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GCC Code Coverage Report

Directory:	.		Exec	Total	Coverage
File:	build-coverage/deps/include/symfpu/core/divide.h	Lines:	43	43	100.0 %
Date:	2021-08-14	Branches:	99	161	61.5 %


/*
** Copyright (C) 2018 Martin Brain
**
** See the file LICENSE for licensing information.
*/

/*
** divide.h
**
** Martin Brain
** martin.brain@cs.ox.ac.uk
** 04/02/16
**
** Division of arbitrary precision floats
**
*/

#include "symfpu/core/unpackedFloat.h"
#include "symfpu/core/ite.h"
#include "symfpu/core/rounder.h"
#include "symfpu/core/operations.h"

#ifndef SYMFPU_DIVIDE
#define SYMFPU_DIVIDE

namespace symfpu {

template <class t>
  unpackedFloat<t> addDivideSpecialCases (const typename t::fpt &format,
					  const unpackedFloat<t> &left,
					  const unpackedFloat<t> &right,
					  const typename t::prop &sign,
					  const unpackedFloat<t> &divideResult) {
  typedef typename t::prop prop;

  prop eitherArgumentNaN(left.getNaN() || right.getNaN());
  prop generateNaN((left.getInf() && right.getInf()) ||
		   (left.getZero() && right.getZero()));

  prop isNaN(eitherArgumentNaN || generateNaN);

  prop isInf((!left.getZero() && right.getZero()) ||
	     (left.getInf() && !right.getInf()));

  prop isZero((!left.getInf() && right.getInf()) ||
	      (left.getZero() && !right.getZero()));

  return ITE(isNaN,
	     unpackedFloat<t>::makeNaN(format),
	     ITE(isInf,
		 unpackedFloat<t>::makeInf(format, sign),
		 ITE(isZero,
		     unpackedFloat<t>::makeZero(format, sign),
		     divideResult)));
 }


 template <class t>
  unpackedFloat<t> arithmeticDivide (const typename t::fpt &format,
				       const unpackedFloat<t> &left,
				       const unpackedFloat<t> &right) {
  typedef typename t::bwt bwt;
  typedef typename t::prop prop;
  typedef typename t::ubv ubv;
  typedef typename t::sbv sbv;
  typedef typename t::fpt fpt;

  PRECONDITION(left.valid(format));
  PRECONDITION(right.valid(format));

  // Compute sign
  prop divideSign(left.getSign() ^ right.getSign());

  // Subtract up exponents
  sbv exponentDiff(expandingSubtract<t>(left.getExponent(),right.getExponent()));
  // Optimisation : do this late and use the increment as a carry in

  sbv min(unpackedFloat<t>::minSubnormalExponent(format));
  sbv max(unpackedFloat<t>::maxNormalExponent(format));
  INVARIANT(expandingSubtract<t>(min,max) <= exponentDiff);
  INVARIANT(exponentDiff <= expandingSubtract<t>(max, min));
  // Optimisation : use the if-then-lazy-else to avoid dividing for underflow and overflow
  //                subnormal / greater-than-2^sigwidth does not need to be evaluated


  // Divide the significands
  // We need significandWidth() + 1 bits in the result but the top one may cancel, so add two bits
  ubv extendedNumerator(left.getSignificand().append(ubv::zero(2)));
  ubv extendedDenominator(right.getSignificand().append(ubv::zero(2)));

  resultWithRemainderBit<t> divided(fixedPointDivide<t>(extendedNumerator, extendedDenominator));


  bwt resWidth(divided.result.getWidth());
  ubv topBit(divided.result.extract(resWidth - 1, resWidth - 1));
  ubv nextBit(divided.result.extract(resWidth - 2, resWidth - 2));

  // Alignment of inputs means at least one of the two MSB is 1
  //  i.e. [1,2) / [1,2) = [0.5,2)
  // Top bit is set by the first round of the divide and thus is 50/50 1 or 0
  prop topBitSet(topBit.isAllOnes());
  INVARIANT(topBitSet || nextBit.isAllOnes());
  INVARIANT(topBitSet == (left.getSignificand() >= right.getSignificand()));


  // Re-align
  sbv alignedExponent(conditionalDecrement<t>(!topBitSet, exponentDiff)); // Will not overflow as previously expanded
  ubv alignedSignificand(conditionalLeftShiftOne<t>(!topBitSet, divided.result)); // Will not loose information

