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  • AI
    Artificial Intelligence

    Unified multimodal access layer for Quora’s Poe using Amazon Bedrock

    Artificial Intelligence

    5 Strategic Steps to a Seamless AI Integration

    Artificial Intelligence

    Streamline access to ISO-rating content changes with Verisk rating insights and Amazon…

    Artificial Intelligence

    How msg enhanced HR workforce transformation with Amazon Bedrock and msg.ProfileMap

    Artificial Intelligence

    Unlock model insights with log probability support for Amazon Bedrock Custom Model…

    Artificial Intelligence

    5 Tips for Building Optimized Hugging Face Transformer Pipelines

    Artificial Intelligence

    How Yichao “Peak” Ji became a global AI app hitmaker

    Artificial Intelligence

    How Amazon Finance built an AI assistant using Amazon Bedrock and Amazon Kendra to…

    Artificial Intelligence

    5 Reasons Why Vibe Coding Threatens Secure Data App Development

  • Apple
    Here’s everything new for the Messages app in iOS 26

    Here’s everything new for the Messages app in iOS 26

    Apple promises software update to fix ‘very rare’ iPhone Air camera glitch

    Apple promises software update to fix ‘very rare’ iPhone Air camera glitch

    Apple prepares suppliers for an iPhone sales boost next year, fueled by the new foldable model

    Apple prepares suppliers for an iPhone sales boost next year, fueled by the new foldable model

    Photographer Tyler Stalman reviews the new iPhone cameras

    Photographer Tyler Stalman reviews the new iPhone cameras

    Here’s Apple’s official method to charge your Apple Watch faster

    Here’s Apple’s official method to charge your Apple Watch faster

    WhatsApp for iOS gets message reminders

    WhatsApp for iOS gets message reminders

    Here’s how the iPhone 17 Pro vapor chamber actually works

    Here’s how the iPhone 17 Pro vapor chamber actually works

    Mac Studio M3 Ultra owners can’t install macOS Tahoe yet

    Mac Studio M3 Ultra owners can’t install macOS Tahoe yet

    Apple’s new generative AI ‘answer engine’ might arrive sooner than we initially thought

    Apple Intelligence’s required iPhone storage in iOS 26 is actually good news

  • Crypto
    India Mandates Cybersecurity Audits for Crypto Firms Under FIU’s Directive

    India Mandates Cybersecurity Audits for Crypto Firms Under FIU’s Directive

    Bullish Wins BitLicense, Expands Crypto Services in New York

    Bullish Wins BitLicense, Expands Crypto Services in New York

    Citi Predicts ETH at $4,300 by End of 2025, Citing Investor Optimism Over Activity

    Citi Predicts ETH at $4,300 by End of 2025, Citing Investor Optimism Over Activity

    CME Unleashing XRP Options After $16B Futures Rally Signals Strong Institutional Demand

    CME Unleashing XRP Options After $16B Futures Rally Signals Strong Institutional Demand

    Circle and Kraken Ignite Stablecoin Shakeup With Game-Changing Partnership

    Circle and Kraken Ignite Stablecoin Shakeup With Game-Changing Partnership

    Powell’s Fed Pulls Trigger on Quarter-Point Cut

    Powell’s Fed Pulls Trigger on Quarter-Point Cut

    BTC Struggles to Hold $115K Despite Dovish Fed Shift

    BTC Struggles to Hold $115K Despite Dovish Fed Shift

    Bitcoin Briefly Shoots Past $116K After Fed Cuts Rates

    Bitcoin Briefly Shoots Past $116K After Fed Cuts Rates

    Global Crypto Market‑Maker Keyrock Acquires Turing Capital to Launch Asset & Wealth Management Division

    Global Crypto Market‑Maker Keyrock Acquires Turing Capital to Launch Asset & Wealth Management Division

  • Gaming
    Mezza Lo Shrine- Ancient Trifecta- The Crowned Beast Quests- Zelda BOTW –  walkthrough

    Mezza Lo Shrine- Ancient Trifecta- The Crowned Beast Quests- Zelda BOTW – walkthrough

    A more expensive rapid trigger version of Logitech’s G515 gaming keyboard has just launched and it’s for low-profile fans

    A more expensive rapid trigger version of Logitech’s G515 gaming keyboard has just launched and it’s for low-profile fans

    This Black Myth Wukong build is absolutely BROKEN! I Lvl 25+ one shot build

    This Black Myth Wukong build is absolutely BROKEN! I Lvl 25+ one shot build

    Helldivers 2’s new bugs are bugged, so Arrowhead’s turning them off for 5 weeks to debug its bugged bugs’ bugs

