Author: claimsbot

1. A pneumatic tire of the present invention comprising:
a tread portion;
a pair of side wall portions;
a pair of bead portions;
a carcass constituted of at least one carcass ply extending in a toroidal shape between bead cores in the respective bead portions;
a belt disposed on the outer peripheral side of a crown region of the carcass and formed by at least one inclined belt layer made of cords extending to be inclined with respect to the equatorial plane of the tire; and
a tread rubber disposed on the radially outer side of the belt,
wherein a ratio of BDBW satisfies the following formula: (0.062\xd7tire aspect ratio\u22120.01)<BDBW<(0.062\xd7tire aspect ratio+0.004), provided that BD is a difference in radial distance measured from the rim diameter line between the maximum-radial distance position and a widthwise end edge position of the outermost layer of the inclined belt and BW is a width of the outermost inclined belt layer in a meridian cross section of the tire in a state where the tire is assembled with an application wheel rim.
2. The pneumatic tire of claim 1, wherein a ratio of BWSW preferably satisfies the following formula: (\u22121.04\xd7tire aspect ratio+1.33)<BWSW<(\u22121.04\xd7tire aspect ratio+1.43), where BW is a width of the outermost inclined belt layer and SW is the maximum width of the tire in a meridian cross section of the tire.
3. The pneumatic tire of claim 1, wherein a ratio of SWhSH is preferably in the range of 0.5-0.8, where SH is a cross sectional height of the tire and SWh is a radial distance measured from the wheel rim line to a position where the tire width reaches the maximum value thereof.
4. The pneumatic tire of claim 1, wherein a ratio of CWhCH is preferably within the range of 0.55-0.9, where CH is a cross sectional full height of the carcass and CWh is a cross sectional partial height of the carcass up to a position where the tire width reaches the maximum value thereof.

The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.

1. A quaternary ammonium compound of the formula
40
and any stereoisomers thereof, wherein
R1, R2 and R3 independently represent C1-C6 alkyl, optionally substituted with phenyl or hydroxyl, or both, and wherein any two of R1, R2 and R3 may form a ring together with the quaternary ammonium nitrogen;
R4 represents
H,
CH3, or
COR4-1,wherein R4-1 represents
(C1-C4 alkyl),
(C1-C4 alkoxy), or
NR4-2R4-3, wherein R4-2 and R4-3 independently represent H or (C1-C4 alkyl);
R5, R6 and R7 independently represent
H,
OCH3,
OH,
CONH2,
SO2NH2,
F, Cl, Br, I,
CF3, or
(C1-C4 alkyl), optionally substituted with one or two
OH,
(C1-C4 alkoxy),
COOH, or
COO(C1-C3 alkyl); and
X represents an anion of a pharmaceutically acceptable acid.
2. A quaternary ammonium compound according to claim 1, wherein the carbon stereocenter is (R).
3. A quaternary ammonium compound according to claim 1, wherein the carbon stereocenter is (S).
4. A quaternary ammonium compound according to claim 1, which is a mixture of stereoisomers.
5. A quaternary ammonium compound according to claim 1, wherein at least one of R1, R2 and R3 represents C1-C3 alkyl.
6. A quaternary ammonium compound according to claim 5, wherein at least one of R1, R2 and R3 represents isopropyl.
7. A quaternary ammonium compound according to claim 6, wherein at least two of R1, R2 and R3 represents isopropyl.
8. A quaternary ammonium compound according to claim 5, wherein at least one of R1, R2 and R3 represents methyl.
9. A quaternary ammonium compound according to claim 5, wherein at least one of R1, R2 and R3 represents ethyl.
10. A quaternary ammonium compound according to claim 1, wherein R1 and R2 jointly form a ring together with the quaternary ammonium nitrogen.
11. A quaternary ammonium compound according to claim 10, wherein said ring comprises from 4 to 6 carbon atoms.
12. A quaternary ammonium compound according to claim 1, wherein R4 represents H, CH3, or COR4-1, wherein R4-1 represents C1-C4 alkyl.
