From 27535dc833ab1a8d098e1ad1adfcac98d0c57fad Mon Sep 17 00:00:00 2001 From: Bill Schmidt Date: Tue, 28 Apr 2020 17:22:29 -0500 Subject: [PATCH] Rewrite section 2.4 for #8. 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b79099a..7b0b1ab 100644 --- a/Intrinsics_Reference/ch_biendian.xml +++ b/Intrinsics_Reference/ch_biendian.xml @@ -552,32 +552,113 @@ a[3] = c; Vector data types consist of a homogeneous sequence of elements of the base data type specified in the vector data type. Individual elements of a vector can be addressed by a - vector element number. Element numbers can be established either - by counting from the “left” of a register and assigning the - left-most element the element number 0, or from the “right” of - the register and assigning the right-most element the element - number 0. + vector element number. To understand how vector elements are + represented in memory and in registers, it is best to start with + some simple concepts of endianness. + +
+ Scalar Quantities and Endianness + + + + + +
+ + shows different representations + of a 64-bit scalar integer with the hexadecimal value + 0x0123456789ABCDEF. We say that the most + significant byte (MSB) of this value is 0x01, and + its least significant byte (LSB) is 0xEF. The scalar + value is stored using eight bytes of memory. On a little-endian + (LE) system, the LSB is stored at the lowest address of these + eight bytes, and the MSB is stored at the highest address. On a + big-endian (BE) system, the MSB is stored at the lowest address + of these eight bytes, and the LSB is stored at the highest + address. Regardless of the memory order, the register + representation of the scalar value is identical; the MSB is + located on the "left" end of the register, and the LSB is + located on the "right" end. + + + Of course, the concept of "left" and "right" is a useful + fiction; there is no guarantee that the circuitry of a hardware + register is laid out this way. However, we will see, as we deal + with vector elements, that the concepts of left and right are + more natural for human understanding than byte and element + significance. Indeed, most programming languages have + instructions, such as shift-left and shift-right, that use this + same terminology. - In big-endian environments, establishing element counts from the - left makes the element stored at the lowest memory address the - lowest-numbered element. Thus, when vectors and arrays of a - given base data type are overlaid, vector element 0 corresponds - to array element 0, vector element 1 corresponds to array - element 1, and so forth. + Let's move from scalars to arrays, which are more interesting to + us since we can map arrays into vector registers. Suppose we + have an array of bytes with values 0 through 15, as shown in + . Note that each byte is a + separate data element with only one possible representation in + memory, so the array of bytes looks identical in memory, + regardless of whether we are using a BE system or an LE system. + But when we load these 16 bytes into a vector register, perhaps + by using the ISA 3.0 lxv + instruction, the byte at the lowest address on an LE system will + be placed in the LSB of the vector register, but on a BE system + will be placed in the MSB of the vector register. Thus the + array elements appear "right to left" in the register on an LE + system, and "left to right" in the register on a BE system. +
+ Byte Arrays and Endianness + + + + + +
- In little-endian environments, establishing element counts from - the right makes the element stored at the lowest memory address - the lowest-numbered element. Thus, when vectors and arrays of a - given base data type are overlaid, vector element 0 will - correspond to array element 0, vector element 1 will correspond - to array element 1, and so forth. + Things become even more interesting when we consider arrays of + larger elements. In , we + see the layout of an array of four 32-bit integers, where the 0th + element has hexadecimal value 0x00010203, the 1st + element has value 0x04050607, the 2nd element has + value 0x08090A0B, and the 3rd element has value + 0x0C0D0E0F. The order of the array elements in + memory is the same for both LE and BE systems; but the layout of + each element itself is reversed. When the lxv instruction is used to load the + memory into a vector register, again the low address is loaded + into the LSB of the register for LE, but loaded into the MSB of + the register for BE. The effect is that the array elements + again appear right-to-left on a LE system and left-to-right on a + BE system. Note that each 32-bit element of the array has its + most significant bit "on the left" whether a LE or BE system is + in use. This is of course necessary for proper arithmetic to be + performed on the array elements by vector instructions. +
+ Word Arrays and Endianness + + + + + +
+ + - Consequently, the vector numbering schemes can be described as - big-endian and little-endian vector layouts and vector element - numberings. + Thus on a BE system, we number vector elements starting with 0 + on the left, while on an LE system, we number vector elements + starting with 0 on the right. We will informally refer to these + as big-endian and little-endian vector element numberings and + vector layouts. This element numbering shall also be used by the [] @@ -619,11 +700,13 @@ a[3] = c; This is no longer as useful as it once was. The primary use case was for big-endian vector layout in little-endian environments, which is now deprecated as discussed in . + linkend="VIPR.biendian.BELE" />. It's generally equivalent to + test for __BIG_ENDIAN__ or + __LITTLE_ENDIAN__. - Note that each element in a vector has the same representation + Remember that each element in a vector has the same representation in both big- and little-endian element orders. That is, an int is always 32 bits, with the sign bit in the high-order position. Programmers must be aware of this when