    Helldivers 2’s new bugs are bugged, so Arrowhead’s turning them off for 5 weeks to debug its bugged bugs’ bugs

    Baldur's Gate 3 – Early Access | Review

    Baldur's Gate 3 – Early Access | Review

    REDRAGON S101 GAMING KEYBOARD

    Logitech’s Astro A20 X gaming headset can swap between audio sources

    Linus Torvalds has apparently met Bill Gates for the first time in person and before you ask, no he didn’t clock him in the face

    After disappointing fans with a time-grated grind in beta, Blizzard turned WoW Legion Remix around just in time for its October release

    Late Review of The Callisto Protocol

    Late Review of The Callisto Protocol

    REDRAGON S101 GAMING KEYBOARD

    Logitech’s Pro X2 Superstrike offers haptic clicks and rapid trigger

  • Retro Rewind
    Retro Rewind: Game Players Issue 80 Magazine January 1996

    Retro Rewind: Game Players Issue 80 Magazine January 1996

    Retro Rewind: Video Game Trader Winter 2014

    Retro Rewind: Video Game Trader Winter 2014

    Retro Rewind: Electronic Games April 1995

    Retro Rewind: Electronic Games April 1995

    Retro Rewind: Electronic Gaming Monthly Magazine Number 55 February 1994

    Retro Rewind: Electronic Gaming Monthly Magazine Number 57 April 1994

    Retro Rewind: Blast from the Past – 35 Iconic Commercials of 1988!

    Retro Rewind: Blast from the Past – 35 Iconic Commercials of 1988!

    Retro Rewind: PC World Magazine August 1998

    Retro Rewind: PC World Magazine August 1998

    Retro Rewind: Computer Shopper Magazine September 1997

    Retro Rewind: Computer Shopper Magazine September 1997

    Retro Rewind: PC Magazine December 2015

    Retro Rewind: PC Magazine December 2015

    Retro Rewind: EDGE Magazine RETRO #1: The Guide to Classic Videogame Playing and Collecting

    Retro Rewind: EDGE Magazine RETRO #1: The Guide to Classic Videogame Playing and Collecting

  • Tech Art
    Viewer Request Print Digital Images From Portrait To Landscape – Digital Collage Club

    Viewer Request Print Digital Images From Portrait To Landscape – Digital Collage Club

    3d drawing easy on paper for beginner

    3d drawing easy on paper for beginner

    Announcing the 2025 Center for Craft Archive Fellows

    Announcing the 2025 Center for Craft Archive Fellows

    Social Media Post Graphic Design   Adobe Photoshop Tutorial

    Social Media Post Graphic Design Adobe Photoshop Tutorial

    Color theory explained

    Color theory explained

    MAGA Is Coming for the Arts!

    MAGA Is Coming for the Arts!

    Computer Art, Cyber Art, Multimedia Art, Digital Art Manipulation, Omni-Manipulation

    Computer Art, Cyber Art, Multimedia Art, Digital Art Manipulation, Omni-Manipulation

    How To Pick the Right Size/Resolution for your Art – Beginner Illustration Tips

    How To Pick the Right Size/Resolution for your Art – Beginner Illustration Tips

    HOW I DRAW DIGITAL ART USING CLIP STUDIO PAINT

    HOW I DRAW DIGITAL ART USING CLIP STUDIO PAINT

  • Tech Deals
    ATARI 7800 Video Game Cartridge Pole Position II

    ATARI 7800 Video Game Cartridge Pole Position II

    Transcend 2TB External SSD, Up to 1,050MB/s, Dual USB Flash Drive for Pixel10, Tesla,…

    Transcend 2TB External SSD, Up to 1,050MB/s, Dual USB Flash Drive for Pixel10, Tesla,…

    Pioneer Air Conditioner WYS012G-22 Wall Mount Ductless Inverter++ Mini Split Heat Pump,…

    Pioneer Air Conditioner WYS012G-22 Wall Mount Ductless Inverter++ Mini Split Heat Pump,…

    Pioneer DMH-WT6000NEX 10.1″ Single DIN Digital Multimedia Receiver w/Bluetooth…

    Pioneer DMH-WT6000NEX 10.1″ Single DIN Digital Multimedia Receiver w/Bluetooth…

    Logitech G920 Driving Force Racing Wheel and Pedals, Force Feedback + Logitech G Driving…

    Logitech G920 Driving Force Racing Wheel and Pedals, Force Feedback + Logitech G Driving…

    Lenovo IdeaPad Laptop with Microsoft Office and 1TB Cloud Storage (1-Year)| 15.6 inch HD…

