EarthBound/ROM map

The following article is a ROM map for EarthBound.

Primary Engine and Critical Data Bank

• 000000-0001FF (000200) = ROM Header Data
• 000200-00043E (00023f) = Important ASM (EDIT AT OWN RISK)
• 00043F-00055A (00011c) = Animated Palette Routines
• 00055B-000590 (000036) = Unclassified Data
• 000591-000829 (000299) = Sprite Palette Adjustment Routines
• 00082A-000977 (00014e) = Unclassified Data
• 000978-000AC2 (00014b) = Map Palette Load Routines
• 000AC3-000CA0 (0001de) = Load Map Tileset/Palette Routine
• 000CA1-000CC4 (000024) = Unclassified ASM
• 000CC5-000EF2 (00022e) = Load Tilemap to Buffers Routines
• 000Ef3-001015 (000123) = Unclassified Data
• 001016-001380 (00036b) = Load Tilemap to VRAM Routines
• 001381-007E03 (006a83) = Unclassified Data
• 007E04-0081FF (0003fb) = Flyover Data and Various GUI Including Text Windows
• 008200-008340 (000141) = SNES Startup routine
• 008341-00834E (00000e) = SNES interrupt redirects
• 00834F-00836F (000021) = IRQ Interrupt routine
• 008370-008590 (000221) = VBLANK Interrupt routine
• 008591-0085B7 (000027) = Unclassified Data
• 0085B8-008700 (000149) = Controller Input Routines
• 008701-0087B6 (0000b6) = Unclassified Data
• 0087B7-008904 (00014e) = VRAM DMA Transfer Routines
• 008905-0090D1 (0007cd) = Unclassified Data
• 0090D2-00918A (0000b9) = Memory And String Util Routines
• 00918B-009197 (00000d) = Unclassified Data
• 009198-0091AF (000018) = CGRAM DMA Transfer Style Table
• 0091B0-0091E5 (000036) = VRAM DMA Transfer Style Table
• 0091E6-009478 (000293) = Math Routines
• 009479-00A3F1 (000f79) = Unclassified Data
• 00A3F2-00A40B (00001a) = Load Animated Palette Routine
• 00A40C-00A41B (000010) = Decompressed Map Animation Palette Pointer Table
• 00A41C-00AD05 (0008ea) = Unclassified Data
• 00AD06-00ADA7 (0000a2) = Music Loading Routine
• 00ADA8-00BA20 (000c79) = Unclassified Data
• 00BA21-00BA23 (000003) = Execute Load Saved Game Pointer
• 00BA24-00BBB7 (000194) = Unclassified Data
• 00BBB8-00BBBA (000003) = Execute Introduction Sequence Pointer
• 00BBBB-0101AF (0045f5) = Unclassified Data
• 0101B0-0101DF (000030) = SNES Rom Header
• 0101E0-0101FF (000020) = CPU Interrupt Vectors
• 010200-0212E5 (0110e6) = Unclassified Data
• 0212E6-0215AB (0002c6) = HP/PP Rolling Routine
• 0215AC-021827 (00027c) = Unclassified Data
• 021828-02185D (000036) = Load Flag Value Routine
• 02185E-0301FF (00e9a2) = Unclassified Data
• 030200-0302FF (000100) = Sprite Palettes
• 030300-03E44F (00e150) = Largely Movement Data, Possibly Incongruous
• 03E450-03E5F7 (0001a8) = Dialog Window Attributes Table
• 03E5F8-03EA73 (00047c) = Unclassified Data
• 03EA74-03EB76 (000103) = Debug Mode Commands
• 03EB77-03F253 (0006dd) = Unclassified Data
• 03F254-03F28F (00003c) = Primary Font Table
• 03F290-03F3EC (00015d) = PSI Submenu Text
• 03F3ED-03F4B1 (0000c5) = ASM Routine - Indeterminate Function
• 03F4B2-03F4B4 (000003) = Unclassified Data
• 03F4B5-03F5C4 (000110) = Character Graphics Control Table
• 03F5C5-03FD2A (000766) = Unclassified Data, Partially ASM
• 03FD2B-03FD46 (00001c) = Name Registration String
• 03FD47-0402D3 (00058d) = Unclassified Data
• 0402D4-040D51 (000a7e) = Movement Pattern Pointer Table
• 040D52-041C9D (000f4c) = Unclassified Data, Partially ASM
• 041C9E-041DC7 (00012a) = Decompression Routine
• 041DC8-043163 (00139c) = Unclassified Data
• 043164-04318B (000028) = Map Data Pointer Table
• 04318C-04374F (0005c4) = Unclassified Data
• 043750-043768 (000019) = Goods Submenu Commands
• 043769-04582E (0020c6) = Unclassified Data
• 04582F-045836 (000008) = Precomputed Powers of 2
• 045837-045D4C (000516) = Unclassified Data
• 045D4D-045E0F (0000c3) = Status Text Strings
• 045E10-045E85 (000076) = Equipment Submenu Text
• 045E86-048186 (002301) = Unclassified Data
• 048187-04820A (000084) = Text/Window Palettes Load Routine
• 04820B-048236 (00002c) = Unclassified Data
• 048237-04830D (0000d7) = Lumine Hall Text
• 04830E-0498F8 (0015eb) = Unclassified Data
• 0498F9-04993F (000047) = Copy Current Palettes Routine
• 049940-04A0A3 (000764) = Unclassified Data
• 04A0A4-04A0C3 (000020) = Movement-Referenced Text String Pointer Table
• 04A0C4-04A1E0 (00011d) = ASM Routine - Indeterminate Function
• 04A1E1-04A28A (0000aa) = Battle Command Strings
• 04A28B-04A508 (00027e) = Unclassified Data
• 04A509-04A530 (000028) = Prayer Command Text Pointers
• 04A531-04C25F (001d2f) = Unclassified Data
• 04C260-04C4DC (00027d) = Startup Menu Text Strings
• 04C4DD-04F909 (00342d) = Unclassified Data
• 04F90A-04FB46 (00023d) = Song Table
• 04FB47-04FD41 (0001fb) = SPC Pack Pointer Table
• 04FD42-04FF4A (000209) = Parsing Routines for 04FB47 Block
• 04FF4B-0501FF (0002b5) = Nullspace

