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Mar 16, 2025
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re-name integration constants #714

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102 changes: 51 additions & 51 deletions code/scipy/integrate/integrate.c
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Original file line number Diff line number Diff line change
Expand Up @@ -41,21 +41,21 @@

#if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_DOUBLE
ULAB_DEFINE_FLOAT_CONST(etolerance, MICROPY_FLOAT_CONST(1e-14), 0x283424dcUL, 0x3e901b2b29a4692bULL);
#define MACHEPS MICROPY_FLOAT_CONST(1e-17)
#define ULAB_MACHEPS MICROPY_FLOAT_CONST(1e-17)
#else
ULAB_DEFINE_FLOAT_CONST(etolerance, MICROPY_FLOAT_CONST(1e-8), 0x358637cfUL, 0x3e7010c6f7d42d18ULL);
#define MACHEPS MICROPY_FLOAT_CONST(1e-8)
#define ULAB_MACHEPS MICROPY_FLOAT_CONST(1e-8)
#endif

#define ZERO MICROPY_FLOAT_CONST(0.0)
#define POINT_TWO_FIVE MICROPY_FLOAT_CONST(0.25)
#define ONE MICROPY_FLOAT_CONST(1.0)
#define TWO MICROPY_FLOAT_CONST(2.0)
#define FOUR MICROPY_FLOAT_CONST(4.0)
#define SIX MICROPY_FLOAT_CONST(6.0)
#define TEN MICROPY_FLOAT_CONST(10.0)
#define FIFTEEN MICROPY_FLOAT_CONST(15.0)
#define EPS_5 MICROPY_FLOAT_CONST(1e-5)
#define ULAB_ZERO MICROPY_FLOAT_CONST(0.0)
#define ULAB_POINT_TWO_FIVE MICROPY_FLOAT_CONST(0.25)
#define ULAB_ONE MICROPY_FLOAT_CONST(1.0)
#define ULAB_TWO MICROPY_FLOAT_CONST(2.0)
#define ULAB_FOUR MICROPY_FLOAT_CONST(4.0)
#define ULAB_SIX MICROPY_FLOAT_CONST(6.0)
#define ULAB_TEN MICROPY_FLOAT_CONST(10.0)
#define ULAB_FIFTEEN MICROPY_FLOAT_CONST(15.0)
#define ULAB_EPSILON_5 MICROPY_FLOAT_CONST(1e-5)


static mp_float_t integrate_python_call(const mp_obj_type_t *type, mp_obj_t fun, mp_float_t x, mp_obj_t *fargs, uint8_t nparams) {
Expand All @@ -68,7 +68,7 @@ static mp_float_t integrate_python_call(const mp_obj_type_t *type, mp_obj_t fun,

