* Further reduction of multiplier width.
* Add more comments.
This commit is contained in:
parent
a3d8939440
commit
9873f91e8e
|
|
@ -14,6 +14,12 @@ use ieee.std_logic_1164.all;
|
|||
use ieee.numeric_std.all;
|
||||
use ieee.math_real.all;
|
||||
|
||||
|
||||
--
|
||||
-- Calculate sine and cosine based on a lookup table with limited size,
|
||||
-- followed by 1st order or 2nd order Taylor interpolation.
|
||||
--
|
||||
|
||||
entity sincos_gen is
|
||||
|
||||
generic (
|
||||
|
|
@ -59,13 +65,13 @@ architecture rtl of sincos_gen is
|
|||
-- Number of bits in signed delta phase term.
|
||||
constant dphase_bits: integer := phase_bits - table_addrbits;
|
||||
|
||||
-- Scaling for 1st order (final) Taylor correction.
|
||||
constant accum1_bits: integer := table_width + phase_bits - 1;
|
||||
constant round_const1: unsigned(phase_bits-3 downto 0) := (others => '1');
|
||||
-- Number of (MSB) bits from lookup table used for Taylor correction.
|
||||
constant coeff_bits: integer := table_width + 4 - table_addrbits;
|
||||
|
||||
-- Scaling for 2nd order Taylor correction.
|
||||
constant accum2_bits: integer := table_width + phase_bits;
|
||||
constant round_const2: unsigned(phase_bits-2 downto 0) := "0" & round_const1;
|
||||
-- Scaling after Taylor correction.
|
||||
constant frac_bits: integer := phase_bits + 4 - table_addrbits;
|
||||
constant accum_bits: integer := data_bits + frac_bits;
|
||||
constant round_const: unsigned(frac_bits-2 downto 0) := (others => '1');
|
||||
|
||||
-- Lookup table type.
|
||||
type table_type is array(0 to table_size-1) of
|
||||
|
|
@ -109,39 +115,39 @@ architecture rtl of sincos_gen is
|
|||
signal r3_dphase: signed(dphase_bits-1 downto 0);
|
||||
signal r3_sin_data: unsigned(table_width-1 downto 0);
|
||||
signal r3_cos_data: unsigned(table_width-1 downto 0);
|
||||
signal r3_sinm2_a: signed(table_width-1 downto 0);
|
||||
signal r3_sinm2_a: signed(coeff_bits-1 downto 0);
|
||||
signal r3_sinm2_b: signed(dphase_bits-1 downto 0);
|
||||
signal r3_cosm2_a: signed(table_width-1 downto 0);
|
||||
signal r3_cosm2_a: signed(coeff_bits-1 downto 0);
|
||||
signal r3_cosm2_b: signed(dphase_bits-1 downto 0);
|
||||
signal r4_quadrant: unsigned(1 downto 0);
|
||||
signal r4_dphase: signed(dphase_bits-1 downto 0);
|
||||
signal r4_sin_data: unsigned(table_width-1 downto 0);
|
||||
signal r4_cos_data: unsigned(table_width-1 downto 0);
|
||||
signal r4_sinm2_m: signed(table_width+dphase_bits-1 downto 0);
|
||||
signal r4_sinm2_c: signed(accum2_bits-1 downto 0);
|
||||
signal r4_cosm2_m: signed(table_width+dphase_bits-1 downto 0);
|
||||
signal r4_cosm2_c: signed(accum2_bits-1 downto 0);
|
||||
signal r4_sinm2_m: signed(coeff_bits+dphase_bits-1 downto 0);
|
||||
signal r4_sinm2_c: signed(accum_bits-1 downto 0);
|
||||
signal r4_cosm2_m: signed(coeff_bits+dphase_bits-1 downto 0);
|
||||
signal r4_cosm2_c: signed(accum_bits-1 downto 0);
|
||||
signal r5_quadrant: unsigned(1 downto 0);
|
||||
signal r5_dphase: signed(dphase_bits-1 downto 0);
|
||||
signal r5_sin_data: unsigned(table_width-1 downto 0);
|
||||
signal r5_cos_data: unsigned(table_width-1 downto 0);
|
||||
signal r5_sinm2_p: signed(accum2_bits-1 downto 0);
