float_fast_print/
lib.rs

1#![cfg_attr(feature = "cargo-clippy", allow(unreadable_literal))]
2
3use std::io::{Write,Result};
4//use std::fmt::{LowerExp, UpperExp, Display, Debug};
5
6const F32_MANTISSA_BITS: u32 = 23;
7const F32_EXP_BITS: u32 = 8;
8const F32_OFFSET: u32 = (1u32 << (F32_EXP_BITS - 1)) - 1;
9const F32_POW5_BIT_COUNT: u32 = 61;
10const F32_POW5_INV_BIT_COUNT: u32 = 59;
11const F64_MANTISSA_BITS: i32 = 52;
12const F64_EXP_BITS: i32 = 11;
13const F64_OFFSET: i32 = (1 << (F64_EXP_BITS - 1)) - 1;
14const F64_POW5_BIT_COUNT: i32 = 121;
15const F64_POW5_INV_BIT_COUNT: u32 = 122;
16
17/// Returns `e == 0 ? 1 : ceil(log_2(5^e))`.
18#[inline]
19fn pow5_bits(e: u32 ) -> u32 {
20    // This function has only been tested for 0 <= e <= 1500.
21    debug_assert!(e <= 1500);
22
23    ((e * 1217359) >> 19) + 1
24}
25
26/// Returns `floor(log10(2^e))`.
27#[inline]
28fn log10_pow2(e: u32 ) -> u32
29{
30    // This function has only been tested for 0 <= e <= 1500.
31    debug_assert!(e <= 1500);
32
33    (e * 78913) >> 18
34}
35
36/// Returns `floor(log10(5^e))`.
37#[inline]
38fn log10_pow5(e: u32 ) -> u32
39{
40    // This function has only been tested for 0 <= e <= 1500.
41    debug_assert!(e <= 1500);
42
43    (e * 732923) >> 20
44}
45
46#[inline]
47fn pow5_factor_32(mut value: u32 ) -> u32 {
48    for count in 0.. {
49        if value == 0 {
50            break;
51        }
52        if value % 5 != 0 {
53            return count;
54        }
55        value /= 5;
56    }
57
58    return 0;
59}
60
61#[inline]
62fn pow5_factor_64(mut value: u64 ) -> u32 {
63    for count in 0.. {
64        if value == 0 {
65            break;
66        }
67        if value % 5 != 0 {
68            return count;
69        }
70        value /= 5;
71    }
72
73    return 0;
74}
75
76/// Returns `true` if `value` is divisible by `5^p`.
77#[inline]
78fn multiple_of_pow5_32(value: u32, p: i32) -> bool {
79    // @@@ Is this necessary? Is p ever negative?
80    if p < 0 { return false; }
81    return pow5_factor_32(value) >= p as u32;
82}
83
84/// Returns `true` if `value` is divisible by `5^p`.
85#[inline]
86fn multiple_of_pow5_64(value: u64, p: i32) -> bool {
87    // @@@ Is this necessary? Is p ever negative?
88    if p < 0 { return false; }
89    return pow5_factor_64(value) >= p as u32;
90}
91
92fn mul_shift_32(m: u32, factor: u64, shift: u32 ) -> u32 {
93    debug_assert!(shift > 32);
94
95    let factor_lo: u32 = factor as u32; // @@@ may need unchecked or something
96    let factor_hi: u32 = (factor >> 32) as u32;
97    let bits_0: u64 = (m as u64) * (factor_lo as u64);
98    let bits_1: u64 = (m as u64) * (factor_hi as u64);
99
100    let sum : u64 = (bits_0 >> 32) + bits_1;
101    let shifted_sum : u64 = sum >> (shift - 32);
102
103    debug_assert!(shifted_sum <= std::u32::MAX as u64);
104
105    return shifted_sum as u32;
106}
107
108/// We need a 64x128-bit multiplication and a subsequent 128-bit shift.
109///
110/// Multiplication:
111///   The 64-bit factor is variable and passed in, the 128-bit factor comes
112///   from a lookup table. We know that the 64-bit factor only has 55
113///   significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
114///   factor only has 124 significant bits (i.e., the 4 topmost bits are
115///   zeros).
116///
117/// Shift:
118///   In principle, the multiplication result requires 55+124=179 bits to
119///   represent. However, we then shift this value to the right by j, which is
120///   at least j >= 115, so the result is guaranteed to fit into 179-115=64
121///   bits. This means that we only need the topmost 64 significant bits of
122///   the 64x128-bit multiplication.
123#[inline]
124fn mul_shift_64( m: u64, mul: (u64,u64), shift: u32 ) -> u64 {
125    debug_assert!(shift > 64);
126
127    let b0: u128 = m as u128 * mul.0 as u128;
128    let b2: u128 = m as u128 * mul.1 as u128;
129    (((b0 >> 64) + b2) >> (shift - 64)) as u64
130}
131
132#[inline]
133fn mul_pow5_inv_div_pow2(m: u32, q: u32, j: u32 ) -> u32 {
134    mul_shift_32(m, F32_POW5_INV_SPLIT[q as usize], j)
135}
136
137#[inline]
138fn mul_pow5_div_pow2(m: u32, i: u32, j: u32 ) -> u32 {
139    mul_shift_32(m, F32_POW5_SPLIT[i as usize], j)
140}
141
142#[inline]
143fn decimal_length_32(v: u32 ) -> u32 {
144    // Function precondition: v is not a 10-digit number.
145    // (9 digits are sufficient for round-tripping.)
146    debug_assert!(v < 1000000000);
147    
148    if      v >= 100000000 { 9 }
149    else if v >= 10000000 { 8 }
150    else if v >= 1000000 { 7 }
151    else if v >= 100000 { 6 }
152    else if v >= 10000 { 5 }
153    else if v >= 1000 { 4 }
154    else if v >= 100 { 3 }
155    else if v >= 10 { 2 }
156    else           { 1 }
157}
158
159#[inline]
160fn decimal_length_64(v: u64) -> u32 {
161
162    // This is slightly faster than a loop.
163    // The average output length is 16.38 digits, so we check high-to-low.
164    // Function precondition: v is not an 18, 19, or 20-digit number.
165    // (17 digits are sufficient for round-tripping.)
166    debug_assert!(v < 100000000000000000u64);
167
168    if      v >= 10000000000000000u64 { 17 }
169    else if v >= 1000000000000000u64 { 16 }
170    else if v >= 100000000000000u64 { 15 }
171    else if v >= 10000000000000u64 { 14 }
172    else if v >= 1000000000000u64 { 13 }
173    else if v >= 100000000000u64 { 12 }
174    else if v >= 10000000000u64 { 11 }
175    else if v >= 1000000000u64 { 10 }
176    else if v >= 100000000u64 { 9 }
177    else if v >= 10000000u64 { 8 }
178    else if v >= 1000000u64 { 7 }
179    else if v >= 100000u64 { 6 }
180    else if v >= 10000u64 { 5 }
181    else if v >= 1000u64 { 4 }
182    else if v >= 100u64 { 3 }
183    else if v >= 10u64 { 2 }
184    else              { 1 }
185}
186
187/// Converts the given `f32` number to a short round-trip base-10 representation
188/// using the efficient Ryū algorithm by Ulf Adams.
189///
190/// This function is ideal for exporting bulk floating-point data to text formats,
191/// such as CSV, JSON, or XLSX (Excel 2007 and later).
192///
193/// # Examples
194///
195/// ```
196/// use float_fast_print::write_f32_shortest;
197///
198/// let mut buffer: Vec<u8> = Vec::with_capacity(32);
199/// write_f32_shortest(&mut buffer, 502.1239e29).unwrap();
200/// assert_eq!(&buffer, b"5.021239e31");
201/// ```
202/// # Safety
203/// Unlike some other similar code such as the `dtoa` crate, this function uses
204/// 100% safe Rust code, does not have any external dependencies, does not include
205/// C code, and does not require a heap.
206///
207/// The `float_fast_print::exhaustive` test can be used to totally validate the
208/// round-trip behaviour and stability (no panics wih all 2^32 distinct `f32` inputs),
209/// guaranteeing safety. Note that this takes some days to complete...
210pub fn write_f32_shortest<W: Write>(mut writer: W, num: f32 ) -> Result<usize> {
211
212    // TODO: may want to extract the bulk of this code to prevent large amounts of code being generated if using multiple Write implementations...
213
214    let bits = num.to_bits();
215
216    let sign: bool = ((bits >> (F32_MANTISSA_BITS + F32_EXP_BITS)) & 1) != 0;
217    let ieee_mantissa: u32 = bits & ((1u32 << F32_MANTISSA_BITS) - 1);
218    let ieee_exponent: u32 = (bits >> F32_MANTISSA_BITS) & ((1u32 << F32_EXP_BITS) - 1);
219
220    let e2: i32;
221    let m2: u32;
222
223    if ieee_exponent == ( 1 << F32_EXP_BITS ) - 1 {
224        if ieee_mantissa != 0 {
225            return writer.write( b"NaN" );
226        } else if sign {
227            return writer.write( b"-inf" );
228        } else {
229            return writer.write( b"inf" );
230        }
231    }
232    else if ieee_exponent == 0 {
233        if ieee_mantissa == 0 {
234            if sign {
235                return writer.write( b"-0e0" );
236            }
237            else {
238                return writer.write( b"0e0" );
239            }
240        }
241
242        // We subtract 2 so that the bounds computation has 2 additional bits.
