CUDA vs OpenCL math builtin precision

CUDA Guarantees

From Appendix E.1 of the CUDA C Programming Guide:

This section specifies the error bounds of each function when executed on the device and also when executed on the host in the case where the host does not supply the function.

The error bounds are generated from extensive but not exhaustive tests, so they are not guaranteed bounds.

In Section 11.1.5 of the CUDA C Best Practices Guide on Math Libraries and Section 11.1.6 of the CUDA C Best Practices Guide on Precision-related Compiler Flags, there are mentions of the precision of math built-ins.

Single Precision

The following table uses the following sources:

• Section 7.4 of the OpenCL 1.2 Specification

• Appendix E.1 of the CUDA C Programming Guide which is referenced from the CUDA Math API documentation

In addition to the following table, the CUDA documentation also includes:

Addition and multiplication are IEEE-compliant, so have a maximum error of 0.5 ulp.

The recommended way to round a single-precision floating-point operand to an integer, with the result being a single-precision floating-point number is rintf(), not roundf(). The reason is that roundf() maps to an 8-instruction sequence on the device, whereas rintf() maps to a single instruction. truncf(), ceilf(), and floorf() each map to a single instruction as well.

OpenCL defines ULP (units in last place) as:

If x is a real number that lies between two finite consecutive floating-point numbers a and b, without being equal to one of them, then ulp(x) = |b − a|, otherwise ulp(x) is the distance between the two non-equal finite floating-point numbers nearest x. Moreover, ulp(NaN) is NaN.

Maximum error is defined in the CUDA documentation as:

The maximum error is stated as the absolute value of the difference in ulps between a correctly rounded single-precision result and the result returned by the CUDA library function.

