AssignDecimal sets f to an approximate value mantissa*10^exp. It returns true if 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.
(mantissa uint64, exp10 int, neg bool, trunc bool, flt *floatInfo)
| 260 | // best approximation of d after being rounded to a float64 or |
| 261 | // float32 depending on flt. |
| 262 | func (f *extFloat) AssignDecimal(mantissa uint64, exp10 int, neg bool, trunc bool, flt *floatInfo) (ok bool) { |
| 263 | const uint64digits = 19 |
| 264 | const errorscale = 8 |
| 265 | errors := 0 // An upper bound for error, computed in errorscale*ulp. |
| 266 | if trunc { |
| 267 | // the decimal number was truncated. |
| 268 | errors += errorscale / 2 |
| 269 | } |
| 270 | |
| 271 | f.mant = mantissa |
| 272 | f.exp = 0 |
| 273 | f.neg = neg |
| 274 | |
| 275 | // Multiply by powers of ten. |
| 276 | i := (exp10 - firstPowerOfTen) / stepPowerOfTen |
| 277 | if exp10 < firstPowerOfTen || i >= len(powersOfTen) { |
| 278 | return false |
| 279 | } |
| 280 | adjExp := (exp10 - firstPowerOfTen) % stepPowerOfTen |
| 281 | |
| 282 | // We multiply by exp%step |
| 283 | if adjExp < uint64digits && mantissa < uint64pow10[uint64digits-adjExp] { |
| 284 | // We can multiply the mantissa exactly. |
| 285 | f.mant *= uint64pow10[adjExp] |
| 286 | f.Normalize() |
| 287 | } else { |
| 288 | f.Normalize() |
| 289 | f.Multiply(smallPowersOfTen[adjExp]) |
| 290 | errors += errorscale / 2 |
| 291 | } |
| 292 | |
| 293 | // We multiply by 10 to the exp - exp%step. |
| 294 | f.Multiply(powersOfTen[i]) |
| 295 | if errors > 0 { |
| 296 | errors += 1 |
| 297 | } |
| 298 | errors += errorscale / 2 |
| 299 | |
| 300 | // Normalize |
| 301 | shift := f.Normalize() |
| 302 | errors <<= shift |
| 303 | |
| 304 | // Now f is a good approximation of the decimal. |
| 305 | // Check whether the error is too large: that is, if the mantissa |
| 306 | // is perturbated by the error, the resulting float64 will change. |
| 307 | // The 64 bits mantissa is 1 + 52 bits for float64 + 11 extra bits. |
| 308 | // |
| 309 | // In many cases the approximation will be good enough. |
| 310 | denormalExp := flt.bias - 63 |
| 311 | var extrabits uint |
| 312 | if f.exp <= denormalExp { |
| 313 | // f.mant * 2^f.exp is smaller than 2^(flt.bias+1). |
| 314 | extrabits = uint(63 - flt.mantbits + 1 + uint(denormalExp-f.exp)) |
| 315 | } else { |
| 316 | extrabits = uint(63 - flt.mantbits) |
| 317 | } |
| 318 | |
| 319 | halfway := uint64(1) << (extrabits - 1) |