Text Bank

• 050200-051D11 (001b12) = Conditional Pointers for Store Dialogue
• 051D12-0A012E (04e41d) = Primary Dialogue Bank
• 0A012F-0A01FF (0000d1) = Nullspace

Animation Bank

• 0A0200-0AD9A0 (00d7a1) = Battle BGs: Primary Data Group
• 0AD9A1-0ADB3C (00019c) = Battle BGs: Graphics Pointer Table
• 0ADB3D-0ADCD8 (00019c) = Battle BGs: Arrangement Pointer Table
• 0ADCD9-0ADEA0 (0001c8) = Battle BGs: Palette Pointer Table
• 0ADEA1-0AF457 (0015b7) = Battle BGs: Rendering Data
• 0AF458-0AF907 (0004b0) = Battle BGs: Scroll Table
• 0AF908-0B01FE (0008f7) = Battle BGs: Distortion Table
• 0B01FF-0B01FF (000001) = Nullspace
• 0B0200-0BDA99 (00d89a) = Battle BGs: Secondary Data Group
• 0BDA9A-0BE229 (000790) = Battle Group BG Association Table
• 0BE22A-0C01FF (001fd6) = Audio Data Block (Unspecified)
• 0C0200-0C19CA (0017cb) = Animation Data: Carpainter's Lightning - Reflected
• 0C19CB-0C215B (000791) = Animation Data: Carpainter's Lightning - Strike
• 0C215C-0C24D7 (00037c) = Animation Data: Starman Junior's Teleport
• 0C24D8-0C2E88 (0009b1) = Animation Data: "BOOM!"
• 0C2E89-0C2EE0 (000058) = Animation Data: Zombie Attack
• 0C2EE1-0C2FE0 (000100) = Animation Data: "The End?"
• 0C2FE1-0C3018 (000038) = Animation Sequence Data Pointers
• 0C3019-0CAE24 (007e0c) = PSI Animation Arrangement - First Block
• 0CAE25-0CB12E (00030a) = PSI Animation Graphics - First Block
• 0CB12F-0CB812 (0006e4) = PSI Animation Arrangement - Second Block
• 0CB813-0CBCC6 (0004b4) = PSI Animation Graphics - Second Block
• 0CBCC7-0CDD26 (002060) = PSI Animation Arrangement - Third Block
• 0CDD27-0CDFF8 (0002d2) = PSI Animation Graphics - Third Block
• 0CDFF9-0CE51C (000524) = PSI Animation Arrangement - Fourth Block
• 0CE51D-0CE76C (000250) = PSI Animation Graphics - Fourth Block
• 0CE76D-0CF24C (000ae0) = PSI Animation Arrangement - Fifth Block
• 0CF24D-0CF3E4 (000198) = PSI Animation Configuration Data
• 0CF3E5-0CF67E (00029a) = PSI Animation Arrangement - Sixth Block
• 0CF67F-0CF78E (000110) = PSI Animation Palettes
• 0CF78F-0CF816 (000088) = PSI Animation Pointers
• 0CF817-0D01FF (0009e9) = Audio Data Block (Unspecified)
• 0D0200-0E64ED (0162ee) = Battle Sprites Graphics
• 0E64EE-0E6713 (000226) = Battle Sprites Pointer Table
• 0E6714-0E6B13 (000400) = Battle Sprites Palettes
• 0E6B14-0EDE44 (007331) = Swirl Animation Data
• 0EDE45-0EDF40 (0000fc) = Swirl Animation Pointer Table
• 0EDF41-0EDF5C (00001c) = Swirl Animation Primary Table <- Please Confirm
• 0EDF5D-0EFA05 (001aa9) = Sound Stone Graphics
• 0EFA06-0EFAC5 (0000c0) = Sound Stone Palette
• 0EFAC6-0F01FF (00073a) = Audio Data Block (Unspecified)