OpenCL Built-in	OpenCL Min Accuracy (ULP)	CUDA Built-in	CUDA Maximum Error (ULP)
x + y	Correctly rounded	x + y	0 ulp (IEEE-754 round-to-nearest-even)
x - y	Correctly rounded	N/A	N/A
x * y	Correctly rounded	x * y	0 ulp (IEEE-754 round-to-nearest-even)
1.0 / x	≤ 2.5 ulp	1.0 / x	0 ulp (if compute capability ≥ 2 when compiled with -prec-div=true), 1 ulp (full range) otherwise
x / y	≤ 2.5 ulp	x / y	0 ulp (if compute capability ≥ 2 when compiled with -prec-div=true), 2 ulp (full range) otherwise
acos	≤ 4 ulp	acosf	3 ulp (full range)
acospi	≤ 5 ulp	N/A	N/A
asin	≤ 4 ulp	asinf	4 ulp (full range)
asinpi	≤ 5 ulp	N/A	N/A
atan	≤ 5 ulp	atanf	2 ulp (full range)
atan2	≤ 6 ulp	atan2f	3 ulp (full range)
atanpi	≤ 5 ulp	N/A	N/A
atan2pi	≤ 6 ulp	N/A	N/A
acosh	≤ 4 ulp	acoshf	4 ulp (full range)
asinh	≤ 4 ulp	asinhf	3 ulp (full range)
atanh	≤ 5 ulp	atanhf	3 ulp (full range)
cbrt	≤ 2 ulp	cbrtf	1 ulp (full range)
ceil	Correctly rounded	ceilf	0 ulp (full range)
copysign	0 ulp	copysignf	Undocumented.
cos	≤ 4 ulp	cosf	2 ulp (full range)
cosh	≤ 4 ulp	coshf	2 ulp (full range)
cospi	≤ 4 ulp	cospi	2 ulp (full range)
N/A	N/A	cyl_bessel_i0f	6 ulp (full range)
N/A	N/A	cyl_bessel_i1f	6 ulp (full range)
erfc	≤ 16 ulp	erfcf	4 ulp (full range)
N/A	N/A	erfcinvf	2 ulp (full range)
N/A	N/A	erfcxf	4 ulp (full range)
N/A	N/A	erfinvf	2 ulp (full range)
erf	≤ 16 ulp	erff	2 ulp (full range)
exp	≤ 3 ulp	expf	2 ulp (full range)
exp2	≤ 3 ulp	exp2f	2 ulp (full range)
exp10	≤ 3 ulp	exp10f	2 ulp (full range)
expm1	≤ 3 ulp	expm1f	1 ulp (full range)
fabs	0 ulp	fabsf	Undocumented.
fdim	Correctly rounded	fdimf	0 ulp (full range)
floor	Correctly rounded	floorf	0 ulp (full range)
fma	Correctly rounded	fmaf	0 ulp (full range)
fmax	0 ulp	fmaxf	Undocumented.
fmin	0 ulp	fminf	Undocumented.
fmod	0 ulp	fmodf	0 ulp (full range)
fract	Correctly rounded	N/A	N/A
frexp	0 ulp	frexpf	0 ulp (full range)
hypot	≤ 4 ulp	hypotf	3 ulp (full range)
ilogb	0 ulp	ilogbf	0 ulp (full range)
N/A	N/A	j0f	9 ulp for abs(x) < 8, otherwise 2.2 x 10^(-6)
N/A	N/A	j1f	9 ulp for abs(x) < 8, otherwise 2.2 x 10^(-6)
N/A	N/A	jnf	For n = 128, 2.2 x 10^(-6)
ldexp	Correctly rounded	ldexpf	0 ulp (full range)
N/A	N/A	lgammaf	6 ulp (outside interval -10.001 ... -2.264; larger inside)
log	≤ 3 ulp	logf	1 ulp (full range)
log2	≤ 3 ulp	log2f	1 ulp (full range)
log10	≤ 3 ulp	log10f	2 ulp (full range)
log1p	≤ 2 ulp	log1pf	1 ulp (full range)
logb	0 ulp	logbf	0 ulp (full range)
N/A	N/A	lrintf	0 ulp (full range)
N/A	N/A	lroundf	0 ulp (full range)
N/A	N/A	llrintf	0 ulp (full range)
N/A	N/A	llroundf	0 ulp (full range)
mad	Any value allowed (infinite ulp)	N/A	N/A
maxmag	0 ulp	N/A	N/A
minmag	0 ulp	N/A	N/A
modf	0 ulp	modff	0 ulp (full range)
nan	0 ulp	nanf	Undocumented.
N/A	N/A	nearbyintf	0 ulp (full range)
nextafter	0 ulp	nextafterf	Undocumented.
N/A	N/A	normf	4 ulp (full range)
N/A	N/A	normcdff	5 ulp (full range)
N/A	N/A	normcdfinvf	5 ulp (full range)
N/A	N/A	norm3df	3 ulp (full range)
N/A	N/A	norm4df	3 ulp (full range)
pow(x, y)	≤ 16 ulp	powf	8 ulp (full range)
pown(x, y)	≤ 16 ulp	N/A	N/A
powr(x, y)	≤ 16 ulp	N/A	N/A
N/A	N/A	rcbrtf	1 ulp (full range)
N/A	N/A	rhypot	2 ulp (full range)
N/A	N/A	rnormf	3 ulp (full range)
N/A	N/A	rnorm3df	2 ulp (full range)
N/A	N/A	rnorm4df	2 ulp (full range)
remainder	0 ulp	remainderf	0 ulp (full range)
remquo	0 ulp	remquof	0 ulp (full range)
rint	Correctly rounded	rintf	0 ulp (full range)
rootn	≤ 16 ulp	N/A	N/A
round	Correctly rounded	roundf	0 ulp (full range)
rsqrt	≤ 2 ulp	rsqrtf	2 ulp (full range) (applies to 1 / sqrtf(x) only when converted to rsqrtf by compiler)
N/A	N/A	scalbnf	0 ulp (full range)
N/A	N/A	scalblnf	0 ulp (full range)
sin	≤ 4 ulp	sinf	2 ulp (full range)
sincos	≤ 4 ulp for sine and cosine values	sincosf	2 ulp (full range)
N/A	N/A	sincospif	2 ulp (full range)
sinh	≤ 4 ulp	sinhf	3 ulp (full range)
sinpi	≤ 4 ulp	sinpif	2 ulp (full range)
sqrt	≤ 3 ulp	sqrtf	0 ulp (when compiled with -prec-sqrt=true) otherwise 1 ulp if compute capability ≥ 5.2 and 3 ulp otherwise.
tan	≤ 5 ulp	tanf	4 ulp (full range)
tanh	≤ 5 ulp	tanhf	2 ulp (full range)
tanpi	≤ 6 ulp	N/A	N/A
tgamma	≤ 16 ulp	tgammaf	11 ulp (full range)
trunc	Correctly rounded	truncf	0 ulp (full range)
N/A	N/A	y0f	9 ulp for abs(x) < 8, otherwise 2.2 x 10^(-6)
N/A	N/A	y1f	9 ulp for abs(x) < 8, otherwise 2.2 x 10^(-6)
N/A	N/A	ynf	ceil(2 + 2.5n) for abs(x) < n, otherwise 2.2 x 10^(-6)
N/A	N/A	isfinite	N/A
N/A	N/A	isinf	N/A
N/A	N/A	isnan	N/A
N/A	N/A	signbit	N/A