    Lenovo IdeaPad Laptop with Microsoft Office and 1TB Cloud Storage (1-Year)| 15.6 inch HD…

    AC Adapter Charger Compatible with LaCie D2 Thunderbolt 2 3TB USB 3.0 3.5inch External…

    AC Adapter Charger Compatible with LaCie D2 Thunderbolt 2 3TB USB 3.0 3.5inch External…

    MIXAGE 128GB MicroSDXC Memory Card U3 V30 A1 UH-I, 100MB/s Read 60MB/s Write 4K UHD for…

    MIXAGE 128GB MicroSDXC Memory Card U3 V30 A1 UH-I, 100MB/s Read 60MB/s Write 4K UHD for…

    [5-Yrs Free Data Recovery] GIGASTONE 256GB SD Card, 4K Camera Pro, A1 V30 SDXC Memory…

    [5-Yrs Free Data Recovery] GIGASTONE 256GB SD Card, 4K Camera Pro, A1 V30 SDXC Memory…

  • Techs Got To Eat
    Spicy Chickpea Shakshuka Mug: 5-Minute Vegetarian Fuel

    Spicy Chickpea Shakshuka Mug: 5-Minute Vegetarian Fuel

    Bacon & Spinach Mug Quiche: 3-Minute Gourmet Breakfast

    Bacon & Spinach Mug Quiche: 3-Minute Gourmet Breakfast

    Cheesy Broccoli Rice Mug: 5-Minute Super Comfort Food

    Cheesy Broccoli Rice Mug: 5-Minute Super Comfort Food

    Top 10 Vegetarian Recipes for 2025: Easy and Nutritious Meals for Busy People

    Top 10 Vegetarian Recipes for 2025: Easy and Nutritious Meals for Busy People

    Bacon Mug Lasagna: 5-Minute Microwave Meat Lover’s Dream

    Bacon Mug Lasagna: 5-Minute Microwave Meat Lover’s Dream

    Bacon Fried Rice Mug: 5-Minute Microwave Meal

    Bacon Fried Rice Mug: 5-Minute Microwave Meal

    Bacon & Cheddar Mug Biscuit: 2-Minute Savory Comfort

    Bacon & Cheddar Mug Biscuit: 2-Minute Savory Comfort

    Loaded Bacon Cheesy Potato Mug: 5-Minute Comfort Food

    Loaded Bacon Cheesy Potato Mug: 5-Minute Comfort Food

    Peanut Butter Banana Mug Muffin: 5-Minute Protein Snack

    Peanut Butter Banana Mug Muffin: 5-Minute Protein Snack

  • Tesla
    KIKIMO Cargo Mat for 2025 Tesla Model Y Juniper, for Tesla New Model Y 5-Seater…

    KIKIMO Cargo Mat for 2025 Tesla Model Y Juniper, for Tesla New Model Y 5-Seater…

    Maoershan EVA Hard Protective Travel Case Carrying Pouch Cover Bag for Tesla Charging…

    Maoershan EVA Hard Protective Travel Case Carrying Pouch Cover Bag for Tesla Charging…

    iJDMTOY 2pc Set Track Racing Style Direct Fit Silver Aluminum Accelerator and Brake Foot…

    iJDMTOY 2pc Set Track Racing Style Direct Fit Silver Aluminum Accelerator and Brake Foot…

    Shakas Motorcycle Accelerator Throttle Seat, Temperature Resistant High Strength Alloy…

    Shakas Motorcycle Accelerator Throttle Seat, Temperature Resistant High Strength Alloy…

    1pc Wolf Pack Badges Emblems 3D Logo Replacement for Tsla Cybertruck 2024 Car Truck…

    1pc Wolf Pack Badges Emblems 3D Logo Replacement for Tsla Cybertruck 2024 Car Truck…

    CAR PASS Leather and 3D Air Mesh Universal Fit Car Seat Covers, for…

    CAR PASS Leather and 3D Air Mesh Universal Fit Car Seat Covers, for…

    CCS1 to Tesla Adapter for Tesla, NOT Compatible with Cybertruck, Supports Charging…

    CCS1 to Tesla Adapter for Tesla, NOT Compatible with Cybertruck, Supports Charging…

    Tesla partners with Uber Freight to offer Tesla Semi electric trucks at discounts

    Tesla partners with Uber Freight to offer Tesla Semi electric trucks at discounts

    Tesla Cybertruck and new Model 3 miss the top marks in latest crash tests

    Tesla Cybertruck and new Model 3 miss the top marks in latest crash tests

  • UFO
    Alien Birthday Party Decorations Door Curtain with Foil Fringe Tinsel Spacecraft Flying Saucer Spaceship Hanging Banner for Alien Halloween Party(Fluorescent Yellow)

