* Increase precision of delta_phase term by 1 bit.
* This improves accuracy of 1st order Taylor variant to less than 1.0 lsb peak deviation. * Add comments.
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@ -57,15 +57,15 @@ architecture rtl of sincos_gen is
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constant table_width: integer := data_bits;
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-- Number of bits in signed delta phase term.
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constant dphase_bits: integer := phase_bits - table_addrbits - 1;
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constant dphase_bits: integer := phase_bits - table_addrbits;
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-- Scaling for 1st order (final) Taylor correction.
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constant accum1_bits: integer := table_width + phase_bits - 1;
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constant round_const1: unsigned(phase_bits-3 downto 0) := (others => '1');
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constant accum1_bits: integer := table_width + phase_bits;
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constant round_const1: unsigned(phase_bits-2 downto 0) := (others => '1');
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-- Scaling for 2nd order Taylor correction.
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constant accum2_bits: integer := table_width + phase_bits;
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constant round_const2: unsigned(phase_bits-2 downto 0) := "0" & round_const1;
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constant accum2_bits: integer := table_width + phase_bits + 1;
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constant round_const2: unsigned(phase_bits-1 downto 0) := "0" & round_const1;
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-- Lookup table type.
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type table_type is array(0 to table_size-1) of
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@ -91,12 +91,12 @@ architecture rtl of sincos_gen is
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-- Internal registers.
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signal r1_quadrant: unsigned(1 downto 0);
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signal r1_rphase: signed(dphase_bits-2 downto 0);
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signal r1_rphase: signed(dphase_bits-3 downto 0);
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signal r1_dphase: signed(dphase_bits-1 downto 0);
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signal r1_sin_addr: unsigned(table_addrbits-1 downto 0);
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signal r1_cos_addr: unsigned(table_addrbits-1 downto 0);
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signal r2_quadrant: unsigned(1 downto 0);
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signal r2_rphase: signed(dphase_bits-2 downto 0);
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signal r2_rphase: signed(dphase_bits-3 downto 0);
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signal r2_dphase: signed(dphase_bits-1 downto 0);
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signal r2_sin_data: unsigned(table_width-1 downto 0);
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signal r2_cos_data: unsigned(table_width-1 downto 0);
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@ -152,7 +152,7 @@ begin
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-- Synchronous process.
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process (clk) is
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variable v1_rphase: signed(dphase_bits-2 downto 0);
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variable v1_rphase: signed(dphase_bits-3 downto 0);
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variable v3_dphase: signed(dphase_bits-1 downto 0);
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variable v9_sin_val: signed(data_bits-1 downto 0);
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variable v9_cos_val: signed(data_bits-1 downto 0);
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@ -163,20 +163,73 @@ begin
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if clk_en = '1' then
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--
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-- "in_phase" is an unsigned integer of width (phase_bits).
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-- We split it into three fields
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--
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-- MSB LSB
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-- (2 bits) (table_addrbits) (remaining bits)
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-- -------------------------------------------
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-- | . . | . . . . . | . . . . . . |
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-- -------------------------------------------
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-- quadrant table index phase remainder
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--
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-- The two most significant bits are the quadrant index
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-- (0 .. 3). We keep this index for later.
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-- Sine and cosine are calculated for the first quadrant,
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-- then modified afterwards to step to the selected quadrant.
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--
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-- The following (table_addrbits) bits form an index into
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-- the lookup table. Each entry in the lookup table represents
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-- the ideal value for the midpoint of the corresponding
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-- range of phase values.
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--
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-- The remaining least signifcant bits form the phase
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-- remainder with respect to the lookup index.
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-- If the phase remainder is "10000...", the lookup table
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-- value is exactly right. Smaller than "10000..." requires
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-- negative phase adjustment, larger than "1000..." requires
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-- positive phase adjustment. The phase remainder can thus
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-- be interpreted as a signed integer with the sign bit
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-- inverted.
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--
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-- The phase remainder must be converted to radians
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-- for use as Taylor correction coeffcient. This conversion
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-- requires multiplication by Pi.