Map Bank

• 0F0200-0F284E (00264f) = Door Destinations Table
• 0F284F-0F5AEE (0032a0) = Door Configuration Table
• 0F5AEF-0F5C38 (00014a) = Overworld Event Music Pointer Table
• 0F5C39-0F63DF (0007a7) = Overworld Event Music Table
• 0F63E0-0F63E6 (000007) = Unclassified Data
• 0F63E7-0F6DE6 (000a00) = NPC Placement Pointer Table
• 0F6DE7-0F8B91 (001dab) = NPC Placement Data Table
• 0F8B92-0FF4B4 (006923) = NPC Dialogue and Configuration Table
• 0FF4B5-1001FF (000d4b) = Audio Data Block (Unspecified)
• 100200-1015FF (001400) = Doors Pointer Table
• 101600-101797 (000198) = Screen Transition Configuration Table
• 101798-1017BF (000028) = Map Tiles: Event Control Pointer Table
• 1017C0-101A7F (0002c0) = Map Tiles: Event Control Table

Battle Bank

• 101A80-10BA7F (00a000) = Map Data: Enemy Placement data
• 10BA80-10BDAB (00032c) = Enemy Placement Groups Pointer Table
• 10BDAC-10C80C (000a61) = Enemy Placement Groups Table
• 10C80D-10D72C (000f20) = Enemy Battle Groups Pointer Table
• 10D72D-10D74B (00001f) = Apparent Garbage Data
• 10D74C-10E1B3 (000a68) = Enemy Battle Groups Table
• 10E1B4-1101A7 (001ff4) = Audio Data Block (Unspecified)
• 1101A8-1101FF (000058) = Nullspace

Primary Data Groups Bank

• 110200-1547BF (0445c0) = Uncompressed Sprite Graphics
• 1547C0-1551FF (000a40) = Nullspace
• 155200-1578B1 (0026b2) = Item Properties Table
• 1578B2-157A7F (0001ce) = Store Inventories Table
• 157A80-157CAD (00022e) = PSI Teleport Destination Table
• 157CAE-157D67 (0000ba) = Telephone Contacts Table
• 157D68-158C4F (000ee8) = Battle Actions Table
• 158C50-158F6A (00031b) = PSI Abilities Table
• 158F6B-158F79 (00000f) = Nullspace
• 158F7A-159122 (0001a9) = PSI Names List
• 159123-159148 (000026) = NPC Battle AI Table
• 159149-159788 (000640) = Level Up Requirements Table
• 159789-15EC5A (0054d2) = Enemy Configuration Table
• 15EC5B-15EC76 (00001c) = Statistic Growth Variables
• 15EC77-15EDAA (000134) = Condiment Configuration Table
• 15EDAB-15F4F2 (000748) = Preset Teleport Destination Table
• 15F4F3-15F6BA (0001c8) = Map Data: Hotspots Table
• 15F6BB-15F6CE (000014) = Timed Item Transformation Table
• 15F6CF-15F7F4 (000126) = "Don't Care" Preset Character Names
• 15F7F5-15F808 (000014) = Starting Statistics: Ness
• 15F809-15F81C (000014) = Starting Statistics: Paula
• 15F81D-15F830 (000014) = Starting Statistics: Jeff
• 15F831-15F844 (000014) = Starting Statistics: Poo
• 15F845-15F90C (0000c8) = Timed Delivery Events Table
• 15F90D-1601FF (0008f3) = Nullspace

