| // Copyright 2020 The Wuffs Authors. |
| // |
| // Licensed under the Apache License, Version 2.0 (the "License"); |
| // you may not use this file except in compliance with the License. |
| // You may obtain a copy of the License at |
| // |
| // https://www.apache.org/licenses/LICENSE-2.0 |
| // |
| // Unless required by applicable law or agreed to in writing, software |
| // distributed under the License is distributed on an "AS IS" BASIS, |
| // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| // See the License for the specific language governing permissions and |
| // limitations under the License. |
| |
| // +build ignore |
| |
| package main |
| |
| // print-mpb-powers-of-10.go prints the medium-precision (128-bit mantissa) |
| // binary (base-2) wuffs_base__private_implementation__powers_of_10 tables. |
| // |
| // When the approximation to (10 ** N) is not exact, the mantissa is truncated, |
| // not rounded to nearest. The base-2 exponent is chosen so that the mantissa's |
| // most signficant bit (bit 127) is set. |
| // |
| // The final uint32_t entry in each row-of-5 is biased by 1214, also known as |
| // 0x04BE, which simplifies its use in f64conv-submodule.c. |
| // |
| // Usage: go run print-mpb-powers-of-10.go -detail |
| // |
| // With -detail set, its output should include: |
| // |
| // 0xF7604B57, 0x014BB630, 0xFE98746D, 0x84A57695, 0x0004, |
| // // 1e-326 ≈ (0x84A57695FE98746D014BB630F7604B57 >> 1210) |
| // |
| // 0x35385E2D, 0x419EA3BD, 0x7E3E9188, 0xA5CED43B, 0x0007, |
| // // 1e-325 ≈ (0xA5CED43B7E3E9188419EA3BD35385E2D >> 1207) |
| // |
| // ... |
| // |
| // 0x0A3D70A3, 0x3D70A3D7, 0x70A3D70A, 0xA3D70A3D, 0x0438, |
| // // 1e-2 ≈ (0xA3D70A3D70A3D70A3D70A3D70A3D70A3 >> 134) |
| // |
| // 0xCCCCCCCC, 0xCCCCCCCC, 0xCCCCCCCC, 0xCCCCCCCC, 0x043B, |
| // // 1e-1 ≈ (0xCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC >> 131) |
| // |
| // 0x00000000, 0x00000000, 0x00000000, 0x80000000, 0x043F, |
| // // 1e0 ≈ (0x80000000000000000000000000000000 >> 127) |
| // |
| // 0x00000000, 0x00000000, 0x00000000, 0xA0000000, 0x0442, |
| // // 1e1 ≈ (0xA0000000000000000000000000000000 >> 124) |
| // |
| // 0x00000000, 0x00000000, 0x00000000, 0xC8000000, 0x0445, |
| // // 1e2 ≈ (0xC8000000000000000000000000000000 >> 121) |
| // |
| // ... |
| // |
| // 0x51E513DA, 0x2CD2CC65, 0x35D63F73, 0xB201833B, 0x0841, |
| // // 1e309 ≈ (0xB201833B35D63F732CD2CC6551E513DA << 899) |
| // |
| // 0xA65E58D1, 0xF8077F7E, 0x034BCF4F, 0xDE81E40A, 0x0844, |
| // // 1e310 ≈ (0xDE81E40A034BCF4FF8077F7EA65E58D1 << 902) |
| |
| import ( |
| "flag" |
| "fmt" |
| "math/big" |
| "os" |
| ) |
| |
| var ( |
| detail = flag.Bool("detail", false, "whether to print detailed comments") |
| ) |
| |
| func main() { |
| if err := main1(); err != nil { |
| os.Stderr.WriteString(err.Error() + "\n") |
| os.Exit(1) |
| } |
| } |
| |
| func main1() error { |
| flag.Parse() |
| |
| const count = 1 + (+310 - -326) |
| fmt.Printf("static const uint32_t "+ |
| "wuffs_base__private_implementation__powers_of_10[%d] = {\n", 5*count) |
| for e := -326; e <= +310; e++ { |
| if err := do(e); err != nil { |
| return err |
| } |
| } |
| fmt.Printf("};\n\n") |
| |
| return nil |
| } |
| |
| var ( |
| one = big.NewInt(1) |
| ten = big.NewInt(10) |
| two128 = big.NewInt(0).Lsh(one, 128) |
| ) |
| |
| // N is large enough so that (1<<N) is easily bigger than 1e310. |
| const N = 2048 |
| |
| // 1214 is 1023 + 191. 1023 is the bias for IEEE 754 double-precision floating |
| // point. 191 is ((3 * 64) - 1) and we work with multiples-of-64-bit mantissas. |
| const bias = 1214 |
| |
| func do(e int) error { |
| z := big.NewInt(0).Lsh(one, N) |
| if e >= 0 { |
| exp := big.NewInt(0).Exp(ten, big.NewInt(int64(+e)), nil) |
| z.Mul(z, exp) |
| } else { |
| exp := big.NewInt(0).Exp(ten, big.NewInt(int64(-e)), nil) |
| z.Div(z, exp) |
| } |
| |
| n := int32(-N) |
| for z.Cmp(two128) >= 0 { |
| z.Rsh(z, 1) |
| n++ |
| } |
| hex := fmt.Sprintf("%X", z) |
| if len(hex) != 32 { |
| return fmt.Errorf("invalid hexadecimal representation %q", hex) |
| } |
| |
| fmt.Printf(" 0x%s, 0x%s, 0x%s, 0x%s, 0x%04X, // 1e%-04d", |
| hex[24:], hex[16:24], hex[8:16], hex[:8], uint32(n)+bias, e) |
| if *detail { |
| fmt.Printf(" ≈ (0x%s ", hex) |
| if n >= 0 { |
| fmt.Printf("<< %4d)", +n) |
| } else { |
| fmt.Printf(">> %4d)", -n) |
| } |
| } |
| |
| fmt.Println() |
| return nil |
| } |