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--
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-- We use the following approximation of Pi with
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-- 10 fractional bits:
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-- Pi =~ 11.0010010001B
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--
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-- Multiplication by this factor is implemented through
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-- shifting and adding:
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-- x * Pi =~ (x << 1) + x + (x >> 3) + (x >> 6) + (x >> 10)
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--
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-- which can be decomposed as follows:
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-- t1 = (x << 1) + (x >> 3)
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-- t2 = t + (t >> 7)
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-- x * Pi =~ x + t
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--
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-- Stage 1
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-- Keep quadrant for later use.
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r1_quadrant <= in_phase(phase_bits-1 downto phase_bits-2);
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-- Extract phase remainder as signed number.
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v1_rphase(dphase_bits-2) := not in_phase(dphase_bits-2);
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v1_rphase(dphase_bits-3 downto 0) := signed(in_phase(dphase_bits-3 downto 0));
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-- Extract phase remainder as signed number
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-- (by simply inverting the sign bit).
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v1_rphase(dphase_bits-3) := not in_phase(dphase_bits-3);
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v1_rphase(dphase_bits-4 downto 0) := signed(in_phase(dphase_bits-4 downto 0));
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-- Keep phase remainder and work on multiplication by Pi/2.
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-- Keep phase remainder for later use.
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r1_rphase <= v1_rphase;
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r1_dphase <= resize(v1_rphase, dphase_bits) +
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resize(v1_rphase(dphase_bits-2 downto 4), dphase_bits) +
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signed("0" & v1_rphase(3 downto 3));
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-- Multiply phase remainder by Pi, step 1.
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-- t1 = (rphase << 1) + (rphase >> 3)
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-- (apply rounding constant for truncation due to shift)
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r1_dphase <= resize(v1_rphase & "0", dphase_bits) +
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resize(v1_rphase(dphase_bits-3 downto 3), dphase_bits) +
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signed("0" & v1_rphase(2 downto 2));
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-- Extract table index for sin and cos.
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r1_sin_addr <= in_phase(phase_bits-3 downto
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@ -186,11 +239,13 @@ begin
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-- Stage 2
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-- Keep quadrant for later use.
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-- Keep quadrant and phase remainder for later use.
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r2_quadrant <= r1_quadrant;
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-- Keep phase remainder and work on multiplication by Pi/2.
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r2_rphase <= r1_rphase;
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-- Multiply phase remainder by Pi, step 2.
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-- t2 = t1 + (t1 >> 7)
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-- (apply rounding constant for truncation due to shift)
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r2_dphase <= r1_dphase +
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resize(r1_dphase(dphase_bits-1 downto 7), dphase_bits) +
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signed("0" & r1_dphase(6 downto 6));
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@ -201,9 +256,10 @@ begin
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-- Stage 3
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-- Finalize multiplication of phase remainder by Pi/2.
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-- Multiply phase remainder by Pi, final step.
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-- dphase = t2 + rphase
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v3_dphase := r2_dphase +
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resize(r2_rphase(dphase_bits-2 downto 1), dphase_bits);
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resize(r2_rphase, dphase_bits);
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if taylor_order = 2 then
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-- Handle 2nd order Taylor correction.
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@ -267,9 +323,9 @@ begin
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r6_cos_data <= r5_cos_data;
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-- Prepare multiplication for 1st order Taylor correction.
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r6_sinm1_a <= r5_sinm2_p(accum2_bits-1 downto phase_bits-1);
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r6_sinm1_a <= r5_sinm2_p(accum2_bits-1 downto phase_bits);
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r6_sinm1_b <= r5_dphase;
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r6_cosm1_a <= r5_cosm2_p(accum2_bits-1 downto phase_bits-1);
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r6_cosm1_a <= r5_cosm2_p(accum2_bits-1 downto phase_bits);
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r6_cosm1_b <= r5_dphase;
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else
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@ -322,8 +378,8 @@ begin
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-- Stage 9
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-- Extract relevant bits of answer.
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v9_sin_val := r8_sinm1_p(accum1_bits-1 downto phase_bits-1);
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v9_cos_val := r8_cosm1_p(accum1_bits-1 downto phase_bits-1);
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v9_sin_val := r8_sinm1_p(accum1_bits-1 downto phase_bits);
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v9_cos_val := r8_cosm1_p(accum1_bits-1 downto phase_bits);
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-- Choose between sin/cos based on quadrant.
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if r8_quadrant(0) = '0' then
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