Map Construction Primary Bank

• 160200-1751FF (015000) = Map Data: Primary Table
• 175200-17A9FF (005800) = Map Data: Local Tileset Table
• 17AA00-17B3FF (000a00) = Map Data: Global Tileset/Palette Table
• 17B400-17C7FF (001400) = Map Data: Per-Sector Attributes Table
• 17C800-17FDE7 (0035e8) = Map Data: Compressed Tile Arrangement Data Block 1
• 17FDE8-1801FF (000418) = Nullspace
• 180200-18914F (008f50) = Map Data: Tile Arrangement Collision Data
• 189150-18F25D (00610e) = Map Data: Tileset Tile Arrangement Collision Pointer Tables

Anti-Piracy Screens Bank

• 18F25E-18F40C (0001af) = Anti-Piracy Notice Screen Arrangement
• 18F40D-18F5BD (0001b1) = Anti-Piracy Notice Screen Graphics
• 18F5BE-18F5C5 (000008) = Palette for Anti-Piracy and Faulty Game Pak Screens
• 18F5C6-18F7C3 (0001fe) = Faulty Game Pak Notice Screen Arrangement
• 18F7C4-18F8B6 (0000f3) = Faulty Game Pak Notice Screen Graphics
• 18F8B7-1901FF (000949) = Audio Data Block (Unspecified)

Map Construction Secondary Bank

• 190200-19D051 (00ce52) = Map Data: Compressed Tile Arrangement Data Block 2
• 19D052-19FE17 (002dc6) = Map Data: Compressed Tileset Character Data Block 1
• 19FE18-1A01FF (0003e8) = Audio Data Block (Unspecified)
• 1A0200-1A7EA6 (007ca7) = Map Data: Compressed Tile Arrangement Data Block 3
• 1A7EA7-1AFCA6 (007e00) = Map Data: Palettes
• 1AFCA7-1AFD06 (000060) = Map Data: Unused Palette Pointer Table
• 1AFD07-1B01FF (0004f9) = Audio Data Block (Unspecified)
• 1B0200-1BF4EA (00f2eb) = Map Data: Compressed Tile Arrangement Data Block 4
• 1BF4EB-1C01FF (000d15) = Audio Data Block (Unspecified)
• 1C0200-1CB222 (00b023) = Map Data: Compressed Tile Arrangement Data Block 5
• 1CB223-1CD836 (002614) = Map Data: Compressed Tileset Character Data Block 2
• 1CD837-1CE236 (000a00) = Map Data: Per-Sector Music Assignments
• 1CE237-1D01FF (001fc9) = Audio Data Block (Unspecified)
• 1D0200-1E00CD (00fece) = Map Data: Compressed Tileset Character Data Block 3
• 1E00CE-1E01FF (000132) = Audio Data Block (Unspecified)
• 1E0200-1EF2E6 (00f0e7) = Map Data: Compressed Tileset Character Data Block 4
• 1EF2E7-1EFEDC (000bf6) = Map Data: Graphics for Animated Tiles Block 1
• 1EFEDD-1F01FF (000323) = Audio Data Block (Unspecified)
• 1F0200-1FC442 (00c243) = Map Data: Compressed Tileset Character Data Block 5
• 1FC443-1FE6E0 (00229e) = Map Data: Graphics for Animated Tiles Block 2
• 1FE6E1-1FE75C (00007c) = Map Data: Palette Animation Pointer Table
• 1FE75D-1FE81A (0000be) = Map Data: Palette Animation Secondary Pointer/Data Table
• 1FE81B-1FEE45 (00062b) = Map Data: Compressed Palette Animation Data
• 1FEE46-2001FF (0013ba) = Audio Data Block (Unspecified)

