Rollup merge of rust-lang#128609 - swenson:smaller-faster-dragon, r=A…

…manieu

Remove unnecessary constants from flt2dec dragon

The "dragon" `flt2dec` algorithm uses multi-precision multiplication by (sometimes large) powers of 10. It has precomputed some values to help with these calculations.

BUT:

* There is no need to store powers of 10 and 2 * powers of 10: it is trivial to compute the second from the first.
* We can save a chunk of memory by storing powers of 5 instead of powers of 10 for the large powers (and just shifting as appropriate).
* This also slightly speeds up the routines (by ~1-3%) since the intermediate products are smaller and the shift is cheap.

In this PR, we remove the unnecessary constants and do the necessary adjustments.

Relevant benchmarks before (on my Threadripper 3970X, x86_64-unknown-linux-gnu):

```
num::flt2dec::bench_big_shortest                      137.92/iter   +/- 2.24
num::flt2dec::strategy::dragon::bench_big_exact_12   2135.28/iter  +/- 38.90
num::flt2dec::strategy::dragon::bench_big_exact_3     904.95/iter  +/- 10.58
num::flt2dec::strategy::dragon::bench_big_exact_inf 47230.33/iter +/- 320.84
num::flt2dec::strategy::dragon::bench_big_shortest   3915.05/iter  +/- 51.37
```

and after:

```
num::flt2dec::bench_big_shortest                      137.40/iter   +/- 2.03
num::flt2dec::strategy::dragon::bench_big_exact_12   2101.10/iter  +/- 25.63
num::flt2dec::strategy::dragon::bench_big_exact_3     873.86/iter   +/- 4.20
num::flt2dec::strategy::dragon::bench_big_exact_inf 47468.19/iter +/- 374.45
num::flt2dec::strategy::dragon::bench_big_shortest   3877.01/iter  +/- 45.74
```

core/src/num/flt2dec/strategy/dragon.rs

@@ -12,48 +12,51 @@ use crate::num::flt2dec::{round_up, Decoded, MAX_SIG_DIGITS};
 
 static POW10: [Digit; 10] =
     [1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000];
-static TWOPOW10: [Digit; 10] =
-    [2, 20, 200, 2000, 20000, 200000, 2000000, 20000000, 200000000, 2000000000];
-
-// precalculated arrays of `Digit`s for 10^(2^n)
-static POW10TO16: [Digit; 2] = [0x6fc10000, 0x2386f2];
-static POW10TO32: [Digit; 4] = [0, 0x85acef81, 0x2d6d415b, 0x4ee];
-static POW10TO64: [Digit; 7] = [0, 0, 0xbf6a1f01, 0x6e38ed64, 0xdaa797ed, 0xe93ff9f4, 0x184f03];
-static POW10TO128: [Digit; 14] = [
-    0, 0, 0, 0, 0x2e953e01, 0x3df9909, 0xf1538fd, 0x2374e42f, 0xd3cff5ec, 0xc404dc08, 0xbccdb0da,
-    0xa6337f19, 0xe91f2603, 0x24e,
+// precalculated arrays of `Digit`s for 5^(2^n).
+static POW5TO16: [Digit; 2] = [0x86f26fc1, 0x23];
+static POW5TO32: [Digit; 3] = [0x85acef81, 0x2d6d415b, 0x4ee];
+static POW5TO64: [Digit; 5] = [0xbf6a1f01, 0x6e38ed64, 0xdaa797ed, 0xe93ff9f4, 0x184f03];
+static POW5TO128: [Digit; 10] = [
+    0x2e953e01, 0x3df9909, 0xf1538fd, 0x2374e42f, 0xd3cff5ec, 0xc404dc08, 0xbccdb0da, 0xa6337f19,
+    0xe91f2603, 0x24e,
 ];
-static POW10TO256: [Digit; 27] = [
-    0, 0, 0, 0, 0, 0, 0, 0, 0x982e7c01, 0xbed3875b, 0xd8d99f72, 0x12152f87, 0x6bde50c6, 0xcf4a6e70,
-    0xd595d80f, 0x26b2716e, 0xadc666b0, 0x1d153624, 0x3c42d35a, 0x63ff540e, 0xcc5573c0, 0x65f9ef17,
-    0x55bc28f2, 0x80dcc7f7, 0xf46eeddc, 0x5fdcefce, 0x553f7,
+static POW5TO256: [Digit; 19] = [
+    0x982e7c01, 0xbed3875b, 0xd8d99f72, 0x12152f87, 0x6bde50c6, 0xcf4a6e70, 0xd595d80f, 0x26b2716e,
+    0xadc666b0, 0x1d153624, 0x3c42d35a, 0x63ff540e, 0xcc5573c0, 0x65f9ef17, 0x55bc28f2, 0x80dcc7f7,
+    0xf46eeddc, 0x5fdcefce, 0x553f7,
 ];
 
 #[doc(hidden)]
 pub fn mul_pow10(x: &mut Big, n: usize) -> &mut Big {
     debug_assert!(n < 512);
+    // Save ourself the left shift for the smallest cases.
+    if n < 8 {
+        return x.mul_small(POW10[n & 7]);
+    }
+    // Multiply by the powers of 5 and shift the 2s in at the end.
+    // This keeps the intermediate products smaller and faster.
     if n & 7 != 0 {
-        x.mul_small(POW10[n & 7]);
+        x.mul_small(POW10[n & 7] >> (n & 7));
     }
     if n & 8 != 0 {
-        x.mul_small(POW10[8]);
+        x.mul_small(POW10[8] >> 8);
     }
     if n & 16 != 0 {
-        x.mul_digits(&POW10TO16);
+        x.mul_digits(&POW5TO16);
     }
     if n & 32 != 0 {
-        x.mul_digits(&POW10TO32);
+        x.mul_digits(&POW5TO32);
     }
     if n & 64 != 0 {
-        x.mul_digits(&POW10TO64);
+        x.mul_digits(&POW5TO64);
     }
     if n & 128 != 0 {
-        x.mul_digits(&POW10TO128);
+        x.mul_digits(&POW5TO128);
     }
     if n & 256 != 0 {
-        x.mul_digits(&POW10TO256);
+        x.mul_digits(&POW5TO256);
     }
-    x
+    x.mul_pow2(n)
 }
 
 fn div_2pow10(x: &mut Big, mut n: usize) -> &mut Big {
@@ -62,7 +65,7 @@ fn div_2pow10(x: &mut Big, mut n: usize) -> &mut Big {
         x.div_rem_small(POW10[largest]);
         n -= largest;
     }
-    x.div_rem_small(TWOPOW10[n]);
+    x.div_rem_small(POW10[n] << 1);
     x
 }