13. A quaternary ammonium compound according to claim 12, wherein R4 represents H.
14. A quaternary ammonium compound according to claim 1, wherein R5 represents H, Br, Cl, CH3, or CH2OH.
15. A quaternary ammonium compound according to claim 14, wherein R5 represents CH3.
16. A quaternary ammonium compound according to claim 1, wherein at least one of R6 and R7 represents H.
17. A quaternary ammonium compound according to claim 1, wherein both R6 and R7 represent H.
18. A quaternary ammonium compound according to claim 1, wherein X is selected from the group consisting of the anions of the following acids: tartaric, hydrochloric, hydrobromic, hydroiodic, sulfuric, phosphoric, nitric, citric, methanesulfonic, CH3(CH2)n-COOH where n is 0 thru 4, HOOC(CH2)n-COOH where n is 1 thru 4, HOOCCHCHCOOH, and benzoic.
19. A quaternary ammonium compound according to claim 18, wherein X is selected from the group consisting of iodide, bromide, and chloride.
20. A quaternary ammonium compound according to claim 19, wherein X represents iodide.
21. A quaternary ammonium compound according to claim 19, wherein X represents chloride.
22. A quaternary ammonium compound according to claim 19, wherein X represents bromide.
23. A quaternary ammonium compound according to claim 1, which is selected from the group consisting of
(3R)-3-(2-hydroxy-5-methylphenyl)-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium iodide,
(3R)-3-(2-hydroxy-5-methylphenyl)-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium bromide,
(3R)-N-ethyl-3-(2-hydroxy-5-methylphenyl)-N,N-diisopropyl-3-phenylpropan-1-aminium iodide,
(3R)-3-(2-hydroxy-5-methylphenyl)-N,N-diisopropyl-3-phenyl-N-propylpropan-1-aminium iodide,
(3R)-N-benzyl-3-(2-hydroxy-5-methylphenyl)-N,N-diisopropyl-3-phenylpropan-1-aminium iodide,
(3R)-N-(tert-butyl)-3-(2-hydroxy-5-methylphenyl)-N,N-dimethyl-3-phenylpropan-1-aminium bromide,
(3R)-3-2-hydroxy-5-(hydroxymethyl)phenyl-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium iodide,
(3R)-3-(2-hydroxyphenyl)-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium bromide,
(3S)-3-(2-hydroxyphenyl)-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium bromide,
(3R)-3-(5-chloro-2-hydroxyphenyl)-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium bromide,
(3R)-3-(5-bromo-2-hydroxyphenyl)-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium bromide,
(3R)-3-2-(acetyloxy)-5-methylphenyl-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium iodide,
(3R)-3-2-(isobutyryloxy)-5-methylphenyl-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium iodide,
(3R)-3-(4-fluorophenyl)-3-(2-hydroxy-5-methylphenyl)-N,N-diisopropyl-N-methylpropan-1-aminium bromide,
(3R)-3-2-hydroxy-5-(trifluoromethyl)phenyl-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium bromide,
(3R)-3-2-(isobutyryloxy)-5-hydroxymethylphenyl-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium bromide,
(3R)-3-2-(acetyloxy)-5-(acetyloxy)methylphenyl-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium bromide,
2-(1R)-3-diisopropyl (methyl)ammonio-1-phenylpropyl-4-methylbenzenolate,
(3R)-N,N-diisopropyl-3-(2-methoxy-5-methylphenyl)-N-methyl-3-phenylpropan-1-aminium iodide,
(3R)-3-2-(butyryloxy)-5-methylphenyl-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium iodide,
(3R)-3-(2-hydroxy-5-methylphenyl)-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium chloride,
5-hydroxy-N-(3R)-3-(2-hydroxy-5-methylphenyl)-3-phenylpropyl-N-isopropyl-N-methylpentan-1-aminium iodide,
(3R)-3-(2-hydroxy-4-methylphenyl)-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium iodide,
3,3-bis(2-hydroxy-5-methylphenyl)-N,N-diisopropyl-N-methylpropan-1-aminium iodide,
(3R)-3-5-(aminocarbonyl)-2-hydroxyphenyl-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium iodide,
3,3-bis(2-methoxyphenyl)-N,N-diisopropyl-N-methylpropan-1-aminium iodide,
1-3-(2-hydroxy-5-methylphenyl)-3-phenylpropyl-1-methylpyrrolidinium iodide,
1-ethyl-1-3-(2-hydroxy-5-methylphenyl)-3-phenylpropylpyrrolidinium iodide,
1-3-(2-hydroxy-5-methylphenyl)-3-phenylpropyl-1-methylpiperidinium iodide, and
1-3-(2-hydroxy-5-methylphenyl)-3-phenylpropyl-1-methylazepanium iodide.
