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// 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
}