|
||||
signal r5_cosm2_p: signed(accum2_bits-1 downto 0);
|
||||
signal r5_sinm2_p: signed(accum_bits-1 downto 0);
|
||||
signal r5_cosm2_p: signed(accum_bits-1 downto 0);
|
||||
signal r6_quadrant: unsigned(1 downto 0);
|
||||
signal r6_sin_data: unsigned(table_width-1 downto 0);
|
||||
signal r6_cos_data: unsigned(table_width-1 downto 0);
|
||||
signal r6_sinm1_a: signed(table_width-1 downto 0);
|
||||
signal r6_sinm1_a: signed(coeff_bits downto 0);
|
||||
signal r6_sinm1_b: signed(dphase_bits-1 downto 0);
|
||||
signal r6_cosm1_a: signed(table_width-1 downto 0);
|
||||
signal r6_cosm1_a: signed(coeff_bits downto 0);
|
||||
signal r6_cosm1_b: signed(dphase_bits-1 downto 0);
|
||||
signal r7_quadrant: unsigned(1 downto 0);
|
||||
signal r7_sinm1_m: signed(table_width+dphase_bits-1 downto 0);
|
||||
signal r7_sinm1_c: signed(accum1_bits-1 downto 0);
|
||||
signal r7_cosm1_m: signed(table_width+dphase_bits-1 downto 0);
|
||||
signal r7_cosm1_c: signed(accum1_bits-1 downto 0);
|
||||
signal r7_sinm1_m: signed(coeff_bits+dphase_bits downto 0);
|
||||
signal r7_sinm1_c: signed(accum_bits-1 downto 0);
|
||||
signal r7_cosm1_m: signed(coeff_bits+dphase_bits downto 0);
|
||||
signal r7_cosm1_c: signed(accum_bits-1 downto 0);
|
||||
signal r8_quadrant: unsigned(1 downto 0);
|
||||
signal r8_sinm1_p: signed(accum1_bits-1 downto 0);
|
||||
signal r8_cosm1_p: signed(accum1_bits-1 downto 0);
|
||||
signal r8_sinm1_p: signed(accum_bits-1 downto 0);
|
||||
signal r8_cosm1_p: signed(accum_bits-1 downto 0);
|
||||
signal r8_sin_neg: std_logic;
|
||||
signal r8_cos_neg: std_logic;
|
||||
|
||||
|
|
@ -223,16 +229,19 @@ begin
|
|||
|
||||
-- Extract phase remainder as signed number
|
||||
-- (by simply inverting the sign bit).
|
||||
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));
|
||||
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 for later use.
|
||||
r1_rphase <= v1_rphase;
|
||||
|
||||
-- Multiply phase remainder by Pi, step 1.
|
||||
-- Multiply phase remainder by Pi, first step.
|
||||
-- t1 = (rphase << 1) + (rphase >> 3)
|
||||
-- (apply rounding constant for truncation due to shift)
|
||||
r1_dphase <= resize(v1_rphase & "0", dphase_bits) +
|
||||
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));
|
||||
|
||||
|
|
@ -248,10 +257,11 @@ begin
|
|||
r2_quadrant <= r1_quadrant;
|
||||
r2_rphase <= r1_rphase;
|
||||
|
||||
-- Multiply phase remainder by Pi, step 2.
|
||||
-- Multiply phase remainder by Pi, next step.
|
||||
-- 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) +
|
||||
signed("0" & r1_dphase(6 downto 6));
|
||||
|
||||
|
|
@ -279,10 +289,29 @@ begin
|
|||
r3_sin_data <= r2_sin_data;
|
||||
r3_cos_data <= r2_cos_data;
|
||||
|
||||
--
|
||||
-- Prepare multiplication for 2nd order Taylor correction.
|
||||
r3_sinm2_a <= signed(resize(r2_sin_data(table_width-1 downto 1), table_width));
|
||||
-- sin_t2 = sin_table + 0.5 * dphase * cos_table
|
||||
-- cos_t2 = cos_table - 0.5 * dphase * sin_table
|
||||
--
|
||||
-- Use only the (coeff_bits-1) MSB bits of the table value
|
||||
-- for the multiplication.
|
||||
--
|
||||
-- Convert table values from unsigned to signed (sign-ext).