243        e2 = 1i32 - ( F32_OFFSET as i32 ) - ( F32_MANTISSA_BITS as i32 ) - 2;
244        m2 = ieee_mantissa;
245    }
246    else
247    {
248        e2 = ( ieee_exponent as i32 ) - ( F32_OFFSET as i32 ) - ( F32_MANTISSA_BITS as i32 ) - 2;
249        m2 = (1u32 << F32_MANTISSA_BITS) | ieee_mantissa;
250    }
251
252    let even = (m2 & 1) == 0;
253    let accept_bounds = even; // @@@ remove?
254
255    // Step 2: Determine the interval of legal decimal representations.
256    let mv: u32 = 4 * m2;
257    let mp: u32 = 4 * m2 + 2;
258    let mm: u32 = 4 * m2 - ( if (m2 != (1u32 << F32_MANTISSA_BITS)) || (ieee_exponent <= 1) { 2 } else { 1 } );
259
260    // Step 3: Convert to a decimal power base using 64-bit arithmetic.
261    let mut vr: u32;
262    let mut vp: u32;
263    let mut vm: u32;
264    let e10: i32;
265    let mut vm_is_trailing_zeros = false;
266    let mut vr_is_trailing_zeros = false;
267    let mut last_removed_digit: u8 = 0;
268
269    if e2 >= 0 {
270        let q = log10_pow2(e2 as u32 );
271        e10 = q as i32;
272        let k = ( F32_POW5_INV_BIT_COUNT as u32 ) + pow5_bits(q ) - 1;
273        let i = -e2 + q as i32 + ( k as i32 );
274        vr = mul_pow5_inv_div_pow2(mv, q, i as u32);
275        vp = mul_pow5_inv_div_pow2(mp, q, i as u32);
276        vm = mul_pow5_inv_div_pow2(mm, q, i as u32);
277
278        if q != 0 && ((vp - 1) / 10 <= vm / 10) {
279            // We need to know one removed digit even if we are not going to loop below. We could use
280            // q = X - 1 above, except that would require 33 bits for the result, and we've found that
281            // 32-bit arithmetic is faster even on 64-bit machines.
282            let l: i32 = ( F32_POW5_INV_BIT_COUNT as i32 ) + ( pow5_bits(q - 1) as i32 ) - 1;
283            last_removed_digit = (mul_pow5_inv_div_pow2(mv, q - 1, (-e2 + ( q as i32) - 1 + l) as u32) % 10) as u8;
284        }
285        if q <= 9 {
286            // Only one of mp, mv, and mm can be a multiple of 5, if any.
287            if mv % 5 == 0 {
288                vr_is_trailing_zeros = multiple_of_pow5_32(mv, q as i32);
289            } else if accept_bounds {
290                vm_is_trailing_zeros = multiple_of_pow5_32(mm, q as i32);
291            } else {
292                vp -= multiple_of_pow5_32(mp, q as i32) as u32;
293            }
294        }
295    } else {
296        let q = log10_pow5((-e2) as u32 ) as i32;
297        e10 = ( q as i32 ) + e2;
298        let i = ( -e2 - ( q as i32 )) as u32;
299        let k: i32 = pow5_bits(i) as i32 - F32_POW5_BIT_COUNT as i32;
300        let mut j= ( q - k ) as u32;
301        vr = mul_pow5_div_pow2(mv, i, j);
302        vp = mul_pow5_div_pow2(mp, i, j);
303        vm = mul_pow5_div_pow2(mm, i, j);
304
305        if q != 0 && ((vp - 1) / 10 <= vm / 10) {
306            j = ( q - 1 - (pow5_bits(i + 1) as i32 - F32_POW5_BIT_COUNT as i32)) as u32;
307            last_removed_digit = (mul_pow5_div_pow2(mv, i + 1, j) % 10) as u8;
308        }
309
310        if q <= 1 {
311            vr_is_trailing_zeros = (!mv & 1) >= q as u32;
312            if accept_bounds {
313                vm_is_trailing_zeros = (!mm & 1) >= q as u32;
314            }
315            else {
316                vp -= 1;
317            }
318        } else if q < 31 { // TODO: @u32fjack: Use a tighter bound here.
319            vr_is_trailing_zeros = (mv & ((1u32 << (q - 1)) - 1)) == 0;
320        }
321    }
322
323    // Step 4: Find the shortest decimal representation in the interval of legal representations.
324    let mut removed: u32 = 0;
325    let mut output: u32;
326    if vm_is_trailing_zeros || vr_is_trailing_zeros {
327        // General case, which happens rarely.
328        while vp / 10 > vm / 10 {
329            vm_is_trailing_zeros &= vm % 10 == 0;
330            vr_is_trailing_zeros &= last_removed_digit == 0;
331            last_removed_digit = (vr % 10) as u8;
332            vr /= 10;
333            vp /= 10;
334            vm /= 10;
335            removed += 1;
336        }
337        if vm_is_trailing_zeros {
338            while vm % 10 == 0 {
339                vr_is_trailing_zeros &= last_removed_digit == 0;
340                last_removed_digit = (vr % 10) as u8;
341                vr /= 10;
342                vp /= 10;
343                vm /= 10;
344                removed += 1;
345            }
346        }
347        if vr_is_trailing_zeros && (last_removed_digit == 5) && (vr % 2 == 0) {
348            // Round down not up if the number ends in X50000.
349            last_removed_digit = 4;
350        }
351        // We need to take vr+1 if vr is outside bounds or we need to round up.
352        output = vr + ((vr == vm && (!accept_bounds || !vm_is_trailing_zeros)) || last_removed_digit >= 5) as u32;
353    } else {
354        // Common case.
355        while vp / 10 > vm / 10 {
356            last_removed_digit = (vr % 10) as u8;
357            vr /= 10;
358            vp /= 10;
359            vm /= 10;
360            removed += 1;
361        }
362        // We need to take vr+1 if vr is outside bounds or we need to round up.
363        output = vr + (vr == vm || last_removed_digit >= 5) as u32;
364    }
365    let o_length: u32 = decimal_length_32(output);
366    let vp_length: u32 = o_length + removed;
367
368    let mut exp: i32 = ( e10 + vp_length  as i32 ) - 1;
369
370    // Step 5: Print the decimal representation.
371    let mut index: usize = 0;
372    let mut result: [u8;24] = [0; 24];
373
374    if sign {
375        result[index] = b'-';
376        index += 1;
377    }
378
379    // @@@ Removed DIGIT_TABLE optimisation
380
381    // Print decimal digits after the decimal point.
382    for i in 0 .. o_length as usize - 1 {
383        let c = ( output % 10 ) as u8;
384        output /= 10;
385        result[index + o_length as usize - i] = b'0' + c;
386    }
387
388    // Print the leading decimal digit.
389    result[index] = b'0' + ( output % 10 ) as u8;
390
391    // Print decimal point if needed.
392    if o_length > 1 {
393        result[index + 1] = b'.';
394        index += o_length as usize + 1;
395    } else {
396        index += 1;
397    }
398
399    // Print the exponent.
400    result[index] = b'e';
401    index += 1;
402    if exp < 0 {
403        result[index] = b'-';
404        index += 1;
405        exp = -exp;
406    }
407
408    // @@@ Removed DIGIT_TABLE optimisation
409
410    if exp >= 10 {
411        result[index] = b'0' + ( (exp / 10) % 10 ) as u8;
412        index += 1;
413    }
414    result[index] = b'0' + ( exp % 10 ) as u8;
415    index += 1;
416
417    writer.write(&result[0..index] )
418}
419
420/// Converts the given `f32` number to a short round-trip base-10 representation
421/// using the efficient Ryū algorithm by Ulf Adams.
422///
423/// This function is ideal for exporting bulk floating-point data to text formats,
424/// such as CSV, JSON, or XLSX (Excel 2007 and later).
425///
426/// # Examples
427///
428/// ```
429/// use float_fast_print::write_f64_shortest;
430///
431/// let mut buffer: Vec<u8> = Vec::with_capacity(32);
432/// write_f64_shortest(&mut buffer, 502.1239e29).unwrap();
433/// assert_eq!(&buffer, b"5.021239e31");
434/// ```
435///
436/// # Safety
437/// Unlike some other similar code such as the `dtoa` crate, this function uses
438/// 100% safe Rust code, does not have any external dependencies, does not include
439/// C code, and does not require a heap.
440///
441/// Unlike `write_f32_shortest`, it is infeasible to test all 2^64 possible input
442/// numbers.
443pub fn write_f64_shortest<W: Write>(mut writer: W, num: f64 ) -> Result<usize> {
444    // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
445     let bits: u64 = num.to_bits();
446
447    // Decode bits into sign, mantissa, and exponent.
