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half.h
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1 
2 //
3 // Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
4 // Digital Ltd. LLC
5 //
6 // All rights reserved.
7 //
8 // Redistribution and use in source and binary forms, with or without
9 // modification, are permitted provided that the following conditions are
10 // met:
11 // * Redistributions of source code must retain the above copyright
12 // notice, this list of conditions and the following disclaimer.
13 // * Redistributions in binary form must reproduce the above
14 // copyright notice, this list of conditions and the following disclaimer
15 // in the documentation and/or other materials provided with the
16 // distribution.
17 // * Neither the name of Industrial Light & Magic nor the names of
18 // its contributors may be used to endorse or promote products derived
19 // from this software without specific prior written permission.
20 //
21 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
22 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
23 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
24 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
25 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
26 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
27 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
28 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
29 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
30 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
31 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
32 //
34 
35 // Primary authors:
36 // Florian Kainz <kainz@ilm.com>
37 // Rod Bogart <rgb@ilm.com>
38 
39 //---------------------------------------------------------------------------
40 //
41 // half -- a 16-bit floating point number class:
42 //
43 // Type half can represent positive and negative numbers whose
44 // magnitude is between roughly 6.1e-5 and 6.5e+4 with a relative
45 // error of 9.8e-4; numbers smaller than 6.1e-5 can be represented
46 // with an absolute error of 6.0e-8. All integers from -2048 to
47 // +2048 can be represented exactly.
48 //
49 // Type half behaves (almost) like the built-in C++ floating point
50 // types. In arithmetic expressions, half, float and double can be
51 // mixed freely. Here are a few examples:
52 //
53 // half a (3.5);
54 // float b (a + sqrt (a));
55 // a += b;
56 // b += a;
57 // b = a + 7;
58 //
59 // Conversions from half to float are lossless; all half numbers
60 // are exactly representable as floats.
61 //
62 // Conversions from float to half may not preserve a float's value
63 // exactly. If a float is not representable as a half, then the
64 // float value is rounded to the nearest representable half. If a
65 // float value is exactly in the middle between the two closest
66 // representable half values, then the float value is rounded to
67 // the closest half whose least significant bit is zero.
68 //
69 // Overflows during float-to-half conversions cause arithmetic
70 // exceptions. An overflow occurs when the float value to be
71 // converted is too large to be represented as a half, or if the
72 // float value is an infinity or a NAN.
73 //
74 // The implementation of type half makes the following assumptions
75 // about the implementation of the built-in C++ types:
76 //
77 // float is an IEEE 754 single-precision number
78 // sizeof (float) == 4
79 // sizeof (unsigned int) == sizeof (float)
80 // alignof (unsigned int) == alignof (float)
81 // sizeof (unsigned short) == 2
82 //
83 //---------------------------------------------------------------------------
84 
85 #ifndef _HALF_H_
86 #define _HALF_H_
87 
88 #include <iostream>
89 
90 #if defined(OPENEXR_DLL)
91  #if defined(HALF_EXPORTS)
92  #define HALF_EXPORT __declspec(dllexport)
93  #else
94  #define HALF_EXPORT __declspec(dllimport)
95  #endif
96  #define HALF_EXPORT_CONST
97 #else
98  #define HALF_EXPORT
99  #define HALF_EXPORT_CONST const
100 #endif
101 
103 {
104  public:
105 
106  //-------------
107  // Constructors
108  //-------------
109 
110  half (); // no initialization
111  half (float f);
112 
113 
114  //--------------------
115  // Conversion to float
116  //--------------------
117 
118  operator float () const;
119 
120 
121  //------------
122  // Unary minus
123  //------------
124 
125  half operator - () const;
126 
127 
128  //-----------
129  // Assignment
130  //-----------
131 
132  half & operator = (half h);
133  half & operator = (float f);
134 
135  half & operator += (half h);
136  half & operator += (float f);
137 
138  half & operator -= (half h);
139  half & operator -= (float f);
140 
141  half & operator *= (half h);
142  half & operator *= (float f);
143 
144  half & operator /= (half h);
145  half & operator /= (float f);
146 
147 
148  //---------------------------------------------------------
149  // Round to n-bit precision (n should be between 0 and 10).
150  // After rounding, the significand's 10-n least significant
151  // bits will be zero.
