| // Copyright 2020 The Wuffs Authors. |
| // |
| // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or |
| // https://www.apache.org/licenses/LICENSE-2.0> or the MIT license |
| // <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your |
| // option. This file may not be copied, modified, or distributed |
| // except according to those terms. |
| |
| //go:build ignore |
| // +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 (an implicit third column) is |
| // chosen so that the mantissa's most signficant bit (bit 127) is set. |
| // |
| // Usage: go run print-mpb-powers-of-10.go -detail |
| // |
| // With -detail set, its output should include: |
| // |
| // {0xA5D3B6D479F8E056, 0x8FD0C16206306BAB}, |
| // // 1e-307 ≈ (0x8FD0C16206306BABA5D3B6D479F8E056 >> 1147) |
| // |
| // {0x8F48A4899877186C, 0xB3C4F1BA87BC8696}, |
| // // 1e-306 ≈ (0xB3C4F1BA87BC86968F48A4899877186C >> 1144) |
| // |
| // ... |
| // |
| // {0x3D70A3D70A3D70A3, 0xA3D70A3D70A3D70A}, |
| // // 1e-2 ≈ (0xA3D70A3D70A3D70A3D70A3D70A3D70A3 >> 134) |
| // |
| // {0xCCCCCCCCCCCCCCCC, 0xCCCCCCCCCCCCCCCC}, |
| // // 1e-1 ≈ (0xCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC >> 131) |
| // |
| // {0x0000000000000000, 0x8000000000000000}, |
| // // 1e0 ≈ (0x80000000000000000000000000000000 >> 127) |
| // |
| // {0x0000000000000000, 0xA000000000000000}, |
| // // 1e1 ≈ (0xA0000000000000000000000000000000 >> 124) |
| // |
| // {0x0000000000000000, 0xC800000000000000}, |
| // // 1e2 ≈ (0xC8000000000000000000000000000000 >> 121) |
| // |
| // ... |
| // |
| // {0x5C68F256BFFF5A74, 0xA81F301449EE8C70}, |
| // // 1e287 ≈ (0xA81F301449EE8C705C68F256BFFF5A74 << 826) |
| // |
| // {0x73832EEC6FFF3111, 0xD226FC195C6A2F8C}, |
| // // 1e288 ≈ (0xD226FC195C6A2F8C73832EEC6FFF3111 << 829) |
| |
| 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 + (+288 - -307) |
| fmt.Printf("static const uint64_t "+ |
| "wuffs_base__private_implementation__powers_of_10[%d][2] = {\n", count) |
| for e := -307; e <= +288; 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) |
| } |
| |
| // Confirm that the linear approximation to the biased-value-of-n is |
| // correct for this particular value of e. |
| approxN := uint32(((217706 * e) >> 16) + 1087) |
| biasedN := bias + uint32(n) |
| if approxN != biasedN { |
| return fmt.Errorf("biased-n approximation: have %d, want %d", approxN, biasedN) |
| } |
| |
| fmt.Printf(" {0x%s, 0x%s}, // 1e%-04d", |
| hex[16:], hex[:16], e) |
| if *detail { |
| fmt.Printf(" ≈ (0x%s ", hex) |
| if n >= 0 { |
| fmt.Printf("<< %4d)", +n) |
| } else { |
| fmt.Printf(">> %4d)", -n) |
| } |
| } |
| |
| fmt.Println() |
| return nil |
| } |