 - {0x98165af37b2153df, 641, false}, // 10^212 - {0xe2a0b5dc971f303a, 667, false}, // 10^220 - {0xa8d9d1535ce3b396, 694, false}, // 10^228 - {0xfb9b7cd9a4a7443c, 720, false}, // 10^236 - {0xbb764c4ca7a44410, 747, false}, // 10^244 - {0x8bab8eefb6409c1a, 774, false}, // 10^252 - {0xd01fef10a657842c, 800, false}, // 10^260 - {0x9b10a4e5e9913129, 827, false}, // 10^268 - {0xe7109bfba19c0c9d, 853, false}, // 10^276 - {0xac2820d9623bf429, 880, false}, // 10^284 - {0x80444b5e7aa7cf85, 907, false}, // 10^292 - {0xbf21e44003acdd2d, 933, false}, // 10^300 - {0x8e679c2f5e44ff8f, 960, false}, // 10^308 - {0xd433179d9c8cb841, 986, false}, // 10^316 - {0x9e19db92b4e31ba9, 1013, false}, // 10^324 - {0xeb96bf6ebadf77d9, 1039, false}, // 10^332 - {0xaf87023b9bf0ee6b, 1066, false}, // 10^340 -} - -// floatBits returns the bits of the float64 that best approximates -// the extFloat passed as receiver. Overflow is set to true if -// the resulting float64 is ±Inf. -func (f *extFloat) floatBits(flt *floatInfo) (bits uint64, overflow bool) { - f.Normalize() - - exp := f.exp + 63 - - // Exponent too small. - if exp < flt.bias+1 { - n := flt.bias + 1 - exp - f.mant >>= uint(n) - exp += n - } - - // Extract 1+flt.mantbits bits from the 64-bit mantissa. - mant := f.mant >> (63 - flt.mantbits) - if f.mant&(1<<(62-flt.mantbits)) != 0 { - // Round up. - mant += 1 - } - - // Rounding might have added a bit; shift down. - if mant == 2<<flt.mantbits { - mant >>= 1 - exp++ - } - - // Infinities. - if exp-flt.bias >= 1<<flt.expbits-1 { - // ±Inf - mant = 0 - exp = 1<<flt.expbits - 1 + flt.bias - overflow = true - } else if mant&(1<<flt.mantbits) == 0 { - // Denormalized? - exp = flt.bias - } - // Assemble bits. - bits = mant & (uint64(1)<<flt.mantbits - 1) - bits |= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits - if f.neg { - bits |= 1 << (flt.mantbits + flt.expbits) - } - return -} - -// AssignComputeBounds sets f to the floating point value -// defined by mant, exp and precision given by flt. It returns -// lower, upper such that any number in the closed interval -// [lower, upper] is converted back to the same floating point number. -func (f *extFloat) AssignComputeBounds(mant uint64, exp int, neg bool, flt *floatInfo) (lower, upper extFloat) { - f.mant = mant - f.exp = exp - int(flt.mantbits) - f.neg = neg - if f.exp <= 0 && mant == (mant>>uint(-f.exp))<<uint(-f.exp) { - // An exact integer - f.mant >>= uint(-f.exp) - f.exp = 0 - return *f, *f - } - expBiased := exp - flt.bias - - upper = extFloat{mant: 2*f.mant + 1, exp: f.exp - 1, neg: f.neg} - if mant != 1<<flt.mantbits || expBiased == 1 { - lower = extFloat{mant: 2*f.mant - 1, exp: f.exp - 1, neg: f.neg} - } else { - lower = extFloat{mant: 4*f.mant - 1, exp: f.exp - 2, neg: f.neg} - } - return -} - -// Normalize normalizes f so that the highest bit of the mantissa is -// set, and returns the number by which the mantissa was left-shifted. -func (f *extFloat) Normalize() (shift uint) { - mant, exp := f.mant, f.exp - if mant == 0 { - return 0 - } - if mant>>(64-32) == 0 { - mant <<= 32 - exp -= 32 - } - if mant>>(64-16) == 0 { - mant <<= 16 - exp -= 16 - } - if mant>>(64-8) == 0 { - mant <<= 8 - exp -= 8 - } - if mant>>(64-4) == 0 { - mant <<= 4 - exp -= 4 - } - if mant>>(64-2) == 0 { - mant <<= 2 - exp -= 2 - } - if mant>>(64-1) == 0 { - mant <<= 1 - exp -= 1 - } - shift = uint(f.exp - exp) - f.mant, f.exp = mant, exp - return -} - -// Multiply sets f to the product f*g: the result is correctly rounded, -// but not normalized. -func (f *extFloat) Multiply(g extFloat) { - fhi, flo := f.mant>>32, uint64(uint32(f.mant)) - ghi, glo := g.mant>>32, uint64(uint32(g.mant)) - - // Cross products. - cross1 := fhi * glo - cross2 := flo * ghi - - // f.mant*g.mant is fhi*ghi << 64 + (cross1+cross2) << 32 + flo*glo - f.mant = fhi*ghi + (cross1 >> 32) + (cross2 >> 32) - rem := uint64(uint32(cross1)) + uint64(uint32(cross2)) + ((flo * glo) >> 32) - // Round up. - rem += (1 << 31) - - f.mant += (rem >> 32) - f.exp = f.exp + g.exp + 64 -} - -var uint64pow10 = [...]uint64{ - 1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, - 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, -} - -// AssignDecimal sets f to an approximate value mantissa*10^exp. It -// reports whether the value represented by f is guaranteed to be the -// best approximation of d after being rounded to a float64 or -// float32 depending on flt. -func (f *extFloat) AssignDecimal(mantissa uint64, exp10 int, neg bool, trunc bool, flt *floatInfo) (ok bool) { - const uint64digits = 19 - const errorscale = 8 - errors := 0 // An upper bound for error, computed in errorscale*ulp. - if trunc { - // the decimal number was truncated. - errors += errorscale / 2 - } - - f.mant = mantissa - f.exp = 0 - f.neg = neg - - // Multiply by powers of ten. - i := (exp10 - firstPowerOfTen) / stepPowerOfTen - if exp10 < firstPowerOfTen || i >= len(powersOfTen) { - return false - } - adjExp := (exp10 - firstPowerOfTen) % stepPowerOfTen - - // We multiply by exp%step - if adjExp < uint64digits && mantissa < uint64pow10[uint64digits-adjExp] { - // We can multiply the mantissa exactly. - f.mant *= uint64pow10[adjExp] - f.Normalize() - } else { - f.Normalize() - f.Multiply(smallPowersOfTen[adjExp]) - errors += errorscale / 2 - } - - // We multiply by 10 to the exp - exp%step. - f.Multiply(powersOfTen[i]) - if errors > 0 { - errors += 1 - } - errors += errorscale / 2 - - // Normalize - shift := f.Normalize() - errors <<= shift - - // Now f is a good approximation of the decimal. - // Check whether the error is too large: that is, if the mantissa - // is perturbated by the error, the resulting float64 will change. - // The 64 bits mantissa is 1 + 52 bits for float64 + 11 extra bits. - // - // In many cases the approximation will be good enough. - denormalExp := flt.bias - 63 - var extrabits uint - if f.exp <= denormalExp { - // f.mant * 2^f.exp is smaller than 2^(flt.bias+1). - extrabits = 63 - flt.mantbits + 1 + uint(denormalExp-f.exp) - } else { - extrabits = 63 - flt.mantbits - } - - halfway := uint64(1) << (extrabits - 1) - mant_extra := f.mant & (1<<extrabits - 1) - - // Do a signed comparison here! If the error estimate could make - // the mantissa round differently for the conversion to double, - // then we can't give a definite answer. - if int64(halfway)-int64(errors) < int64(mant_extra) && - int64(mant_extra) < int64(halfway)+int64(errors) { - return false - } - return true -} - -// Frexp10 is an analogue of math.Frexp for decimal powers. It scales -// f by an approximate power of ten 10^-exp, and returns exp10, so -// that f*10^exp10 has the same value as the old f, up to an ulp, -// as well as the index of 10^-exp in the powersOfTen table. -func (f *extFloat) frexp10() (exp10, index int) { - // The constants expMin and expMax constrain the final value of the - // binary exponent of f. We want a small integral part in the result - // because finding digits of an integer requires divisions, whereas - // digits of the fractional part can be found by repeatedly multiplying - // by 10. - const expMin = -60 - const expMax = -32 - // Find power of ten such that x * 10^n has a binary exponent - // between expMin and expMax. - approxExp10 := ((expMin+expMax)/2 - f.exp) * 28 / 93 // log(10)/log(2) is close to 93/28. - i := (approxExp10 - firstPowerOfTen) / stepPowerOfTen -Loop: - for { - exp := f.exp + powersOfTen[i].exp + 64 - switch { - case exp < expMin: - i++ - case exp > expMax: - i-- - default: - break Loop - } - } - // Apply the desired decimal shift on f. It will have exponent - // in the desired range. This is multiplication by 10^-exp10. - f.Multiply(powersOfTen[i]) - - return -(firstPowerOfTen + i*stepPowerOfTen), i -} - -// frexp10Many applies a common shift by a power of ten to a, b, c. -func frexp10Many(a, b, c *extFloat) (exp10 int) { - exp10, i := c.frexp10() - a.Multiply(powersOfTen[i]) - b.Multiply(powersOfTen[i]) - return -} - -// FixedDecimal stores in d the first n significant digits -// of the decimal representation of f. It returns false -// if it