152  //---------------------------------------------------------
153 
154  half round (unsigned int n) const;
155 
156 
157  //--------------------------------------------------------------------
158  // Classification:
159  //
160  // h.isFinite() returns true if h is a normalized number,
161  // a denormalized number or zero
162  //
163  // h.isNormalized() returns true if h is a normalized number
164  //
165  // h.isDenormalized() returns true if h is a denormalized number
166  //
167  // h.isZero() returns true if h is zero
168  //
169  // h.isNan() returns true if h is a NAN
170  //
171  // h.isInfinity() returns true if h is a positive
172  // or a negative infinity
173  //
174  // h.isNegative() returns true if the sign bit of h
175  // is set (negative)
176  //--------------------------------------------------------------------
177 
178  bool isFinite () const;
179  bool isNormalized () const;
180  bool isDenormalized () const;
181  bool isZero () const;
182  bool isNan () const;
183  bool isInfinity () const;
184  bool isNegative () const;
185 
186 
187  //--------------------------------------------
188  // Special values
189  //
190  // posInf() returns +infinity
191  //
192  // negInf() returns -infinity
193  //
194  // qNan() returns a NAN with the bit
195  // pattern 0111111111111111
196  //
197  // sNan() returns a NAN with the bit
198  // pattern 0111110111111111
199  //--------------------------------------------
200 
201  static half posInf ();
202  static half negInf ();
203  static half qNan ();
204  static half sNan ();
205 
206 
207  //--------------------------------------
208  // Access to the internal representation
209  //--------------------------------------
210 
211  unsigned short bits () const;
212  void setBits (unsigned short bits);
213 
214 
215  public:
216 
217  union uif
218  {
219  unsigned int i;
220  float f;
221  };
222 
223  private:
224 
225  static short convert (int i);
226  static float overflow ();
227 
228  unsigned short _h;
229 
230  static HALF_EXPORT_CONST uif _toFloat[1 << 16];
231  static HALF_EXPORT_CONST unsigned short _eLut[1 << 9];
232 };
233 
234 //-----------
235 // Stream I/O
236 //-----------
237 
238 HALF_EXPORT std::ostream & operator << (std::ostream &os, half h);
239 HALF_EXPORT std::istream & operator >> (std::istream &is, half &h);
240 
241 
242 //----------
243 // Debugging
244 //----------
245 
246 HALF_EXPORT void printBits (std::ostream &os, half h);
247 HALF_EXPORT void printBits (std::ostream &os, float f);
248 HALF_EXPORT void printBits (char c[19], half h);
249 HALF_EXPORT void printBits (char c[35], float f);
250 
251 
252 //-------------------------------------------------------------------------
253 // Limits
254 //
255 // Visual C++ will complain if HALF_MIN, HALF_NRM_MIN etc. are not float
256 // constants, but at least one other compiler (gcc 2.96) produces incorrect
257 // results if they are.
258 //-------------------------------------------------------------------------
259 
260 #if (defined _WIN32 || defined _WIN64) && defined _MSC_VER
261 
262  #define HALF_MIN 5.96046448e-08f // Smallest positive half
263 
264  #define HALF_NRM_MIN 6.10351562e-05f // Smallest positive normalized half
265 
266  #define HALF_MAX 65504.0f // Largest positive half
267 
268  #define HALF_EPSILON 0.00097656f // Smallest positive e for which
269  // half (1.0 + e) != half (1.0)
270 #else
271 
272  #define HALF_MIN 5.96046448e-08 // Smallest positive half
273 
274  #define HALF_NRM_MIN 6.10351562e-05 // Smallest positive normalized half
275 
276  #define HALF_MAX 65504.0 // Largest positive half
277 
278  #define HALF_EPSILON 0.00097656 // Smallest positive e for which
279  // half (1.0 + e) != half (1.0)
280 #endif
281 
282 
283 #define HALF_MANT_DIG 11 // Number of digits in mantissa
284  // (significand + hidden leading 1)
285 
286 #define HALF_DIG 2 // Number of base 10 digits that
287  // can be represented without change
288 
289 #define HALF_RADIX 2 // Base of the exponent
290 
291 #define HALF_MIN_EXP -13 // Minimum negative integer such that
292  // HALF_RADIX raised to the power of
293  // one less than that integer is a
294  // normalized half
295 
296 #define HALF_MAX_EXP 16 // Maximum positive integer such that
297  // HALF_RADIX raised to the power of
298  // one less than that integer is a
299  // normalized half
300 
301 #define HALF_MIN_10_EXP -4 // Minimum positive integer such
302  // that 10 raised to that power is
303  // a normalized half
304 
305 #define HALF_MAX_10_EXP 4 // Maximum positive integer such
306  // that 10 raised to that power is
307  // a normalized half
308 
309 
310 //---------------------------------------------------------------------------
311 //
312 // Implementation --
313 //
314 // Representation of a float:
315 //
316 // We assume that a float, f, is an IEEE 754 single-precision
317 // floating point number, whose bits are arranged as follows:
318 //
319 // 31 (msb)
320 // |
321 // | 30 23
322 // | | |
323 // | | | 22 0 (lsb)
324 // | | | | |
325 // X XXXXXXXX XXXXXXXXXXXXXXXXXXXXXXX
326 //
327 // s e m
328 //
329 // S is the sign-bit, e is the exponent and m is the significand.