24. A quaternary ammonium compound according to claim 23, which is selected from the group consisting of
(3R)-3-(2-hydroxy-5-methylphenyl)-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium iodide,
(3R)-3-(2-hydroxy-5-methylphenyl)-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium bromide, and
(3R)-3-(2-hydroxy-5-methylphenyl)-N,N-diisopropyl-N-methyl-3-phenylpropan-1-aminium chloride.
25. A pharmaceutical composition comprising a therapeutically effective amount of a quaternary ammonium compound according to any one of claims 1-24, and a suitable pharmaceutical carrier therefor.
26. A quaternary ammonium compound according to any one of claims 1-24 for use as a medicament.
27. Use of a quaternary ammonium compound according to any one of claims 1-24 for the manufacture of a medicament for treating asthma.
28. Use of a quaternary ammonium compound according to any one of claims 1-24 for the manufacture of a medicament for treating chronic obstructive pulmonary disease (COPD).
29. Use of a quaternary ammonium compound according to any one of claims 1-24 for the manufacture of a medicament for treating rhinorrhea due to the common cold.
30. Use of a quaternary ammonium compound according to any one of claims 1-24 for the manufacture of a medicament for treating allergic rhinitis.
31. A method of treating asthma in a mammal, including man, comprising administering to said mammal, in need of such a treatment, a therapeutically effective amount of a quaternary ammonium compound according to any one of claims 1-24.
32. A method of treating chronic obstructive pulmonary disease (COPD) in a mammal, including man, comprising administering to said mammal, in need of such a treatment, a therapeutically effective amount of a quaternary ammonium compound according to any one of claims 1-24.
33. A method of treating allergic rhinitis in a mammal, including man, comprising administering to said mammal, in need of such a treatment, a therapeutically effective amount of a quaternary ammonium compound according to any one of claims 1-24.
34. A method of treating rhinorrhea due to the common cold in a mammal, including man, comprising administering to said mammal, in need of such a treatment, a therapeutically effective amount of a quaternary ammonium compound according to any one of claims 1-24.

1. A fuel cell system comprising:
a fuel generator configured to generate a hydrogen-rich fuel gas by reforming a feed gas;
a material supply means configured to supply the feed gas to said fuel generator;
a fuel cell configured to generate electric power using the fuel gas supplied from said fuel generator and an oxidizing gas;
a bypass means configured to supply the feed gas to an anode of said fuel cell by bypassing said fuel generator;
a material supply switch means configured to switch a destination of the feed gas supplied from said material supply means between said fuel generator and said bypass means;
a material flow rate meter disposed at a position of a feed gas passage to be located between said material supply means and the anode and configured to measure a flow rate of the feed gas flowing through said bypass means; and
a controller,
wherein, at start-up of said fuel cell system, the feed gas is injected to the anode through said bypass means,
and said controller is configured to cause said material supply switch means to operate based on a value output from said material flow rate meter to stop supply of the feed gas to the anode, and to then start the supply of the feed gas to said fuel generator.
2. The fuel cell system according to claim 1, further comprising:
a desulfurization device provided in the feed gas passage and configured to remove a sulfur component from a city gas which is the feed gas.
3. The fuel cell system according to claim 1, further comprising:
a combustor configured to heat said fuel generator by combusting the feed gas supplied to the anode through said bypass means and exhausted from the anode, or the feed gas supplied from said material supply means.
4. The fuel cell system according to claim 1, further comprising:
a material flow rate adjusting means provided upstream of said material supply switch means and configured to adjust a flow rate of the feed gas supplied from said material supply means.
5. The fuel cell system according to claim 1, further comprising:
an air supply means configured to supply air to at least one of the anode and said fuel generator, wherein after said air supply means supplies the air to at least one of the anode and said fuel generator and stops the supply of the air, the feed gas is supplied to the anode through said bypass means.