    Alien Birthday Party Decorations Door Curtain with Foil Fringe Tinsel Spacecraft Flying Saucer Spaceship Hanging Banner for Alien Halloween Party(Fluorescent Yellow)

    What is “Alive” in Alien Stage’s Wiege Music Video? THEORY #alienstage analysis

    What is “Alive” in Alien Stage’s Wiege Music Video? THEORY #alienstage analysis

    YJYart Home Decor Pink Blossom Hand Painted 30×60 Inch Colorful Wall Art Large Canvas Wall Art for Living Room Bedroom Office Kitchen

    YJYart Home Decor Pink Blossom Hand Painted 30×60 Inch Colorful Wall Art Large Canvas Wall Art for Living Room Bedroom Office Kitchen

    The Proof Is Out There: UFO Encounters Terrify Witnesses

    The Proof Is Out There: UFO Encounters Terrify Witnesses

    Womens Roswell High School Hornets V-Neck T-Shirt

    Womens Roswell High School Hornets V-Neck T-Shirt

    SOJOS Retro Polarized Square Aviator Sunglasses for Women Men Vintage 70s UV400 Protection Shade SJ2609

    SOJOS Retro Polarized Square Aviator Sunglasses for Women Men Vintage 70s UV400 Protection Shade SJ2609

    Mind-Blowing Moon Encounters: Unveiling the UFO Mystery

    Mind-Blowing Moon Encounters: Unveiling the UFO Mystery

    300PC Gold Glitter and Sage Green Happy 40th Birthday Decorations for Men/Women Greenery 40th Birthday Confetti for Table Forty Party Decor Supplies

    300PC Gold Glitter and Sage Green Happy 40th Birthday Decorations for Men/Women Greenery 40th Birthday Confetti for Table Forty Party Decor Supplies

    FOREO Call It A Night Revitalizing & Nourishing UFO Activated Mask, 7 count

    FOREO Call It A Night Revitalizing & Nourishing UFO Activated Mask, 7 count

  • AI
    Artificial Intelligence

    Unified multimodal access layer for Quora’s Poe using Amazon Bedrock

    Artificial Intelligence

    5 Strategic Steps to a Seamless AI Integration

    Artificial Intelligence

    Streamline access to ISO-rating content changes with Verisk rating insights and Amazon…

    Artificial Intelligence

    How msg enhanced HR workforce transformation with Amazon Bedrock and msg.ProfileMap

    Artificial Intelligence

    Unlock model insights with log probability support for Amazon Bedrock Custom Model…

    Artificial Intelligence

    5 Tips for Building Optimized Hugging Face Transformer Pipelines

    Artificial Intelligence

    How Yichao “Peak” Ji became a global AI app hitmaker

    Artificial Intelligence

    How Amazon Finance built an AI assistant using Amazon Bedrock and Amazon Kendra to…

    Artificial Intelligence

    5 Reasons Why Vibe Coding Threatens Secure Data App Development

  • Apple
    Here’s everything new for the Messages app in iOS 26

    Here’s everything new for the Messages app in iOS 26

    Apple promises software update to fix ‘very rare’ iPhone Air camera glitch

    Apple promises software update to fix ‘very rare’ iPhone Air camera glitch

    Apple prepares suppliers for an iPhone sales boost next year, fueled by the new foldable model

    Apple prepares suppliers for an iPhone sales boost next year, fueled by the new foldable model

    Photographer Tyler Stalman reviews the new iPhone cameras

    Photographer Tyler Stalman reviews the new iPhone cameras

    Here’s Apple’s official method to charge your Apple Watch faster

    Here’s Apple’s official method to charge your Apple Watch faster

    WhatsApp for iOS gets message reminders

    WhatsApp for iOS gets message reminders

    Here’s how the iPhone 17 Pro vapor chamber actually works

    Here’s how the iPhone 17 Pro vapor chamber actually works

    Mac Studio M3 Ultra owners can’t install macOS Tahoe yet

    Mac Studio M3 Ultra owners can’t install macOS Tahoe yet

    Apple’s new generative AI ‘answer engine’ might arrive sooner than we initially thought

    Apple Intelligence’s required iPhone storage in iOS 26 is actually good news

  • Crypto
    India Mandates Cybersecurity Audits for Crypto Firms Under FIU’s Directive