OpenCL’s native_ math built-ins map to the same CUDA built-in as the equivalent non-native_ OpenCL built-in and the precision is implementation-defined:

• native_cos

• native_divide

• native_exp

• native_exp2

• native_exp10

• native_log

• native_log2

• native_log10

• native_powr

• native_recip

• native_rsqrt

• native_sin

• native_sqrt

• native_tan

In section 7.4 of the OpenCL 2.1 Specification, mad has a different requirement, namely:

Implemented either as a correctly rounded fma or as a multiply followed by an add both of which are correctly rounded.

Precision of SPIR-V math instructions for use in an OpenCL environment, can be found in this document.

Double Precision

The following table uses the following sources:

• Section 7.4 of the OpenCL 1.2 Specification

• Appendix E.1 of the CUDA C Programming Guide which is referenced from the CUDA Math API documentation

CUDA defines maximum error in the same way as for single precision, and also includes:

The recommended way to round a double-precision floating-point operand to an integer, with the result being a double-precision floating-point number is rint(), not round(). The reason is that round() maps to an 8-instruction sequence on the device, whereas rint() maps to a single instruction. trunc(), ceil(), and floor() each map to a single instruction as well.

Only differences from single precision are included. There are only changes to 1.0 / x, x / y and sqrt from OpenCL. All built-in names changed for CUDA and many precisions too.

