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tablegen_mpfr.c
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tablegen_mpfr.c
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// gcc tablegen_mpfr.c -o tablegen_mpfr.exe -std=c99 -lm -lmpfr -lgmp -lwinmm -lcomdlg32 -lole32 -Wno-incompatible-pointer-types -O0 -DRL_STOREU_SI32 && ./tablegen_mpfr.exe
// clang tablegen_mpfr.c -o tablegen_mpfr.exe -std=c99 -lm -lmpfr -lgmp -lwinmm -lcomdlg32 -lole32 -Wno-incompatible-pointer-types -Wno-dangling-else -Wno-parentheses -Wno-pointer-sign -Wno-shift-op-parentheses -O0 && ./tablegen_mpfr.exe
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
#include <math.h>
#include <float.h>
//#include <windows.h>
#define RL_MPFR
#include "../rouziclib/rouziclib.h"
#include "../rouziclib/rouziclib.c"
#define COEF_COUNT 100
double get_double_impl_error(void (*f)(real_t,real_t), double (*g)(double), real_t start, real_t end, int errmode)
{
int32_t i;
static int init=1;
static real_t a, b;
static real_t x, err;
if (init)
{
init = 0;
r_init(a);
r_init(b);
r_init(x);
r_init(err);
}
r_setd(err, 0.);
for (i=0; i<=1000; i++)
{
r_mix(x, (double) i / 1000., start, end);
r_setd(a, g(r_todouble(x))); // double implementation
f(b, x);
if (errmode==DIVMODE)
{
if (mpfr_cmp(a, b) < 0) //if (a < b)
{
r_rdiv(a, b, a); //a = b / a - 1.;
r_subd(a, 1.);
}
else
{
r_div(a, b); //a = a / b - 1.;
r_subd(a, 1.);
}
}
else
r_rsub(a, b, a); //a = b - a;
r_abs(a);
if (mpfr_cmp(err, a) < 0)
r_set(err, a);
}
return r_todouble(err);
}
double get_float_impl_error(void (*f)(real_t,real_t), float (*g)(float), real_t start, real_t end, int errmode)
{
int32_t i;
static int init=1;
static real_t a, b;
static real_t x, err;
if (init)
{
init = 0;
r_init(a);
r_init(b);
r_init(x);
r_init(err);
}
r_setd(err, 0.);
for (i=0; i<=1000; i++)
{
r_mix(x, (double) i / 1000., start, end);
r_setd(a, g(r_todouble(x))); // float implementation
f(b, x);
if (errmode==DIVMODE)
{
if (mpfr_cmp(a, b) < 0) //if (a < b)
{
r_rdiv(a, b, a); //a = b / a - 1.;
r_subd(a, 1.);
}
else
{
r_div(a, b); //a = a / b - 1.;
r_subd(a, 1.);
}
}
else
r_rsub(a, b, a); //a = b - a;
r_abs(a);
if (mpfr_cmp(err, a) < 0)
r_set(err, a);
}
return r_todouble(err);
}
double f_cosd(double x)
{
return cos(2.*pi*x);
}
float f_cosf(float x)
{
return cosf(2.*pi*x);
}
void f_cos(real_t y, real_t x)
{
static int init=1;
static real_t a;
if (init)
{
init = 0;
r_init(a);
}
r_pi(a);
r_muld(a, 2.);
r_mul(a, x);
r_cos(y, a);
}
void f_cos_sq(real_t y, real_t x)
{
r_sqrt(y, x);
f_cos(y, y);
}
double find_max_intermediary_value(real_t *c_r, real_t segstart_r, real_t segend_r)
{
int32_t i, ic;
double c[COEF_COUNT], start=r_todouble(segstart_r), end=r_todouble(segend_r), x, v, maxv=0.;
for (ic=0; ic<COEF_COUNT; ic++)
c[ic] = r_todouble(c_r[ic]);
for (i=0; i<=1000; i++) // evaluate the polynomial for many different values of x in the given range