330 //
331 // If e is between 1 and 254, f is a normalized number:
332 //
333 // s e-127
334 // f = (-1) * 2 * 1.m
335 //
336 // If e is 0, and m is not zero, f is a denormalized number:
337 //
338 // s -126
339 // f = (-1) * 2 * 0.m
340 //
341 // If e and m are both zero, f is zero:
342 //
343 // f = 0.0
344 //
345 // If e is 255, f is an "infinity" or "not a number" (NAN),
346 // depending on whether m is zero or not.
347 //
348 // Examples:
349 //
350 // 0 00000000 00000000000000000000000 = 0.0
351 // 0 01111110 00000000000000000000000 = 0.5
352 // 0 01111111 00000000000000000000000 = 1.0
353 // 0 10000000 00000000000000000000000 = 2.0
354 // 0 10000000 10000000000000000000000 = 3.0
355 // 1 10000101 11110000010000000000000 = -124.0625
356 // 0 11111111 00000000000000000000000 = +infinity
357 // 1 11111111 00000000000000000000000 = -infinity
358 // 0 11111111 10000000000000000000000 = NAN
359 // 1 11111111 11111111111111111111111 = NAN
360 //
361 // Representation of a half:
362 //
363 // Here is the bit-layout for a half number, h:
364 //
365 // 15 (msb)
366 // |
367 // | 14 10
368 // | | |
369 // | | | 9 0 (lsb)
370 // | | | | |
371 // X XXXXX XXXXXXXXXX
372 //
373 // s e m
374 //
375 // S is the sign-bit, e is the exponent and m is the significand.
376 //
377 // If e is between 1 and 30, h is a normalized number:
378 //
379 // s e-15
380 // h = (-1) * 2 * 1.m
381 //
382 // If e is 0, and m is not zero, h is a denormalized number:
383 //
384 // S -14
385 // h = (-1) * 2 * 0.m
386 //
387 // If e and m are both zero, h is zero:
388 //
389 // h = 0.0
390 //
391 // If e is 31, h is an "infinity" or "not a number" (NAN),
392 // depending on whether m is zero or not.
393 //
394 // Examples:
395 //
396 // 0 00000 0000000000 = 0.0
397 // 0 01110 0000000000 = 0.5
398 // 0 01111 0000000000 = 1.0
399 // 0 10000 0000000000 = 2.0
400 // 0 10000 1000000000 = 3.0
401 // 1 10101 1111000001 = -124.0625
402 // 0 11111 0000000000 = +infinity
403 // 1 11111 0000000000 = -infinity
404 // 0 11111 1000000000 = NAN
405 // 1 11111 1111111111 = NAN
406 //
407 // Conversion:
408 //
409 // Converting from a float to a half requires some non-trivial bit
410 // manipulations. In some cases, this makes conversion relatively
411 // slow, but the most common case is accelerated via table lookups.
412 //
413 // Converting back from a half to a float is easier because we don't
414 // have to do any rounding. In addition, there are only 65536
415 // different half numbers; we can convert each of those numbers once
416 // and store the results in a table. Later, all conversions can be
417 // done using only simple table lookups.
418 //
419 //---------------------------------------------------------------------------
420 
421 
422 //--------------------
423 // Simple constructors
424 //--------------------
425 
426 inline
428 {
429  // no initialization
430 }
431 
432 
433 //----------------------------
434 // Half-from-float constructor
435 //----------------------------
436 
437 inline
438 half::half (float f)
439 {
440  uif x;
441 
442  x.f = f;
443 
444  if (f == 0)
445  {
446  //
447  // Common special case - zero.
448  // Preserve the zero's sign bit.
449  //
450 
451  _h = (x.i >> 16);
452  }
453  else
454  {
455  //
456  // We extract the combined sign and exponent, e, from our
457  // floating-point number, f. Then we convert e to the sign
458  // and exponent of the half number via a table lookup.
459  //
460  // For the most common case, where a normalized half is produced,
461  // the table lookup returns a non-zero value; in this case, all
462  // we have to do is round f's significand to 10 bits and combine
463  // the result with e.
464  //
465  // For all other cases (overflow, zeroes, denormalized numbers
466  // resulting from underflow, infinities and NANs), the table
467  // lookup returns zero, and we call a longer, non-inline function
468  // to do the float-to-half conversion.
469  //
470 
471  int e = (x.i >> 23) & 0x000001ff;
472 
473  e = _eLut[e];
474 
475  if (e)
476  {
477  //
478  // Simple case - round the significand, m, to 10
479  // bits and combine it with the sign and exponent.
480  //
481 
482  int m = x.i & 0x007fffff;
483  _h = e + ((m + 0x00000fff + ((m >> 13) & 1)) >> 13);
484  }
485  else
486  {
487  //
488  // Difficult case - call a function.