OpenCL Built-in	OpenCL Min Accuracy (ULP)	CUDA Built-in	CUDA Maximum Error (ULP)
x + y	Correctly rounded	x + y	0 ulp (IEEE-754 round-to-nearest-even)
x - y	Correctly rounded	N/A	N/A
x * y	Correctly rounded	x * y	0 ulp (IEEE-754 round-to-nearest-even)
1.0 / x	Correctly rounded	1.0 / x	0 ulp (IEEE-754 round-to-nearest-even
x / y	Correctly rounded	x / y	0 ulp (IEEE-754 round-to-nearest-even)
acos	≤ 4 ulp	acos	1 ulp (full range)
acospi	≤ 5 ulp	N/A	N/A
asin	≤ 4 ulp	asin	2 ulp (full range)
asinpi	≤ 5 ulp	N/A	N/A
atan	≤ 5 ulp	atan	2 ulp (full range)
atan2	≤ 6 ulp	atan2	2 ulp (full range)
atanpi	≤ 5 ulp	N/A	N/A
atan2pi	≤ 6 ulp	N/A	N/A
acosh	≤ 4 ulp	acosh	2 ulp (full range)
asinh	≤ 4 ulp	asinh	2 ulp (full range)
atanh	≤ 5 ulp	atanh	2 ulp (full range)
cbrt	≤ 2 ulp	cbrt	1 ulp (full range)
ceil	Correctly rounded	ceil	0 ulp (full range)
copysign	0 ulp	copysign	Undocumented.
cos	≤ 4 ulp	cos	1 ulp (full range)
cosh	≤ 4 ulp	cosh	1 ulp (full range)
cospi	≤ 4 ulp	cospi	1 ulp (full range)
N/A	N/A	cyl_bessel_i0	6 ulp (full range)
N/A	N/A	cyl_bessel_i1	6 ulp (full range)
erfc	≤ 16 ulp	erfc	4 ulp (full range)
N/A	N/A	erfcinv	6 ulp (full range)
N/A	N/A	erfcx	3 ulp (full range)
N/A	N/A	erfinv	5 ulp (full range)
erf	≤ 16 ulp	erf	2 ulp (full range)
exp	≤ 3 ulp	exp	1 ulp (full range)
exp2	≤ 3 ulp	exp2	1 ulp (full range)
exp10	≤ 3 ulp	exp10	1 ulp (full range)
expm1	≤ 3 ulp	expm1	1 ulp (full range)
fabs	0 ulp	fabs	Undocumented.
fdim	Correctly rounded	fdim	0 ulp (full range)
floor	Correctly rounded	floor	0 ulp (full range)
fma	Correctly rounded	fma	0 ulp (IEEE-754 round-to-nearest-even)
fmax	0 ulp	fmax	Undocumented.
fmin	0 ulp	fmin	Undocumented.
fmod	0 ulp	fmod	0 ulp (full range)
fract	Correctly rounded	N/A	N/A
frexp	0 ulp	frexp	0 ulp (full range)
hypot	≤ 4 ulp	hypot	2 ulp (full range)
ilogb	0 ulp	ilogb	0 ulp (full range)
N/A	N/A	j0	7 ulp for abs(x) < 8, otherwise 5 x 10^(-12)
N/A	N/A	j1	7 ulp for abs(x) < 8, otherwise 5 x 10^(-12)
N/A	N/A	jn	For n = 128, 5 x 10^(-12)
ldexp	Correctly rounded	ldexp	0 ulp (full range)
N/A	N/A	lgamma	4 ulp (outside interval -11.0001 ... -2.2637; larger inside)
log	≤ 3 ulp	log	1 ulp (full range)
log2	≤ 3 ulp	log2	1 ulp (full range)
log10	≤ 3 ulp	log10	1 ulp (full range)
log1p	≤ 2 ulp	log1p	1 ulp (full range)
logb	0 ulp	logb	0 ulp (full range)
N/A	N/A	lrint	0 ulp (full range)
N/A	N/A	lround	0 ulp (full range)
N/A	N/A	llrint	0 ulp (full range)
N/A	N/A	llround	0 ulp (full range)
mad	Any value allowed (infinite ulp)	N/A	N/A
maxmag	0 ulp	N/A	N/A
minmag	0 ulp	N/A	N/A
modf	0 ulp	mod (might be called modf, the documentation is inconsistent)	0 ulp (full range)
nan	0 ulp	nan	Undocumented.
N/A	N/A	nearbyint	0 ulp (full range)
nextafter	0 ulp	nextafter	Undocumented.
N/A	N/A	norm	3 ulp (full range)
N/A	N/A	normcdf	5 ulp (full range)
N/A	N/A	normcdfinv	7 ulp (full range)
N/A	N/A	norm3d	2 ulp (full range)
N/A	N/A	norm4d	2 ulp (full range)
pow(x, y)	≤ 16 ulp	pow	2 ulp (full range)
pown(x, y)	≤ 16 ulp	N/A	N/A
powr(x, y)	≤ 16 ulp	N/A	N/A
N/A	N/A	rcbrt	1 ulp (full range)
N/A	N/A	rhypot	1 ulp (full range)
N/A	N/A	rnorm	2 ulp (full range)
N/A	N/A	rnorm3d	1 ulp (full range)
N/A	N/A	rnorm4d	1 ulp (full range)
remainder	0 ulp	remainder	0 ulp (full range)
remquo	0 ulp	remquo	0 ulp (full range)
rint	Correctly rounded	rint	0 ulp (full range)
rootn	≤ 16 ulp	N/A	N/A
round	Correctly rounded	round	0 ulp (full range)
rsqrt	≤ 2 ulp	rsqrt	1 ulp (full range)
N/A	N/A	scalbn	0 ulp (full range)
N/A	N/A	scalbln	0 ulp (full range)
sin	≤ 4 ulp	sin	1 ulp (full range)
sincos	≤ 4 ulp for sine and cosine values	sincos	1 ulp (full range)
N/A	N/A	sincospi	1 ulp (full range)
sinh	≤ 4 ulp	sinh	1 ulp (full range)
sinpi	≤ 4 ulp	sinpi	1 ulp (full range)
sqrt	Correctly rounded	sqrt	0 ulp (IEEE-754 round-to-nearest-even)
tan	≤ 5 ulp	tan	2 ulp (full range)
tanh	≤ 5 ulp	tanh	1 ulp (full range)
tanpi	≤ 6 ulp	N/A	N/A
tgamma	≤ 16 ulp	tgamma	8 ulp (full range)
trunc	Correctly rounded	trunc	0 ulp (full range)
N/A	N/A	y0	7 ulp for abs(x) < 8, otherwise 5 x 10^(-12)
N/A	N/A	y1	7 ulp for abs(x) < 8, otherwise 5 x 10^(-12)
N/A	N/A	yn	For abs(x) > 1.5n, otherwise 5 x 10^(-12)
N/A	N/A	isfinite	N/A
N/A	N/A	isinf	N/A
N/A	N/A	isnan	N/A
N/A	N/A	signbit	N/A