{
x = (double) i / 1000. * (end-start) + start;
if (fabs(x) > maxv) maxv = fabs(x);
v = c[COEF_COUNT-1];
if (fabs(v) > maxv) maxv = fabs(v);
for (ic=COEF_COUNT-2; ic>=0; ic--)
{
v *= x;
if (fabs(v) > maxv) maxv = fabs(v);
v += c[ic];
if (fabs(v) > maxv) maxv = fabs(v);
if (fabs(c[ic]) > maxv) maxv = fabs(c[ic]);
}
}
return maxv;
}
void make_cos_table(const int cos_order, const int lutsp, const int quads) // cos_order is <= 6, lutsp can only be <= 15
{
int32_t i, is, segcount, prec;
real_t c[COEF_COUNT];
real_t start, segstep, segstart, segend;
double end, step, err, errd, errf, maxerr=0., maxerrd=0., maxerrf=0., v, maxv=0.;
double k=0., errmin=1., mink;
FILE *file;
char header_path[64];
sprintf(header_path, "../rouziclib/approximations/tables/fastcos_d%d.h", cos_order);
file = fopen(header_path, "wb");
fprintf(file, "{");
end = (double) quads * 0.25;
step = 0.25 / pow(2., (double) lutsp);
segcount = ceil(end / step);
if (quads < 4)
segcount++; // +1 for the only lookup for x==0.25 or x==0.5
r_init(start);
r_init(segstep);
r_setd(segstep, step);
r_init(segstart);
r_init(segend);
for (i=0; i<COEF_COUNT; i++)
r_init(c[i]);
for (is=0; is<segcount; is++)
{
r_set(segstart, segend);
r_add(segend, segstep);
//if (is==segcount-1) // only useful if the last segment only needs to cover a shorter range than usual
// r_setd(segend, end);
for (i=0; i<COEF_COUNT; i++)
r_setd(c[i], 0.);
if (quads==2 && is==segcount-1) // if the final segment is at x = 0.5
r_setd(c[0], -1);
if (quads==4 || is!=segcount-1) // let the final segment be 0
{
polynomial_fit_on_function_by_dct_mpfr(f_cos, segstart, segend, c, cos_order);
err = get_polynomial_error_mpfr(f_cos, segstart, segend, c, cos_order, NEGMODE);
if (err > maxerr)
maxerr = err;
}
errd = get_double_impl_error(f_cos, f_cosd, segstart, segend, NEGMODE);
if (errd > maxerrd)
maxerrd = errd;
errf = get_float_impl_error(f_cos, f_cosf, segstart, segend, NEGMODE);
if (errf > maxerrf)
maxerrf = errf;
v = find_max_intermediary_value(c, segstart, segend);
if (v > maxv)
maxv = v;
//if (is==segcount/2)
/*for (i=cos_order; i>=1; i--)
if (i==1)
mpfr_printf("%+.16Rf*x", c[i]);
else
mpfr_printf("%+.16Rf*x^%d", c[i], i);
mpfr_printf("%+.16Rf\n[%.7Rf , %.7Rf]\terr %g\n", c[0], segstart, segend, err);*/
//mpfr_printf("%+.16Rf err %g\n\tdouble err:%g\ti=%3d (segratio 1/%.0f) [%.7Rf , %.7Rf]\n", c[0], err, errd, is, 1./step, segstart, segend);
for (i=0; i<cos_order; i++)
mpfr_fprintf(file, "%.17Rg, ", c[i]);
mpfr_fprintf(file, "%.17Rg%s", c[cos_order], (is==segcount-1 && quads < 4) ? "};\n" : ", \n");
}
if (quads==4)
{
for (i=0; i<cos_order; i++)
mpfr_fprintf(file, (i==0) ? "1., " : "0., ");
mpfr_fprintf(file, "0.};\n");
}
fprintf(file, "const uint32_t lutsp = %d;\n", lutsp);
fprintf(file, "const int quads = %d;", quads);
fclose (file);
if (maxv <= 2047.)