cannot be sure of the answer. -func (f *extFloat) FixedDecimal(d *decimalSlice, n int) bool { - if f.mant == 0 { - d.nd = 0 - d.dp = 0 - d.neg = f.neg - return true - } - if n == 0 { - panic("strconv: internal error: extFloat.FixedDecimal called with n == 0") - } - // Multiply by an appropriate power of ten to have a reasonable - // number to process. - f.Normalize() - exp10, _ := f.frexp10() - - shift := uint(-f.exp) - integer := uint32(f.mant >> shift) - fraction := f.mant - (uint64(integer) << shift) - ε := uint64(1) // ε is the uncertainty we have on the mantissa of f. - - // Write exactly n digits to d. - needed := n // how many digits are left to write. - integerDigits := 0 // the number of decimal digits of integer. - pow10 := uint64(1) // the power of ten by which f was scaled. - for i, pow := 0, uint64(1); i < 20; i++ { - if pow > uint64(integer) { - integerDigits = i - break - } - pow *= 10 - } - rest := integer - if integerDigits > needed { - // the integral part is already large, trim the last digits. - pow10 = uint64pow10[integerDigits-needed] - integer /= uint32(pow10) - rest -= integer * uint32(pow10) - } else { - rest = 0 - } - - // Write the digits of integer: the digits of rest are omitted. - var buf [32]byte - pos := len(buf) - for v := integer; v > 0; { - v1 := v / 10 - v -= 10 * v1 - pos-- - buf[pos] = byte(v + '0') - v = v1 - } - for i := pos; i < len(buf); i++ { - d.d[i-pos] = buf[i] - } - nd := len(buf) - pos - d.nd = nd - d.dp = integerDigits + exp10 - needed -= nd - - if needed > 0 { - if rest != 0 || pow10 != 1 { - panic("strconv: internal error, rest != 0 but needed > 0") - } - // Emit digits for the fractional part. Each time, 10*fraction - // fits in a uint64 without overflow. - for needed > 0 { - fraction *= 10 - ε *= 10 // the uncertainty scales as we multiply by ten. - if 2*ε > 1<<shift { - // the error is so large it could modify which digit to write, abort. - return false - } - digit := fraction >> shift - d.d[nd] = byte(digit + '0') - fraction -= digit << shift - nd++ - needed-- - } - d.nd = nd - } - - // We have written a truncation of f (a numerator / 10^d.dp). The remaining part - // can be interpreted as a small number (< 1) to be added to the last digit of the - // numerator. - // - // If rest > 0, the amount is: - // (rest<<shift | fraction) / (pow10 << shift) - // fraction being known with a ±ε uncertainty. - // The fact that n > 0 guarantees that pow10 << shift does not overflow a uint64. - // - // If rest = 0, pow10 == 1 and the amount is - // fraction / (1 << shift) - // fraction being known with a ±ε uncertainty. - // - // We pass this information to the rounding routine for adjustment. - - ok := adjustLastDigitFixed(d, uint64(rest)<<shift|fraction, pow10, shift, ε) - if !ok { - return false - } - // Trim trailing zeros. - for i := d.nd - 1; i >= 0; i-- { - if d.d[i] != '0' { - d.nd = i + 1 - break - } - } - return true -} - -// adjustLastDigitFixed assumes d contains the representation of the integral part -// of some number, whose fractional part is num / (den << shift). The numerator -// num is only known up to an uncertainty of size ε, assumed to be less than -// (den << shift)/2. -// -// It will increase the last digit by one to account for correct rounding, typically -// when the fractional part is greater than 1/2, and will return false if ε is such -// that no correct answer can be given. -func adjustLastDigitFixed(d *decimalSlice, num, den uint64, shift uint, ε uint64) bool { - if num > den<<shift { - panic("strconv: num > den<<shift in adjustLastDigitFixed") - } - if 2*ε > den<<shift { - panic("strconv: ε > (den<<shift)/2") - } - if 2*(num+ε) < den<<shift { - return true - } - if 2*(num-ε) > den<<shift { - // increment d by 1. - i := d.nd - 1 - for ; i >= 0; i-- { - if d.d[i] == '9' { - d.nd-- - } else { - break - } - } - if i < 0 { - d.d[0] = '1' - d.nd = 1 - d.dp++ - } else { - d.d[i]++ - } - return true - } - return false -} - -// ShortestDecimal stores in d the shortest decimal representation of f -// which