A round-for-reround mode (preferably in a BID encoded Decimal format) of a floating point instruction prepares a result for later rounding to a variable number of digits by detecting that the least significant digit may be a 0, and if so changing it to 1 when the trailing digits are not all 0. A subsequent reround instruction is then able to round the result to any number of digits at least 2 fewer than the number of digits of the result. An optional embodiment saves a tag indicating the fact that the low order digit of the result is 0 or 5 if the trailing bits are non-zero in a tag field rather than modify the result. Another optional embodiment also saves a half-way-and-above indicator when the trailing digits represent a decimal with a most significant digit having a value of 5. An optional subsequent reround instruction is able to round the result to any number of digits fewer or equal to the number of digits of the result using the saved tags.

A recommended order quantity determining device 80 includes a recommended order quantity determination unit 81. The recommended order quantity determination unit 81 determines a recommended order quantity of each commodity from a required quantity of the commodity expressed by a decimal, depending on an order unit of the commodity. The recommended order quantity determination unit 81 determines the recommended order quantity of each commodity, depending on a total required quantity of a commodity category including the commodity.

Setting or updating of floating point controls is managed. Floating point controls include controls used for floating point operations, such as rounding mode and/or other controls. Further, floating point controls include status associated with floating point operations, such as floating point exceptions and/or others. The management of the floating point controls includes efficiently updating the controls, while reducing costs associated therewith.

Setting or updating of floating point controls is managed. Floating point controls include controls used for floating point operations, such as rounding mode and/or other controls. Further, floating point controls include status associated with floating point operations, such as floating point exceptions and/or others. The management of the floating point controls includes efficiently updating the controls, while reducing costs associated therewith.

A machine learning tool uses dithered quantization of parameters during training of a machine learning model such as a neural network. The machine learning tool receives training data and initializes certain parameters of the machine learning model (e.g., weights for connections between nodes of a neural network, biases for nodes). The machine learning tool trains the parameters in one or more iterations based on the training data. In particular, in a given iteration, the machine learning tool applies the machine learning model to at least some of the training data and, based at least in part on the results, determines parameter updates to the parameters. The machine learning tool updates the parameters using the parameter updates and a dithered quantizer function, which can add random values before a rounding or truncation operation.

A round-for-reround mode (preferably in a BID encoded Decimal format) of a floating point instruction prepares a result for later rounding to a variable number of digits by detecting that the least significant digit may be a 0, and if so changing it to 1 when the trailing digits are not all 0. A subsequent reround instruction is then able to round the result to any number of digits at least 2 fewer than the number of digits of the result. An optional embodiment saves a tag indicating the fact that the low order digit of the result is 0 or 5 if the trailing bits are non-zero in a tag field rather than modify the result. Another optional embodiment also saves a half-way-and-above indicator when the trailing digits represent a decimal with a most significant digit having a value of 5. An optional subsequent reround instruction is able to round the result to any number of digits fewer or equal to the number of digits of the result using the saved tags.

A round-for-reround mode (preferably in a BID encoded Decimal format) of a floating point instruction prepares a result for later rounding to a variable number of digits by detecting that the least significant digit may be a 0, and if so changing it to 1 when the trailing digits are not all 0. A subsequent reround instruction is then able to round the result to any number of digits at least 2 fewer than the number of digits of the result. An optional embodiment saves a tag indicating the fact that the low order digit of the result is 0 or 5 if the trailing bits are non-zero in a tag field rather than modify the result. Another optional embodiment also saves a half-way-and-above indicator when the trailing digits represent a decimal with a most significant digit having a value of 5. An optional subsequent reround instruction is able to round the result to any number of digits fewer or equal to the number of digits of the result using the saved tags.

The information processing apparatus: generates PDL data by calculating, in a case where a drawing-target object within XPS format drawing data is a text-attribute character object that is drawn by using a font, a character advance width from font data; and performing rendering for the XPS format drawing data by using the calculated character advance width.

Apparatus for processing data includes processing circuitry 16, 18, 20, 22, 24, 26 and decoder circuitry 14 for decoding program instructions. The program instructions decoded include a floating point pre-conversion instruction which performs round-to-nearest ties to even rounding upon the mantissa field of an input floating number to generate an output floating point number with the same mantissa length but with the mantissa rounded to a position corresponding to a shorter mantissa field. The output mantissa field includes a suffix of zero values concatenated the rounded value. The decoder for circuitry 14 is also responsive to an integer pre-conversion instruction to quantise and input integer value using round-to-nearest ties to even rounding to form an output integer operand with a number of significant bits matched to the mantissa size of a floating point number to which the integer is later to be converted using an integer-to-floating point conversion instruction.

A round-for-reround mode (preferably in a BID encoded Decimal format) of a floating point instruction prepares a result for later rounding to a variable number of digits by detecting that the least significant digit may be a 0, and if so changing it to 1 when the trailing digits are not all 0. A subsequent reround instruction is then able to round the result to any number of digits at least 2 fewer than the number of digits of the result. An optional embodiment saves a tag indicating the fact that the low order digit of the result is 0 or 5 if the trailing bits are non-zero in a tag field rather than modify the result. Another optional embodiment also saves a half-way-and-above indicator when the trailing digits represent a decimal with a most significant digit having a value of 5. An optional subsequent reround instruction is able to round the result to any number of digits fewer or equal to the number of digits of the result using the saved tags.