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vhdl-sincos-gen
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* Further reduction of multiplier width. 

* Add more comments.
This commit is contained in:
Joris van Rantwijk 2016-04-14 22:49:32 +02:00
parent a3d8939440
commit 9873f91e8e
1 changed files with 127 additions and 51 deletions
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178
rtl/sincos_gen.vhdl
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@ -14,6 +14,12 @@ use ieee.std_logic_1164.all;
use ieee.numeric_std.all; use ieee.numeric_std.all;
use ieee.math_real.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 entity sincos_gen is
generic ( generic (
@ -59,13 +65,13 @@ architecture rtl of sincos_gen is
-- Number of bits in signed delta phase term. -- Number of bits in signed delta phase term.
constant dphase_bits: integer := phase_bits - table_addrbits; constant dphase_bits: integer := phase_bits - table_addrbits;
-- Scaling for 1st order (final) Taylor correction. -- Number of (MSB) bits from lookup table used for Taylor correction.
constant accum1_bits: integer := table_width + phase_bits - 1; constant coeff_bits: integer := table_width + 4 - table_addrbits;
constant round_const1: unsigned(phase_bits-3 downto 0) := (others => '1');
-- Scaling for 2nd order Taylor correction. -- Scaling after Taylor correction.
constant accum2_bits: integer := table_width + phase_bits; constant frac_bits: integer := phase_bits + 4 - table_addrbits;
constant round_const2: unsigned(phase_bits-2 downto 0) := "0" & round_const1; constant accum_bits: integer := data_bits + frac_bits;
constant round_const: unsigned(frac_bits-2 downto 0) := (others => '1');
-- 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
@ -109,39 +115,39 @@ architecture rtl of sincos_gen is
signal r3_dphase: signed(dphase_bits-1 downto 0); signal r3_dphase: signed(dphase_bits-1 downto 0);
signal r3_sin_data: unsigned(table_width-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_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_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 r3_cosm2_b: signed(dphase_bits-1 downto 0);
signal r4_quadrant: unsigned(1 downto 0); signal r4_quadrant: unsigned(1 downto 0);
signal r4_dphase: signed(dphase_bits-1 downto 0); signal r4_dphase: signed(dphase_bits-1 downto 0);
signal r4_sin_data: unsigned(table_width-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_cos_data: unsigned(table_width-1 downto 0);
signal r4_sinm2_m: signed(table_width+dphase_bits-1 downto 0); signal r4_sinm2_m: signed(coeff_bits+dphase_bits-1 downto 0);
signal r4_sinm2_c: signed(accum2_bits-1 downto 0); signal r4_sinm2_c: signed(accum_bits-1 downto 0);
signal r4_cosm2_m: signed(table_width+dphase_bits-1 downto 0); signal r4_cosm2_m: signed(coeff_bits+dphase_bits-1 downto 0);
signal r4_cosm2_c: signed(accum2_bits-1 downto 0); signal r4_cosm2_c: signed(accum_bits-1 downto 0);
signal r5_quadrant: unsigned(1 downto 0); signal r5_quadrant: unsigned(1 downto 0);
signal r5_dphase: signed(dphase_bits-1 downto 0); signal r5_dphase: signed(dphase_bits-1 downto 0);
signal r5_sin_data: unsigned(table_width-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_cos_data: unsigned(table_width-1 downto 0);
signal r5_sinm2_p: signed(accum2_bits-1 downto 0); signal r5_sinm2_p: signed(accum_bits-1 downto 0);
signal r5_cosm2_p: signed(accum2_bits-1 downto 0); signal r5_cosm2_p: signed(accum_bits-1 downto 0);
signal r6_quadrant: unsigned(1 downto 0); signal r6_quadrant: unsigned(1 downto 0);
signal r6_sin_data: unsigned(table_width-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_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_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 r6_cosm1_b: signed(dphase_bits-1 downto 0);
signal r7_quadrant: unsigned(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_m: signed(coeff_bits+dphase_bits downto 0);
signal r7_sinm1_c: signed(accum1_bits-1 downto 0); signal r7_sinm1_c: signed(accum_bits-1 downto 0);
signal r7_cosm1_m: signed(table_width+dphase_bits-1 downto 0); signal r7_cosm1_m: signed(coeff_bits+dphase_bits downto 0);
signal r7_cosm1_c: signed(accum1_bits-1 downto 0); signal r7_cosm1_c: signed(accum_bits-1 downto 0);
signal r8_quadrant: unsigned(1 downto 0); signal r8_quadrant: unsigned(1 downto 0);
signal r8_sinm1_p: signed(accum1_bits-1 downto 0); signal r8_sinm1_p: signed(accum_bits-1 downto 0);
signal r8_cosm1_p: signed(accum1_bits-1 downto 0); signal r8_cosm1_p: signed(accum_bits-1 downto 0);
signal r8_sin_neg: std_logic; signal r8_sin_neg: std_logic;
signal r8_cos_neg: std_logic; signal r8_cos_neg: std_logic;
@ -223,18 +229,21 @@ begin
-- Extract phase remainder as signed number -- Extract phase remainder as signed number
-- (by simply inverting the sign bit). -- (by simply inverting the sign bit).