448    let sign: bool =  ((bits >> (F64_MANTISSA_BITS + F64_EXP_BITS)) & 1) != 0;
449    let ieee_mantissa: u64 = bits & ((1u64 << F64_MANTISSA_BITS) - 1);
450    let ieee_exponent: u32 = ((bits >> F64_MANTISSA_BITS) & ((1u64 << F64_EXP_BITS) - 1)) as u32;
451
452    let e2: i32;
453    let m2: u64;
454    // Case distinction; exit early for the easy cases.
455    if ieee_exponent == ((1u32 << F64_EXP_BITS) - 1u32) || (ieee_exponent == 0 && ieee_mantissa == 0) {
456        if ieee_mantissa != 0 {
457            return writer.write( b"NaN" );
458        }
459        if ieee_exponent != 0 {
460            if sign {
461                return writer.write( b"-inf" );
462            }  else {
463                return writer.write( b"inf" );
464            }
465        }
466        if sign {
467            return writer.write( b"-0e0" );
468        } else {
469            return writer.write( b"0e0" );
470        }
471    } else if ieee_exponent == 0 {
472        // We subtract 2 so that the bounds computation has 2 additional bits.
473        e2 = 1 - F64_OFFSET - F64_MANTISSA_BITS - 2;
474        m2 = ieee_mantissa;
475    } else {
476        e2 = ieee_exponent as i32 - F64_OFFSET - F64_MANTISSA_BITS - 2;
477        m2 = (1u64 << F64_MANTISSA_BITS) | ieee_mantissa;
478    }
479    let even: bool =  (m2 & 1) == 0;
480    let accept_bounds: bool =  even;
481
482    // Step 2: Determine the interval of legal decimal representations.
483    let mv: u64 =  4 * m2;
484    // Explicit bool -> int conversion. True is 1, false is 0.
485    let mm_shift: u64 = ((m2 != (1u64 << F64_MANTISSA_BITS)) || (ieee_exponent <= 1)) as u64;
486    // We would compute mp and mm like this:
487    //  u64 mp = 4 * m2 + 2;
488    //  u64 mm = mv - 1 - mm_shift;
489
490    // Step 3: Convert to a decimal power base using 128-bit arithmetic.
491    let mut vr: u64;
492    let mut vp: u64;
493    let mut vm: u64;
494    let e10: i32;
495    let mut vm_is_trailing_zeros = false;
496    let mut vr_is_trailing_zeros = false;
497    if e2 >= 0 {
498        // I tried special-casing q == 0, but there was no effect on performance.
499        // This expression is slightly faster than max(0, log10Pow2(e2) - 1).
500        let q: i32 = log10_pow2(e2 as u32) as i32 - (e2 > 3) as i32;
501        e10 = q;
502        let k: i32 = ( F64_POW5_INV_BIT_COUNT + pow5_bits(q as u32 )) as i32 - 1;
503        let i: i32 = -e2 + q + k;
504
505        let mul = DOUBLE_POW5_INV_SPLIT[q as usize];
506        vr = mul_shift_64(4 * m2,                mul, i as u32);
507        vp = mul_shift_64(4 * m2 + 2,            mul, i as u32);
508        vm = mul_shift_64(4 * m2 - 1 - mm_shift, mul, i as u32);
509
510        if q <= 21 {
511            // Only one of mp, mv, and mm can be a multiple of 5, if any.
512            if mv % 5 == 0 {
513                vr_is_trailing_zeros = multiple_of_pow5_64(mv, q);
514            } else if accept_bounds {
515                vm_is_trailing_zeros = multiple_of_pow5_64(mv - 1 - mm_shift, q);
516            } else {
517                // Same as min(e2 + 1, pow5Factor(mp)) >= q.
518                vp -= multiple_of_pow5_64(mv + 2, q) as u64;
519            }
520        }
521    } else {
522        // This expression is slightly faster than max(0, log10_pow5_64(-e2) - 1).
523        let q: i32 = log10_pow5(( -e2 ) as u32) as i32 - ((-e2 > 1) as i32 );
524        e10 = q + e2;
525        let i: i32 = -e2 - q;
526        let k: i32 = pow5_bits(i as u32 ) as i32 - F64_POW5_BIT_COUNT;
527        let j: i32 = q - k;
528
529        let mul = DOUBLE_POW5_SPLIT[i as usize];
530        vr = mul_shift_64(4 * m2,                       mul, j as u32);
531        vp = mul_shift_64(4 * m2 + 2,                   mul, j as u32);
532        vm = mul_shift_64(4 * m2 - 1 - mm_shift as u64, mul, j as u32);
533
534        if q <= 1 {
535            vr_is_trailing_zeros = (!(mv as u32) & 1) >= q as u32;
536            if accept_bounds {
537                vm_is_trailing_zeros = (!((mv - 1 - mm_shift as u64) as u32) & 1) >= q as u32;
538            } else {
539                vp -= 1;
540            }
541        }  else if q < 63 { // TODO(u32fjack): Use a tighter bound here.
542            // We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q-1
543            // <=> ntz(mv) >= q-1  &&  pow5Factor(mv) - e2 >= q-1
544            // <=> ntz(mv) >= q-1
545            // <=> (mv & ((1 << (q-1)) - 1)) == 0
546            // We also need to make sure that the left shift does not overflow.
547            vr_is_trailing_zeros = (mv & ((1u64 << (q - 1)) - 1)) == 0;
548        }
549    }
550
551    // Step 4: Find the shortest decimal representation in the interval of legal representations.
552    let mut removed: usize = 0;
553    let mut last_removed_digit: u8 = 0;
554    let mut output: u64;
555    // On average, we remove ~2 digits.
556    if vm_is_trailing_zeros || vr_is_trailing_zeros {
557        // General case, which happens rarely (<1%).
558        while vp / 10 > vm / 10 {
559            // https://bugs.llvm.org/show_bug.cgi?id=23106
560            // The compiler does not realize that vm % 10 can be computed from vm / 10
561            // as vm - (vm / 10) * 10.
562            vm_is_trailing_zeros &= vm - (vm / 10) * 10 == 0;
563            // vm_is_trailing_zeros &= vm % 10 == 0;
564            vr_is_trailing_zeros &= last_removed_digit == 0;
565            last_removed_digit = (vr % 10) as u8;
566            vr /= 10;
567            vp /= 10;
568            vm /= 10;
569            removed += 1;
570        }
571
572        if vm_is_trailing_zeros {
573            while vm % 10 == 0 {
574                vr_is_trailing_zeros &= last_removed_digit == 0;
575                last_removed_digit = (vr % 10) as u8;
576                vr /= 10;
577                vp /= 10;
578                vm /= 10;
579                removed += 1;
580            }
581        }
582
583        if vr_is_trailing_zeros && (last_removed_digit == 5) && (vr % 2 == 0) {
584            // Round down not up if the number ends in X50000.
585            last_removed_digit = 4;
586        }
587
588        // We need to take vr+1 if vr is outside bounds or we need to round up.
589        output = vr + ((vr == vm && (!accept_bounds || !vm_is_trailing_zeros)) || (last_removed_digit >= 5)) as u64;
590    } else {
591        // Specialized for the common case (>99%).
592        while vp / 10 > vm / 10 {
593            last_removed_digit = (vr % 10) as u8;
594            vr /= 10;
595            vp /= 10;
596            vm /= 10;
597            removed += 1;
598        }
599
600        // We need to take vr+1 if vr is outside bounds or we need to round up.
601        output = vr + ( (vr == vm) || (last_removed_digit >= 5)) as u64;
602    }
603    // The average output length is 16.38 digits.
604    let o_length: usize =  decimal_length_64(output) as usize;
605    let vp_length: usize =  o_length + removed;
606    let mut exp: i32 = e10 + vp_length as i32 - 1;
607
608    // Step 5: Print the decimal representation.
609    let mut result: [u8;24] = [0; 24]; // the longest required is apparently: -2.2250738585072020E−308
610    let mut index: usize = 0;
611    if sign {
612        result[index] = b'-';
613        index += 1;
614    }
615
616    // Print decimal digits after the decimal point.
617    for i in 0 .. o_length - 1 {
618        let c = output % 10;
619        output /= 10;
620        result[index + o_length - i] = b'0' + c as u8;
621    }
622    // Print the leading decimal digit.
623    result[index] = b'0' + ( output % 10 ) as u8;
624
625    // Print decimal point if needed.
626    if o_length > 1 {
627        result[index + 1] = b'.';
628        index += o_length + 1;
629    } else {
630        index += 1;
631    }
632
633    // Print the exponent.