489  //
490 
491  _h = convert (x.i);
492  }
493  }
494 }
495 
496 
497 //------------------------------------------
498 // Half-to-float conversion via table lookup
499 //------------------------------------------
500 
501 inline
502 half::operator float () const
503 {
504  return _toFloat[_h].f;
505 }
506 
507 
508 //-------------------------
509 // Round to n-bit precision
510 //-------------------------
511 
512 inline half
513 half::round (unsigned int n) const
514 {
515  //
516  // Parameter check.
517  //
518 
519  if (n >= 10)
520  return *this;
521 
522  //
523  // Disassemble h into the sign, s,
524  // and the combined exponent and significand, e.
525  //
526 
527  unsigned short s = _h & 0x8000;
528  unsigned short e = _h & 0x7fff;
529 
530  //
531  // Round the exponent and significand to the nearest value
532  // where ones occur only in the (10-n) most significant bits.
533  // Note that the exponent adjusts automatically if rounding
534  // up causes the significand to overflow.
535  //
536 
537  e >>= 9 - n;
538  e += e & 1;
539  e <<= 9 - n;
540 
541  //
542  // Check for exponent overflow.
543  //
544 
545  if (e >= 0x7c00)
546  {
547  //
548  // Overflow occurred -- truncate instead of rounding.
549  //
550 
551  e = _h;
552  e >>= 10 - n;
553  e <<= 10 - n;
554  }
555 
556  //
557  // Put the original sign bit back.
558  //
559 
560  half h;
561  h._h = s | e;
562 
563  return h;
564 }
565 
566 
567 //-----------------------
568 // Other inline functions
569 //-----------------------
570 
571 inline half
573 {
574  half h;
575  h._h = _h ^ 0x8000;
576  return h;
577 }
578 
579 
580 inline half &
582 {
583  _h = h._h;
584  return *this;
585 }
586 
587 
588 inline half &
590 {
591  *this = half (f);
592  return *this;
593 }
594 
595 
596 inline half &
598 {
599  *this = half (float (*this) + float (h));
600  return *this;
601 }
602 
603 
604 inline half &
606 {
607  *this = half (float (*this) + f);
608  return *this;
609 }
610 
611 
612 inline half &
614 {
615  *this = half (float (*this) - float (h));
616  return *this;
617 }
618 
619 
620 inline half &
622 {
623  *this = half (float (*this) - f);
624  return *this;
625 }
626 
627 
628 inline half &
630 {
631  *this = half (float (*this) * float (h));
632  return *this;
633 }
634 
635 
636 inline half &
638 {
639  *this = half (float (*this) * f);
640  return *this;
641 }
642 
643 
644 inline half &
646 {
647  *this = half (float (*this) / float (h));
648  return *this;
649 }
650 
651 
652 inline half &
654 {
655  *this = half (float (*this) / f);
656  return *this;
657 }
658 
659 
660 inline bool
662 {
663  unsigned short e = (_h >> 10) & 0x001f;
664  return e < 31;
665 }
666 
667 
668 inline bool
670 {
671  unsigned short e = (_h >> 10) & 0x001f;
672  return e > 0 && e < 31;
673 }
674 
675 
676 inline bool
678 {
679  unsigned short e = (_h >> 10) & 0x001f;
680  unsigned short m = _h & 0x3ff;
681  return e == 0 && m != 0;
682 }
683 
684 
685 inline bool
686 half::isZero () const
687 {
688  return (_h & 0x7fff) == 0;
689 }
690 
691 
692 inline bool
693 half::isNan () const
694 {
695  unsigned short e = (_h >> 10) & 0x001f;
696  unsigned short m = _h & 0x3ff;
697  return e == 31 && m != 0;
698 }
699 
700 
701 inline bool
703 {
704  unsigned short e = (_h >> 10) & 0x001f;
705  unsigned short m = _h & 0x3ff;
706  return e == 31 && m == 0;
707 }
708 
709 
710 inline bool
712 {
713  return (_h & 0x8000) != 0;
714 }
715 
716 
717 inline half
719 {
720  half h;
721  h._h = 0x7c00;
722  return h;
723 }
724 
725 
726 inline half
728 {
729  half h;
730  h._h = 0xfc00;
731  return h;
732 }
733 
734 
735 inline half
737 {
738  half h;
739  h._h = 0x7fff;
740  return h;
741 }
742 
743 
744 inline half
746 {
747  half h;
748  h._h = 0x7dff;
749  return h;
750 }
751 
752 
753 inline unsigned short
754 half::bits () const
755 {
756  return _h;
757 }
758 
759 
760 inline void
761 half::setBits (unsigned short bits)
762 {
763  _h = bits;
764 }
765 
766 #endif