ARM1156T2F-S™ Technical Reference Manual 23.12.10. FTOUI, FTOUIZ, FTOSI, and FTOSIZ

23.12.10. FTOUI, FTOUIZ, FTOSI, and FTOSIZ

Float-to-integer conversions generate Invalid Operation exceptions rather than Overflow or Underflow exceptions. To support signed conversions with round-towards-zero rounding in the maximum range possible for C, C++, and Java compiled code, the thresholds for pessimistic bouncing are different for the various rounding modes.

Table 23.12 and Table 23.13 use the following notation:

In the VFP Response column, the response notations are:

all: These input values are bounced for all rounding modes.
S: These input values are bounced for signed conversions in all rounding modes.
SnZ: These input values are bounced for signed conversions in all rounding modes except round-towards-zero.
U: These input values are bounced for unsigned conversions in all rounding modes.
UnZ: These input values are bounced for unsigned conversions in all rounding modes except round-towards-zero.

In the Unsigned results and Signed results columns, the rounding mode notations are:

N: Round-to-nearest mode.
P: Round-towards-plus-infinity mode.
M: Round-towards-minus infinity mode.
Z: Round-towards-zero mode.

Table 23.12 shows the single-precision float-to-integer bounce range and the results returned for exceptional conditions. The exponent values shown in Table 23.12 are in biased format.

Table 23.12. Single-precision float-to-integer bounce thresholds and stored results

Floating-point value	Integer value	Unsigned result	Status	Signed result	Status	VFP11 response
NaN	-	`0x00000000`	Invalid	`0x00000000`	Invalid	Bounce all
`0x7F800000`	+infinity	`0xFFFFFFFF`	Invalid	`0x7FFFFFFF`	Invalid	Bounce all
`0x7F7FFFFF` to 0x4F800000	+maximum SP^[1] to 2³²	`0xFFFFFFFF`	Invalid	`0x7FFFFFFF`	Invalid	Bounce all
`0x4F7FFFFF` to 0x`4F000000`	2³² - 2⁸ to 2³¹	`0xFFFFFF00` to `0x80000000`	Valid	`0x7FFFFFFF`	Invalid	Bounce S UnZ
`0x4EFFFFFF` to `0x4E800000`	2³¹ - 2⁷ to 2³⁰	`0x7FFFFF80` to `0x40000000`	Valid	`0x7FFFFF80` to `0x40000000`	Valid	Bounce SnZ
`0x4E7FFFFF` to `0x00000000`	2³⁰ - 2⁶ to +0	`0x3FFFFFC0` to `0x00000000`	Valid	`0x3FFFFFC0` to `0x00000000`	Valid	No bounce
`0x80000000` to `0xCE7FFFFF`	-0 to -2³⁰ + 2⁶	`0x00000000`	Invalid^[2]	`0x00000000` to `0xC0000040`	Valid	Bounce U
`0xCE800000` to `0xCEFFFFFF`	-2³⁰ to -2³¹ +2⁷	`0x00000000`	Invalid	`0xC0000000` to `0x80000080`	Valid	Bounce U
`0xCF000000`	-2³¹	`0x00000000`	Invalid	`0x80000000`	Valid	Bounce U SnZ
`0xCF000000` to `0xFF7FFFFF`	-2³¹ to -maximum SP	`0x00000000`	Invalid	`0x80000000`	Invalid	Bounce all
`0xFF800000`	-infinity	`0x00000000`	Invalid	`0x80000000`	Invalid	Bounce all
^[1]SP = single-precision. ^[2]A negative input value that rounds to a zero result returns zero and is not invalid.

Table 23.13 shows the double-precision float-to-integer bounce range and the results returned for exceptional conditions.