    India Mandates Cybersecurity Audits for Crypto Firms Under FIU’s Directive

    Bullish Wins BitLicense, Expands Crypto Services in New York

    Bullish Wins BitLicense, Expands Crypto Services in New York

    Citi Predicts ETH at $4,300 by End of 2025, Citing Investor Optimism Over Activity

    Citi Predicts ETH at $4,300 by End of 2025, Citing Investor Optimism Over Activity

    CME Unleashing XRP Options After $16B Futures Rally Signals Strong Institutional Demand

    CME Unleashing XRP Options After $16B Futures Rally Signals Strong Institutional Demand

    Circle and Kraken Ignite Stablecoin Shakeup With Game-Changing Partnership

    Circle and Kraken Ignite Stablecoin Shakeup With Game-Changing Partnership

    Powell’s Fed Pulls Trigger on Quarter-Point Cut

    Powell’s Fed Pulls Trigger on Quarter-Point Cut

    BTC Struggles to Hold $115K Despite Dovish Fed Shift

    BTC Struggles to Hold $115K Despite Dovish Fed Shift

    Bitcoin Briefly Shoots Past $116K After Fed Cuts Rates

    Bitcoin Briefly Shoots Past $116K After Fed Cuts Rates

    Global Crypto Market‑Maker Keyrock Acquires Turing Capital to Launch Asset & Wealth Management Division

    Global Crypto Market‑Maker Keyrock Acquires Turing Capital to Launch Asset & Wealth Management Division

  • Gaming
    Mezza Lo Shrine- Ancient Trifecta- The Crowned Beast Quests- Zelda BOTW –  walkthrough

    Mezza Lo Shrine- Ancient Trifecta- The Crowned Beast Quests- Zelda BOTW – walkthrough

    A more expensive rapid trigger version of Logitech’s G515 gaming keyboard has just launched and it’s for low-profile fans

    A more expensive rapid trigger version of Logitech’s G515 gaming keyboard has just launched and it’s for low-profile fans

    This Black Myth Wukong build is absolutely BROKEN! I Lvl 25+ one shot build

    This Black Myth Wukong build is absolutely BROKEN! I Lvl 25+ one shot build

    Helldivers 2’s new bugs are bugged, so Arrowhead’s turning them off for 5 weeks to debug its bugged bugs’ bugs

    Helldivers 2’s new bugs are bugged, so Arrowhead’s turning them off for 5 weeks to debug its bugged bugs’ bugs

    Baldur's Gate 3 – Early Access | Review

    Baldur's Gate 3 – Early Access | Review

    REDRAGON S101 GAMING KEYBOARD

    Logitech’s Astro A20 X gaming headset can swap between audio sources

    Linus Torvalds has apparently met Bill Gates for the first time in person and before you ask, no he didn’t clock him in the face

    After disappointing fans with a time-grated grind in beta, Blizzard turned WoW Legion Remix around just in time for its October release

    Late Review of The Callisto Protocol

    Late Review of The Callisto Protocol

    REDRAGON S101 GAMING KEYBOARD

    Logitech’s Pro X2 Superstrike offers haptic clicks and rapid trigger

  • Retro Rewind
    Retro Rewind: Game Players Issue 80 Magazine January 1996

    Retro Rewind: Game Players Issue 80 Magazine January 1996

    Retro Rewind: Video Game Trader Winter 2014

    Retro Rewind: Video Game Trader Winter 2014

    Retro Rewind: Electronic Games April 1995

    Retro Rewind: Electronic Games April 1995

    Retro Rewind: Electronic Gaming Monthly Magazine Number 55 February 1994

    Retro Rewind: Electronic Gaming Monthly Magazine Number 57 April 1994

    Retro Rewind: Blast from the Past – 35 Iconic Commercials of 1988!

    Retro Rewind: Blast from the Past – 35 Iconic Commercials of 1988!

    Retro Rewind: PC World Magazine August 1998

    Retro Rewind: PC World Magazine August 1998

    Retro Rewind: Computer Shopper Magazine September 1997

    Retro Rewind: Computer Shopper Magazine September 1997

    Retro Rewind: PC Magazine December 2015

    Retro Rewind: PC Magazine December 2015

    Retro Rewind: EDGE Magazine RETRO #1: The Guide to Classic Videogame Playing and Collecting

    Retro Rewind: EDGE Magazine RETRO #1: The Guide to Classic Videogame Playing and Collecting

  • Tech Art
    Viewer Request Print Digital Images From Portrait To Landscape – Digital Collage Club

    Viewer Request Print Digital Images From Portrait To Landscape – Digital Collage Club

    3d drawing easy on paper for beginner

    3d drawing easy on paper for beginner

    Announcing the 2025 Center for Craft Archive Fellows

    Announcing the 2025 Center for Craft Archive Fellows

    Social Media Post Graphic Design   Adobe Photoshop Tutorial

    Social Media Post Graphic Design Adobe Photoshop Tutorial

    Color theory explained

    Color theory explained

    MAGA Is Coming for the Arts!