The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.

1. A computer-implemented method for unrolling loops in a loop nest, said loop nest iterating aver an actual iteration space of n-dimension, said method comprising:
accounting for residues, said residues comprising portions of said actual iteration space falling outside of, or incompletely overlapping with, cuts of a virtual iteration space, said virtual iteration space comprising said actual iteration space and said virtual iteration space evenly divided by an unrolling factor, said cuts and said virtual iteration space having n-dimensions;
unrolling at least one outer loop of said loop nest, said unrolled outer loop bounded by cuts of said virtual iteration space falling completely within said actual iteration space;
calculating a boundary of said virtual iteration space using said unrolling factor, wherein said unrolling factor is used to determine a next integer value greater than an upper bound of the outer loop which is evenly divisible by said unrolling factor.
2. The method of claim 1 wherein said accounting for residues comprises:
generating a residue loop nest, said residue loop nest iterating over said portion of said actual iteration space falling outside of, or incompletely overlapping with, cuts of said virtual iteration space.
3. The method of claim 2 wherein said residue loop nest comprises a perfect loop nest.
4. The method of claim 1 wherein said unrolling at least one outer loop of said loop nest comprises:
iterating over said at least one outer loop of said loop neat, the induction variable of said at least one outer loop being incremented by said unrolling factor;
replicating an inner portion of said loop nest, whereby the total number of said inner portions of said loop nest equal said unrolling factor.
5. The method of claim 1 wherein said loop nest comprises a two dimensional loop nest.
6. The method of claim 5 wherein said loop nest comprises a perfect triangular loop where at least one of an upper and lower bound of an inner loop is a linear function of an outer loop induction variable.
7. The method of claim 6 wherein said virtual iteration space is bounded by the modulus of an upper bound of the induction variable of said outer loop and said unrolling factor.
8. The method of claim 6 wherein said accounting for residues comprises:
generating a residue loop nest iterating over said portion of said actual iteration space falling outside of, or incompletely overlapping with, outs of said virtual iteration space, said residue loop nest comprising:
an outer residue loop; and
an inner residue loop;
an induction variable \u201ci\u201d for said outer residue loop bounded by the bounds of the induction variable of said outer loop; and
an induction variable \u201cj\u201d for said inner residue loop having a lower bound governed by the equation:
jlower bound=max (0,i\u2212mod(+UF\u2212mod(n, UF),UF)):
where \u201cn\u201d is the upper bound of said outer loop;
and said induction variable \u201cj\u201d for said inner residue loop having an upper bound governed by said induction variable for said outer residue loop.
9. The method of claim 5 wherein said loop nest comprises a rectangular loop.
10. The method of claim 9 wherein said virtual iteration space is bounded by the modulus of an upper bound of the induction variable of said outer loop and said unrolling factor.
11. The method of claim 10 wherein said accounting for residues comprises:
generating a residue loop nest iterating over said portion of sold actual Iteration space felling outside of, or incompletely overlapping with, cuts of said virtual iteration space, said residue loop nest comprising:
an outer residue loop; and
an inner residue loop;
an induction variable \u201ci\u201d for said outer residue loop comprising a lower bound of the induction variable of said outer loop and an upper bound governed by the modulus of an upper bound of the induction variable of said outer loop and said unrolling factor.
12. The method of claim 1 wherein said loop nest comprises at least one of: a rectangular and a triangular loop nest.
13. A computer readable media storing data and instructions, said data and instructions, when executed, adapting a computer system to unroll loops in a loop nest, said nested loop nest iterating over an actual iteration space of n-dimension, said computer system adapted to:
account for residues, said residues comprising portions of said actual iteration space falling outside of, or incompletely overlapping with, cuts of a virtual iteration space, said virtual iteration apace comprising said actual iteration space and said virtual iteration space evenly divided by an unrolling factor, said cuts and said virtual iteration space having n-dimensions;
unroll at least one outer loop of said nested loop nest, said unrolled outer loop bounded by cutsslices of said virtual iteration space falling completely within said actual iteration space;
calculate a boundary of said virtual iteration space using said unrolling factor, wherein said unrolling factor is used to determine a next integer value greater than an upper bound of the outer loop which is evenly divisible by said unrolling factor.
