VREDUCEPD — Perform Reduction Transformation on Packed Float64 Values

Instruction Operand Encoding ¶

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 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 normalized significand and ‘p’ is the unbiased exponent

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

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

Handling of special case of input values are listed in Table 5-24.

* 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←0;// 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 Exceptions Type E2, additionally