    MAGA Is Coming for the Arts!

    Computer Art, Cyber Art, Multimedia Art, Digital Art Manipulation, Omni-Manipulation

    Computer Art, Cyber Art, Multimedia Art, Digital Art Manipulation, Omni-Manipulation

    How To Pick the Right Size/Resolution for your Art – Beginner Illustration Tips

    How To Pick the Right Size/Resolution for your Art – Beginner Illustration Tips

    HOW I DRAW DIGITAL ART USING CLIP STUDIO PAINT

    HOW I DRAW DIGITAL ART USING CLIP STUDIO PAINT

  • Tech Deals
    ATARI 7800 Video Game Cartridge Pole Position II

    ATARI 7800 Video Game Cartridge Pole Position II

    Transcend 2TB External SSD, Up to 1,050MB/s, Dual USB Flash Drive for Pixel10, Tesla,…

    Transcend 2TB External SSD, Up to 1,050MB/s, Dual USB Flash Drive for Pixel10, Tesla,…

    Pioneer Air Conditioner WYS012G-22 Wall Mount Ductless Inverter++ Mini Split Heat Pump,…

    Pioneer Air Conditioner WYS012G-22 Wall Mount Ductless Inverter++ Mini Split Heat Pump,…

    Pioneer DMH-WT6000NEX 10.1″ Single DIN Digital Multimedia Receiver w/Bluetooth…

    Pioneer DMH-WT6000NEX 10.1″ Single DIN Digital Multimedia Receiver w/Bluetooth…

    Logitech G920 Driving Force Racing Wheel and Pedals, Force Feedback + Logitech G Driving…

    Logitech G920 Driving Force Racing Wheel and Pedals, Force Feedback + Logitech G Driving…

    Lenovo IdeaPad Laptop with Microsoft Office and 1TB Cloud Storage (1-Year)| 15.6 inch HD…

    Lenovo IdeaPad Laptop with Microsoft Office and 1TB Cloud Storage (1-Year)| 15.6 inch HD…

    AC Adapter Charger Compatible with LaCie D2 Thunderbolt 2 3TB USB 3.0 3.5inch External…

    AC Adapter Charger Compatible with LaCie D2 Thunderbolt 2 3TB USB 3.0 3.5inch External…

    MIXAGE 128GB MicroSDXC Memory Card U3 V30 A1 UH-I, 100MB/s Read 60MB/s Write 4K UHD for…

    MIXAGE 128GB MicroSDXC Memory Card U3 V30 A1 UH-I, 100MB/s Read 60MB/s Write 4K UHD for…

    [5-Yrs Free Data Recovery] GIGASTONE 256GB SD Card, 4K Camera Pro, A1 V30 SDXC Memory…

    [5-Yrs Free Data Recovery] GIGASTONE 256GB SD Card, 4K Camera Pro, A1 V30 SDXC Memory…

  • Techs Got To Eat
    Spicy Chickpea Shakshuka Mug: 5-Minute Vegetarian Fuel

    Spicy Chickpea Shakshuka Mug: 5-Minute Vegetarian Fuel

    Bacon & Spinach Mug Quiche: 3-Minute Gourmet Breakfast

    Bacon & Spinach Mug Quiche: 3-Minute Gourmet Breakfast

    Cheesy Broccoli Rice Mug: 5-Minute Super Comfort Food

    Cheesy Broccoli Rice Mug: 5-Minute Super Comfort Food

    Top 10 Vegetarian Recipes for 2025: Easy and Nutritious Meals for Busy People

    Top 10 Vegetarian Recipes for 2025: Easy and Nutritious Meals for Busy People

    Bacon Mug Lasagna: 5-Minute Microwave Meat Lover’s Dream

    Bacon Mug Lasagna: 5-Minute Microwave Meat Lover’s Dream

    Bacon Fried Rice Mug: 5-Minute Microwave Meal

    Bacon Fried Rice Mug: 5-Minute Microwave Meal

    Bacon & Cheddar Mug Biscuit: 2-Minute Savory Comfort

    Bacon & Cheddar Mug Biscuit: 2-Minute Savory Comfort

    Loaded Bacon Cheesy Potato Mug: 5-Minute Comfort Food

    Loaded Bacon Cheesy Potato Mug: 5-Minute Comfort Food

    Peanut Butter Banana Mug Muffin: 5-Minute Protein Snack

    Peanut Butter Banana Mug Muffin: 5-Minute Protein Snack

  • Tesla
    KIKIMO Cargo Mat for 2025 Tesla Model Y Juniper, for Tesla New Model Y 5-Seater…