prec = 63 - ffo_lut[(int) ceil(maxv)];
else
prec = -1;
printf("\nMax error: %g\tMax double implementation error: %g, float implementation error: %g\nMax intermediary value: %g, prec: %d fractional bits\n", maxerr, maxerrd, maxerrf, maxv, prec);
}
void make_cos_table_human(const int cos_order, const double step) // cos_order is <= 6
{
int32_t i, is, segcount;
real_t c[COEF_COUNT];
real_t segstep, segstart, segend, maxseg;
double end=1., err, maxerr=0.;
FILE *file;
char header_path[64];
segcount = nearbyint(ceil(end / step));
sprintf(header_path, "cos_d%d_step_%g_human new.dat", cos_order, step);
file = fopen(header_path, "wb");
r_init(segstep);
r_setd(segstep, step);
r_init(segstart);
r_init(segend);
r_init(maxseg);
for (i=0; i<COEF_COUNT; i++)
r_init(c[i]);
for (is=0; is<segcount; is++)
{
r_set(segstart, segend);
r_add(segend, segstep);
for (i=0; i<COEF_COUNT; i++)
r_setd(c[i], 0.);
// Fit
polynomial_fit_on_function_by_dct_mpfr(f_cos, segstart, segend, c, cos_order);
//err = get_polynomial_error_mpfr(f_cos, segstart, segend, c, cos_order, NEGMODE);
// Reduce digits
err = reduce_digits_mpfr(f_cos, segstart, segend, c, cos_order, NEGMODE, 1.1, 30.);
if (err > maxerr)
{
maxerr = err;
r_set(maxseg, segstart);
}
// Print to file
mpfr_fprintf(file, "%Rg ", segstart);
for (i=cos_order; i > 0; i--)
mpfr_fprintf(file, "% .17Rg ", c[i]);
mpfr_fprintf(file, "% .17Rg\n", c[0]);
fflush(file);
}
mpfr_fprintf(file, "\nMax error: %g at segment %Rg\n", maxerr, maxseg);
fclose (file);
printf("\nMax error: %g\n", maxerr);
}
void compare_chebyshev_arithmetics(void (*f)(real_t,real_t), real_t *cm, int degree, double xd)
{
int id;
real_t xr, yr, x2r;
ddouble_t xq={0};
xd *= 4.;
r_init(xr);
r_init(yr);
r_setd(xr, xd);
xq.hi = xd;
ddouble_t b1q={0}, b2q, yq, x2q = mul_qd_simple(xq, 2.);
real_t b1r, b2r;
r_init(b1r);
r_init(b2r);
r_init(x2r);
r_rmuld(x2r, xr, 2.);
// Clenshaw evaluation
yq = mpfr_to_ddouble(cm[degree]);
r_set(yr, cm[degree]);
for (id = degree-1; id >= 1; id--)
{
fprintf(stdout, "id %2d:\n", id);
b2q = b1q;
b1q = yq;
r_set(b2r, b1r);
r_set(b1r, yr);
//y = cm[id] + x2*b1 - b2q;
yq = mul_qq(x2q, b1q);
r_rmul(yr, x2r, b1r);
mpfr_fprintf(stdout, " x2 %Rg (diff %g) * b1 %Rg (diff %g) => y %Rg (diff %g)\n", x2r, sub_qq(x2q, mpfr_to_ddouble(x2r)).hi, b1r, sub_qq(b1q, mpfr_to_ddouble(b1r)).hi, yr, sub_qq(yq, mpfr_to_ddouble(yr)).hi);
yq = add_qq(mpfr_to_ddouble(cm[id]), yq);
r_add(yr, cm[id]);
mpfr_fprintf(stdout, " cm[%d] %Rg + y => y %Rg (diff %g)\n", id, cm[id], yr, sub_qq(yq, mpfr_to_ddouble(yr)).hi);
yq = sub_qq(yq, b2q);
r_sub(yr, b2r);
mpfr_fprintf(stdout, " y - b2 %Rg (diff %g) => y %Rg (diff %g)\n", b2r, sub_qq(b2q, mpfr_to_ddouble(b2r)).hi, yr, sub_qq(yq, mpfr_to_ddouble(yr)).hi);
}
//y = cm[0] + x*y - b1q;
yq = mul_qq(xq, yq);