14. The computer readable media of claim 13 wherein said adaptation to account for residues comprises adapting said computer system to:
generate a residue loop nest, said residue loop nest iterating over said portion of said actual iteration space falling outside of, or incompletely overlapping with, cuts of said virtual iteration space.
15. The computer readable media of claim 14 wherein said residue loop nest comprises a perfect loop nest.
16. The computer readable media of claim 13 wherein said adaptation to unroll at least one outer loop of said loop nest comprises adapting said computer system to:
iterate over said at least one outer loop of said loop nest, the induction variable of said at least one outer loop being incremented by said unrolling factor,
replicate an inner potion of said loop nest, whereby the total number of said inner portions of said loop nest equal said unrolling factor.
17. The computer readable media of claim 13 wherein said loop nest comprises a two dimensional loop nest.
18. The computer readable media of claim 17 wherein said loop nest comprises a perfect triangular loop where at least one of an upper and lower bound of an inner loop is a linear function of an outer loop induction variable.
19. The computer readable media of claim 18 wherein said virtual iteration space is bounded by the modulus of an upper bound of the induction variable of said outer loop and said unrolling factor.
20. The computer readable media of claim 18 wherein said adaptation to account for residues comprises adapting said computer system to:
create a residue, loop neat iterating over said portion of said actual iteration space falling outside of, or incompletely overlapping with, cuts of said virtual iteration apace, said residue loop nest comprising:
an outer residue loop; and
an inner residue loop;
an induction variable \u201ci\u201d for said outer residue loop bounded by the bounds of the induction variable of said outer loop; and
an induction variable \u201cj\u201d for said inner residue loop having a lower bound governed by the equation:
jlower bound=max (0,i \u2212mod(i+UF\u2212mod(n, UF),UF));
where \u201cn\u201d is the upper bound of said outer loop;
and said induction variable \u201cj\u201d for said inner residue loop having an upper bound governed by said induction variable for said outer residue loop.
21. The computer readable media of claim 17 wherein said loop nest comprises a rectangular loop.
22. The computer readable media of claim 21 wherein said virtual iteration space is bounded by the modulus of an upper bound of the induction variable of said outer loop and said unrolling factor.
23. The computer readable media of claim 22 wherein said adaptation to account for residues comprises adapting said computer system to:
generate a residue loop nest iterating over said portion of said actual iteration space falling outside of, or incompletely overlapping with, cuts of said virtual iteration space, said residue loop nest comprising:
an outer residue loop; and
an inner residue loop;
an induction variable \u201ci\u201d for said outer residue loop comprising a lower bound of the induction variable of said outer loop and an upper bound governed by the modulus of an upper bound of the induction variable of said outer loop and said unrolling factor.
24. The computer readable media of claim 13 wherein said loop nest comprises at least one of: a rectangular and a triangular loop nest.
25. A computer-implemented method for unrolling loops in a loop nest, said nested loop nest iterating over an actual iteration space of n-dimension, said method comprising:
means accounting for residues, said residues comprising portions of said actual iteration space failing outside of, or incompletely overlapping with, cuts of a virtual iteration space, said virtual iteration space comprising said actual iteration space and said virtual iteration space evenly divided by an unrolling factor, said cuts and said virtual iteration space having n-dimensions;
means unrolling at least one outer loop of said nested loop nest, said unrolled outer loop bounded by cutsslices of said virtual iteration space falling completely within said actual iteration space;
means for calculating a boundary of said virtual iteration space using said unrolling factor, wherein said unrolling factor is used to determine a next integer value greater than an upper bound of the outer loop which is evenly divisible by said unrolling factor.
26. The method of claim 25 wherein said means for accounting for residues comprises:
moans for generating a residue loop nest, said residue loop nest iterating over said portion of said actual iteration space falling outside of or incompletely overlapping with, cuts of said virtual iteration space.
27. The method of claim 26 wherein said residue loop nest comprises a perfect loop nest.
28. The method of claim 25 wherein said means for unrolling at least one outer loop of said loop nest comprises:
means for iterating over said at least one outer loop of said loop nest, the induction variable of said at least one outer loop being incremented by said unrolling factor;
means for replicating an inner portion of said loop nest whereby the total number of said inner portions of said loop nest equal said unrolling factor.