634    result[index] = b'e';
635    index += 1;
636    if exp < 0 {
637        result[index] = b'-';
638        index += 1;
639        exp = -exp;
640    }
641
642    if exp >= 100 {
643        result[index] = b'0' + ( exp / 100 ) as u8;
644        index += 1;
645    }
646    if exp >= 10 {
647        result[index] = b'0' + ((exp / 10) % 10) as u8;
648        index += 1;
649    }
650    result[index] = b'0' + ( exp % 10 ) as u8;
651    index += 1;
652    
653    writer.write(&result[0..index] )
654}
655
656const F32_POW5_INV_SPLIT: [u64;31] = [
657    576460752303423489u64, 461168601842738791u64, 368934881474191033u64, 295147905179352826u64,
658    472236648286964522u64, 377789318629571618u64, 302231454903657294u64, 483570327845851670u64,
659    386856262276681336u64, 309485009821345069u64, 495176015714152110u64, 396140812571321688u64,
660    316912650057057351u64, 507060240091291761u64, 405648192073033409u64, 324518553658426727u64,
661    519229685853482763u64, 415383748682786211u64, 332306998946228969u64, 531691198313966350u64,
662    425352958651173080u64, 340282366920938464u64, 544451787073501542u64, 435561429658801234u64,
663    348449143727040987u64, 557518629963265579u64, 446014903970612463u64, 356811923176489971u64,
664    570899077082383953u64, 456719261665907162u64, 365375409332725730u64
665];
666
667const F32_POW5_SPLIT: [u64;47] = [
668    1152921504606846976u64, 1441151880758558720u64, 1801439850948198400u64, 2251799813685248000u64,
669    1407374883553280000u64, 1759218604441600000u64, 2199023255552000000u64, 1374389534720000000u64,
670    1717986918400000000u64, 2147483648000000000u64, 1342177280000000000u64, 1677721600000000000u64,
671    2097152000000000000u64, 1310720000000000000u64, 1638400000000000000u64, 2048000000000000000u64,
672    1280000000000000000u64, 1600000000000000000u64, 2000000000000000000u64, 1250000000000000000u64,
673    1562500000000000000u64, 1953125000000000000u64, 1220703125000000000u64, 1525878906250000000u64,
674    1907348632812500000u64, 1192092895507812500u64, 1490116119384765625u64, 1862645149230957031u64,
675    1164153218269348144u64, 1455191522836685180u64, 1818989403545856475u64, 2273736754432320594u64,
676    1421085471520200371u64, 1776356839400250464u64, 2220446049250313080u64, 1387778780781445675u64,
677    1734723475976807094u64, 2168404344971008868u64, 1355252715606880542u64, 1694065894508600678u64,
678    2117582368135750847u64, 1323488980084844279u64, 1654361225106055349u64, 2067951531382569187u64,
679    1292469707114105741u64, 1615587133892632177u64, 2019483917365790221u64
680];
681
682const DOUBLE_POW5_INV_SPLIT: [(u64,u64);292] = [
683    (                    1u64, 288230376151711744u64 ), (  3689348814741910324u64, 230584300921369395u64 ),
684    (  2951479051793528259u64, 184467440737095516u64 ), ( 17118578500402463900u64, 147573952589676412u64 ),
685    ( 12632330341676300947u64, 236118324143482260u64 ), ( 10105864273341040758u64, 188894659314785808u64 ),
686    ( 15463389048156653253u64, 151115727451828646u64 ), ( 17362724847566824558u64, 241785163922925834u64 ),
687    ( 17579528692795369969u64, 193428131138340667u64 ), (  6684925324752475329u64, 154742504910672534u64 ),
688    ( 18074578149087781173u64, 247588007857076054u64 ), ( 18149011334012135262u64, 198070406285660843u64 ),
689    (  3451162622983977240u64, 158456325028528675u64 ), (  5521860196774363583u64, 253530120045645880u64 ),
690    (  4417488157419490867u64, 202824096036516704u64 ), (  7223339340677503017u64, 162259276829213363u64 ),
691    (  7867994130342094503u64, 259614842926741381u64 ), (  2605046489531765280u64, 207691874341393105u64 ),
692    (  2084037191625412224u64, 166153499473114484u64 ), ( 10713157136084480204u64, 265845599156983174u64 ),
693    ( 12259874523609494487u64, 212676479325586539u64 ), ( 13497248433629505913u64, 170141183460469231u64 ),
694    ( 14216899864323388813u64, 272225893536750770u64 ), ( 11373519891458711051u64, 217780714829400616u64 ),
695    (  5409467098425058518u64, 174224571863520493u64 ), (  4965798542738183305u64, 278759314981632789u64 ),
696    (  7661987648932456967u64, 223007451985306231u64 ), (  2440241304404055250u64, 178405961588244985u64 ),
697    (  3904386087046488400u64, 285449538541191976u64 ), ( 17880904128604832013u64, 228359630832953580u64 ),
698    ( 14304723302883865611u64, 182687704666362864u64 ), ( 15133127457049002812u64, 146150163733090291u64 ),
699    ( 16834306301794583852u64, 233840261972944466u64 ), (  9778096226693756759u64, 187072209578355573u64 ),
700    ( 15201174610838826053u64, 149657767662684458u64 ), (  2185786488890659746u64, 239452428260295134u64 ),
701    (  5437978005854438120u64, 191561942608236107u64 ), ( 15418428848909281466u64, 153249554086588885u64 ),
702    (  6222742084545298729u64, 245199286538542217u64 ), ( 16046240111861969953u64, 196159429230833773u64 ),
703    (  1768945645263844993u64, 156927543384667019u64 ), ( 10209010661905972635u64, 251084069415467230u64 ),
704    (  8167208529524778108u64, 200867255532373784u64 ), ( 10223115638361732810u64, 160693804425899027u64 ),
705    (  1599589762411131202u64, 257110087081438444u64 ), (  4969020624670815285u64, 205688069665150755u64 ),
706    (  3975216499736652228u64, 164550455732120604u64 ), ( 13739044029062464211u64, 263280729171392966u64 ),
707    (  7301886408508061046u64, 210624583337114373u64 ), ( 13220206756290269483u64, 168499666669691498u64 ),
708    ( 17462981995322520850u64, 269599466671506397u64 ), (  6591687966774196033u64, 215679573337205118u64 ),
709    ( 12652048002903177473u64, 172543658669764094u64 ), (  9175230360419352987u64, 276069853871622551u64 ),
710    (  3650835473593572067u64, 220855883097298041u64 ), ( 17678063637842498946u64, 176684706477838432u64 ),
711    ( 13527506561580357021u64, 282695530364541492u64 ), (  3443307619780464970u64, 226156424291633194u64 ),
712    (  6443994910566282300u64, 180925139433306555u64 ), (  5155195928453025840u64, 144740111546645244u64 ),
713    ( 15627011115008661990u64, 231584178474632390u64 ), ( 12501608892006929592u64, 185267342779705912u64 ),
714    (  2622589484121723027u64, 148213874223764730u64 ), (  4196143174594756843u64, 237142198758023568u64 ),
715    ( 10735612169159626121u64, 189713759006418854u64 ), ( 12277838550069611220u64, 151771007205135083u64 ),
716    ( 15955192865369467629u64, 242833611528216133u64 ), (  1696107848069843133u64, 194266889222572907u64 ),
717    ( 12424932722681605476u64, 155413511378058325u64 ), (  1433148282581017146u64, 248661618204893321u64 ),
718    ( 15903913885032455010u64, 198929294563914656u64 ), (  9033782293284053685u64, 159143435651131725u64 ),
719    ( 14454051669254485895u64, 254629497041810760u64 ), ( 11563241335403588716u64, 203703597633448608u64 ),
720    ( 16629290697806691620u64, 162962878106758886u64 ), (   781423413297334329u64, 260740604970814219u64 ),
721    (  4314487545379777786u64, 208592483976651375u64 ), (  3451590036303822229u64, 166873987181321100u64 ),
722    (  5522544058086115566u64, 266998379490113760u64 ), (  4418035246468892453u64, 213598703592091008u64 ),
723    ( 10913125826658934609u64, 170878962873672806u64 ), ( 10082303693170474728u64, 273406340597876490u64 ),
724    (  8065842954536379782u64, 218725072478301192u64 ), ( 17520720807854834795u64, 174980057982640953u64 ),
725    (  5897060404116273733u64, 279968092772225526u64 ), (  1028299508551108663u64, 223974474217780421u64 ),
726    ( 15580034865808528224u64, 179179579374224336u64 ), ( 17549358155809824511u64, 286687326998758938u64 ),
727    (  2971440080422128639u64, 229349861599007151u64 ), ( 17134547323305344204u64, 183479889279205720u64 ),
728    ( 13707637858644275364u64, 146783911423364576u64 ), ( 14553522944347019935u64, 234854258277383322u64 ),
729    (  4264120725993795302u64, 187883406621906658u64 ), ( 10789994210278856888u64, 150306725297525326u64 ),
730    (  9885293106962350374u64, 240490760476040522u64 ), (   529536856086059653u64, 192392608380832418u64 ),
