### Table 1. Boundary cases for multiplication

"... In PAGE 3: ... And since it is plausible to test IEEE single precision exhaustively in a reasonable time it does no harm to require DC AL DD too. Examples are shown in Table1 , using decimal form atop the conventional hexadecimal format, itself with an under-... In PAGE 4: ... Boundary cases for multiplication 4 Division Each valid pair of unequal multiplicands provides further tests for directed division at no cost, derived briefly thus: Given DCDD BPBE D2A0CX D4A6CZ, it is immediate that BE D2A0CX D4 DC BP DD A6 AF DC and BE D2A0CX D4 DD BP DC A6 AF DD for tiny AF DC BP CZBPDC and AF DD BP CZBPDD.SinceDCDD BPBE D2A0CX D4A0CZ is a test case for multiplication, four corresponding tests for directed division are BE D2A0CX minfB4D4BPDCB5BPDDBN BE D2A0CX infB4D4BPDCB5BPDDB7BDBN BE D2A0CX minfB4D4BPDDB5BPDCBN BE D2A0CX infB4D4BPDDB5BPDCB7BD With DCDD BPBE D2A0CX D4B7CZ, check for BE D2A0CX minfB4D4BPDCB5BPDDA0BDBN BE D2A0CX infB4D4BPDCB5BPDDBN BE D2A0CX minfB4D4BPDDB5BPDCA0BDBN BE D2A0CX infB4D4BPDDB5BPDC The examples shown in Table 2 correspond to various rows in Table1 . Each has at least 21 consecutive like bits after the binary point; the first has 23, which is provably maximal.... In PAGE 4: ... Certainly BED4 is representable if D4 is, and so BE D1 minfB4 D4 BED4B5BPDCBN BE D1 infB4 D4 BED4B5BPDCB7BD More tests associated with the equation DC BE A0CZ BPBE D2A0CX D4are obtained in a similar manner. For an even exponent, check BE D1 minfB4 D4 D4B5BPDCA0BDBN BE D1 infB4 D4 D4B5BPDCBN and for odd exponent BE D1 minfB4 D4 BED4B5BPDCA0BDBN BE D1 infB4 D4 BED4B5BPDC For example, from Table1 , we know that BKBFBKBKBIBCBL BE A0 BDBPBE BEBF A2 BKBFBKBKBIBDBC,andso BE BDBD D4 BE A2 BKBFBKBKBIBDBC BP BKBFBKBKBIBCBKBMBLBLBLBLBLBLBLBGBMBMBM Another case is BDBIBJBJBJBEBDBH BE A0 BDBPBE BEBG A2 BDBIBJBJBJBEBDBG, with BE BDBE D4 BDBIBJBJBJBEBDBG BP BDBIBJBJBJBEBDBGBMBLBLBLBLBLBLBLBJBMBMBM This trick can not be exploited to find division or square root boundary cases for mode to-nearest, because for that problem DCDD (or DC BE ) must nearly equal the average of consecutive D2-bit floating-point numbers, a midpoint whose... ..."

### Table 1: Classification of reconstruction algorithms for surfaces with boundaries.

2002

"... In PAGE 4: ... Changes in these stages include strengthening of the sampling condition in the sampling stage and providing additional information to the reconstruction stage. The Table1 enumerates the classification. All classes of algorithms, except Class BT, can be designed to reconstruct surfaces with boundaries.... ..."

Cited by 3

### Table 1: Classification of reconstruction algorithms for surfaces with boundaries.

"... In PAGE 4: ... Changes in these stages include strengthening of the sampling condition in the sampling stage and providing additional information to the reconstruction stage. The Table1 enumerates the classification. All classes of algorithms, except Class BT, can be designed to reconstruct surfaces with boundaries.... ..."

### Table 1: Classification of reconstruction algorithms for surfaces with boundaries.

"... In PAGE 4: ... Changes in these stages include strengthening of the sampling condition in the sampling stage and providing additional information to the reconstruction stage. The Table1 enumerates the classification. All classes of algorithms, except Class a0 , can be designed to reconstruct surfaces with boundaries.... ..."

### TABLE II Self-Motion Surface Boundary Data

1997

Cited by 12

### Table 1: Surfaces created by drilling and end-milling features. Type of feature Portion of feature boundary Surface type

"... In PAGE 12: ... Each machining feature is capable of creating cer- tain types of surfaces. For example, Table1 presents the types of surfaces that can be created by drilling (shown in Fig.... ..."

### Table 1: Surfaces created by drilling and end-milling features. Type of feature Portion of feature boundary Surface type

"... In PAGE 12: ... Each machining feature is capable of creating cer- tain types of surfaces. For example, Table1 presents the types of surfaces that can be created by drilling (shown in Fig.... ..."

### Table 1: Look-up table for surface contruction in tetrahedra 4-bit index surface boundary

"... In PAGE 34: ... Edges along which z0?Z changes sign clearly must have a point at which it is zero, and which is therefore a corner of the surface z0 = Z. This index is therefore used as an entry into a lookup table which gives the logical structure of the surface z0 =Z, by listing the edges which it intersects; see Table1 in which 1=2 means the edge between nodes 1 and 2. Figure 6 shows the shape of the cut surfaces.... ..."

### Table II. Calculation of the traction-displacement integrals for all loaded boundary surfaces and traction- loaded crack surfaces.

### Table 3: Complexity boundary involving multiple machine chain scheduling problems and the

1989

"... In PAGE 7: ...Thus, Pmjchain;p j =1j P w j C j is strongly NP-complete. Table3 presents the known boundary involving multiple machine unit execution time chain scheduling problems and makespan, mean #0Dow time, and weighted mean #0Dow time objective func- tions. 3 Arbitrary Precedence Structured Tasks Wenow examine the complexity of several problems involving tree and prec precedence constraint topologies.... ..."