This chapter is from the book
This chapter is from the book
This chapter is from the book
Explicit Conversions
In the preceding sections we learned that implicit conversions and explicit casts do not allow conversions between vector types. However, there are many cases where we need to convert a vector type to another type. In addition, it may be necessary to specify the rounding mode that should be used to perform the conversion and whether the results of the conversion are to be saturated. This is useful for both scalar and vector data types.
Consider the following example:
float x; int i = (int)x;
In this example the value in x is truncated to an integer value and stored in i; that is, the cast performs round-toward-zero rounding when converting the floating-point value to an integer value.
Sometimes we need to round the floating-point value to the nearest integer. The following example shows how this is typically done:
float x; int i = (int)(x + 0.5f);
This works correctly for most values of x except when x is 0.5f – 1 ulp 5 or if x is a negative number. When x is 0.5f – 1 ulp, (int)(x + 0.5f) returns 1; that is, it rounds up instead of rounding down. When x is a negative number, (int)(x + 0.5f) rounds down instead of rounding up.
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <float.h>
int
main(void)
{
float a = 0.5f;
float b = a – nextafterf(a, (float)-INFINITY); // a – 1 ulp
printf("a = %8x, b = %8x\n",
*(unsigned int *)&a, *(unsigned int *)&b);
printf("(int)(a + 0.5f) = %d \n", (int)(a + 0.5f));
printf("(int)(b + 0.5f) = %d \n", (int)(b + 0.5f));
}
The printed values are:
a = 3f000000, b = 3effffff // where b = a – 1 ulp.
(int)(a + 0.5f) = 1,
(int)(b + 0.5f) = 1
We could fix these issues by adding appropriate checks to see what value x is and then perform the correct conversion, but there is hardware to do these conversions with rounding and saturation on most devices. It is important from a performance perspective that OpenCL C allows developers to perform these conversions using the appropriate hardware ISA as opposed to emulating in software. This is why OpenCL implements builtin functions that perform conversions from one type to another with options that select saturation and one of four rounding modes.
Explicit conversions may be performed using either of the following:
destType convert_destType<_sat><_roundingMode> (sourceType) destType convert_destTypen <_sat><_roundingMode> (sourceTypen)
These provide a full set of type conversions for the following scalar types: char, uchar, short, ushort, int, uint, long, ulong, float, double,6half,7 and the built-in vector types derived therefrom. The operand and result type must have the same number of elements. The operand and result type may be the same type, in which case the conversion has no effect on the type or value.
In the following example, convert_int4 converts a uchar4 vector u to an int4 vector c:
uchar4 u; int4 c = convert_int4(u);
In the next example, convert_int converts a float scalar f to an int scalar i:
float f; int i = convert_int(f);
The optional rounding mode modifier can be set to one of the values described in Table 4.7.
Table 4.7. Rounding Modes for Conversions
|
Rounding Mode Modifier |
Rounding Mode Description |
|
_rte |
Round to nearest even. |
|
_rtz |
Round toward zero. |
|
_rtp |
Round toward positive infinity. |
|
_rtn |
Round toward negative infinity. |
|
No modifier specified |
Use the default rounding mode for this destination type: _rtz for conversion to integers or _rte for conversion to floating-point types. |
The optional saturation modifier (_sat) can be used to specify that the results of the conversion must be saturated to the result type. When the conversion operand is either greater than the greatest representable destination value or less than the least representable destination value, it is said to be out of range. When converting between integer types, the resulting value for out-of-range inputs will be equal to the set of least significant bits in the source operand element that fits in the corresponding destination element. When converting from a floating-point type to an integer type, the behavior is implementation-defined.
Conversions to integer type may opt to convert using the optional saturated mode by appending the _sat modifier to the conversion function name. When in saturated mode, values that are outside the representable range clamp to the nearest representable value in the destination format. (NaN should be converted to 0.)
Conversions to a floating-point type conform to IEEE 754 rounding rules. The _sat modifier may not be used for conversions to floating-point formats.
Following are a few examples of using explicit conversion functions.
The next example shows a conversion of a float4 to a ushort4 with round-to-nearest rounding mode and saturation. Figure 4.2 describes the values in f and the result of conversion in c.
float4 f = (float4)(-5.0f, 254.5f, 254.6f, 1.2e9f); ushort4 c = convert_uchar4_sat_rte(f);
)
Figure 4.2 Converting a float4 to a ushort4 with round-to-nearest rounding and saturation
The next example describes the behavior of the saturation modifier when converting a signed value to an unsigned value or performing a down-conversion with integer types:
short4 s; // negative values clamped to 0 ushort4 u = convert_ushort4_sat(s); // values > CHAR_MAX converted to CHAR_MAX // values < CHAR_MIN converted to CHAR_MIN char4 c = convert_char4_sat(s);
The following example illustrates conversion from a floating-point to an integer with saturation and rounding mode modifiers:
float4 f; // values implementation-defined for f > INT_MAX, f < INT_MAX, or NaN int4 i = convert_int4(f); // values > INT_MAX clamp to INT_MAX, // values < INT_MIN clamp to INT_MIN // NaN should produce 0. // The _rtz rounding mode is used to produce the integer values. int4 i2 = convert_int4_sat(f); // similar to convert_int4 except that floating-point values // are rounded to the nearest integer instead of truncated int4 i3 = convert_int4_rte(f); // similar to convert_int4_sat except that floating-point values // are rounded to the nearest integer instead of truncated int4 i4 = convert_int4_sat_rte(f);
The final conversion example given here shows conversions from an integer to a floating-point value with and without the optional rounding mode modifier:
int4 i; // convert ints to floats using the round-to-nearest rounding mode float4 f = convert_float4(i); // convert ints to floats; integer values that cannot be // exactly represented as floats should round up to the next // representable float float4 f = convert_float4_rtp(i);