731    (  7802327114352668369u64, 153914086704665934u64 ), (  1415676938738538420u64, 246262538727465495u64 ),
732    (  1132541550990830736u64, 197010030981972396u64 ), ( 15663428499760305882u64, 157608024785577916u64 ),
733    ( 17682787970132668764u64, 252172839656924666u64 ), ( 10456881561364224688u64, 201738271725539733u64 ),
734    ( 15744202878575200397u64, 161390617380431786u64 ), ( 17812026976236499989u64, 258224987808690858u64 ),
735    (  3181575136763469022u64, 206579990246952687u64 ), ( 13613306553636506187u64, 165263992197562149u64 ),
736    ( 10713244041592678929u64, 264422387516099439u64 ), ( 12259944048016053467u64, 211537910012879551u64 ),
737    (  6118606423670932450u64, 169230328010303641u64 ), (  2411072648389671274u64, 270768524816485826u64 ),
738    ( 16686253377679378312u64, 216614819853188660u64 ), ( 13349002702143502650u64, 173291855882550928u64 ),
739    ( 17669055508687693916u64, 277266969412081485u64 ), ( 14135244406950155133u64, 221813575529665188u64 ),
740    (   240149081334393137u64, 177450860423732151u64 ), ( 11452284974360759988u64, 283921376677971441u64 ),
741    (  5472479164746697667u64, 227137101342377153u64 ), ( 11756680961281178780u64, 181709681073901722u64 ),
742    (  2026647139541122378u64, 145367744859121378u64 ), ( 18000030682233437097u64, 232588391774594204u64 ),
743    ( 18089373360528660001u64, 186070713419675363u64 ), (  3403452244197197031u64, 148856570735740291u64 ),
744    ( 16513570034941246220u64, 238170513177184465u64 ), ( 13210856027952996976u64, 190536410541747572u64 ),
745    (  3189987192878576934u64, 152429128433398058u64 ), (  1414630693863812771u64, 243886605493436893u64 ),
746    (  8510402184574870864u64, 195109284394749514u64 ), ( 10497670562401807014u64, 156087427515799611u64 ),
747    (  9417575270359070576u64, 249739884025279378u64 ), ( 14912757845771077107u64, 199791907220223502u64 ),
748    (  4551508647133041040u64, 159833525776178802u64 ), ( 10971762650154775986u64, 255733641241886083u64 ),
749    ( 16156107749607641435u64, 204586912993508866u64 ), (  9235537384944202825u64, 163669530394807093u64 ),
750    ( 11087511001168814197u64, 261871248631691349u64 ), ( 12559357615676961681u64, 209496998905353079u64 ),
751    ( 13736834907283479668u64, 167597599124282463u64 ), ( 18289587036911657145u64, 268156158598851941u64 ),
752    ( 10942320814787415393u64, 214524926879081553u64 ), ( 16132554281313752961u64, 171619941503265242u64 ),
753    ( 11054691591134363444u64, 274591906405224388u64 ), ( 16222450902391311402u64, 219673525124179510u64 ),
754    ( 12977960721913049122u64, 175738820099343608u64 ), ( 17075388340318968271u64, 281182112158949773u64 ),
755    (  2592264228029443648u64, 224945689727159819u64 ), (  5763160197165465241u64, 179956551781727855u64 ),
756    (  9221056315464744386u64, 287930482850764568u64 ), ( 14755542681855616155u64, 230344386280611654u64 ),
757    ( 15493782960226403247u64, 184275509024489323u64 ), (  1326979923955391628u64, 147420407219591459u64 ),
758    (  9501865507812447252u64, 235872651551346334u64 ), ( 11290841220991868125u64, 188698121241077067u64 ),
759    (  1653975347309673853u64, 150958496992861654u64 ), ( 10025058185179298811u64, 241533595188578646u64 ),
760    (  4330697733401528726u64, 193226876150862917u64 ), ( 14532604630946953951u64, 154581500920690333u64 ),
761    (  1116074521063664381u64, 247330401473104534u64 ), (  4582208431592841828u64, 197864321178483627u64 ),
762    ( 14733813189500004432u64, 158291456942786901u64 ), ( 16195403473716186445u64, 253266331108459042u64 ),
763    (  5577625149489128510u64, 202613064886767234u64 ), (  8151448934333213131u64, 162090451909413787u64 ),
764    ( 16731667109675051333u64, 259344723055062059u64 ), ( 17074682502481951390u64, 207475778444049647u64 ),
765    (  6281048372501740465u64, 165980622755239718u64 ), (  6360328581260874421u64, 265568996408383549u64 ),
766    (  8777611679750609860u64, 212455197126706839u64 ), ( 10711438158542398211u64, 169964157701365471u64 ),
767    (  9759603424184016492u64, 271942652322184754u64 ), ( 11497031554089123517u64, 217554121857747803u64 ),
768    ( 16576322872755119460u64, 174043297486198242u64 ), ( 11764721337440549842u64, 278469275977917188u64 ),
769    ( 16790474699436260520u64, 222775420782333750u64 ), ( 13432379759549008416u64, 178220336625867000u64 ),
770    (  3045063541568861850u64, 285152538601387201u64 ), ( 17193446092222730773u64, 228122030881109760u64 ),
771    ( 13754756873778184618u64, 182497624704887808u64 ), ( 18382503128506368341u64, 145998099763910246u64 ),
772    (  3586563302416817083u64, 233596959622256395u64 ), (  2869250641933453667u64, 186877567697805116u64 ),
773    ( 17052795772514404226u64, 149502054158244092u64 ), ( 12527077977055405469u64, 239203286653190548u64 ),
774    ( 17400360011128145022u64, 191362629322552438u64 ), (  2852241564676785048u64, 153090103458041951u64 ),
775    ( 15631632947708587046u64, 244944165532867121u64 ), (  8815957543424959314u64, 195955332426293697u64 ),
776    ( 18120812478965698421u64, 156764265941034957u64 ), ( 14235904707377476180u64, 250822825505655932u64 ),
777    (  4010026136418160298u64, 200658260404524746u64 ), ( 17965416168102169531u64, 160526608323619796u64 ),
778    (  2919224165770098987u64, 256842573317791675u64 ), (  2335379332616079190u64, 205474058654233340u64 ),
779    (  1868303466092863352u64, 164379246923386672u64 ), (  6678634360490491686u64, 263006795077418675u64 ),
780    (  5342907488392393349u64, 210405436061934940u64 ), (  4274325990713914679u64, 168324348849547952u64 ),
781    ( 10528270399884173809u64, 269318958159276723u64 ), ( 15801313949391159694u64, 215455166527421378u64 ),
782    (  1573004715287196786u64, 172364133221937103u64 ), ( 17274202803427156150u64, 275782613155099364u64 ),
783    ( 17508711057483635243u64, 220626090524079491u64 ), ( 10317620031244997871u64, 176500872419263593u64 ),
784    ( 12818843235250086271u64, 282401395870821749u64 ), ( 13944423402941979340u64, 225921116696657399u64 ),
785    ( 14844887537095493795u64, 180736893357325919u64 ), ( 15565258844418305359u64, 144589514685860735u64 ),
786    (  6457670077359736959u64, 231343223497377177u64 ), ( 16234182506113520537u64, 185074578797901741u64 ),
787    (  9297997190148906106u64, 148059663038321393u64 ), ( 11187446689496339446u64, 236895460861314229u64 ),
788    ( 12639306166338981880u64, 189516368689051383u64 ), ( 17490142562555006151u64, 151613094951241106u64 ),
789    (  2158786396894637579u64, 242580951921985771u64 ), ( 16484424376483351356u64, 194064761537588616u64 ),
790    (  9498190686444770762u64, 155251809230070893u64 ), ( 11507756283569722895u64, 248402894768113429u64 ),
791    ( 12895553841597688639u64, 198722315814490743u64 ), ( 17695140702761971558u64, 158977852651592594u64 ),
792    ( 17244178680193423523u64, 254364564242548151u64 ), ( 10105994129412828495u64, 203491651394038521u64 ),
793    (  4395446488788352473u64, 162793321115230817u64 ), ( 10722063196803274280u64, 260469313784369307u64 ),
794    (  1198952927958798777u64, 208375451027495446u64 ), ( 15716557601334680315u64, 166700360821996356u64 ),
795    ( 17767794532651667857u64, 266720577315194170u64 ), ( 14214235626121334286u64, 213376461852155336u64 ),
796    (  7682039686155157106u64, 170701169481724269u64 ), (  1223217053622520399u64, 273121871170758831u64 ),
797    ( 15735968901865657612u64, 218497496936607064u64 ), ( 16278123936234436413u64, 174797997549285651u64 ),
798    (   219556594781725998u64, 279676796078857043u64 ), (  7554342905309201445u64, 223741436863085634u64 ),
799    (  9732823138989271479u64, 178993149490468507u64 ), (   815121763415193074u64, 286389039184749612u64 ),
800    ( 11720143854957885429u64, 229111231347799689u64 ), ( 13065463898708218666u64, 183288985078239751u64 ),
801    (  6763022304224664610u64, 146631188062591801u64 ), (  3442138057275642729u64, 234609900900146882u64 ),
802    ( 13821756890046245153u64, 187687920720117505u64 ), ( 11057405512036996122u64, 150150336576094004u64 ),
803    (  6623802375033462826u64, 240240538521750407u64 ), ( 16367088344252501231u64, 192192430817400325u64 ),