Table 23.13. Double-precision float-to-integer bounce thresholds and stored results

Floating-point value	Integer value	Unsigned result	Status	Signed result	Status	VFP11 response
NaN	-	`0x00000000`	Invalid	`0x00000000`	Invalid	Bounce all
`0x7FF00000 00000000`	+infinity	`0xFFFFFFFF`	Invalid	`0x7FFFFFFF`	Invalid	Bounce all
`0x7FEFFFFF FFFFFFFF` to `0x41F00000 00000000`	+max DP^[1] to 2³²	`0xFFFFFFFF`	Invalid	`0x7FFFFFFF`	Invalid	Bounce all
`0x41EFFFFF FFFFFFFF` to `0x41EFFFFF FFF00000`	2³² - 2²¹ to 2³² - 2^-1	`0xFFFFFFFF` N, P `0xFFFFFFFF` Z, M	Invalid Valid	`0x7FFFFFFF`	Invalid	Bounce S UnZ
`0x41EFFFFF FFEFFFFF` to `0x41EFFFFF FFE00001`	2³² - 2^-1 - 2²¹ to 2³² - 2⁰ + 2^-21	`0xFFFFFFFF` P `0xFFFFFFFF` N, Z, M	Invalid Valid	`0x7FFFFFFF`	Invalid	Bounce S UnZ
`0x41EFFFFF FFE00000` to `0x41E00000 00000000`	2³² - 2⁰ to 2³¹	`0xFFFFFFFF` to `0x80000000`	Valid	`0x7FFFFFFF`	Invalid	Bounce S UnZ
`0x41DFFFFF FFFFFFFF` to `0x41DFFFFF FFE00000`	2³¹ - 2²² to 2³¹ - 2^-1	`0x80000000` N, P `0x7FFFFFFF` Z, M	Valid Valid	`0x7FFFFFFF` N, P `0x7FFFFFFF` Z, M	Invalid Valid	Bounce SnZ
`0x41DFFFFF FFDFFFFF` to `0x41DFFFFF FFC00001`	2³¹ - 2^-1 - 2^-22 to 2³¹ - 2⁰ + 2^-22	`0x80000000` P `0x7FFFFFFF` N, Z, M	Valid Valid	`0x7FFFFFFF` P `0x7FFFFFFF` N,Z,M	Invalid Valid	Bounce SnZ
`0x41DFFFFF FFC00000` to `0x41D00000 00000000`	2³¹ - 2⁰ to 2³⁰	`0x7FFFFFFF` to `0x40000000`	Valid Valid	`0x7FFFFFFF` to `0x40000000`	Valid Valid	Bounce SnZ
`0x41CFFFFF FFFFFFFF` to `0x00000000 00000000`	2³⁰ - 2²³ to +0	`0x40000000` N, P `0x3FFFFFFF` Z, M to `0x00000000`	Valid Valid Valid	`0x40000000` N, P `0x3FFFFFFF` Z, M to `0x00000000`	Valid Valid Valid	Bounce none
`0x80000000 00000000` to `0xC1CFFFFF FFFFFFFF`	-0 to -2³⁰ + 2^-23	`0x00000000`^[2]	Invalid	`0x00000000` to `0xC0000001` Z, P `0xC0000000` N, M	Valid Valid Valid	Bounce U
`0xC1D00000 00000000` to `0xC1DFFFFF FFFFFFFF`	-2³⁰ to -2³¹ + 2^-22	`0x00000000`	Invalid	`0xC0000000` to `0x80000001` Z, P `0x80000000` N, M	Valid Valid Valid	Bounce U
`0xC1E00000 00000000`	-2³¹	`0x00000000`	Invalid	`0x80000000`	Valid	Bounce U SnZ
`0xC1E00000 00000001` to `0xC1E00000 00100000`	-2³¹ - 2^-21 to -2³¹ - 2^-1	`0x00000000`	Invalid	`0x80000000` N, Z, P `0x80000000` M	Valid Invalid	Bounce U SnZ
`0xC1E00000 00100001` to `0xC1E00000 001FFFFF`	-2³¹ - 2^-1 - 2^-21 to 2³¹ - 2⁰ + 2^-21	`0x00000000`	Invalid	`0x80000000` Z, P `0x80000000` N, M	Valid Invalid	Bounce U SnZ
`0xC1E00000 00200000` to `0xFFEFFFFF FFFFFFFF`	2³¹ - 2⁰ to -max DP ^[1]	`0x00000000`	Invalid	`0x80000000`	Invalid	Bounce all
`0xFFF00000 00000000`	-infinity	`0x00000000`	Invalid	`0x00000000`	Invalid	Bounce all
^[1]max DP = maximum double-precision. ^[2]A negative input value that rounds to a zero result returns zero and is not invalid.

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