belongs to the open interval (lower, upper), where f is supposed -// to lie. It returns false whenever the result is unsure. The implementation -// uses the Grisu3 algorithm. -func (f *extFloat) ShortestDecimal(d *decimalSlice, lower, upper *extFloat) bool { - if f.mant == 0 { - d.nd = 0 - d.dp = 0 - d.neg = f.neg - return true - } - if f.exp == 0 && *lower == *f && *lower == *upper { - // an exact integer. - var buf [24]byte - n := len(buf) - 1 - for v := f.mant; v > 0; { - v1 := v / 10 - v -= 10 * v1 - buf[n] = byte(v + '0') - n-- - v = v1 - } - nd := len(buf) - n - 1 - for i := 0; i < nd; i++ { - d.d[i] = buf[n+1+i] - } - d.nd, d.dp = nd, nd - for d.nd > 0 && d.d[d.nd-1] == '0' { - d.nd-- - } - if d.nd == 0 { - d.dp = 0 - } - d.neg = f.neg - return true - } - upper.Normalize() - // Uniformize exponents. - if f.exp > upper.exp { - f.mant <<= uint(f.exp - upper.exp) - f.exp = upper.exp - } - if lower.exp > upper.exp { - lower.mant <<= uint(lower.exp - upper.exp) - lower.exp = upper.exp - } - - exp10 := frexp10Many(lower, f, upper) - // Take a safety margin due to rounding in frexp10Many, but we lose precision. - upper.mant++ - lower.mant-- - - // The shortest representation of f is either rounded up or down, but - // in any case, it is a truncation of upper. - shift := uint(-upper.exp) - integer := uint32(upper.mant >> shift) - fraction := upper.mant - (uint64(integer) << shift) - - // How far we can go down from upper until the result is wrong. - allowance := upper.mant - lower.mant - // How far we should go to get a very precise result. - targetDiff := upper.mant - f.mant - - // Count integral digits: there are at most 10. - var integerDigits int - for i, pow := 0, uint64(1); i < 20; i++ { - if pow > uint64(integer) { - integerDigits = i - break - } - pow *= 10 - } - for i := 0; i < integerDigits; i++ { - pow := uint64pow10[integerDigits-i-1] - digit := integer / uint32(pow) - d.d[i] = byte(digit + '0') - integer -= digit * uint32(pow) - // evaluate whether we should stop. - if currentDiff := uint64(integer)<<shift + fraction; currentDiff < allowance { - d.nd = i + 1 - d.dp = integerDigits + exp10 - d.neg = f.neg - // Sometimes allowance is so large the last digit might need to be - // decremented to get closer to f. - return adjustLastDigit(d, currentDiff, targetDiff, allowance, pow<<shift, 2) - } - } - d.nd = integerDigits - d.dp = d.nd + exp10 - d.neg = f.neg - - // Compute digits of the fractional part. At each step fraction does not - // overflow. The choice of minExp implies that fraction is less than 2^60. - var digit int - multiplier := uint64(1) - for { - fraction *= 10 - multiplier *= 10 - digit = int(fraction >> shift) - d.d[d.nd] = byte(digit + '0') - d.nd++ - fraction -= uint64(digit) << shift - if fraction < allowance*multiplier { - // We are in the admissible range. Note that if allowance is about to - // overflow, that is, allowance > 2^64/10, the condition is automatically - // true due to the limited range of fraction. - return adjustLastDigit(d, - fraction, targetDiff*multiplier, allowance*multiplier, - 1<<shift, multiplier*2) - } - } -} - -// adjustLastDigit modifies d = x-currentDiff*ε, to get closest to -// d = x-targetDiff*ε, without becoming smaller than x-maxDiff*ε. -// It assumes that a decimal digit is worth ulpDecimal*ε, and that -// all data is known with a error estimate of ulpBinary*ε. -func adjustLastDigit(d *decimalSlice, currentDiff, targetDiff, maxDiff, ulpDecimal, ulpBinary uint64) bool { - if ulpDecimal < 2*ulpBinary { - // Approximation is too wide. - return false - } - for currentDiff+ulpDecimal/2+ulpBinary < targetDiff { - d.d[d.nd-1]-- - currentDiff += ulpDecimal - } - if currentDiff+ulpDecimal <= targetDiff+ulpDecimal/2+ulpBinary { - // we have two choices, and don't know what to do. - return false - } - if currentDiff < ulpBinary || currentDiff > maxDiff-ulpBinary { - // we went too far - return false - } - if d.nd == 1 && d.d[0] == '0' { - // the number has actually reached zero. - d.nd = 0 - d.dp = 0 - } - return true -} |