VREDUCEPD—Perform Reduction Transformation on Packed Float64 Values

Opcode/Instruction Op /En 64/32 bit Mode Support CPUID Feature Flag Description
EVEX.128.66.0F3A.W1 56 /r ib VREDUCEPD xmm1 {k1}{z}, xmm2/m128/m64bcst, imm8 A V/V AVX512VL AVX512DQ Perform reduction transformation on packed double-precision floating point values in xmm2/m128/m32bcst by subtracting a number of fraction bits specified by the imm8 field. Stores the result in xmm1 register under writemask k1.
EVEX.256.66.0F3A.W1 56 /r ib VREDUCEPD ymm1 {k1}{z}, ymm2/m256/m64bcst, imm8 A V/V AVX512VL AVX512DQ Perform reduction transformation on packed double-precision floating point values in ymm2/m256/m32bcst by subtracting a number of fraction bits specified by the imm8 field. Stores the result in ymm1 register under writemask k1.
EVEX.512.66.0F3A.W1 56 /r ib VREDUCEPD zmm1 {k1}{z}, zmm2/m512/m64bcst{sae}, imm8 A V/V AVX512DQ Perform reduction transformation on double-precision floating point values in zmm2/m512/m32bcst by subtracting a number of fraction bits specified by the imm8 field. Stores the result in zmm1 register under writemask k1.

Instruction Operand Encoding

Op/En Tuple Type Operand 1 Operand 2 Operand 3 Operand 4
A Full ModRM:reg (w) ModRM:r/m (r) Imm8 NA

Description

Perform reduction transformation of the packed binary encoded double-precision FP 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], see Figure 5-28. Specifically, the reduction transfor-mation can be expressed as:

dest = src – (ROUND(2M*src))*2-M;

where “Round()” treats “src”, “2M”, and their product as binary FP numbers with normalized significand and bi-ased exponents.

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

Then if RC = RNE: 0<=|Reduced Result|<=2p-M-1

Then if RC ≠ RNE: 0<=|Reduced Result|<2p-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.

EVEX.vvvv is reserved and must be 1111b otherwise instructions will #UD.

7

imm8

Imm8[7:4] : Number of fixed points to subtract

6

Fixed point length

5

4

Suppress Precision Exception: Imm8[3]

Imm8[3] = 0b : Use MXCSR exception mask

Imm8[3] = 1b : Suppress

3

SPE

2

RS

Round Select: Imm8[2]

1

Imm8[2] = 0b : Use Imm8[1:0]

Imm8[2] = 1b : Use MXCSR

0

Round Control Override

Imm8[1:0] = 00b : Round nearest even

Imm8[1:0] = 01b : Round down

Imm8[1:0] = 10b : Round up

Imm8[1:0] = 11b : Truncate

Figure 5-28. Imm8 Controls for VREDUCEPD/SD/PS/SS

Handling of special case of input values are listed in Table 5-15.

Table 5-15. VREDUCEPD/SD/PS/SS Special Cases

Round Mode Returned value
|Src1| < 2-M-1 RNE Src1
RPI, Src1 > 0 Round (Src1-2-M) *
RPI, Src1 ≤ 0 Src1
RNI, Src1 ≥ 0 Src1
|Src1| < 2-M RNI, Src1 < 0 Round (Src1+2-M) *
Src1 = ±0, or NOT RNI +0.0
Dest = ±0 (Src1!=INF) RNI -0.0
Src1 = ±INF any +0.0
Src1= ±NAN n/a QNaN(Src1)

* Round control = (imm8.MS1)? MXCSR.RC: imm8.RC

Operation

ReduceArgumentDP(SRC[63:0], imm8[7:0])

{

// Check for NaN

IF (SRC [63:0] = NAN) THEN

RETURN (Convert SRC[63:0] to QNaN); FI;

M := imm8[7:4]; // Number of fraction bits of the normalized significand to be subtracted

RC := imm8[1:0];// Round Control for ROUND() operation

RC source := imm[2];

SPE := imm[3];// Suppress Precision Exception

TMP[63:0] := 2-M *{ROUND(2M*SRC[63:0], SPE, RC_source, RC)}; // ROUND() treats SRC and 2M as standard binary FP values

TMP[63:0] := SRC[63:0] – TMP[63:0]; // subtraction under the same RC,SPE controls

RETURN TMP[63:0]; // binary encoded FP with biased exponent and normalized significand

}

VREDUCEPD

(KL, VL) = (2, 128), (4, 256), (8, 512)

FOR j := 0 TO KL-1

i := j * 64

IF k1[j] OR *no writemask* THEN

IF (EVEX.b == 1) AND (SRC *is memory*)

THEN DEST[i+63:i] := ReduceArgumentDP(SRC[63:0], imm8[7:0]);

ELSE DEST[i+63:i] := ReduceArgumentDP(SRC[i+63:i], imm8[7:0]);

FI;

ELSE

IF *merging-masking*

; merging-masking

THEN *DEST[i+63:i] remains unchanged*

ELSE

; zeroing-masking

DEST[i+63:i] = 0

FI;

FI;

ENDFOR;

DEST[MAXVL-1:VL] := 0

Intel C/C++ Compiler Intrinsic Equivalent

VREDUCEPD __m512d _mm512_mask_reduce_pd( __m512d a, int imm, int sae)

VREDUCEPD __m512d _mm512_mask_reduce_pd(__m512d s, __mmask8 k, __m512d a, int imm, int sae)

VREDUCEPD __m512d _mm512_maskz_reduce_pd(__mmask8 k, __m512d a, int imm, int sae)

VREDUCEPD __m256d _mm256_mask_reduce_pd( __m256d a, int imm)

VREDUCEPD __m256d _mm256_mask_reduce_pd(__m256d s, __mmask8 k, __m256d a, int imm)

VREDUCEPD __m256d _mm256_maskz_reduce_pd(__mmask8 k, __m256d a, int imm)

VREDUCEPD __m128d _mm_mask_reduce_pd( __m128d a, int imm)

VREDUCEPD __m128d _mm_mask_reduce_pd(__m128d s, __mmask8 k, __m128d a, int imm)

VREDUCEPD __m128d _mm_maskz_reduce_pd(__mmask8 k, __m128d a, int imm)

SIMD Floating-Point Exceptions

Invalid, Precision

If SPE is enabled, precision exception is not reported (regardless of MXCSR exception mask).

Other Exceptions

See Table 2-46, “Type E2 Class Exception Conditions”; additionally:

#UD If EVEX.vvvv != 1111B.