Miscellaneous Graphics Bank

• 200200-200953 (000754) = Text Window Graphics
• 200954-20099F (00004c) = Flavored Text Window Graphics
• 2009A0-200BB3 (000214) = 8x16 (Large) Romaji Font Graphics from MOTHER 2
• 200BB4-201558 (0009a5) = Compressed SRAM Data
• 201559-2015B8 (000060) = Mr. Saturn Font Character Data
• 2015B9-2021B8 (000c00) = Mr. Saturn Font Graphics
• 2021B9-2021C7 (00000f) = Text Window Properties Table
• 2021C8-202387 (0001c0) = Text Window Flavor Palettes
• 202388-20238F (000008) = Movement-Referenced Text String Palette
• 202390-2023A7 (000018) = Town Map Graphics Pointer Table
• 2023A8-204B1F (002778) = Onett Town Map Data
• 204B20-206921 (001e02) = Twoson Town Map Data
• 206922-208578 (001c58) = Threed Town Map Data
• 208579-20AFB3 (002a3b) = Fourside Town Map Data
• 20AFB4-20C9F0 (001a3d) = Scaraba Town Map Data
• 20C9F1-20EF02 (002512) = Summers Town Map Data
• 20EF03-2101FF (0012fd) = Audio Data Block (Unspecified)
• 210200-210851 (000652) = Coffee Sequence Text
• 210852-210D85 (000534) = Tea Sequence Text
• 210D86-210E79 (0000f4) = Movement-Referenced Text Strings
• 210E7A-210ED9 (000060) = Main Font Character Data
• 210EDA-211AD9 (000c00) = Main Font Graphics
• 211ADA-211B39 (000060) = 8x16 (Battle) Font Character Data
• 211B3A-212139 (000600) = 8x16 (Battle) Font Graphics
• 21213A-212199 (000060) = 8x8 (Tiny) Font Character Data
• 21219A-212499 (000300) = 8x8 (Tiny) Font Font Graphics
• 21249A-2124F9 (000060) = Large Font Character Data
• 2124FA-2130F9 (000c00) = Large Font Graphics
• 2130FA-213189 (000090) = Formatting For Cast Sequence Text
• 21318A-213949 (0007c0) = Wandering Photographer Configuration Table
• 21394A-21433E (0009f5) = Compressed Palette Data for End Credits Photos
• 21433F-214FE7 (000ca9) = Staff Credits Sequence Text
• 214FE8-2150C0 (0000d9) = Unclassified Code
• 2150C1-215129 (000069) = "APE" Logo Screen Arrangement
• 21512A-21532F (000206) = "APE" Logo Screen Graphics
• 215330-215373 (000044) = "APE" Logo Screen Palette
• 215374-2153E7 (000074) = "Halken" Logo Screen Arrangement
• 2153E8-2155B7 (0001d0) = "Halken" Logo Screen Graphics
• 2155B8-215654 (00009d) = "Halken" Logo Screen Palette
• 215655-21569D (000049) = "Nintendo" Logo Screen Arrangement
• 21569E-21578E (0000f1) = "Nintendo" Logo Screen Graphics
• 21578F-2157D2 (000044) = "Nintendo" Logo Screen Palette
• 2157D3-215D32 (000560) = "Gas Station" Screen Arrangement
• 215D33-21ABB6 (004e84) = "Gas Station" Screen Graphics
• 21ABB7-21AC5C (0000a6) = "Gas Station" Screen Palette
• 21AC5D-21ACDE (000082) = "Gas Station" Screen Alternate Palette
• 21ACDF-21AD4A (00006c) = "Produced by Shigesato Itoi" Graphics Arrangement
• 21AD4B-21AF00 (0001b6) = "Produced by Shigesato Itoi" Graphics
• 21AF01-21AF4D (00004d) = "Presented by Nintendo" Graphics Arrangement
• 21AF4E-21B06E (000121) = "Presented by Nintendo" Graphics
• 21B06F-21B07B (00000d) = Shared Palette"Produced by Shigesato Itoi" and "Presented by Nintendo" Graphics
• 21B07C-21B082 (000007) = Title Screen Text (Static) Palette
• 21B083-21B0FC (00007a) = Title Screen Text (Animated) Palette
• 21B0FD-21B17C (000080) = Title Screen Highlight (Animated) Palette
• 21B17D-21B410 (000294) = Title Screen Static Layer Arrangement
• 21B411-21C8E4 (0014d4) = Title Screen Static Layer Graphics
• 21C8E5-21CFE0 (0006fc) = Title Screen Text Layer Graphics
• 21CFE1-21D007 (000027) = Title Screen Copyright Text Palette
• 21D008-21D1AE (0001a7) = Animation Control Data for Title Screen
• 21D1AF-21D6F3 (000545) = Death Screen Graphics
• 21D6F4-21D7E7 (0000f4) = Death Screen Palette
• 21D7E8-21D8E0 (0000f9) = Death Screen Arrangement
• 21D8E1-21DA14 (000134) = "Cast" and "Mr. Saturn" Graphics for Cast Sequence
• 21DA15-21DA34 (000020) = "Cast" Graphic Palette
• 21DA35-21E6E6 (000cb2) = Character Names for Cast Sequence
• 21E6E7-21E727 (000041) = Insane Cultist Palette for Cast Sequence
• 21E728-21EB13 (0003ec) = Staff Credits Sequence Font Graphics
• 21EB14-21EB23 (000010) = Staff Credits Sequence Font Palette
• 21EB24-21EB49 (000026) = Unclassified Data
• 21EB4A-21EC4F (000106) = Staff Credits Sequence Border Data
• 21EC50-21F3C2 (000773) = Town Map Point of Interest Graphics
• 21F3C3-21F780 (0003be) = Unclassified Data
• 21F781-261408 (041c88) = Audio Data
• 261409-261505 (0000fc) = SFX Pointers
• 26156C-2629F1 (001485) = SFX Sequence Data
• 2629F2-262B8B (00019B) = Audio Data
• 262B8C-262D09 (00017E) = Song SPC Pointer Table
• 262D0A-2E9400 (0866f7) = Audio Data
• 2E9401-2F01FF (006dff) = PK Hack System Area of Doom
• 2F0200-2F121A (00101b) = Unclassified Data