|
||||
--
|
||||
|
||||
r3_sinm2_a <=
|
||||
signed(
|
||||
resize(r2_cos_data(table_width-1 downto
|
||||
table_width-coeff_bits+1),
|
||||
coeff_bits));
|
||||
r3_cosm2_a <=
|
||||
signed(
|
||||
resize(r2_sin_data(table_width-1 downto
|
||||
table_width-coeff_bits+1),
|
||||
coeff_bits));
|
||||
|
||||
r3_sinm2_b <= v3_dphase;
|
||||
r3_cosm2_a <= signed(resize(r2_cos_data(table_width-1 downto 1), table_width));
|
||||
r3_cosm2_b <= v3_dphase;
|
||||
|
||||
-- Stage 4
|
||||
|
|
@ -300,9 +329,10 @@ begin
|
|||
r4_cosm2_m <= r3_cosm2_a * r3_cosm2_b;
|
||||
|
||||
-- Prepare to add Taylor correction to base value.
|
||||
-- Add a rounding constant.
|
||||
r4_sinm2_c <= signed(resize(r3_cos_data & round_const2, accum2_bits));
|
||||
r4_cosm2_c <= signed(resize(r3_sin_data & round_const2, accum2_bits));
|
||||
r4_sinm2_c <= signed(resize(r3_sin_data & round_const,
|
||||
accum_bits));
|
||||
r4_cosm2_c <= signed(resize(r3_cos_data & round_const,
|
||||
accum_bits));
|
||||
|
||||
-- Stage 5
|
||||
|
||||
|
|
@ -315,8 +345,8 @@ begin
|
|||
r5_cos_data <= r4_cos_data;
|
||||
|
||||
-- Add Taylor correction to base value.
|
||||
r5_sinm2_p <= r4_sinm2_c - resize(r4_sinm2_m, accum2_bits);
|
||||
r5_cosm2_p <= r4_cosm2_c + resize(r4_cosm2_m, accum2_bits);
|
||||
r5_sinm2_p <= r4_sinm2_c + resize(r4_sinm2_m, accum_bits);
|
||||
r5_cosm2_p <= r4_cosm2_c - resize(r4_cosm2_m, accum_bits);
|
||||
|
||||
-- Stage 6
|
||||
|
||||
|
|
@ -327,10 +357,21 @@ begin
|
|||
r6_sin_data <= r5_sin_data;
|
||||
r6_cos_data <= r5_cos_data;
|
||||
|
||||
-- Prepare multiplication for 1st order Taylor correction.
|
||||
r6_sinm1_a <= r5_sinm2_p(accum2_bits-1 downto phase_bits);
|
||||
--
|
||||
-- Prepare multiplication for final Taylor correction.
|
||||
-- sin_corr = sin_table + dphase * cos_t2
|
||||
-- cos_corr = cos_table - dphase * sin_t2
|
||||
--
|
||||
-- Use only the coeff_bits MSB bits of the intermediate
|
||||
-- sin/cos values for the multiplication.
|
||||
--
|
||||
|
||||
r6_sinm1_a <= r5_sinm2_p(accum_bits-1 downto
|
||||
accum_bits-coeff_bits-1);
|
||||
r6_cosm1_a <= r5_cosm2_p(accum_bits-1 downto
|
||||
accum_bits-coeff_bits-1);
|
||||
|
||||
r6_sinm1_b <= r5_dphase;
|
||||
r6_cosm1_a <= r5_cosm2_p(accum2_bits-1 downto phase_bits);
|
||||
r6_cosm1_b <= r5_dphase;
|
||||
|
||||
else
|
||||
|
|
@ -345,10 +386,29 @@ begin
|
|||
r6_sin_data <= r2_sin_data;
|
||||
r6_cos_data <= r2_cos_data;
|
||||
|
||||
--
|
||||
-- Prepare multiplication for 1st order Taylor correction.
|
||||
r6_sinm1_a <= signed(resize(r2_cos_data(table_width-1 downto 1), table_width));
|
||||
-- sin_corr = sin_table + dphase * cos_table
|
||||
-- cos_corr = cos_table - dphase * sin_table
|
||||
--
|
||||
-- Use only the coeff_bits MSB bits of the table value
|
||||
-- for the multiplication.
|
||||
--
|
||||
-- Convert table values from unsigned to signed (sign-ext).
