From its introduction in the 1980s, the IEEE-754 standard for floating-point arithmetic has ably served a wide range of scientists and engineers. Even today, the vast majority of numerical computations employ either IEEE single or IEEE double, typically one or the other exclusively in a single application. However, recent developments have exhibited the need for a broader range of precision levels, and a varying level of precision within a single application. There are clear performance advantages to a variable precision framework: faster processing, better cache utilization, lower memory usage, and lower long-term data storage. But effective usage of variable precision requires a more sophisticated mathematical framework, together with corresponding software tools and diagnostic facilities.
At the low end, the explosive rise of graphics, artificial intelligence, and machine learning has underscored the utility of reduced precision levels. Accordingly, an IEEE 16-bit "half" precision standard has been specified, with five exponent bits and ten mantissa bits. Many in the machine learning community are using the "bfloat16" format, which has eight exponent bits and seven mantissa bits. Hardware such as NVIDIA's tensor core units can take advantage of these formats to significantly increase processing rates.
At the same time, researchers in the high-performance computing (HPC) field, in a drive to achieve exascale computing, are considering mixed-precision, such as in iterative refinement calculations where initial iterations are performed using half- or single-precision. Along this line, recognizing that for many simulations much of the data stored in a IEEE 64-bit double precision variable has low information content, researchers are exploring the use of lossy floating point compression, not only for I/O, but also for storing solution state variables.
Exascale computing has also exposed the need for even greater precision than IEEE 64-bit double in some cases, because greatly magnified numerical sensitivities often mean that one can no longer be certain that results are numerically reliable. One remedy is to use IEEE 128-bit quad precision in selected portions of the computation, which is now available via software in some compilers, notably the gfortran compiler. As a single example, researchers at Stanford have had remarkable success in using quad precision in multiscale linear programming applications in biology.
There has also been a rise in the usage of very high precision (hundreds or even thousands of digits). For example, numerous new results have been discovered by computing mathematical expressions to very high precision, and then using integer relation algorithms such as the "PSLQ" algorithm to recognize these numerical values in terms of simple mathematical formulas. Among the results that have been discovered in this fashion are new formulas connecting mathematical constants and the elucidation of polynomials connected to the Poisson potential function of mathematical physics (the latter requiring up to 64,000-digit precision). Such computations are most efficiently performed using a dynamically varying level of precision, doing as much computation as possible with standard precision and only invoking very high precision when necessary.
In summary, although the IEEE 754 floating-point standard has served the mathematical, scientific and engineering world very well for over 30 years, we now are seeing rapidly growing demand for reduced precision (machine learning, neural nets, graphics, etc.), a growing need for mixed 32-64-bit precision, and also a need for greater than 64-bit, all typically varying within a given application. To the extent that IEEE-754 fails to adequately meet new demands such as these, researchers are considering completely different alternatives, for which a flexible precision level is a fundamental feature of the design, and are exploring new mathematical and software frameworks to better understand and utilize such facilities.
This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.
Confirmed Speakers & Participants
- Poster Presenter
University of California, Davis
Florent de Dinechin
University of Lyon, INSA
Lawrence Livermore National Laboratory
University of Utah
National University of Singapore
Lawrence Livermore National Laboratory
Argonne National Laboratory
University of Tennessee
University of Vermont
Lawrence Livermore National Laboratory
University of California Davis
Worcester Polytechnic Institute
ICERM welcomes applications from faculty, postdocs, graduate students, industry scientists, and other researchers who wish to participate. Some funding may be available for travel and lodging. Graduate students who apply must have their advisor submit a statement of support in order to be considered.
Your Visit to ICERM
- ICERM Facilities
- ICERM is located on the 10th & 11th floors of 121 South Main Street in Providence, Rhode Island. ICERM's business hours are 8:30am - 5:00pm during this event. See our facilities page for more info about ICERM and Brown's available facilities.
- Traveling to ICERM
- ICERM is located at Brown University in Providence, Rhode Island. Providence's T.F. Green Airport (15 minutes south) and Boston's Logan Airport (1 hour north) are the closest airports. Providence is also on Amtrak's Northeast Corridor. In-depth directions and transportation information are available on our travel page.
- To secure ICERM's preferred hotel rate at the Hampton Inn & Suites Providence Downtown, use this link. ICERM regularly works with two additional area hotels for short visits. The Graduate Hotel and Hilton Garden Inn both have discounted rates available. Contact firstname.lastname@example.org before booking outside of the preferred rate or if you would like to book alternate accommodations.
The only way ICERM participants should book a room is through the hotel reservation links located on this page or through links emailed to them from an ICERM email address (email@example.com). ICERM never works with any conference booking vendors and never collects credit card information.
- Those traveling with family who are interested in information about childcare and/or schools should contact firstname.lastname@example.org.
- Technology Resources
- Wireless internet access ("Brown-Guest") and wireless printing is available for all ICERM visitors. Eduroam is available for members of participating institutions. Thin clients in all offices and common areas provide open access to a web browser, SSH terminal, and printing capability. See our Technology Resources page for setup instructions and to learn about all available technology.
- Discrimination and Harassment Policy
- ICERM is committed to creating a safe, professional, and welcoming environment that benefits from the diversity and experiences of all its participants. Both the Brown University "Code of Conduct" and the "Discrimination and Workplace Harassment Policy" apply to all ICERM participants and staff. Participants with concerns or requests for assistance on a discrimination or harassment issue should contact the ICERM Director or Assistant Director; they are the responsible employees at ICERM under this policy.
- Exploring Providence
- Providence's world-renowned culinary scene provides ample options for lunch and dinner. Neighborhoods near campus, including College Hill Historic District, have many local attractions. Check out the map on our Explore Providence page to see what's near ICERM.
Contact email@example.com for assistance.
- Eligible to be reimbursed
- B-1 or Visa Waiver Business (WB)
- Ineligible to be reimbursed
- B-2 or Visa Waiver Tourist (WT)
- Already in the US?
F-1 and J-1 not sponsored by ICERM: need to obtain a letter approving reimbursement from the International Office of your home institution PRIOR to travel.
H-1B holders do not need letter of approval.
All other visas: alert ICERM staff immediately about your situation.
ICERM does not reimburse visa fees. This chart is to inform visitors whether the visa they enter the US on allows them to receive reimbursement for the items outlined in their invitation letter.
- Acceptable Costs
- 1 roundtrip between your home institute and ICERM
- Flights in economy class to either Providence airport (PVD) or Boston airport (BOS)
- Ground Transportation to and from airports and ICERM.
- Unacceptable Costs
- Seats in economy plus, business class, or first class
- Change ticket fees of any kind
- Multi-use bus passes
- Meals or incidentals
- Advance Approval Required
- Personal car travel to ICERM from outside New England
- Multiple-destination plane ticket; does not include layovers to reach ICERM
- Arriving or departing from ICERM more than a day before or day after the program
- Multiple trips to ICERM
- Rental car to/from ICERM
- Arriving or departing from airport other than PVD/BOS or home institution's local airport
- 2 one-way plane tickets to create a roundtrip (often purchased from Expedia, Orbitz, etc.)
- Reimbursement Request Form
Refer to the back of your ID badge for more information. Checklists are available at the front desk.
- Reimbursement Tips
- Scanned original receipts are required for all expenses
- Airfare receipt must show full itinerary and payment
- ICERM does not offer per diem or meal reimbursement
- Allowable mileage is reimbursed at prevailing IRS Business Rate and trip documented via pdf of Google Maps result
- Keep all documentation until you receive your reimbursement!
- Reimbursement Timing
6 - 8 weeks after all documentation is sent to ICERM. All reimbursement requests are reviewed by numerous central offices at Brown who may request additional documentation.
- Reimbursement Deadline
Submissions must be received within 30 days of ICERM departure to avoid applicable taxes. Submissions after thirty days will incur applicable taxes. No submissions are accepted more than six months after the program end.