yq = add_qq(mpfr_to_ddouble(cm[0]), yq);
yq = sub_qq(yq, b1q);
r_mul(yr, xr);
r_add(yr, cm[0]);
r_sub(yr, b1r);
//yq = cos_tr_q(mul_qd_simple(xq, 0.25));
// Compare yr with yq
mpfr_fprintf(stdout, "id %2d: %g\n", id, sub_qq(yq, mpfr_to_ddouble(yr)).hi);
r_free(b1r);
r_free(b2r);
r_free(xr);
r_free(yr);
r_free(x2r);
}
//#define COSQ_EVEN
void make_cos_double_double_approx()
{
int i;
#ifdef COSQ_EVEN
const int step=2, degree = 28;
#else
const int step=1, degree = 14;
#endif
const int p_count = 1000;
real_t *c, *cm;
real_t start, end, v;
double err;
cm = r_init_array(degree+1);
c = r_init_array(degree+1);
r_init(v);
r_init(start);
r_init(end);
#ifdef COSQ_EVEN
r_setd(start, -0.25);
r_setd(end, 0.25);
chebyshev_analysis_on_function_mpfr(f_cos, start, end, cm, degree, p_count);
polynomial_fit_on_function_by_dct_mpfr(f_cos, start, end, c, degree);
err = get_polynomial_error_mpfr(f_cos, start, end, c, degree, NEGMODE);
#else
r_setd(start, 0.);
r_setd(end, 0.0625);
chebyshev_analysis_on_function_mpfr(f_cos_sq, start, end, cm, degree, p_count);
polynomial_fit_on_function_by_dct_mpfr(f_cos_sq, start, end, c, degree);
err = get_polynomial_error_mpfr(f_cos_sq, start, end, c, degree, NEGMODE);
#endif
fprintf(stdout, "Polynomial error: %.5e\n", err);
// Print Chebyshev multipliers
for (i=0; i <= degree; i++)
{
mpfr_abs(v, cm[i], MPFR_RNDN);
if (mpfr_cmp_d(v, 1e-150) > 0)
{
//mpfr_fprintf(stdout, "T_%d(x) * % .32Rg\n", i, cm[i]);
ddouble_t q = mpfr_to_ddouble(cm[i]);
fprintf(stdout, "{%.17g, %.17g}, // T_%d (err %.3g)\n", q.hi, q.lo, i, diff_mpfr_ddouble(cm[i], q));
}
}
// Print polynomial coefficients
for (i=0; i <= degree; i+=step)
{
ddouble_t q = mpfr_to_ddouble(c[i]);
fprintf(stdout, "{%.17g, %.17g}, // c%d\n", q.hi, q.lo, i);
}
// Print Horner form of polynomial
for (i=degree; i > step; i-=step)
mpfr_fprintf(stdout, "(");
for (i=degree; i > 0; i-=step)
if (i==degree)
mpfr_fprintf(stdout, "%.17Rg*x2 + ", c[i]);
else
mpfr_fprintf(stdout, "%.17Rg)*x2 + %s", c[i], (i%8) ? "" : "\n\t");
mpfr_fprintf(stdout, "%.17Rg\n", c[0]);
// Compare arithmetics
//compare_chebyshev_arithmetics(f_cos, cm, degree, 0.24998772);
r_free(v);
r_free_array(&cm, degree+1);
r_free_array(&c, degree+1);
}
rlip_t expr_prog={0};
real_t expr_prog_x;
int f_expr_init(const char *expr)
{
static int init = 1;
rlip_inputs_t inputs[] = { RLIP_REAL_MPFR, {"x", &expr_prog_x, "pr"} };
// Init or reset
if (init)
{
init = 0;
r_init(expr_prog_x);
}
else
{
free_rlip(&expr_prog);
}
// Compile
buffer_t comp_log={0};
expr_prog = rlip_expression_compile(expr, inputs, sizeof(inputs)/sizeof(*inputs), 1, &comp_log);
if (expr_prog.valid_prog == 0)
{
fprintf_rl(stdout, "Compilation log: %s\n", comp_log.buf);
free_buf(&comp_log);
free_rlip(&expr_prog);
return -1;
}