    KIKIMO Cargo Mat for 2025 Tesla Model Y Juniper, for Tesla New Model Y 5-Seater…

    Maoershan EVA Hard Protective Travel Case Carrying Pouch Cover Bag for Tesla Charging…

    Maoershan EVA Hard Protective Travel Case Carrying Pouch Cover Bag for Tesla Charging…

    iJDMTOY 2pc Set Track Racing Style Direct Fit Silver Aluminum Accelerator and Brake Foot…

    iJDMTOY 2pc Set Track Racing Style Direct Fit Silver Aluminum Accelerator and Brake Foot…

    Shakas Motorcycle Accelerator Throttle Seat, Temperature Resistant High Strength Alloy…

    Shakas Motorcycle Accelerator Throttle Seat, Temperature Resistant High Strength Alloy…

    1pc Wolf Pack Badges Emblems 3D Logo Replacement for Tsla Cybertruck 2024 Car Truck…

    1pc Wolf Pack Badges Emblems 3D Logo Replacement for Tsla Cybertruck 2024 Car Truck…

    CAR PASS Leather and 3D Air Mesh Universal Fit Car Seat Covers, for…

    CAR PASS Leather and 3D Air Mesh Universal Fit Car Seat Covers, for…

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    CCS1 to Tesla Adapter for Tesla, NOT Compatible with Cybertruck, Supports Charging…

    Tesla partners with Uber Freight to offer Tesla Semi electric trucks at discounts

    Tesla partners with Uber Freight to offer Tesla Semi electric trucks at discounts

    Tesla Cybertruck and new Model 3 miss the top marks in latest crash tests

    Tesla Cybertruck and new Model 3 miss the top marks in latest crash tests

  • UFO
    Alien Birthday Party Decorations Door Curtain with Foil Fringe Tinsel Spacecraft Flying Saucer Spaceship Hanging Banner for Alien Halloween Party(Fluorescent Yellow)

    Alien Birthday Party Decorations Door Curtain with Foil Fringe Tinsel Spacecraft Flying Saucer Spaceship Hanging Banner for Alien Halloween Party(Fluorescent Yellow)

    What is “Alive” in Alien Stage’s Wiege Music Video? THEORY #alienstage analysis

    What is “Alive” in Alien Stage’s Wiege Music Video? THEORY #alienstage analysis

    YJYart Home Decor Pink Blossom Hand Painted 30×60 Inch Colorful Wall Art Large Canvas Wall Art for Living Room Bedroom Office Kitchen

    YJYart Home Decor Pink Blossom Hand Painted 30×60 Inch Colorful Wall Art Large Canvas Wall Art for Living Room Bedroom Office Kitchen

    The Proof Is Out There: UFO Encounters Terrify Witnesses

    The Proof Is Out There: UFO Encounters Terrify Witnesses

    Womens Roswell High School Hornets V-Neck T-Shirt

    Womens Roswell High School Hornets V-Neck T-Shirt

    SOJOS Retro Polarized Square Aviator Sunglasses for Women Men Vintage 70s UV400 Protection Shade SJ2609

    SOJOS Retro Polarized Square Aviator Sunglasses for Women Men Vintage 70s UV400 Protection Shade SJ2609

    Mind-Blowing Moon Encounters: Unveiling the UFO Mystery

    Mind-Blowing Moon Encounters: Unveiling the UFO Mystery

    300PC Gold Glitter and Sage Green Happy 40th Birthday Decorations for Men/Women Greenery 40th Birthday Confetti for Table Forty Party Decor Supplies

    300PC Gold Glitter and Sage Green Happy 40th Birthday Decorations for Men/Women Greenery 40th Birthday Confetti for Table Forty Party Decor Supplies

    FOREO Call It A Night Revitalizing & Nourishing UFO Activated Mask, 7 count

    FOREO Call It A Night Revitalizing & Nourishing UFO Activated Mask, 7 count

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Home Hacker News

Why Does Integer Addition Approximate Float Multiplication?