804    ( 13093670675402000985u64, 153753944653920260u64 ), (  2503129006933649959u64, 246006311446272417u64 ),
805    ( 13070549649772650937u64, 196805049157017933u64 ), ( 17835137349301941396u64, 157444039325614346u64 ),
806    (  2710778055689733971u64, 251910462920982955u64 ), (  2168622444551787177u64, 201528370336786364u64 ),
807    (  5424246770383340065u64, 161222696269429091u64 ), (  1300097203129523457u64, 257956314031086546u64 ),
808    ( 15797473021471260058u64, 206365051224869236u64 ), (  8948629602435097724u64, 165092040979895389u64 ),
809    (  3249760919670425388u64, 264147265567832623u64 ), (  9978506365220160957u64, 211317812454266098u64 ),
810    ( 15361502721659949412u64, 169054249963412878u64 ), (  2442311466204457120u64, 270486799941460606u64 ),
811    ( 16711244431931206989u64, 216389439953168484u64 ), ( 17058344360286875914u64, 173111551962534787u64 ),
812    ( 12535955717491360170u64, 276978483140055660u64 ), ( 10028764573993088136u64, 221582786512044528u64 ),
813    ( 15401709288678291155u64, 177266229209635622u64 ), (  9885339602917624555u64, 283625966735416996u64 ),
814    (  4218922867592189321u64, 226900773388333597u64 ), ( 14443184738299482427u64, 181520618710666877u64 ),
815    (  4175850161155765295u64, 145216494968533502u64 ), ( 10370709072591134795u64, 232346391949653603u64 ),
816    ( 15675264887556728482u64, 185877113559722882u64 ), (  5161514280561562140u64, 148701690847778306u64 ),
817    (   879725219414678777u64, 237922705356445290u64 ), (   703780175531743021u64, 190338164285156232u64 ),
818    ( 11631070584651125387u64, 152270531428124985u64 ), (   162968861732249003u64, 243632850284999977u64 ),
819    ( 11198421533611530172u64, 194906280227999981u64 ), (  5269388412147313814u64, 155925024182399985u64 ),
820    (  8431021459435702103u64, 249480038691839976u64 ), (  3055468352806651359u64, 199584030953471981u64 ),
821    ( 17201769941212962380u64, 159667224762777584u64 ), ( 16454785461715008838u64, 255467559620444135u64 ),
822    ( 13163828369372007071u64, 204374047696355308u64 ), ( 17909760324981426303u64, 163499238157084246u64 ),
823    (  2830174816776909822u64, 261598781051334795u64 ), (  2264139853421527858u64, 209279024841067836u64 ),
824    ( 16568707141704863579u64, 167423219872854268u64 ), (  4373838538276319787u64, 267877151796566830u64 ),
825    (  3499070830621055830u64, 214301721437253464u64 ), (  6488605479238754987u64, 171441377149802771u64 ),
826    (  3003071137298187333u64, 274306203439684434u64 ), (  6091805724580460189u64, 219444962751747547u64 ),
827    ( 15941491023890099121u64, 175555970201398037u64 ), ( 10748990379256517301u64, 280889552322236860u64 ),
828    (  8599192303405213841u64, 224711641857789488u64 ), ( 14258051472207991719u64, 179769313486231590u64 )
829];
830
831const DOUBLE_POW5_SPLIT: [(u64,u64);326] = [
832    (                    0u64,  72057594037927936u64 ), (                    0u64,  90071992547409920u64 ),
833    (                    0u64, 112589990684262400u64 ), (                    0u64, 140737488355328000u64 ),
834    (                    0u64,  87960930222080000u64 ), (                    0u64, 109951162777600000u64 ),
835    (                    0u64, 137438953472000000u64 ), (                    0u64,  85899345920000000u64 ),
836    (                    0u64, 107374182400000000u64 ), (                    0u64, 134217728000000000u64 ),
837    (                    0u64,  83886080000000000u64 ), (                    0u64, 104857600000000000u64 ),
838    (                    0u64, 131072000000000000u64 ), (                    0u64,  81920000000000000u64 ),
839    (                    0u64, 102400000000000000u64 ), (                    0u64, 128000000000000000u64 ),
840    (                    0u64,  80000000000000000u64 ), (                    0u64, 100000000000000000u64 ),
841    (                    0u64, 125000000000000000u64 ), (                    0u64,  78125000000000000u64 ),
842    (                    0u64,  97656250000000000u64 ), (                    0u64, 122070312500000000u64 ),
843    (                    0u64,  76293945312500000u64 ), (                    0u64,  95367431640625000u64 ),
844    (                    0u64, 119209289550781250u64 ), (  4611686018427387904u64,  74505805969238281u64 ),
845    ( 10376293541461622784u64,  93132257461547851u64 ), (  8358680908399640576u64, 116415321826934814u64 ),
846    (   612489549322387456u64,  72759576141834259u64 ), ( 14600669991935148032u64,  90949470177292823u64 ),
847    ( 13639151471491547136u64, 113686837721616029u64 ), (  3213881284082270208u64, 142108547152020037u64 ),
848    (  4314518811765112832u64,  88817841970012523u64 ), (   781462496279003136u64, 111022302462515654u64 ),
849    ( 10200200157203529728u64, 138777878078144567u64 ), ( 13292654125893287936u64,  86736173798840354u64 ),
850    (  7392445620511834112u64, 108420217248550443u64 ), (  4628871007212404736u64, 135525271560688054u64 ),
851    ( 16728102434789916672u64,  84703294725430033u64 ), (  7075069988205232128u64, 105879118406787542u64 ),
852    ( 18067209522111315968u64, 132348898008484427u64 ), (  8986162942105878528u64,  82718061255302767u64 ),
853    (  6621017659204960256u64, 103397576569128459u64 ), (  3664586055578812416u64, 129246970711410574u64 ),
854    ( 16125424340018921472u64,  80779356694631608u64 ), (  1710036351314100224u64, 100974195868289511u64 ),
855    ( 15972603494424788992u64, 126217744835361888u64 ), (  9982877184015493120u64,  78886090522101180u64 ),
856    ( 12478596480019366400u64,  98607613152626475u64 ), ( 10986559581596820096u64, 123259516440783094u64 ),
857    (  2254913720070624656u64,  77037197775489434u64 ), ( 12042014186943056628u64,  96296497219361792u64 ),
858    ( 15052517733678820785u64, 120370621524202240u64 ), (  9407823583549262990u64,  75231638452626400u64 ),
859    ( 11759779479436578738u64,  94039548065783000u64 ), ( 14699724349295723422u64, 117549435082228750u64 ),
860    (  4575641699882439235u64,  73468396926392969u64 ), ( 10331238143280436948u64,  91835496157991211u64 ),
861    (  8302361660673158281u64, 114794370197489014u64 ), (  1154580038986672043u64, 143492962746861268u64 ),
862    (  9944984561221445835u64,  89683101716788292u64 ), ( 12431230701526807293u64, 112103877145985365u64 ),
863    (  1703980321626345405u64, 140129846432481707u64 ), ( 17205888765512323542u64,  87581154020301066u64 ),
864    ( 12283988920035628619u64, 109476442525376333u64 ), (  1519928094762372062u64, 136845553156720417u64 ),
865    ( 12479170105294952299u64,  85528470722950260u64 ), ( 15598962631618690374u64, 106910588403687825u64 ),
866    (  5663645234241199255u64, 133638235504609782u64 ), ( 17374836326682913246u64,  83523897190381113u64 ),
867    (  7883487353071477846u64, 104404871487976392u64 ), (  9854359191339347308u64, 130506089359970490u64 ),
868    ( 10770660513014479971u64,  81566305849981556u64 ), ( 13463325641268099964u64, 101957882312476945u64 ),
869    (  2994098996302961243u64, 127447352890596182u64 ), ( 15706369927971514489u64,  79654595556622613u64 ),
870    (  5797904354682229399u64,  99568244445778267u64 ), (  2635694424925398845u64, 124460305557222834u64 ),
871    (  6258995034005762182u64,  77787690973264271u64 ), (  3212057774079814824u64,  97234613716580339u64 ),
872    ( 17850130272881932242u64, 121543267145725423u64 ), ( 18073860448192289507u64,  75964541966078389u64 ),
873    (  8757267504958198172u64,  94955677457597987u64 ), (  6334898362770359811u64, 118694596821997484u64 ),
874    ( 13182683513586250689u64,  74184123013748427u64 ), ( 11866668373555425458u64,  92730153767185534u64 ),
875    (  5609963430089506015u64, 115912692208981918u64 ), ( 17341285199088104971u64,  72445432630613698u64 ),
876    ( 12453234462005355406u64,  90556790788267123u64 ), ( 10954857059079306353u64, 113195988485333904u64 ),
877    ( 13693571323849132942u64, 141494985606667380u64 ), ( 17781854114260483896u64,  88434366004167112u64 ),