  // Create the sticky bit, it is important that this is after alignment
  ubv finishedSignificand(alignedSignificand | ubv(divided.remainderBit).extend(resWidth - 1));

  // Put back together
  fpt extendedFormat(format.exponentWidth() + 1, format.significandWidth() + 2);
  unpackedFloat<t> divideResult(extendedFormat, divideSign, alignedExponent, finishedSignificand);

  // A brief word about formats.
  // You might think that the extend above is unnecessary : it is from a overflow point of view.
  // It's needed so that it is a valid number with exponentWidth() + 2.
  // +1 is sufficient in almost all cases.  However:
  //    very large normal / very small subnormal
  // can have an exponent greater than very large normal * 2 ( + 1)
  // because the exponent range is asymmetric with more subnormal than normal.

  POSTCONDITION(divideResult.valid(extendedFormat));

  return divideResult;
 }


// Put it all together...
template <class t>
  unpackedFloat<t> divide (const typename t::fpt &format,
			   const typename t::rm &roundingMode,
			   const unpackedFloat<t> &left,
			   const unpackedFloat<t> &right) {
  //typedef typename t::bwt bwt;
  //typedef typename t::prop prop;
  //typedef typename t::ubv ubv;
  //typedef typename t::sbv sbv;

  PRECONDITION(left.valid(format));
  PRECONDITION(right.valid(format));

  unpackedFloat<t> divideResult(arithmeticDivide(format, left, right));

  unpackedFloat<t> roundedDivideResult(rounder(format, roundingMode, divideResult));

  unpackedFloat<t> result(addDivideSpecialCases(format, left, right, roundedDivideResult.getSign(), roundedDivideResult));

  POSTCONDITION(result.valid(format));

  return result;
 }


}

#endif


Generated by: GCOVR (Version 3.2)