Hacker News by Hacker News
February 13, 2025
in Hacker News
Reading Time: 8 mins read
121
A A
0

2025-02-09 13:36:00
probablydance.com

Here is a rough approximation of float multiplication (source):

float rough_float_multiply(float a, float b) {
    constexpr uint32_t bias = 0x3f76d000;
    return bit_cast(bit_cast(a) + bit_cast(b) - bias);
}

We’re casting the floats to ints, adding them, adjusting the exponent, and returning as float. If you think about it for a second you will realize that since the float contains the exponent, this won’t be too wrong: You can multiply two numbers by adding their exponents. So just with the exponent-addition you will be within a factor of 2 of the right result. But this will actually be much better and get within 7.5% of the right answer. Why?

It’s not the magic number. Even if you only adjust the exponent (subtract 127 to get it back into range after the addition) you get within 12.5% of the right result. There is also a mantissa offset in that constant which helps a little, but 12.5% is surprisingly good as a default.

I should also say that the above fails catastrophically when you overflow or underflow the exponent. I think the source paper doesn’t handle that, even though underflowing is really easy by doing e.g. 0.5 * 0. It’s probably fine to ignore overflow, so here is a version that just handles underflow:

float custom_multiply(float a, float b) {
    constexpr uint32_t sign_bit = 0x8000'0000;
    constexpr uint32_t exp_offset =    0b0'01111111'0000000'00000000'00000000;
    constexpr uint32_t mantissa_bias = 0b0'00000000'0001001'00110000'00000000;
    constexpr uint32_t offset = exp_offset - mantissa_bias;
    uint32_t bits_a = std::bit_cast(a);
    uint32_t bits_b = std::bit_cast(b);
    uint32_t c = (bits_a & ~sign_bit) + (bits_b & ~sign_bit);
    if (c (c);
}

Clang compiles this to a branchless version that doesn’t perform too far off from float multiplication. Is this ever worth using? The paper talks about using this to save power, but that’s probably not worth it for a few reasons:

  1. Most of the power-consumption comes from moving bits around, the actual float multiplication is a small power drain compared to loading the float and saving the result
  2. You wouldn’t be able to use tensor cores
  3. I don’t think you can actually be faster than float multiplication because there are so many edge cases to handle

It feels close to being worth it though, so I wouldn’t be surprised if someone found a use case.

But there is still the question of why this works so well. The mantissa is not stored in log-space, it’s just stored in plain old linear space where addition does not do multiplication. But lets think about how to get the exponent from the mantissa.

In general how do you get the remaining exponent-fraction from the remaining bits? This is easier to think about for integers where you can get the log2 by determining the highest set bit:

log2(20) = log2(0b10100) ~= highest_set_bit(0b10100) = 4

The actual correct value is log2(20)=4.322. The question we need to answer is: How do you get the remaining exponent-fraction, 0.322 from the remaining bits, 0b0100?

To make this work for any number of bits we should normalize the remaining bits into the range 0 to 1, which in this case means doing the division 0b0100/float(1

After we brought the numbers into the range from 0 to 1, you can get the remaining exponent fraction with log2(1+x). In this case it’s log2(1+0.25) = 0.322.

If you plot y=log2(1+x) for the range from 0 to 1 you will find that it doesn’t deviate too far from y=x. So if you just want an approximate solution you might as well skip this step.

And then the mantissa is already interpreted as a fraction on floats, so you also don’t have to divide. So the whole operation cancels out and you can just add.

You still need to handle

  1. The sign bit
  2. Overflowing mantissa
  3. Overflowing exponent
  4. Underflowing exponent

Number 1 and 2 also work out naturally using addition because of how floats are represented:

  • Since the sign bit is the highest bit, overflow is ignored so addition is the same as xor, which is what you want
  • When the mantissa overflows you end up increasing the exponent, which is what you want. (e.g. 1.5 * 1.5 = 2.25, which has a higher base-2 exponent)

Number 3 can be ignored for most floats you care about.

Number 4 is the one that required me to write that more complicated version of the code. It’s really easy to underflow the exponent, which will wrap around and give you large numbers instead. In neural networks lots of activation functions like to return 0 or close to 0 and when you multiply with that you will underflow the initial function and get very wrong results. So you need to handle underflow. I have not found an elegant way of doing it because you only have a few cycles to work in, otherwise you might as well use float multiplication.

The last open question is that mantissa-adjustment: You can see in the graph above that the approximation y=x is never too big, so by default you will always bias towards 0. But you can add a little bias to the mantissa to shift the whole line up. I tried a few analytic ways to arrive at a good constant, but they all gave terrible results when I actually tried this on a bunch of floats. So I just tried many different constants and stuck with the one that gave the least error on 10,000 randomly generated test floats.

So even though this is probably not useful and I haven’t found a really elegant way of doing it, it’s still neat how the whole thing almost works out as a one-liner because so many things cancel out once you approximate y=log2(1+x) as y=x.

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