878    (  3780573569116053255u64, 110542957505208891u64 ), (   114030942967678664u64, 138178696881511114u64 ),
879    (  4682955357782187069u64,  86361685550944446u64 ), ( 15077066234082509644u64, 107952106938680557u64 ),
880    (  5011274737320973344u64, 134940133673350697u64 ), ( 14661261756894078100u64,  84337583545844185u64 ),
881    (  4491519140835433913u64, 105421979432305232u64 ), (  5614398926044292391u64, 131777474290381540u64 ),
882    ( 12732371365632458552u64,  82360921431488462u64 ), (  6692092170185797382u64, 102951151789360578u64 ),
883    ( 17588487249587022536u64, 128688939736700722u64 ), ( 15604490549419276989u64,  80430587335437951u64 ),
884    ( 14893927168346708332u64, 100538234169297439u64 ), ( 14005722942005997511u64, 125672792711621799u64 ),
885    ( 15671105866394830300u64,  78545495444763624u64 ), (  1142138259283986260u64,  98181869305954531u64 ),
886    ( 15262730879387146537u64, 122727336632443163u64 ), (  7233363790403272633u64,  76704585395276977u64 ),
887    ( 13653390756431478696u64,  95880731744096221u64 ), (  3231680390257184658u64, 119850914680120277u64 ),
888    (  4325643253124434363u64,  74906821675075173u64 ), ( 10018740084832930858u64,  93633527093843966u64 ),
889    (  3300053069186387764u64, 117041908867304958u64 ), ( 15897591223523656064u64,  73151193042065598u64 ),
890    ( 10648616992549794273u64,  91438991302581998u64 ), (  4087399203832467033u64, 114298739128227498u64 ),
891    ( 14332621041645359599u64, 142873423910284372u64 ), ( 18181260187883125557u64,  89295889943927732u64 ),
892    (  4279831161144355331u64, 111619862429909666u64 ), ( 14573160988285219972u64, 139524828037387082u64 ),
893    ( 13719911636105650386u64,  87203017523366926u64 ), (  7926517508277287175u64, 109003771904208658u64 ),
894    (   684774848491833161u64, 136254714880260823u64 ), (  7345513307948477581u64,  85159196800163014u64 ),
895    ( 18405263671790372785u64, 106448996000203767u64 ), ( 18394893571310578077u64, 133061245000254709u64 ),
896    ( 13802651491282805250u64,  83163278125159193u64 ), (  3418256308821342851u64, 103954097656448992u64 ),
897    (  4272820386026678563u64, 129942622070561240u64 ), (  2670512741266674102u64,  81214138794100775u64 ),
898    ( 17173198981865506339u64, 101517673492625968u64 ), (  3019754653622331308u64, 126897091865782461u64 ),
899    (  4193189667727651020u64,  79310682416114038u64 ), ( 14464859121514339583u64,  99138353020142547u64 ),
900    ( 13469387883465536574u64, 123922941275178184u64 ), (  8418367427165960359u64,  77451838296986365u64 ),
901    ( 15134645302384838353u64,  96814797871232956u64 ), (   471562554271496325u64, 121018497339041196u64 ),
902    (  9518098633274461011u64,  75636560836900747u64 ), (  7285937273165688360u64,  94545701046125934u64 ),
903    ( 18330793628311886258u64, 118182126307657417u64 ), (  4539216990053847055u64,  73863828942285886u64 ),
904    ( 14897393274422084627u64,  92329786177857357u64 ), (  4786683537745442072u64, 115412232722321697u64 ),
905    ( 14520892257159371055u64,  72132645451451060u64 ), ( 18151115321449213818u64,  90165806814313825u64 ),
906    (  8853836096529353561u64, 112707258517892282u64 ), (  1843923083806916143u64, 140884073147365353u64 ),
907    ( 12681666973447792349u64,  88052545717103345u64 ), (  2017025661527576725u64, 110065682146379182u64 ),
908    ( 11744654113764246714u64, 137582102682973977u64 ), (   422879793461572340u64,  85988814176858736u64 ),
909    (   528599741826965425u64, 107486017721073420u64 ), (   660749677283706782u64, 134357522151341775u64 ),
910    (  7330497575943398595u64,  83973451344588609u64 ), ( 13774807988356636147u64, 104966814180735761u64 ),
911    (  3383451930163631472u64, 131208517725919702u64 ), ( 15949715511634433382u64,  82005323578699813u64 ),
912    (  6102086334260878016u64, 102506654473374767u64 ), (  3015921899398709616u64, 128133318091718459u64 ),
913    ( 18025852251620051174u64,  80083323807324036u64 ), (  4085571240815512351u64, 100104154759155046u64 ),
914    ( 14330336087874166247u64, 125130193448943807u64 ), ( 15873989082562435760u64,  78206370905589879u64 ),
915    ( 15230800334775656796u64,  97757963631987349u64 ), (  5203442363187407284u64, 122197454539984187u64 ),
916    (   946308467778435600u64,  76373409087490117u64 ), (  5794571603150432404u64,  95466761359362646u64 ),
917    ( 16466586540792816313u64, 119333451699203307u64 ), (  7985773578781816244u64,  74583407312002067u64 ),
918    (  5370530955049882401u64,  93229259140002584u64 ), (  6713163693812353001u64, 116536573925003230u64 ),
919    ( 18030785363914884337u64,  72835358703127018u64 ), ( 13315109668038829614u64,  91044198378908773u64 ),
920    (  2808829029766373305u64, 113805247973635967u64 ), ( 17346094342490130344u64, 142256559967044958u64 ),
921    (  6229622945628943561u64,  88910349979403099u64 ), (  3175342663608791547u64, 111137937474253874u64 ),
922    ( 13192550366365765242u64, 138922421842817342u64 ), (  3633657960551215372u64,  86826513651760839u64 ),
923    ( 18377130505971182927u64, 108533142064701048u64 ), (  4524669058754427043u64, 135666427580876311u64 ),
924    (  9745447189362598758u64,  84791517238047694u64 ), (  2958436949848472639u64, 105989396547559618u64 ),
925    ( 12921418224165366607u64, 132486745684449522u64 ), ( 12687572408530742033u64,  82804216052780951u64 ),
926    ( 11247779492236039638u64, 103505270065976189u64 ), (   224666310012885835u64, 129381587582470237u64 ),
927    (  2446259452971747599u64,  80863492239043898u64 ), ( 12281196353069460307u64, 101079365298804872u64 ),
928    ( 15351495441336825384u64, 126349206623506090u64 ), ( 14206370669262903769u64,  78968254139691306u64 ),
929    (  8534591299723853903u64,  98710317674614133u64 ), ( 15279925143082205283u64, 123387897093267666u64 ),
930    ( 14161639232853766206u64,  77117435683292291u64 ), ( 13090363022639819853u64,  96396794604115364u64 ),
931    ( 16362953778299774816u64, 120495993255144205u64 ), ( 12532689120651053212u64,  75309995784465128u64 ),
932    ( 15665861400813816515u64,  94137494730581410u64 ), ( 10358954714162494836u64, 117671868413226763u64 ),
933    (  4168503687137865320u64,  73544917758266727u64 ), (   598943590494943747u64,  91931147197833409u64 ),
934    (  5360365506546067587u64, 114913933997291761u64 ), ( 11312142901609972388u64, 143642417496614701u64 ),
935    (  9375932322719926695u64,  89776510935384188u64 ), ( 11719915403399908368u64, 112220638669230235u64 ),
936    ( 10038208235822497557u64, 140275798336537794u64 ), ( 10885566165816448877u64,  87672373960336121u64 ),
937    ( 18218643725697949000u64, 109590467450420151u64 ), ( 18161618638695048346u64, 136988084313025189u64 ),
938    ( 13656854658398099168u64,  85617552695640743u64 ), ( 12459382304570236056u64, 107021940869550929u64 ),
939    (  1739169825430631358u64, 133777426086938662u64 ), ( 14922039196176308311u64,  83610891304336663u64 ),
940    ( 14040862976792997485u64, 104513614130420829u64 ), (  3716020665709083144u64, 130642017663026037u64 ),
941    (  4628355925281870917u64,  81651261039391273u64 ), ( 10397130925029726550u64, 102064076299239091u64 ),
942    (  8384727637859770284u64, 127580095374048864u64 ), (  5240454773662356427u64,  79737559608780540u64 ),
943    (  6550568467077945534u64,  99671949510975675u64 ), (  3576524565420044014u64, 124589936888719594u64 ),
944    (  6847013871814915412u64,  77868710555449746u64 ), ( 17782139376623420074u64,  97335888194312182u64 ),
945    ( 13004302183924499284u64, 121669860242890228u64 ), ( 17351060901807587860u64,  76043662651806392u64 ),
946    (  3242082053549933210u64,  95054578314757991u64 ), ( 17887660622219580224u64, 118818222893447488u64 ),
947    ( 11179787888887237640u64,  74261389308404680u64 ), ( 13974734861109047050u64,  92826736635505850u64 ),
948    (  8245046539531533005u64, 116033420794382313u64 ), ( 16682369133275677888u64,  72520887996488945u64 ),
949    (  7017903361312433648u64,  90651109995611182u64 ), ( 17995751238495317868u64, 113313887494513977u64 ),
950    (  8659630992836983623u64, 141642359368142472u64 ), (  5412269370523114764u64,  88526474605089045u64 ),