Half Precision

The following tables uses the following sources:

• Section 7.4 of the OpenCL 1.2 Specification

• CUDA Math API documentation

CUDA doesn’t specify the ULP values for any of its half precision math builtins:

OpenCL Built-in	OpenCL Min Accuracy (ULP)	CUDA Built-in	CUDA Maximum Error (ULP)
N/A	N/A	_hadd	Undocumented (only specifies “round-to-nearest-even mode”)
N/A	N/A	_hadd_sat	Undocumented (only specifies “round-to-nearest-even mode”)
N/A	N/A	hceil	Undocumented
half_cos	≤ 8192 ulp	hcos	Undocumented (only specifies “round-to-nearest-even mode”)
half_divide	≤ 8192 ulp	_hdiv	Undocumented (only specifies “round-to-nearest mode”)
N/A	N/A	_heq	Undocumented
N/A	N/A	_hequ	Undocumented
half_exp	≤ 8192 ulp	hexp	Undocumented (only specifies “round-to-nearest-even mode”)
half_exp2	≤ 8192 ulp	hexp2	Undocumented (only specifies “round-to-nearest-even mode”)
half_exp10	≤ 8192 ulp	hexp10	Undocumented (only specifies “round-to-nearest-even mode”)
N/A	N/A	hfloor	Undocumented
N/A	N/A	_hfma	Undocumented (only specifies “round-to-nearest-even mode”)
N/A	N/A	_hfma_sat	Undocumented (only specifies “round-to-nearest-even mode”)
N/A	N/A	_hge	Undocumented
N/A	N/A	_hgeu	Undocumented
N/A	N/A	_hgt	Undocumented
N/A	N/A	_hgtu	Undocumented
N/A	N/A	_hisinf	Undocumented
N/A	N/A	_hisnan	Undocumented
N/A	N/A	_hle	Undocumented
N/A	N/A	_hleu	Undocumented
half_log	≤ 8192 ulp	hlog	Undocumented (only specifies “round-to-nearest-even mode”)
half_log2	≤ 8192 ulp	hlog2	Undocumented (only specifies “round-to-nearest-even mode”)
half_log10	≤ 8192 ulp	hlog10	Undocumented (only specifies “round-to-nearest-even mode”)
N/A	N/A	_hlt	Undocumented
N/A	N/A	_hltu	Undocumented
N/A	N/A	_hmul	Undocumented (only specifies “round-to-nearest mode”)
N/A	N/A	_hmul_sat	Undocumented (only specifies “round-to-nearest mode”)
N/A	N/A	_hneg	Undocumented
N/A	N/A	_hne	Undocumented
N/A	N/A	_hneu	Undocumented
half_powr	≤ 8192 ulp	N/A	N/A
half_recip	≤ 8192 ulp	hrcp	Undocumented (only specifies “round-to-nearest-even mode”)
N/A	N/A	hrint	Undocumented (only specifies “halfway cases rounded to nearest even integer value”)
half_rsqrt	≤ 8192 ulp	hrqsrt	Undocumented (only specifies “round-to-nearest mode”)
half_sin	≤ 8192 ulp	hsin	Undocumented (only specifies “round-to-nearest-even mode”)
half_sqrt	≤ 8192 ulp	hsqrt	Undocumented (only specifies “round-to-nearest-even mode”)
N/A	N/A	_hsub	Undocumented (only specifies “round-to-nearest mode”)
N/A	N/A	_hsub_sat	Undocumented (only specifies “round-to-nearest mode”)
half_tan	≤ 8192 ulp	N/A	N/A
N/A	N/A	htrunc	Undocumented

