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vhdl-sincos-gen
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Make internal phase accuracy configurable. 

* Add generic "phase_extrabits" to set internal accuracy of phase remainder.
* Increase default value of phase_extrabits from 1 to 2.
This commit is contained in:
Joris van Rantwijk 2016-04-20 09:13:34 +02:00
parent 8719b47c6f
commit ba096abf16
3 changed files with 48 additions and 35 deletions
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81
rtl/sincos_gen.vhdl
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@ -33,6 +33,9 @@ entity sincos_gen is
-- Number of address bits for lookup table.
table_addrbits: integer := 10;
-- Number of extra phase bits used internally.
phase_extrabits: integer := 1;
-- Select 1st order or 2nd order Taylor correction.
taylor_order: integer range 1 to 2 := 1 );
@ -63,13 +66,15 @@ architecture rtl of sincos_gen is
constant table_width: integer := data_bits;
-- Number of bits in signed delta phase term.
constant dphase_bits: integer := phase_bits - table_addrbits;
constant rphase_bits: integer := phase_bits - table_addrbits - 2;
constant dphase_bits: integer := rphase_bits + phase_extrabits + 1;
-- Number of (MSB) bits from lookup table used for Taylor correction.
constant coeff_bits: integer := table_width + 3 - table_addrbits;
-- Scaling after Taylor correction.
constant frac_bits: integer := phase_bits + coeff_bits - table_width;
constant frac_bits: integer := phase_bits + phase_extrabits - 1 +
coeff_bits - table_width;
constant accum_bits: integer := data_bits + frac_bits;
constant round_const: unsigned(frac_bits-2 downto 0) := (others => '1');
@ -105,12 +110,12 @@ architecture rtl of sincos_gen is
-- Internal registers.
signal r1_quadrant: unsigned(1 downto 0);
signal r1_rphase: signed(dphase_bits-3 downto 0);
signal r1_rphase: signed(rphase_bits-1 downto 0);
signal r1_dphase: signed(dphase_bits-1 downto 0);
signal r1_sin_addr: std_logic_vector(table_addrbits-1 downto 0);
signal r1_cos_addr: std_logic_vector(table_addrbits-1 downto 0);
signal r2_quadrant: unsigned(1 downto 0);
signal r2_rphase: signed(dphase_bits-3 downto 0);
signal r2_rphase: signed(rphase_bits-1 downto 0);
signal r2_dphase: signed(dphase_bits-1 downto 0);
signal r2_sin_data: std_logic_vector(table_width-1 downto 0);
signal r2_cos_data: std_logic_vector(table_width-1 downto 0);
@ -172,7 +177,9 @@ begin
-- Synchronous process.
process (clk) is
variable v1_rphase: signed(dphase_bits-3 downto 0);
variable v1_rphase: signed(rphase_bits-1 downto 0);
variable v1_xphase: signed(rphase_bits+phase_extrabits-1 downto 0);
variable v3_xphase: signed(rphase_bits+phase_extrabits-1 downto 0);
variable v3_dphase: signed(dphase_bits-1 downto 0);
variable v9_sin_val: signed(data_bits-1 downto 0);
variable v9_cos_val: signed(data_bits-1 downto 0);
@ -199,36 +206,36 @@ begin
-- 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 middle (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
-- If the phase remainder is "1000..0", the lookup table
-- value is exactly right. Smaller than "1000..0" requires
-- negative phase adjustment, larger than "100..0" 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.
-- requires multiplication by Pi/2.
--
-- We use the following approximation of Pi with
-- 10 fractional bits:
-- Pi =~ 11.0010010001B
-- We use the following approximation of Pi/2 with
-- 11 fractional bits:
-- Pi/2 =~ 1.5708 =~ 1.10010010001B
--
-- Multiplication by this factor is implemented through
-- shifting and adding:
-- x * Pi =~ (x << 1) + x + (x >> 3) + (x >> 6) + (x >> 10)
-- x * Pi/2 =~ x + (x >> 1) + (x >> 4) + (x >> 7) + (x >> 11)
--
-- which can be decomposed as follows:
-- t1 = (x << 1) + (x >> 3)
-- t2 = t + (t >> 7)
-- x * Pi =~ x + t
-- t1 = x + (x >> 4)
-- t2 = t + (t >> 7)
-- x * Pi/2 =~ (x >> 1) + t
--
-- Stage 1
@ -238,21 +245,22 @@ 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(rphase_bits-1 downto 0) :=
not in_phase(rphase_bits-1);
v1_rphase(rphase_bits-2 downto 0) :=
signed(in_phase(rphase_bits-2 downto 0));
-- Keep phase remainder for later use.
r1_rphase <= v1_rphase;
-- Multiply phase remainder by Pi, first step.
-- t1 = (rphase << 1) + (rphase >> 3)
-- Multiply phase remainder by Pi/2, first step.
-- t1 = rphase + (rphase >> 4)
-- (left-shift to add extra phase bits to increase accuracy)
-- (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));
v1_xphase := shift_left(v1_rphase, phase_extrabits);
r1_dphase <= resize(v1_xphase, dphase_bits) +
resize(shift_right(v1_xphase, 4), dphase_bits) +
signed("0" & v1_xphase(3 downto 3));
-- Extract table index for sin and cos.
r1_sin_addr <=
@ -268,13 +276,12 @@ begin
r2_quadrant <= r1_quadrant;
r2_rphase <= r1_rphase;
-- Multiply phase remainder by Pi, next step.
-- Multiply phase remainder by Pi/2, next step.
-- t2 = t1 + (t1 >> 7)
-- (apply rounding constant for truncation due to shift)
r2_dphase <=
r1_dphase +
resize(r1_dphase(dphase_bits-1 downto 7), dphase_bits) +
signed("0" & r1_dphase(6 downto 6));
r2_dphase <= r1_dphase +
resize(shift_right(r1_dphase, 7), dphase_bits) +
signed("0" & r1_dphase(6 downto 6));
-- Table lookup.
r2_sin_data <= lookup_table(to_integer(unsigned(r1_sin_addr)));
@ -282,10 +289,14 @@ begin
-- Stage 3
-- Multiply phase remainder by Pi, final step.
-- dphase = t2 + rphase
-- Multiply phase remainder by Pi/2, final step.
-- dphase = t2 + (rphase >> 1)
-- (left-shift to add extra phase bits to increase accuracy)
-- (apply rounding constant for truncation due to shift)
v3_xphase := shift_left(r2_rphase, phase_extrabits);
v3_dphase := r2_dphase +
resize(r2_rphase, dphase_bits);
resize(shift_right(v3_xphase, 1), dphase_bits) +
signed("0" & v3_xphase(0 downto 0));
if taylor_order = 2 then
-- Handle 2nd order Taylor correction.

1
rtl/sincos_gen_d18_p20.vhdl
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@ -51,6 +51,7 @@ begin
generic map (
data_bits => 18,
phase_bits => 20,
phase_extrabits => 2,
table_addrbits => 10,
taylor_order => 1 )
port map (

1
rtl/sincos_gen_d24_p26.vhdl
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@ -53,6 +53,7 @@ begin
generic map (
data_bits => 24,
phase_bits => 26,
phase_extrabits => 2,
table_addrbits => 10,
taylor_order => 2 )
port map (