951    ( 11377022731581281359u64, 110658093256361306u64 ), (  4997906377621825891u64, 138322616570451633u64 ),
952    ( 14652906532082110942u64,  86451635356532270u64 ), (  9092761128247862869u64, 108064544195665338u64 ),
953    (  2142579373455052779u64, 135080680244581673u64 ), ( 12868327154477877747u64,  84425425152863545u64 ),
954    (  2250350887815183471u64, 105531781441079432u64 ), (  2812938609768979339u64, 131914726801349290u64 ),
955    (  6369772649532999991u64,  82446704250843306u64 ), ( 17185587848771025797u64, 103058380313554132u64 ),
956    (  3035240737254230630u64, 128822975391942666u64 ), (  6508711479211282048u64,  80514359619964166u64 ),
957    ( 17359261385868878368u64, 100642949524955207u64 ), ( 17087390713908710056u64, 125803686906194009u64 ),
958    (  3762090168551861929u64,  78627304316371256u64 ), (  4702612710689827411u64,  98284130395464070u64 ),
959    ( 15101637925217060072u64, 122855162994330087u64 ), ( 16356052730901744401u64,  76784476871456304u64 ),
960    (  1998321839917628885u64,  95980596089320381u64 ), (  7109588318324424010u64, 119975745111650476u64 ),
961    ( 13666864735807540814u64,  74984840694781547u64 ), ( 12471894901332038114u64,  93731050868476934u64 ),
962    (  6366496589810271835u64, 117163813585596168u64 ), (  3979060368631419896u64,  73227383490997605u64 ),
963    (  9585511479216662775u64,  91534229363747006u64 ), (  2758517312166052660u64, 114417786704683758u64 ),
964    ( 12671518677062341634u64, 143022233380854697u64 ), (  1002170145522881665u64,  89388895863034186u64 ),
965    ( 10476084718758377889u64, 111736119828792732u64 ), ( 13095105898447972362u64, 139670149785990915u64 ),
966    (  5878598177316288774u64,  87293843616244322u64 ), ( 16571619758500136775u64, 109117304520305402u64 ),
967    ( 11491152661270395161u64, 136396630650381753u64 ), (   264441385652915120u64,  85247894156488596u64 ),
968    (   330551732066143900u64, 106559867695610745u64 ), (  5024875683510067779u64, 133199834619513431u64 ),
969    ( 10058076329834874218u64,  83249896637195894u64 ), (  3349223375438816964u64, 104062370796494868u64 ),
970    (  4186529219298521205u64, 130077963495618585u64 ), ( 14145795808130045513u64,  81298727184761615u64 ),
971    ( 13070558741735168987u64, 101623408980952019u64 ), ( 11726512408741573330u64, 127029261226190024u64 ),
972    (  7329070255463483331u64,  79393288266368765u64 ), ( 13773023837756742068u64,  99241610332960956u64 ),
973    ( 17216279797195927585u64, 124052012916201195u64 ), (  8454331864033760789u64,  77532508072625747u64 ),
974    (  5956228811614813082u64,  96915635090782184u64 ), (  7445286014518516353u64, 121144543863477730u64 ),
975    (  9264989777501460624u64,  75715339914673581u64 ), ( 16192923240304213684u64,  94644174893341976u64 ),
976    (  1794409976670715490u64, 118305218616677471u64 ), (  8039035263060279037u64,  73940761635423419u64 ),
977    (  5437108060397960892u64,  92425952044279274u64 ), ( 16019757112352226923u64, 115532440055349092u64 ),
978    (   788976158365366019u64,  72207775034593183u64 ), ( 14821278253238871236u64,  90259718793241478u64 ),
979    (  9303225779693813237u64, 112824648491551848u64 ), ( 11629032224617266546u64, 141030810614439810u64 ),
980    ( 11879831158813179495u64,  88144256634024881u64 ), (  1014730893234310657u64, 110180320792531102u64 ),
981    ( 10491785653397664129u64, 137725400990663877u64 ), (  8863209042587234033u64,  86078375619164923u64 ),
982    (  6467325284806654637u64, 107597969523956154u64 ), ( 17307528642863094104u64, 134497461904945192u64 ),
983    ( 10817205401789433815u64,  84060913690590745u64 ), ( 18133192770664180173u64, 105076142113238431u64 ),
984    ( 18054804944902837312u64, 131345177641548039u64 ), ( 18201782118205355176u64,  82090736025967524u64 ),
985    (  4305483574047142354u64, 102613420032459406u64 ), ( 14605226504413703751u64, 128266775040574257u64 ),
986    (  2210737537617482988u64,  80166734400358911u64 ), ( 16598479977304017447u64, 100208418000448638u64 ),
987    ( 11524727934775246001u64, 125260522500560798u64 ), (  2591268940807140847u64,  78287826562850499u64 ),
988    ( 17074144231291089770u64,  97859783203563123u64 ), ( 16730994270686474309u64, 122324729004453904u64 ),
989    ( 10456871419179046443u64,  76452955627783690u64 ), (  3847717237119032246u64,  95566194534729613u64 ),
990    (  9421332564826178211u64, 119457743168412016u64 ), (  5888332853016361382u64,  74661089480257510u64 ),
991    ( 16583788103125227536u64,  93326361850321887u64 ), ( 16118049110479146516u64, 116657952312902359u64 ),
992    ( 16991309721690548428u64,  72911220195563974u64 ), ( 12015765115258409727u64,  91139025244454968u64 ),
993    ( 15019706394073012159u64, 113923781555568710u64 ), (  9551260955736489391u64, 142404726944460888u64 ),
994    (  5969538097335305869u64,  89002954340288055u64 ), (  2850236603241744433u64, 111253692925360069u64 )
995];
996
997#[cfg(test)]
998mod tests {
999    use super::*;
1000
1001    fn f32_test_text(number: f32, text: &str) {
1002        let mut buffer: Vec<u8> = Vec::with_capacity(32);
1003        write_f32_shortest(&mut buffer, number).unwrap();
1004
1005        assert_eq!(std::str::from_utf8(&buffer).unwrap(), text);
1006    }
1007
1008    fn f64_test_text(number: f64, text: &str) {
1009        let mut buffer: Vec<u8> = Vec::with_capacity(32);
1010        write_f64_shortest(&mut buffer, number).unwrap();
1011
1012        assert_eq!(std::str::from_utf8(&buffer).unwrap(), text);
1013    }
1014
1015    fn f32_test_roundtrip(number: f32) {
1016        let mut buffer: Vec<u8> = Vec::with_capacity(32);
1017        write_f32_shortest(&mut buffer, number).unwrap();
1018        let text = std::str::from_utf8(&buffer).unwrap();
1019        let parsed = text.parse::<f32>().unwrap();
1020
1021        assert_eq!(number, parsed);
1022    }
1023
1024    fn f64_test_roundtrip(number: f64) {
1025        let mut buffer: Vec<u8> = Vec::with_capacity(32);
1026        write_f64_shortest(&mut buffer, number).unwrap();
1027        let text = std::str::from_utf8(&buffer).unwrap();
1028        let parsed = text.parse::<f64>().unwrap();
1029
1030        assert_eq!(number, parsed);
1031    }
1032
1033
1034    #[test]
1035    fn f32_special_cases() {
1036        f32_test_text(1.0, "1e0");
1037        f32_test_text(-1.0, "-1e0");
1038        f32_test_text(0.0, "0e0");
1039        f32_test_text(std::f32::INFINITY, "inf");
1040        f32_test_text(std::f32::NEG_INFINITY, "-inf");
1041    }
1042
1043    #[test]
1044    fn f64_special_cases() {
1045        f64_test_text(1.0, "1e0");
1046        f64_test_text(-1.0, "-1e0");
1047        f64_test_text(0.0, "0e0");
1048        f64_test_text(std::f64::INFINITY, "inf");
1049        f64_test_text(std::f64::NEG_INFINITY, "-inf");
1050    }
1051
1052    #[test]
1053    fn f32_special_cases_roundtrip() {
1054        f32_test_roundtrip(0.0);
1055        f32_test_roundtrip(1.0);
1056        f32_test_roundtrip(-1.0);
1057        f32_test_roundtrip(0.1);
1058        f32_test_roundtrip(-0.1);
1059        f32_test_roundtrip(std::f32::INFINITY);
1060        f32_test_roundtrip(std::f32::NEG_INFINITY);
1061        f32_test_roundtrip(std::f32::MAX);
1062        f32_test_roundtrip(std::f32::MIN);
1063        f32_test_roundtrip(std::f32::EPSILON);
1064        f32_test_roundtrip(std::f32::MIN_POSITIVE);
1065    }
1066
1067    #[test]
1068    fn f64_special_cases_roundtrip() {
1069        f64_test_roundtrip(0.0);
1070        f64_test_roundtrip(1.0);
1071        f64_test_roundtrip(-1.0);
1072        f64_test_roundtrip(0.1);
1073        f64_test_roundtrip(-0.1);
1074        f64_test_roundtrip(std::f64::INFINITY);
1075        f64_test_roundtrip(std::f64::NEG_INFINITY);
1076        f64_test_roundtrip(std::f64::MAX);
1077        f64_test_roundtrip(std::f64::MIN);
1078        f64_test_roundtrip(std::f64::EPSILON);
1079        f64_test_roundtrip(std::f64::MIN_POSITIVE);
1080    }
1081}
float_fast_print/lib.rs

float_fast_print/
lib.rs