CUDA also defines math builtins that operate on a half2 type to which there is no OpenCL parallel:

CUDA Built-in	CUDA Maximum Error (ULP)
_h2div	Undocumented (only specifies “round-to-nearest mode”)
_hadd2_sat	Undocumented (only specifies “round-to-nearest-even mode”)
_hadd2	Undocumented (only specifies “round-to-nearest-even mode”)
_hbeg2	Undocumented
_hbegu2	Undocumented
_hbge2	Undocumented
_hbgeu2	Undocumented
_hbgt2	Undocumented
_hbgtu2	Undocumented
_hble2	Undocumented
_hbleu2	Undocumented
_hblt2	Undocumented
_hbltu2	Undocumented
_hbne2	Undocumented
_hbneu2	Undocumented
_heq2	Undocumented
_hequ2	Undocumented
_hfma2_sat	Undocumented (only specifies “round-to-nearest-even mode”)
_hfma2	Undocumented (only specifies “round-to-nearest-even mode”)
_hge2	Undocumented
_hgeu2	Undocumented
_hgt2	Undocumented
_hgtu2	Undocumented
_hisnan2	Undocumented
_hle2	Undocumented
_hleu2	Undocumented
_hlt2	Undocumented
_hltu2	Undocumented
_hmul2_sat	Undocumented (only specifies “round-to-nearest-even mode”)
_hmul2	Undocumented (only specifies “round-to-nearest-even mode”)
_hne2	Undocumented
_hneg2	Undocumented
_hneu2	Undocumented
_hsub2_sat	Undocumented (only specifies “round-to-nearest-even mode”)
_hsub2	Undocumented (only specifies “round-to-nearest-even mode”)
h2ceil	Undocumented
h2cos	Undocumented (only specifies “round-to-nearest-even mode”)
h2exp10	Undocumented (only specifies “round-to-nearest-even mode”)
h2exp2	Undocumented (only specifies “round-to-nearest-even mode”)
h2exp	Undocumented (only specifies “round-to-nearest mode”)
h2floor	Undocumented
h2log10	Undocumented (only specifies “round-to-nearest-even mode”)
h2log2	Undocumented (only specifies “round-to-nearest-even mode”)
h2log	Undocumented (only specifies “round-to-nearest-even mode”)
h2rcp	Undocumented (only specifies “round-to-nearest-even mode”)
h2rint	Undocumented (only specifies “halfway cases rounded to nearest even integer value”)
h2rsqrt	Undocumented (only specifies “round-to-nearest-even mode”)
h2trunc	Undocumented

Further, CUDA defines conversion and data movement functions:

CUDA Built-in	CUDA Maximum Error (ULP)
__float22half2_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__float2half2_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__float2half_rd	Undocumented (only specifies “round-down mode”)
__float2half_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__float2half_ru	Undocumented (only specifies “round-up mode”)
__float2half_rz	Undocumented (only specifies “round-towards-zero mode”)
__float2half	Undocumented (only specifies “round-to-nearest-even mode”)
__floats2half2_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__half22float2	Undocumented
__half2float	Undocumented
__half2half2	Undocumented
__half2int_rd	Undocumented (only specifies “round-down mode”)
__half2int_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__half2int_ru	Undocumented (only specifies “round-up mode”)
__half2int_rz	Undocumented (only specifies “round-towards-zero mode”)
__half2ll_rd	Undocumented (only specifies “round-down mode”)
__half2ll_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__half2ll_ru	Undocumented (only specifies “round-up mode”)
__half2ll_rz	Undocumented (only specifies “round-towards-zero mode”)
__half2short_rd	Undocumented (only specifies “round-down mode”)
__half2short_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__half2short_ru	Undocumented (only specifies “round-up mode”)
__half2short_rz	Undocumented (only specifies “round-towards-zero mode”)
__half2uint_rd	Undocumented (only specifies “round-down mode”)
__half2uint_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__half2uint_ru	Undocumented (only specifies “round-up mode”)
__half2uint_rz	Undocumented (only specifies “round-towards-zero mode”)
__half2ull_rd	Undocumented (only specifies “round-down mode”)
__half2ull_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__half2ull_ru	Undocumented (only specifies “round-up mode”)
__half2ull_rz	Undocumented (only specifies “round-towards-zero mode”)
__half2ushort_rd	Undocumented (only specifies “round-down mode”)
__half2ushort_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__half2ushort_ru	Undocumented (only specifies “round-up mode”)
__half2ushort_rz	Undocumented (only specifies “round-towards-zero mode”)
__half_as_short	Undocumented
__half_as_ushort	Undocumented
__halves2half2	Undocumented
__high2float	Undocumented
__high2half2	Undocumented
__high2half	Undocumented
__highs2half2	Undocumented
__int2half_rd	Undocumented (only specifies “round-down mode”)
__int2half_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__int2half_ru	Undocumented (only specifies “round-up mode”)
__int2half_rz	Undocumented (only specifies “round-towards-zero mode”)
__ll2half_rd	Undocumented (only specifies “round-down mode”)
__ll2half_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__ll2half_ru	Undocumented (only specifies “round-up mode”)
__ll2half_rz	Undocumented (only specifies “round-towards-zero mode”)
__low2float	Undocumented
__low2half2	Undocumented
__low2half	Undocumented
__lowhigh2highlow	Undocumented
__lows2half2	Undocumented
__shfl_down_sync	Undocumented
__shfl_sync	Undocumented
__shfl_up_sync	Undocumented
__shfl_xor_sync	Undocumented
__short2half_rd	Undocumented (only specifies “round-down mode”)
__short2half_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__short2half_ru	Undocumented (only specifies “round-up mode”)
__short2half_rz	Undocumented (only specifies “round-towards-zero mode”)
__short_as_half	Undocumented
__uint2half_rd	Undocumented (only specifies “round-down mode”)
__uint2half_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__uint2half_ru	Undocumented (only specifies “round-up mode”)
__uint2half_rz	Undocumented (only specifies “round-towards-zero mode”)
__ull2half_rd	Undocumented (only specifies “round-down mode”)
__ull2half_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__ull2half_ru	Undocumented (only specifies “round-up mode”)
__ull2half_rz	Undocumented (only specifies “round-towards-zero mode”)
__ushort2half_rd	Undocumented (only specifies “round-down mode”)
__ushort2half_rn	Undocumented (only specifies “round-to-nearest-even mode”)
__ushort2half_ru	Undocumented (only specifies “round-up mode”)
__ushort2half_rz	Undocumented (only specifies “round-towards-zero mode”)
__ushort_as_half	Undocumented