Map Construction Tertiary Bank

• 2F121B-2F125A (000040) = Map Data: Tileset Table
• 2F125B-2F12AA (000050) = Map Data: Tileset Pointer Table
• 2F12AB-2F12FA (000050) = Map Data: Tile Arrangement Pointer Table
• 2F12FB-2F137A (000080) = Map Data: Palette Pointer Table
• 2F137B-2F13CA (000050) = Map Data: Collision Tileset Pointer Table
• 2F13CB-2F141A (000050) = Map Data: Tile Animation Tiles Pointer Table
• 2F141B-2F146A (000050) = Map Data: Tile Animation Properties Pointer Table
• 2F146B-2F153E (0000d4) = Map Data: Tile Animation Properties Table

Secondary Engine and Critical Data Bank

• 2F153F-2F1C7E (000740) = Sprite Grouping Pointer Table
• 2F1C7F-2F4C3F (002fc1) = Sprite Grouping Table
• 2F4C40-2F501F (0003e0) = Unclassified Data
• 2F5020-2FA579 (00555a) = Battle Text and PSI Aesthetic Effects Coding
• 2FA57A-2FA5B5 (00003c) = Commands Window Text Strings
• 2FA5B6-2FA65F (0000aa) = Status Window Text
• 2FA660-2FA8EB (00028c) = Name Input Window Selection Layout
• 2FA8EC-2FD71A (002e2f) = Unclassified Data

Debug Menu Assembly Bank

• 2FD71B-2FD76E (000054) = Programmers' Sound Mode Menu Text
• 2FD76F-2FDAB4 (000346) = Unclassified Data
• 2FDAB5-2FDB5D (0000a9) = Programmers' Debug Mode Menu Text
• 2FDB5E-2FED6F (001212) = Unclassified Data
• 2FED70-2FF1B6 (000447) = Programmers' Debug Mode Font Graphics
• 2FF1B7-2FF2D6 (000120) = Programmers' Debug Mode Selection Cursor Graphics (Kirby!)
• 2FF2D7-2FF3B6 (0000e0) = Nullspace
• 2FF3B7-2FF7F6 (000440) = Unclassified Data
• 2FF7F7-3001FF (000a09) = Nullspace