Line	Exec	Source
1		/*
2		** Copyright (C) 2018 Martin Brain
3		**
4		** See the file LICENSE for licensing information.
5		*/
6
7		/*
8		** divide.h
9		**
10		** Martin Brain
11		** martin.brain@cs.ox.ac.uk
12		** 04/02/16
13		**
14		** Division of arbitrary precision floats
15		**
16		*/
17
18		#include "symfpu/core/unpackedFloat.h"
19		#include "symfpu/core/ite.h"
20		#include "symfpu/core/rounder.h"
21		#include "symfpu/core/operations.h"
22
23		#ifndef SYMFPU_DIVIDE
24		#define SYMFPU_DIVIDE
25
26		namespace symfpu {
27
28		template <class t>
29	202	unpackedFloat<t> addDivideSpecialCases (const typename t::fpt &format,
30		const unpackedFloat<t> &left,
31		const unpackedFloat<t> &right,
32		const typename t::prop &sign,
33		const unpackedFloat<t> &divideResult) {
34		typedef typename t::prop prop;
35
36	208	prop eitherArgumentNaN(left.getNaN() \|\| right.getNaN());
37	429	prop generateNaN((left.getInf() && right.getInf()) \|\|
38	250	(left.getZero() && right.getZero()));
39
40	208	prop isNaN(eitherArgumentNaN \|\| generateNaN);
41
42	425	prop isInf((!left.getZero() && right.getZero()) \|\|
43	198	(left.getInf() && !right.getInf()));
44
45	431	prop isZero((!left.getInf() && right.getInf()) \|\|
46	208	(left.getZero() && !right.getZero()));
47
48		return ITE(isNaN,
49		unpackedFloat<t>::makeNaN(format),
50		ITE(isInf,
51		unpackedFloat<t>::makeInf(format, sign),
52		ITE(isZero,
53		unpackedFloat<t>::makeZero(format, sign),
54	208	divideResult)));
55		}
56
57
58		template <class t>
59	202	unpackedFloat<t> arithmeticDivide (const typename t::fpt &format,
60		const unpackedFloat<t> &left,
61		const unpackedFloat<t> &right) {
62		typedef typename t::bwt bwt;
63		typedef typename t::prop prop;
64		typedef typename t::ubv ubv;
65		typedef typename t::sbv sbv;
66		typedef typename t::fpt fpt;
67
68	202	PRECONDITION(left.valid(format));
69	202	PRECONDITION(right.valid(format));
70
71		// Compute sign
72	208	prop divideSign(left.getSign() ^ right.getSign());
73
74		// Subtract up exponents
75	404	sbv exponentDiff(expandingSubtract<t>(left.getExponent(),right.getExponent()));
76		// Optimisation : do this late and use the increment as a carry in
77
78	404	sbv min(unpackedFloat<t>::minSubnormalExponent(format));
79	404	sbv max(unpackedFloat<t>::maxNormalExponent(format));
80	202	INVARIANT(expandingSubtract<t>(min,max) <= exponentDiff);
81	202	INVARIANT(exponentDiff <= expandingSubtract<t>(max, min));
82		// Optimisation : use the if-then-lazy-else to avoid dividing for underflow and overflow
83		// subnormal / greater-than-2^sigwidth does not need to be evaluated
84
85
86		// Divide the significands
87		// We need significandWidth() + 1 bits in the result but the top one may cancel, so add two bits
88	404	ubv extendedNumerator(left.getSignificand().append(ubv::zero(2)));
89	404	ubv extendedDenominator(right.getSignificand().append(ubv::zero(2)));
90
91	404	resultWithRemainderBit<t> divided(fixedPointDivide<t>(extendedNumerator, extendedDenominator));
92
93
94	202	bwt resWidth(divided.result.getWidth());
95	404	ubv topBit(divided.result.extract(resWidth - 1, resWidth - 1));
96	404	ubv nextBit(divided.result.extract(resWidth - 2, resWidth - 2));
97
98		// Alignment of inputs means at least one of the two MSB is 1
99		// i.e. [1,2) / [1,2) = [0.5,2)
100		// Top bit is set by the first round of the divide and thus is 50/50 1 or 0
101	208	prop topBitSet(topBit.isAllOnes());
102	202	INVARIANT(topBitSet \|\| nextBit.isAllOnes());
103	202	INVARIANT(topBitSet == (left.getSignificand() >= right.getSignificand()));
104
105
106		// Re-align
107	404	sbv alignedExponent(conditionalDecrement<t>(!topBitSet, exponentDiff)); // Will not overflow as previously expanded
108	404	ubv alignedSignificand(conditionalLeftShiftOne<t>(!topBitSet, divided.result)); // Will not loose information
109
110		// Create the sticky bit, it is important that this is after alignment
111	404	ubv finishedSignificand(alignedSignificand \| ubv(divided.remainderBit).extend(resWidth - 1));
112
113		// Put back together
114	202	fpt extendedFormat(format.exponentWidth() + 1, format.significandWidth() + 2);
115	202	unpackedFloat<t> divideResult(extendedFormat, divideSign, alignedExponent, finishedSignificand);
116
117		// A brief word about formats.
118		// You might think that the extend above is unnecessary : it is from a overflow point of view.
119		// It's needed so that it is a valid number with exponentWidth() + 2.
120		// +1 is sufficient in almost all cases. However:
121		// very large normal / very small subnormal
122		// can have an exponent greater than very large normal * 2 ( + 1)
123		// because the exponent range is asymmetric with more subnormal than normal.
124
125	202	POSTCONDITION(divideResult.valid(extendedFormat));
126
127	404	return divideResult;
128		}
129
130
131		// Put it all together...
132		template <class t>
133	202	unpackedFloat<t> divide (const typename t::fpt &format,
134		const typename t::rm &roundingMode,
135		const unpackedFloat<t> &left,
136		const unpackedFloat<t> &right) {
137		//typedef typename t::bwt bwt;
138		//typedef typename t::prop prop;
139		//typedef typename t::ubv ubv;
140		//typedef typename t::sbv sbv;
141
142	202	PRECONDITION(left.valid(format));
143	202	PRECONDITION(right.valid(format));
144
145	404	unpackedFloat<t> divideResult(arithmeticDivide(format, left, right));
146
147	404	unpackedFloat<t> roundedDivideResult(rounder(format, roundingMode, divideResult));
148
149	202	unpackedFloat<t> result(addDivideSpecialCases(format, left, right, roundedDivideResult.getSign(), roundedDivideResult));
150
151	202	POSTCONDITION(result.valid(format));
152
153	404	return result;
154		}
155
156
157		}
158
159		#endif