v1_rphase(dphase_bits-3) := not in_phase(dphase_bits-3); v1_rphase(dphase_bits-3) :=
v1_rphase(dphase_bits-4 downto 0) := signed(in_phase(dphase_bits-4 downto 0)); 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. -- Keep phase remainder for later use.
r1_rphase <= v1_rphase; r1_rphase <= v1_rphase;
-- Multiply phase remainder by Pi, step 1. -- Multiply phase remainder by Pi, first step.
-- t1 = (rphase << 1) + (rphase >> 3) -- t1 = (rphase << 1) + (rphase >> 3)
-- (apply rounding constant for truncation due to shift) -- (apply rounding constant for truncation due to shift)
r1_dphase <= resize(v1_rphase & "0", dphase_bits) + r1_dphase <=
resize(v1_rphase(dphase_bits-3 downto 3), dphase_bits) + resize(v1_rphase & "0", dphase_bits) +
signed("0" & v1_rphase(2 downto 2)); 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
@ -248,12 +257,13 @@ begin
r2_quadrant <= r1_quadrant; r2_quadrant <= r1_quadrant;
r2_rphase <= r1_rphase; r2_rphase <= r1_rphase;
-- Multiply phase remainder by Pi, step 2. -- Multiply phase remainder by Pi, next step.
-- t2 = t1 + (t1 >> 7) -- t2 = t1 + (t1 >> 7)
-- (apply rounding constant for truncation due to shift) -- (apply rounding constant for truncation due to shift)
r2_dphase <= r1_dphase + r2_dphase <=
resize(r1_dphase(dphase_bits-1 downto 7), dphase_bits) + r1_dphase +
signed("0" & r1_dphase(6 downto 6)); resize(r1_dphase(dphase_bits-1 downto 7), dphase_bits) +
signed("0" & r1_dphase(6 downto 6));
-- Table lookup. -- Table lookup.
r2_sin_data <= unsigned(lookup_table(to_integer(r1_sin_addr))); r2_sin_data <= unsigned(lookup_table(to_integer(r1_sin_addr)));
@ -279,10 +289,29 @@ begin
r3_sin_data <= r2_sin_data; r3_sin_data <= r2_sin_data;
r3_cos_data <= r2_cos_data; r3_cos_data <= r2_cos_data;
--
-- Prepare multiplication for 2nd order Taylor correction. -- 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_sinm2_b <= v3_dphase;
r3_cosm2_a <= signed(resize(r2_cos_data(table_width-1 downto 1), table_width));
r3_cosm2_b <= v3_dphase; r3_cosm2_b <= v3_dphase;
-- Stage 4 -- Stage 4
@ -300,9 +329,10 @@ begin
r4_cosm2_m <= r3_cosm2_a * r3_cosm2_b; r4_cosm2_m <= r3_cosm2_a * r3_cosm2_b;
-- Prepare to add Taylor correction to base value. -- Prepare to add Taylor correction to base value.