|
||||
--
|
||||
|
||||
r6_sinm1_a <=
|
||||
signed(
|
||||
resize(r2_cos_data(table_width-1 downto
|
||||
table_width-coeff_bits),
|
||||
coeff_bits+1));
|
||||
r6_cosm1_a <=
|
||||
signed(
|
||||
resize(r2_sin_data(table_width-1 downto
|
||||
table_width-coeff_bits),
|
||||
coeff_bits+1));
|
||||
|
||||
r6_sinm1_b <= v3_dphase;
|
||||
r6_cosm1_a <= signed(resize(r2_sin_data(table_width-1 downto 1), table_width));
|
||||
r6_cosm1_b <= v3_dphase;
|
||||
|
||||
end if;
|
||||
|
|
@ -364,8 +424,10 @@ begin
|
|||
|
||||
-- Prepare to add Taylor correction to base value.
|
||||
-- Add a rounding constant.
|
||||
r7_sinm1_c <= signed(resize(r6_sin_data & round_const1, accum1_bits));
|
||||
r7_cosm1_c <= signed(resize(r6_cos_data & round_const1, accum1_bits));
|
||||
r7_sinm1_c <= signed(resize(r6_sin_data & round_const,
|
||||
accum_bits));
|
||||
r7_cosm1_c <= signed(resize(r6_cos_data & round_const,
|
||||
accum_bits));
|
||||
|
||||
-- Stage 8
|
||||
|
||||
|
|
@ -373,8 +435,8 @@ begin
|
|||
r8_quadrant <= r7_quadrant;
|
||||
|
||||
-- Add Taylor correction to base value.
|
||||
r8_sinm1_p <= r7_sinm1_c + resize(r7_sinm1_m, accum1_bits);
|
||||
r8_cosm1_p <= r7_cosm1_c - resize(r7_cosm1_m, accum1_bits);
|
||||
r8_sinm1_p <= r7_sinm1_c + resize(r7_sinm1_m, accum_bits);
|
||||
r8_cosm1_p <= r7_cosm1_c - resize(r7_cosm1_m, accum_bits);
|
||||
|
||||
-- Decide positive/negative value based on quadrant.
|
||||
r8_sin_neg <= r7_quadrant(1);
|
||||
|
|
@ -383,28 +445,42 @@ begin
|
|||
-- Stage 9
|
||||
|
||||
-- Extract relevant bits of answer.
|
||||
v9_sin_val := r8_sinm1_p(accum1_bits-1 downto phase_bits-1);
|
||||
v9_cos_val := r8_cosm1_p(accum1_bits-1 downto phase_bits-1);
|
||||
v9_sin_val := r8_sinm1_p(accum_bits-1 downto frac_bits);
|
||||
v9_cos_val := r8_cosm1_p(accum_bits-1 downto frac_bits);
|
||||
|
||||
--
|
||||
-- Up to now all computations were done for the first quadrant.
|
||||
-- Therefore v9_sin_val and v9_cos_val are the correct final
|
||||
-- results iff r8_quadrant = 0.
|
||||
-- Otherwise adjustments are needed.
|
||||
--
|
||||
|
||||
-- Choose between sin/cos based on quadrant.
|
||||
if r8_quadrant(0) = '0' then
|
||||
-- First or third quadrant; do not swap sin and cos.
|
||||
v9_sin_mag := v9_sin_val;
|
||||
v9_cos_mag := v9_cos_val;
|
||||
else
|
||||
-- Second or fourth quadrant; swap sin and cos.
|
||||
v9_sin_mag := v9_cos_val;
|
||||
v9_cos_mag := v9_sin_val;
|
||||
end if;
|
||||
|
||||
-- Choose positive/negative value based on quadrant.
|
||||
-- Choose positive/negative sine value based on quadrant.
|
||||
if r8_sin_neg = '0' then
|
||||
-- First or second quadrant; sine value is positive.
|
||||
r_outsin <= 0 + v9_sin_mag;
|
||||
else
|
||||
-- Third or fourth quadrant; sine value is negative.
|
||||
r_outsin <= 0 - v9_sin_mag;
|
||||
end if;
|
||||
|
||||
-- Choose positive/negative cosine value based on quadrant.
|
||||
if r8_cos_neg = '0' then
|
||||
-- First or fourth quadrant; cosine value is positive.
|
||||
r_outcos <= 0 + v9_cos_mag;
|
||||
else
|
||||
-- Second or third quadrant; cosine value is negative.
|
||||
r_outcos <= 0 - v9_cos_mag;
|
||||
end if;
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue