joris
/
vhdl-sincos-gen
1
0
Fork 0
Code Issues Pull Requests Activity

* 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.
This commit is contained in:
Joris van Rantwijk 2016-04-13 23:32:02 +02:00
parent 12b896c2df
commit 9f4bb7f9b0
1 changed files with 80 additions and 24 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

104
rtl/sincos_gen.vhdl
View File

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