free_buf(&comp_log);
return 0;
}
void f_expr(real_t y, real_t x)
{
// Set x input
r_set(expr_prog_x, x);
// Execute
volatile int exec_on = 1;
expr_prog.exec_on = &exec_on;
rlip_execute_opcode(&expr_prog);
// Copy result
r_set(y, *(mpfr_t *) &expr_prog.return_real[0]);
}
void make_expr_double_double_approx(const char *expr, double startd, double endd, int degree)
{
int i;
const int p_count = 1000;
real_t *c, *cm;
real_t start, end, v;
double err;
// Init expression
if (f_expr_init(expr))
return;
// Init coef arrays and variables
cm = r_init_array(degree+1);
c = r_init_array(degree+1);
r_init(v);
r_init(start);
r_init(end);
r_setd(start, startd);
r_setd(end, endd);
fprintf_rl(stdout, "\n%s, x = [%g , %g], degree %d:\n\n", expr, startd, endd, degree);
// Fit
chebyshev_analysis_on_function_mpfr(f_expr, start, end, cm, degree, p_count);
polynomial_fit_on_function_by_dct_mpfr(f_expr, start, end, c, degree);
err = get_polynomial_error_mpfr(f_expr, start, end, c, degree, NEGMODE);
fprintf(stdout, "Polynomial error: %.5e\n", err);
// Print Chebyshev multipliers
for (i=0; i <= degree; i++)
{
mpfr_abs(v, cm[i], MPFR_RNDN);
if (mpfr_cmp_d(v, 1e-150) > 0)
{
//mpfr_fprintf(stdout, "T_%d(x) * % .32Rg\n", i, cm[i]);
ddouble_t q = mpfr_to_ddouble(cm[i]);
fprintf(stdout, "{%.17g, %.17g}, // T_%d (err %.3g)\n", q.hi, q.lo, i, diff_mpfr_ddouble(cm[i], q));
fflush(stdout);
}
}
r_free(v);
r_free_array(&cm, degree+1);
r_free_array(&c, degree+1);
}
void test_expr_ddouble(const char *expr, double start, double end, double step, int print_new_err)
{
int i;
real_t x, ym, yq;
ddouble_t r, xq;
double err, maxerr=0., maxerr_x=NAN, maxerr_y=NAN;
rlip_inputs_t inputs_ddouble[] = { RLIP_REAL_DOUBLEDOUBLE, {"x", &xq, "pr"} };
rlip_inputs_t inputs_mpfr[] = { RLIP_REAL_MPFR, {"x", &x, "pr"} };
rlip_t prog_ddouble, prog_mpfr;
prog_ddouble = rlip_expression_compile(expr, inputs_ddouble, sizeof(inputs_ddouble)/sizeof(*inputs_ddouble), 1, NULL);
prog_mpfr = rlip_expression_compile(expr, inputs_mpfr, sizeof(inputs_mpfr)/sizeof(*inputs_mpfr), 1, NULL);
if (prog_ddouble.valid_prog == 0 || prog_mpfr.valid_prog == 0)
{
free_rlip(&prog_ddouble);
free_rlip(&prog_mpfr);
fprintf_rl(stderr, "Invalid compiled program for expression '%s' in test_expr_ddouble()\n", expr);
return;
}
volatile int exec_on = 1;
prog_ddouble.exec_on = &exec_on;
prog_mpfr.exec_on = &exec_on;
r_init(x);
r_init(ym);
r_init(yq);
r_setd(x, start);
for (; mpfr_cmp_d(x, end) < 0; r_addd(x, step))
{
xq = mpfr_to_ddouble(x);
ddouble_to_mpfr(x, xq); // round it to an exact double-double value
// Execution
rlip_execute_opcode(&prog_ddouble);
rlip_execute_opcode(&prog_mpfr);
r = *(ddouble_t *) &prog_ddouble.return_real[0];
r_set(ym, *(mpfr_t *) &prog_mpfr.return_real[0]);
// Comparison
ddouble_to_mpfr(yq, r);
r_sub(yq, ym);
r_abs(yq);
err = r_todouble(yq);
if (err > maxerr)
{
maxerr = err;
maxerr_x = xq.hi;
maxerr_y = r.hi;
if (print_new_err)
{
fprintf_rl(stdout, "\tnew error of '%s': %.5e at %.16g (value %.16g)\n", expr, maxerr, maxerr_x, maxerr_y);
fflush(stdout);
}
}
}
fprintf(stdout, "Max error of '%s': %.5e at %.16g (value %.16g)\n", expr, maxerr, maxerr_x, maxerr_y);
fflush(stdout);
r_free(x);
r_free(ym);
r_free(yq);
free_rlip(&prog_ddouble);
free_rlip(&prog_mpfr);
}
void expr_eval_to_ddouble(const char *expr)
{
ddouble_t result;
rlip_inputs_t inputs_mpfr[] = { RLIP_REAL_MPFR };
rlip_t prog_mpfr;
// Compile
buffer_t comp_log={0};
prog_mpfr = rlip_expression_compile(expr, inputs_mpfr, sizeof(inputs_mpfr)/sizeof(*inputs_mpfr), 1, &comp_log);
if (prog_mpfr.valid_prog == 0)
{
fprintf_rl(stdout, "Compilation log: %s\n", comp_log.buf);
free_buf(&comp_log);
free_rlip(&prog_mpfr);
return;
}
free_buf(&comp_log);
// Execute
volatile int exec_on = 1;
prog_mpfr.exec_on = &exec_on;
rlip_execute_opcode(&prog_mpfr);
result = mpfr_to_ddouble(*(mpfr_t *) &prog_mpfr.return_real[0]);
// Print
mpfr_fprintf(stdout, "%s = %.60Rg = {%.17g, %.17g}\n", expr, *(mpfr_t *) &prog_mpfr.return_real[0], result.hi, result.lo);
fflush(stdout);
free_rlip(&prog_mpfr);
}
// Sinc windowed with squared gaussian window
void r_squared_gaussian_window(real_t y, real_t x, real_t w)
{
static int init=1;
static real_t a, b;
if (init)
{
init = 0;
r_init(a);
r_init(b);
}
// sq(gaussian(x*w) - gaussian(w)) / sq(gaussian(0.) - gaussian(w));
// = sq(gaussian(x*w) - gaussian(w)) / sq(1. - gaussian(w));
// a = x*w
r_rmul(a, x, w);
// = sq(gaussian(a) - gaussian(w)) / sq(1. - gaussian(w));
// a = gaussian(a)
// b = gaussian(w)
r_gaussian(a, a);
r_gaussian(b, w);
// = sq(a - b) / sq(1. - b)
// a = a - b
r_sub(a, b);
// b = 1 - b
r_setd(y, 1.);
r_rsub(b, y, b);
// a = sq(a)
// b = sq(b)
r_sq(a, a);
r_sq(b, b);
// y = a / b
r_rdiv(y, a, b);
}
real_t ws_range, ws_sigma_range;
int no_sine=0;
void f_wsinc(real_t y, real_t x)
{
static int init=1;
static real_t a;
if (init)
{
init = 0;
r_init(a);
}
r_abs(x);
if (mpfr_cmp(x, ws_range) >= 0) // if x is outside of the wsinc range
{
r_setd(y, 0.);
return ;
}
if (mpfr_cmp_d(x, 0.)==0) // if x == 0
{
r_setd(y, 1.);
return ;
}
if (no_sine)
r_setd(y, 1.);
else
{
// sin(pi*x)
r_pi(a);
r_mul(a, x);
r_sin(y, a);
}
// * 1/(pi*x)
r_pi(a);
r_mul(a, x);
r_div(y, a);
// Windowing
r_rdiv(a, x, ws_range);
r_squared_gaussian_window(a, a, ws_sigma_range);
r_mul(y, a);
}
void make_wsinc_table(const int order, const int lutsp, double wsinc_range, double sigma_range) // order is <= 6, lutsp can only be <= 15
{
int32_t i, is, segcount, prec;
real_t c[COEF_COUNT];
real_t segstep, segstart, segend;
double end=wsinc_range, step=1./pow(2., lutsp), err, maxerr=0.;
FILE *file;
char header_path[64];
sprintf(header_path, "../rouziclib/approximations/tables/fastwsinc.h", order);
file = fopen(header_path, "wb");
fprintf(file, "{");
r_init(ws_range);
r_setd(ws_range, wsinc_range);
r_init(ws_sigma_range);
r_setd(ws_sigma_range, sigma_range);
segcount = ceil(end / step);
r_init(segstep);
r_setd(segstep, step);
r_init(segstart);
r_init(segend);
for (i=0; i<COEF_COUNT; i++)
r_init(c[i]);
for (is=0; is<segcount; is++)
{
r_set(segstart, segend);
r_add(segend, segstep);
if (is==segcount-1) // only useful if the last segment only needs to cover a shorter range than usual
r_setd(segend, end);
for (i=0; i<COEF_COUNT; i++)
r_setd(c[i], 0.);
//if (r_todouble(segstart)==1.)
// no_sine = 1;
// Fitting
polynomial_fit_on_function_by_dct_mpfr(f_wsinc, segstart, segend, c, order);
err = get_polynomial_error_mpfr(f_wsinc, segstart, segend, c, order, no_sine==0 ? NEGMODE : DIVMODE);
if (err > maxerr)
maxerr = err;
// Printing
mpfr_printf("[%.7Rf , %.7Rf]\terr %e\n", segstart, segend, err);
for (i=0; i<order; i++)
mpfr_fprintf(file, "%.17Rg, ", c[i]);
mpfr_fprintf(file, "%.17Rg%s", c[order], (is==segcount-1) ? "};\n" : ", \n");
}
double ind_off = exp2(double_get_exponent(wsinc_range)); // offset to calculate the LUT index from the offset mantissa
if (double_get_mantissa(wsinc_range))
ind_off *= 2.;
int ish = 52 - (double_get_exponent(ind_off) + lutsp);
fprintf(file, "const uint32_t order = %d, lutsp = %d, ish = %d;\n", order, lutsp, ish);
fprintf(file, "const double wsinc_range = %g, ind_off = %g;", wsinc_range, ind_off);
fclose (file);
printf("\nMax error: %g\n", maxerr);
printf("LUT size (double): %zu bytes\n", segcount * (order+1) * sizeof(double));
}
void test_matrix()
{
double /*a[COEF_COUNT*COEF_COUNT],*/ b[COEF_COUNT*COEF_COUNT], c[COEF_COUNT*COEF_COUNT];
double a[] = {3., 3.2, 3.5, 3.6};
matrix_inverse(a, b, 2);
a[0] = 118.4;
a[1] = 135.2;
matrix_multiplication(b, a, c, 2, 2, 1);
printf("\n\nInverse matrix:\n%4f\t%4f\n%4f\t%4f\n\n", b[0], b[1], b[2], b[3]);
printf("\n\nResult matrix:\n%4f\t%4f\n", c[0], c[1]);
}
void cos_error_curve()
{
double x;
real_t xr, vd, vr, d;
r_init(xr);
r_init(vd);
r_init(vr);
r_init(d);
FILE *file = fopen("error_curves/cosd_err.dat", "wb");
for (x=0.; x <= 2*pi; x += 1e-4)
{
r_setd(xr, x);
r_setd(vd, cos(x));
r_cos(vr, xr);
r_rsub(d, vd, vr);
mpfr_fprintf(file, "%g\t% Rg\n", x, d);
//mpfr_fprintf(file, "%g\t% g\n", x, r_todouble(vd) - r_todouble(vr));
}
fclose(file);
}
// erf_radlim
double radlim, seg_offset=0.;
double erf_radlim(double x, double in_radlim, double in_step)
{
int i;
static double step=0.;
static double radlim=0.;
static double *v=NULL;
static size_t v_count=0, v_as=0;
double t, v_prev;
if (in_radlim <= 0. || in_step <= 0.)
return NAN;
if (radlim != in_radlim || step != in_step)
{
radlim = in_radlim;
step = in_step;
v_count = 0;
v_prev = 0.;
for (i=0, t=-radlim; t < radlim; t+=step, i++)
{
alloc_enough(&v, v_count = i+1, &v_as, sizeof(double), 2.);
if (i > 0)
v_prev = v[i-1];
v[i] = v_prev + erf(radlim*sqrt(1.-sq(t/radlim))) * gaussian(t) * step / sqrt(pi);
}
}
double p = (x + radlim) / step;
int i0, i1;
i0 = rangelimit_i32(p, 0, v_count-1);
i1 = rangelimit_i32(p+1., 0, v_count-1);
t = p - floor(p);
return v[i0] * (1.-t) + v[i1] * t;
}
double radlim_x_remap(double x) // remaps x from [-1 , 1] to [-radlim , radlim] non-linearly
{
double xa, xn;
x += seg_offset; // remaps [0 , step] to within [-1 , 1]
// Delinearise
xa = fabs(x);
xn = x;
if (radlim <= 1.66)
//xn = (3. - x*x) * x * 0.5;
xn = (2.*xa - sq(xa)) * sign(x); // inverse of this is (1. - sqrt(1. - fabs(x))) * sign(x)
xn *= radlim; // remaps [-1 , 1] to [-radlim , radlim]
return xn;
}
void f_erf_radlim(real_t y, real_t x)
{
r_setd(y, erf_radlim(radlim_x_remap(r_todouble(x)), radlim, 1e-7 * radlim));
}
/*int order_index_glo, order_glo;
real_t zero_glo, segstep;
void f_erf_radlim_coef(real_t y, real_t x)
{
real_t c[COEF_COUNT];
for (i=0; i<COEF_COUNT; i++)
r_init(c[i]);
find_polynomial_fit_old(f_erf_radlim, zero_glo, segstep_glo, c, order_glo, 0.);
r_set(y, c[order_index_glo]);
for (i=0; i<COEF_COUNT; i++)
r_free(c[i]);
}
void make_erf_radlim_table2(const int order, const double step, int order_index)
{
int32_t i, is, segcount, prec;
real_t c[COEF_COUNT];
real_t segstart, segend, maxseg;
double start=0., end=1.66, err, maxerr=0.;
FILE *file;
char header_path[64];
segcount = nearbyint(ceil((end-start) / step));
sprintf(header_path, "erf_radlim2_%g_d%d_step_%g_human.dat", radlim, order, step);
file = fopen(header_path, "wb");
r_init(segstep);
r_setd(segstep, step);
r_init(segstart);
r_init(segend);
r_init(maxseg);
r_init(zero_glo);
order_index_glo = order_index;
order_glo = 3;
r_setd(segend, start);
for (i=0; i<COEF_COUNT; i++)
r_init(c[i]);
for (is=0; is<segcount; is++)
{
r_set(segstart, segend);
r_add(segend, segstep);
for (i=0; i<COEF_COUNT; i++)
r_setd(c[i], 0.);
seg_offset = r_todouble(segstart);
// Fit
find_polynomial_fit_old(f_erf_radlim_coef, segstart, segend, c, order, 0.);
err = get_polynomial_error_mpfr(f_erf_radlim_coef, segstart, segend, c, order, NEGMODE);
// Reduce digits
err = reduce_digits_mpfr(f_erf_radlim_coef, segstart, segend, c, order, NEGMODE, 1.01, 10.);
if (err > maxerr)
{
maxerr = err;
r_set(maxseg, segstart);
}