29. The method of claim 25 wherein said loop nest comprises a two dimensional loop nest.
30. The method of claim 29 wherein said loop nest comprises a perfect triangular loop where at least one of an upper and lower bound of an inner loop is a linear function of an outer loop induction variable.
31. The method of claim 30 wherein said virtual iteration space is bounded by the modulus of an upper bound of the induction variable of said outer loop and said unrolling factor.
32. A compiled file corresponding to a source code file, said source code file comprising a nested loop nest iterating over an actual iteration space of n-dimension, said compiled file comprising machine readable instructions corresponding to said nested loop, said machine readable instructions tangibly embodied in a tangle computer readable medium and comprising:
machine readable instructions accounting for residues, said residues comprising portions of said actual iteration space falling outside of, or incompletely overlapping with, curs of a virtual iteration space, said virtual iteration space comprising said actual iteration space and said virtual iteration space evenly divided by an unrolling factor, said cuts and said virtual iteration space having n-dimensions;
machine readable instructions unrolling at least one outer loop of said loop nest said unrolled outer loop bounded by cuts of said virtual iteration space falling completely within said actual iteration space;
machine readable instructions for calculating a boundary of said virtual iteration space using said unrolling factor, wherein said unrolling factor is used to determine a next integer value greater than an upper bound of the outer loop which is evenly divisible by said unrolling factor.
33. The compiled file of claim 32 wherein sold machine readable instructions accounting for residues comprises:
machine readable instructions for a residue loop nest, said residue loop nest iterating over said portion of said actual iteration space falling outside of or incompletely overlapping with, cuts of said virtual iteration space.
34. The compiled file of claim 33 wherein said residue loop nest comprises a perfect loop nest.
35. The compiled file of claim 32 wherein said machine readable instructions unrolling at least one outer loop of said loop nest comprises:
machine readable instructions iterating over said at least one outer loop of said loop nest, the induction variable of said at least one outer loop being incremented by said unrolling factor;
machine readable instructions iterating over replicated inner portions of said loop nest, whereby the total number of said inner portions of said loop nest equal said unrolling factor.
36. The compiled file of claim 35 wherein said loop nest comprises a two dimensional loop nest.
37. The compiled file of claim 36 wherein said loop nest comprises a perfect triangular loop where at least one of an upper and lower bound of an inner loop is a linear function of an outer loop induction variable.
38. The compiled file of claim 37 wherein said virtual iteration space is bounded by the modulus of an upper bound of the induction variable of said outer loop and said unrolling factor.
39. The compiled file of claim 37 wherein said machine readable instructions accounting for residues comprises:
machine readable instructions for a residue loop nest iterating over said portion of said actual iteration space falling outside of, or incompletely overlapping with, cuts of said virtual iteration space, said residue loop nest comprising:
an outer residue loop; and
an inner residue loop;
an induction variable \u201ci\u201d for said outer residue loop bounded by the bounds of the induction variable of said outer loop; and
an induction variable \u201cj\u201d for said inner residue loop having a lower bound governed by the equation:
jlower bound=max (0,i\u2212mod(i+UF\u2212mod(n, UF),UF));
where \u201cn\u201d is the upper bound of said outer loop;
and said induction variable \u201cj\u201d for said inner residue loop having an upper bound governed by said induction variable for said outer residue loop.
40. The compiled file of claim 37 wherein said loop nest comprises a rectangular loop.
41. The compiled file of claim 40 wherein said virtual iteration space is bounded by the modulus of an upper bound of the induction variable of said outer loop and said unrolling factor.
42. The compiled file of claim 41 wherein said machine readable instructions accounting for residues comprises:
machine readable instructions for a residue loop nest iterating over said portion of said actual iteration space falling outside of, or incompletely overlapping with, cuts of said virtual iteration space, said residue loop nest comprising;
an outer residue loop; and
an inner residue loop;
an induction variable \u201ci\u201d for said outer residue loop comprising a lower bound of the induction variable of said outer loop and an upper bound governed by the modulus of an upper bound of the induction variable of said outer loop and said unrolling factor.
43. The compiled file claim 32 wherein said loop nest comprises at least one of: a rectangular and a triangular loop nest.