x86doc › VREDUCEPH - Perform Reduction Transformation on Packed FP16 Values

VREDUCEPH—Perform Reduction Transformation on Packed FP16 Values

Opcode/Instruction	Op/En	64/32 bit Mode Support	CPUID Feature Flag	Description
EVEX.128.NP.0F3A.W0 56 /r /ib VREDUCEPH xmm1{k1}{z}, xmm2/ imm8 m128/m16bcst,	A	V/V	AVX512-FP16 AVX512VL	Perform reduction transformation on packed FP16 values in xmm2/m128/m16bcst by subtracting a number of fraction bits specified by the imm8 field. Store the result in xmm1 subject to writemask k1.
EVEX.256.NP.0F3A.W0 56 /r /ib VREDUCEPH ymm1{k1}{z}, ymm2/m256/m16bcst, imm8	A	V/V	AVX512-FP16 AVX512VL	Perform reduction transformation on packed FP16 values in ymm2/m256/m16bcst by subtracting a number of fraction bits specified by the imm8 field. Store the result in ymm1 subject to writemask k1.
EVEX.512.NP.0F3A.W0 56 /r /ib VREDUCEPH zmm1{k1}{z}, zmm2/m512/m16bcst {sae}, imm8	A	V/V	AVX512-FP16	Perform reduction transformation on packed FP16 values in zmm2/m512/m16bcst by subtracting a number of fraction bits specified by the imm8 field. Store the result in zmm1 subject to writemask k1.

Instruction Operand Encoding

Op/En	Tuple	Operand 1	Operand 2	Operand 3	Operand 4
A	Full	ModRM:reg (w)	ModRM:r/m (r)	imm8 (r)	N/A

Description

This instruction performs a reduction transformation of the packed binary encoded FP16 values in the source operand (the second operand) and store the reduced results in binary FP format to the destination operand (the first operand) under the writemask k1.

The reduction transformation subtracts the integer part and the leading M fractional bits from the binary FP source value, where M is a unsigned integer specified by imm8[7:4]. Specifically, the reduction transformation can be expressed as:

dest = src − (ROUND(2^M * src)) * 2^−M

where ROUND() treats src, 2^M, and their product as binary FP numbers with normalized significand and biased exponents.

The magnitude of the reduced result can be expressed by considering src = 2^p * man2, where ‘man2’ is the normal-ized significand and ‘p’ is the unbiased exponent.

Then if RC=RNE: 0 ≤ |ReducedResult| ≤ 2^−M−1.

Then if RC ≠ RNE: 0 ≤ |ReducedResult| < 2^−M.

This instruction might end up with a precision exception set. However, in case of SPE set (i.e., Suppress Precision Exception, which is imm8[3]=1), no precision exception is reported.

This instruction may generate tiny non-zero result. If it does so, it does not report underflow exception, even if underflow exceptions are unmasked (UM flag in MXCSR register is 0).

For special cases, see Table 5-20.

Table 5-20. VREDUCEPH/VREDUCESH Special Cases

Input value	Round Mode	Returned Value
|Src1| < 2−M−1

Dest = ±0 (Src1 ≠ ∞)	NOT RD	−0.0 +0.0
Src1 = ±∞	RD
Src1 = ±NAN	Any	+0.0
	Any	QNaN (Src1)

NOTES:

1. The Round(.) function uses rounding controls specified by (imm8[2]? MXCSR.RC: imm8[1:0]).

Operation

def reduce_fp16(src, imm8):

nan := (src.exp = 0x1F) and (src.fraction != 0)

if nan:

return QNAN(src)

m := imm8[7:4]

rc := imm8[1:0]

rc_source := imm8[2]

spe := imm[3] // suppress precision exception

tmp := 2^(-m) * ROUND(2^m * src, spe, rc_source, rc)

tmp := src - tmp // using same RC, SPE controls

return tmp

VREDUCEPH dest{k1}, src, imm8

VL = 128, 256 or 512

KL := VL/16

FOR i := 0 to KL-1:

IF k1[i] or *no writemask*:

IF SRC is memory and (EVEX.b = 1):

tsrc := src.fp16[0]

ELSE:

tsrc := src.fp16[i]

DEST.fp16[i] := reduce_fp16(tsrc, imm8)

ELSE IF *zeroing*:

DEST.fp16[i] := 0

//else DEST.fp16[i] remains unchanged

DEST[MAXVL-1:VL] := 0

Intel C/C++ Compiler Intrinsic Equivalent

VREDUCEPH __m128h _mm_mask_reduce_ph (__m128h src, __mmask8 k, __m128h a, int imm8);

VREDUCEPH __m128h _mm_maskz_reduce_ph (__mmask8 k, __m128h a, int imm8);

VREDUCEPH __m128h _mm_reduce_ph (__m128h a, int imm8);

VREDUCEPH __m256h _mm256_mask_reduce_ph (__m256h src, __mmask16 k, __m256h a, int imm8);

VREDUCEPH __m256h _mm256_maskz_reduce_ph (__mmask16 k, __m256h a, int imm8);

VREDUCEPH __m256h _mm256_reduce_ph (__m256h a, int imm8);

VREDUCEPH __m512h _mm512_mask_reduce_ph (__m512h src, __mmask32 k, __m512h a, int imm8);

VREDUCEPH __m512h _mm512_maskz_reduce_ph (__mmask32 k, __m512h a, int imm8);

VREDUCEPH __m512h _mm512_reduce_ph (__m512h a, int imm8);

VREDUCEPH __m512h _mm512_mask_reduce_round_ph (__m512h src, __mmask32 k, __m512h a, int imm8, const int sae);

VREDUCEPH __m512h _mm512_maskz_reduce_round_ph (__mmask32 k, __m512h a, int imm8, const int sae);

VREDUCEPH __m512h _mm512_reduce_round_ph (__m512h a, int imm8, const int sae);

SIMD Floating-Point Exceptions

Invalid, Precision.

Other Exceptions

EVEX-encoded instruction, see Table 2-46, “Type E2 Class Exception Conditions.”