-- Add a rounding constant. r4_sinm2_c <= signed(resize(r3_sin_data & round_const,
r4_sinm2_c <= signed(resize(r3_cos_data & round_const2, accum2_bits)); accum_bits));
r4_cosm2_c <= signed(resize(r3_sin_data & round_const2, accum2_bits)); r4_cosm2_c <= signed(resize(r3_cos_data & round_const,
accum_bits));
-- Stage 5 -- Stage 5
@ -315,8 +345,8 @@ begin
r5_cos_data <= r4_cos_data; r5_cos_data <= r4_cos_data;
-- Add Taylor correction to base value. -- Add Taylor correction to base value.
r5_sinm2_p <= r4_sinm2_c - resize(r4_sinm2_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, accum2_bits); r5_cosm2_p <= r4_cosm2_c - resize(r4_cosm2_m, accum_bits);
-- Stage 6 -- Stage 6
@ -327,10 +357,21 @@ begin
r6_sin_data <= r5_sin_data; r6_sin_data <= r5_sin_data;
r6_cos_data <= r5_cos_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_sinm1_b <= r5_dphase;
r6_cosm1_a <= r5_cosm2_p(accum2_bits-1 downto phase_bits);
r6_cosm1_b <= r5_dphase; r6_cosm1_b <= r5_dphase;
else else
@ -345,10 +386,29 @@ begin
r6_sin_data <= r2_sin_data; r6_sin_data <= r2_sin_data;
r6_cos_data <= r2_cos_data; r6_cos_data <= r2_cos_data;
--
-- Prepare multiplication for 1st order Taylor correction. -- 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_sinm1_b <= v3_dphase;
r6_cosm1_a <= signed(resize(r2_sin_data(table_width-1 downto 1), table_width));
r6_cosm1_b <= v3_dphase; r6_cosm1_b <= v3_dphase;
end if; end if;
@ -364,8 +424,10 @@ begin
-- Prepare to add Taylor correction to base value. -- Prepare to add Taylor correction to base value.
-- Add a rounding constant. -- Add a rounding constant.
r7_sinm1_c <= signed(resize(r6_sin_data & round_const1, accum1_bits)); r7_sinm1_c <= signed(resize(r6_sin_data & round_const,
r7_cosm1_c <= signed(resize(r6_cos_data & round_const1, accum1_bits)); accum_bits));
r7_cosm1_c <= signed(resize(r6_cos_data & round_const,
accum_bits));
-- Stage 8 -- Stage 8
@ -373,8 +435,8 @@ begin
r8_quadrant <= r7_quadrant; r8_quadrant <= r7_quadrant;
-- Add Taylor correction to base value. -- Add Taylor correction to base value.
r8_sinm1_p <= r7_sinm1_c + resize(r7_sinm1_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, accum1_bits); r8_cosm1_p <= r7_cosm1_c - resize(r7_cosm1_m, accum_bits);
-- Decide positive/negative value based on quadrant. -- Decide positive/negative value based on quadrant.
r8_sin_neg <= r7_quadrant(1); r8_sin_neg <= r7_quadrant(1);
@ -383,28 +445,42 @@ 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(accum_bits-1 downto frac_bits);
v9_cos_val := r8_cosm1_p(accum1_bits-1 downto phase_bits-1); 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. -- Choose between sin/cos based on quadrant.
if r8_quadrant(0) = '0' then if r8_quadrant(0) = '0' then
-- First or third quadrant; do not swap sin and cos.
v9_sin_mag := v9_sin_val; v9_sin_mag := v9_sin_val;
v9_cos_mag := v9_cos_val; v9_cos_mag := v9_cos_val;
else else
-- Second or fourth quadrant; swap sin and cos.
v9_sin_mag := v9_cos_val; v9_sin_mag := v9_cos_val;
v9_cos_mag := v9_sin_val; v9_cos_mag := v9_sin_val;
end if; end if;
-- Choose positive/negative value based on quadrant. -- Choose positive/negative sine value based on quadrant.
if r8_sin_neg = '0' then if r8_sin_neg = '0' then
-- First or second quadrant; sine value is positive.
r_outsin <= 0 + v9_sin_mag; r_outsin <= 0 + v9_sin_mag;
else else
-- Third or fourth quadrant; sine value is negative.
r_outsin <= 0 - v9_sin_mag; r_outsin <= 0 - v9_sin_mag;
end if; end if;
-- Choose positive/negative cosine value based on quadrant.
if r8_cos_neg = '0' then if r8_cos_neg = '0' then
-- First or fourth quadrant; cosine value is positive.
r_outcos <= 0 + v9_cos_mag; r_outcos <= 0 + v9_cos_mag;
else else
-- Second or third quadrant; cosine value is negative.
r_outcos <= 0 - v9_cos_mag; r_outcos <= 0 - v9_cos_mag;
end if; end if;