OpenVDB: openvdb/math/Half.h Source File

OpenVDB 9.0.0

Half.h
Go to the documentation of this file.
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//
33///////////////////////////////////////////////////////////////////////////
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 OPENVDB_MATH_HALF_HAS_BEEN_INCLUDED
86#define OPENVDB_MATH_HALF_HAS_BEEN_INCLUDED
87
88#include <openvdb/Platform.h>
89#include <openvdb/version.h>
90#include <iostream>
91
92namespace openvdb {
93 OPENVDB_USE_VERSION_NAMESPACE
94namespace OPENVDB_VERSION_NAME {
95namespace math {
96 namespace internal {
97
98 class OPENVDB_API half
99{
100 public:
101
102 //-------------
103 // Constructors
104 //-------------
105
106 half () = default; // no initialization
107 half (float f);
108 // rule of 5
109 ~half () = default;
110 half (const half &) = default;
111 half (half &&) noexcept = default;
112
113 //--------------------
114 // Conversion to float
115 //--------------------
116
117 operator float () const;
118
119
120 //------------
121 // Unary minus
122 //------------
123
124 half operator - () const;
125
126
127 //-----------
128 // Assignment
129 //-----------
130
131 half & operator = (const half &h) = default;
132 half & operator = (half &&h) noexcept = default;
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 const uif _toFloat[1 << 16];
231 static const unsigned short _eLut[1 << 9];
232};
233
234
235
236//-----------
237// Stream I/O
238//-----------
239
240 OPENVDB_API std::ostream & operator << (std::ostream &os, half h);
241 OPENVDB_API std::istream & operator >> (std::istream &is, half &h);
242
243
244//----------
245// Debugging
246//----------
247
248 OPENVDB_API void printBits (std::ostream &os, half h);
249 OPENVDB_API void printBits (std::ostream &os, float f);
250 OPENVDB_API void printBits (char c[19], half h);
251 OPENVDB_API void printBits (char c[35], float f);
252
253
254//-------------------------------------------------------------------------
255// Limits
256//
257// Visual C++ will complain if HALF_MIN, HALF_NRM_MIN etc. are not float
258// constants, but at least one other compiler (gcc 2.96) produces incorrect
259// results if they are.
260//-------------------------------------------------------------------------
261
262#if (defined _WIN32 || defined _WIN64) && defined _MSC_VER
263
264 #define VDB_HALF_MIN 5.96046448e-08f // Smallest positive half
265
266 #define VDB_HALF_NRM_MIN 6.10351562e-05f // Smallest positive normalized half
267
268 #define VDB_HALF_MAX 65504.0f // Largest positive half
269
270 #define VDB_HALF_EPSILON 0.00097656f // Smallest positive e for which
271 // half (1.0 + e) != half (1.0)
272#else
273
274 #define VDB_HALF_MIN 5.96046448e-08 // Smallest positive half
275
276 #define VDB_HALF_NRM_MIN 6.10351562e-05 // Smallest positive normalized half
277
278 #define VDB_HALF_MAX 65504.0 // Largest positive half
279
280 #define VDB_HALF_EPSILON 0.00097656 // Smallest positive e for which
281 // half (1.0 + e) != half (1.0)
282#endif
283
284
285#define VDB_HALF_MANT_DIG 11 // Number of digits in mantissa
286 // (significand + hidden leading 1)
287
288//
289// floor( (VDB_HALF_MANT_DIG - 1) * log10(2) ) => 3.01... -> 3
290#define VDB_HALF_DIG 3 // Number of base 10 digits that
291 // can be represented without change
292
293// ceil(VDB_HALF_MANT_DIG * log10(2) + 1) => 4.31... -> 5
294#define VDB_HALF_DECIMAL_DIG 5 // Number of base-10 digits that are
295 // necessary to uniquely represent all
296 // distinct values
297
298#define VDB_HALF_RADIX 2 // Base of the exponent
299
300#define VDB_HALF_MIN_EXP -13 // Minimum negative integer such that
301 // HALF_RADIX raised to the power of
302 // one less than that integer is a
303 // normalized half
304
305#define VDB_HALF_MAX_EXP 16 // Maximum positive integer such that
306 // HALF_RADIX raised to the power of
307 // one less than that integer is a
308 // normalized half
309
310#define VDB_HALF_MIN_10_EXP -4 // Minimum positive integer such
311 // that 10 raised to that power is
312 // a normalized half
313
314#define VDB_HALF_MAX_10_EXP 4 // Maximum positive integer such
315 // that 10 raised to that power is
316 // a normalized half
317
318
319//---------------------------------------------------------------------------
320//
321// Implementation --
322//
323// Representation of a float:
324//
325// We assume that a float, f, is an IEEE 754 single-precision
326// floating point number, whose bits are arranged as follows:
327//
328// 31 (msb)
329// |
330// | 30 23
331// | | |
332// | | | 22 0 (lsb)
333// | | | | |
334// X XXXXXXXX XXXXXXXXXXXXXXXXXXXXXXX
335//
336// s e m
337//
338// S is the sign-bit, e is the exponent and m is the significand.
339//
340// If e is between 1 and 254, f is a normalized number:
341//
342// s e-127
343// f = (-1) * 2 * 1.m
344//
345// If e is 0, and m is not zero, f is a denormalized number:
346//
347// s -126
348// f = (-1) * 2 * 0.m
349//
350// If e and m are both zero, f is zero:
351//
352// f = 0.0
353//
354// If e is 255, f is an "infinity" or "not a number" (NAN),
355// depending on whether m is zero or not.
356//
357// Examples:
358//
359// 0 00000000 00000000000000000000000 = 0.0
360// 0 01111110 00000000000000000000000 = 0.5
361// 0 01111111 00000000000000000000000 = 1.0
362// 0 10000000 00000000000000000000000 = 2.0
363// 0 10000000 10000000000000000000000 = 3.0
364// 1 10000101 11110000010000000000000 = -124.0625
365// 0 11111111 00000000000000000000000 = +infinity
366// 1 11111111 00000000000000000000000 = -infinity
367// 0 11111111 10000000000000000000000 = NAN
368// 1 11111111 11111111111111111111111 = NAN
369//
370// Representation of a half:
371//
372// Here is the bit-layout for a half number, h:
373//
374// 15 (msb)
375// |
376// | 14 10
377// | | |
378// | | | 9 0 (lsb)
379// | | | | |
380// X XXXXX XXXXXXXXXX
381//
382// s e m
383//
384// S is the sign-bit, e is the exponent and m is the significand.
385//
386// If e is between 1 and 30, h is a normalized number:
387//
388// s e-15
389// h = (-1) * 2 * 1.m
390//
391// If e is 0, and m is not zero, h is a denormalized number:
392//
393// S -14
394// h = (-1) * 2 * 0.m
395//
396// If e and m are both zero, h is zero:
397//
398// h = 0.0
399//
400// If e is 31, h is an "infinity" or "not a number" (NAN),
401// depending on whether m is zero or not.
402//
403// Examples:
404//
405// 0 00000 0000000000 = 0.0
406// 0 01110 0000000000 = 0.5
407// 0 01111 0000000000 = 1.0
408// 0 10000 0000000000 = 2.0
409// 0 10000 1000000000 = 3.0
410// 1 10101 1111000001 = -124.0625
411// 0 11111 0000000000 = +infinity
412// 1 11111 0000000000 = -infinity
413// 0 11111 1000000000 = NAN
414// 1 11111 1111111111 = NAN
415//
416// Conversion:
417//
418// Converting from a float to a half requires some non-trivial bit
419// manipulations. In some cases, this makes conversion relatively
420// slow, but the most common case is accelerated via table lookups.
421//
422// Converting back from a half to a float is easier because we don't
423// have to do any rounding. In addition, there are only 65536
424// different half numbers; we can convert each of those numbers once
425// and store the results in a table. Later, all conversions can be
426// done using only simple table lookups.
427//
428//---------------------------------------------------------------------------
429
430
431//----------------------------
432// Half-from-float constructor
433//----------------------------
434
435inline
436 half::half (float f)
437{
438 uif x;
439
440 x.f = f;
441
442 if (f == 0)
443 {
444 //
445 // Common special case - zero.
446 // Preserve the zero's sign bit.
447 //
448
449 _h = (unsigned short)(x.i >> 16);
450 }
451 else
452 {
453 //
454 // We extract the combined sign and exponent, e, from our
455 // floating-point number, f. Then we convert e to the sign
456 // and exponent of the half number via a table lookup.
457 //
458 // For the most common case, where a normalized half is produced,
459 // the table lookup returns a non-zero value; in this case, all
460 // we have to do is round f's significand to 10 bits and combine
461 // the result with e.
462 //
463 // For all other cases (overflow, zeroes, denormalized numbers
464 // resulting from underflow, infinities and NANs), the table
465 // lookup returns zero, and we call a longer, non-inline function
466 // to do the float-to-half conversion.
467 //
468
469 int e = (x.i >> 23) & 0x000001ff;
470
471 e = _eLut[e];
472
473 if (e)
474 {
475 //
476 // Simple case - round the significand, m, to 10
477 // bits and combine it with the sign and exponent.
478 //
479
480 int m = x.i & 0x007fffff;
481 _h = (unsigned short)(e + ((m + 0x00000fff + ((m >> 13) & 1)) >> 13));
482 }
483 else
484 {
485 //
486 // Difficult case - call a function.
487 //
488
489 _h = convert (x.i);
490 }
491 }
492}
493
494
495//------------------------------------------
496// Half-to-float conversion via table lookup
497//------------------------------------------
498
499inline
500half::operator float () const
501{
502 return _toFloat[_h].f;
503}
504
505
506//-------------------------
507// Round to n-bit precision
508//-------------------------
509
510inline half
511half::round (unsigned int n) const
512{
513 //
514 // Parameter check.
515 //
516
517 if (n >= 10)
518 return *this;
519
520 //
521 // Disassemble h into the sign, s,
522 // and the combined exponent and significand, e.
523 //
524
525 unsigned short s = _h & 0x8000;
526 unsigned short e = _h & 0x7fff;
527
528 //
529 // Round the exponent and significand to the nearest value
530 // where ones occur only in the (10-n) most significant bits.
531 // Note that the exponent adjusts automatically if rounding
532 // up causes the significand to overflow.
533 //
534
535 e = (unsigned short)(e >> (9 - n));
536 e = (unsigned short)(e + (e & 1));
537 e = (unsigned short)(e << (9 - n));
538
539 //
540 // Check for exponent overflow.
541 //
542
543 if (e >= 0x7c00)
544 {
545 //
546 // Overflow occurred -- truncate instead of rounding.
547 //
548
549 e = _h;
550 e = (unsigned short)(e >> (10 - n));
551 e = (unsigned short)(e << (10 - n));
552 }
553
554 //
555 // Put the original sign bit back.
556 //
557
558 half h;
559 h._h = (unsigned short)(s | e);
560
561 return h;
562}
563
564
565//-----------------------
566// Other inline functions
567//-----------------------
568
569inline half
570 half::operator - () const
571{
572 half h;
573 h._h = _h ^ 0x8000;
574 return h;
575}
576
577
578inline half &
579half::operator = (float f)
580{
581 *this = half (f);
582 return *this;
583}
584
585
586inline half &
587half::operator += (half h)
588{
589 *this = half (float (*this) + float (h));
590 return *this;
591}
592
593
594inline half &
595half::operator += (float f)
596{
597 *this = half (float (*this) + f);
598 return *this;
599}
600
601
602inline half &
603half::operator -= (half h)
604{
605 *this = half (float (*this) - float (h));
606 return *this;
607}
608
609
610inline half &
611half::operator -= (float f)
612{
613 *this = half (float (*this) - f);
614 return *this;
615}
616
617
618inline half &
619half::operator *= (half h)
620{
621 *this = half (float (*this) * float (h));
622 return *this;
623}
624
625
626inline half &
627half::operator *= (float f)
628{
629 *this = half (float (*this) * f);
630 return *this;
631}
632
633
634inline half &
635half::operator /= (half h)
636{
637 *this = half (float (*this) / float (h));
638 return *this;
639}
640
641
642inline half &
643half::operator /= (float f)
644{
645 *this = half (float (*this) / f);
646 return *this;
647}
648
649
650inline bool
651 half::isFinite () const
652{
653 unsigned short e = (_h >> 10) & 0x001f;
654 return e < 31;
655}
656
657
658inline bool
659half::isNormalized () const
660{
661 unsigned short e = (_h >> 10) & 0x001f;
662 return e > 0 && e < 31;
663}
664
665
666inline bool
667half::isDenormalized () const
668{
669 unsigned short e = (_h >> 10) & 0x001f;
670 unsigned short m = _h & 0x3ff;
671 return e == 0 && m != 0;
672}
673
674
675inline bool
676 half::isZero () const
677{
678 return (_h & 0x7fff) == 0;
679}
680
681
682inline bool
683 half::isNan () const
684{
685 unsigned short e = (_h >> 10) & 0x001f;
686 unsigned short m = _h & 0x3ff;
687 return e == 31 && m != 0;
688}
689
690
691inline bool
692half::isInfinity () const
693{
694 unsigned short e = (_h >> 10) & 0x001f;
695 unsigned short m = _h & 0x3ff;
696 return e == 31 && m == 0;
697}
698
699
700inline bool
701 half::isNegative () const
702{
703 return (_h & 0x8000) != 0;
704}
705
706
707inline half
708half::posInf ()
709{
710 half h;
711 h._h = 0x7c00;
712 return h;
713}
714
715
716inline half
717half::negInf ()
718{
719 half h;
720 h._h = 0xfc00;
721 return h;
722}
723
724
725inline half
726half::qNan ()
727{
728 half h;
729 h._h = 0x7fff;
730 return h;
731}
732
733
734inline half
735half::sNan ()
736{
737 half h;
738 h._h = 0x7dff;
739 return h;
740}
741
742
743inline unsigned short
744half::bits () const
745{
746 return _h;
747}
748
749
750inline void
751half::setBits (unsigned short bits)
752{
753 _h = bits;
754}
755
756} // namespace internal
757} // namespace math
758} // namespace OPENVDB_VERSION_NAME
759} // namespace openvdb
760
761#endif // OPENVDB_MATH_HALF_HAS_BEEN_INCLUDED
Platform.h
OPENVDB_API
#define OPENVDB_API
Definition: Platform.h:254
openvdb::v9_0::math::internal::half
Definition: Half.h:99
openvdb::v9_0::math::internal::half::half
half()=default
openvdb::v9_0::math::internal::half::~half
~half()=default
openvdb::v9_0::math::internal::half::half
half(half &&) noexcept=default
openvdb::v9_0::math::internal::half::half
half(const half &)=default
openvdb::v9_0::math::internal::operator<<
OPENVDB_API std::ostream & operator<<(std::ostream &os, half h)
openvdb::v9_0::math::internal::operator>>
OPENVDB_API std::istream & operator>>(std::istream &is, half &h)
openvdb::v9_0::math::internal::printBits
OPENVDB_API void printBits(char c[35], float f)
openvdb::v9_0::math::operator-
Vec3< typename promote< T, Coord::ValueType >::type > operator-(const Vec3< T > &v0, const Coord &v1)
Allow a Coord to be subtracted from a Vec3.
Definition: Coord.h:550
openvdb::v9_0::math::isFinite
bool isFinite(const float x)
Return true if x is finite.
Definition: Math.h:376
openvdb::v9_0::math::isZero
bool isZero(const Type &x)
Return true if x is exactly equal to zero.
Definition: Math.h:338
openvdb::v9_0::math::isNegative
bool isNegative(const Type &x)
Return true if x is less than zero.
Definition: Math.h:368
openvdb::v9_0::math::half
internal::half half
Definition: Types.h:29
openvdb::v9_0::math::isNan
bool isNan(const float x)
Return true if x is a NaN (Not-A-Number) value.
Definition: Math.h:396
openvdb
Definition: Exceptions.h:13
openvdb::v9_0::math::internal::half::uif
Definition: Half.h:218
openvdb::v9_0::math::internal::half::uif::i
unsigned int i
Definition: Half.h:219
openvdb::v9_0::math::internal::half::uif::f
float f
Definition: Half.h:220
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h.in:116
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h.in:202