// sign helper function
int sign(mp_float_t x) {
if (x >= ZERO)
if (x >= ULAB_ZERO)
return 1;
else
return -1;
Expand All @@ -85,7 +85,7 @@ mp_float_t exp_sinh_opt_d(mp_float_t (*fun)(mp_float_t), mp_float_t a, mp_float_
mp_obj_t fargs[1];
mp_float_t h2 = integrate_python_call(type, fun, a + d/2, fargs, 0) - integrate_python_call(type, fun, (a + d*2)*4, fargs, 0);
int i = 1, j = 32; // j=32 is optimal to find r
if (isfinite(h2) && MICROPY_FLOAT_C_FUN(fabs)(h2) > EPS_5) { // if |h2| > 2^-16
if (isfinite(h2) && MICROPY_FLOAT_C_FUN(fabs)(h2) > ULAB_EPSILON_5) { // if |h2| > 2^-16
mp_float_t r, fl, fr, h, s = 0, lfl, lfr, lr = 2;
do { // find max j such that fl and fr are finite
j /= 2;
Expand Down Expand Up @@ -118,8 +118,8 @@ mp_float_t exp_sinh_opt_d(mp_float_t (*fun)(mp_float_t), mp_float_t a, mp_float_
if (s > eps) { // if sum of |h| > eps
h = lfl - lfr; // use last fl and fr before the sign change
r = lr; // use last r before the sign change
if (h != ZERO) // if last diff != 0, back up r by one step
r /= TWO;
if (h != ULAB_ZERO) // if last diff != 0, back up r by one step
r /= ULAB_TWO;
if (MICROPY_FLOAT_C_FUN(fabs)(lfl) < MICROPY_FLOAT_C_FUN(fabs)(lfr))
d /= r; // move d closer to the finite endpoint
else
Expand All @@ -135,8 +135,8 @@ mp_float_t exp_sinh_opt_d(mp_float_t (*fun)(mp_float_t), mp_float_t a, mp_float_
mp_float_t tanhsinh(mp_float_t (*fun)(mp_float_t), mp_float_t a, mp_float_t b, uint16_t n, mp_float_t eps, mp_float_t *e) {
const mp_obj_type_t *type = mp_obj_get_type(fun);
mp_obj_t fargs[1];
const mp_float_t tol = TEN*eps;
mp_float_t c = ZERO, d = ONE, s, sign = ONE, v, h = TWO;
const mp_float_t tol = ULAB_TEN * eps;
mp_float_t c = ULAB_ZERO, d = ULAB_ONE, s, sign = ULAB_ONE, v, h = ULAB_TWO;
int k = 0, mode = 0; // Tanh-Sinh = 0, Exp-Sinh = 1, Sinh-Sinh = 2
if (b < a) { // swap bounds
v = b;
Expand All @@ -145,8 +145,8 @@ mp_float_t tanhsinh(mp_float_t (*fun)(mp_float_t), mp_float_t a, mp_float_t b, u
sign = -1;
}
if (isfinite(a) && isfinite(b)) {
c = (a+b)/TWO;
d = (b-a)/TWO;
c = (a+b) / ULAB_TWO;
d = (b-a) / ULAB_TWO;
v = c;
}
else if (isfinite(a)) {
Expand All @@ -165,20 +165,20 @@ mp_float_t tanhsinh(mp_float_t (*fun)(mp_float_t), mp_float_t a, mp_float_t b, u
}
else {
mode = 2; // Sinh-Sinh
v = ZERO;
v = ULAB_ZERO;
}
s = integrate_python_call(type, fun, v, fargs, 0);
do {
mp_float_t p = ZERO, q, fp = ZERO, fm = ZERO, t, eh;
h /= TWO;
mp_float_t p = ULAB_ZERO, q, fp = ULAB_ZERO, fm = ULAB_ZERO, t, eh;
h /= ULAB_TWO;
t = eh = MICROPY_FLOAT_C_FUN(exp)(h);
if (k > ZERO)
if (k > ULAB_ZERO)
eh *= eh;
if (mode == 0) { // Tanh-Sinh
do {
mp_float_t u = MICROPY_FLOAT_C_FUN(exp)(ONE / t - t); // = exp(-2*sinh(j*h)) = 1/exp(sinh(j*h))^2
mp_float_t r = TWO * u / (ONE + u); // = 1 - tanh(sinh(j*h))
mp_float_t w = (t + ONE / t) * r / (ONE + u); // = cosh(j*h)/cosh(sinh(j*h))^2
mp_float_t u = MICROPY_FLOAT_C_FUN(exp)(ULAB_ONE / t - t); // = exp(-2*sinh(j*h)) = 1/exp(sinh(j*h))^2
mp_float_t r = ULAB_TWO * u / (ULAB_ONE + u); // = 1 - tanh(sinh(j*h))
mp_float_t w = (t + ULAB_ONE / t) * r / (ULAB_ONE + u); // = cosh(j*h)/cosh(sinh(j*h))^2
mp_float_t x = d*r;
if (a+x > a) { // if too close to a then reuse previous fp
mp_float_t y = integrate_python_call(type, fun, a+x, fargs, 0);
Expand All @@ -196,11 +196,11 @@ mp_float_t tanhsinh(mp_float_t (*fun)(mp_float_t), mp_float_t a, mp_float_t b, u
} while (MICROPY_FLOAT_C_FUN(fabs)(q) > eps*MICROPY_FLOAT_C_FUN(fabs)(p));
}
else {
t /= TWO;
t /= ULAB_TWO;
do {
mp_float_t r = MICROPY_FLOAT_C_FUN(exp)(t - POINT_TWO_FIVE / t); // = exp(sinh(j*h))
mp_float_t r = MICROPY_FLOAT_C_FUN(exp)(t - ULAB_POINT_TWO_FIVE / t); // = exp(sinh(j*h))
mp_float_t x, y, w = r;
q = ZERO;
q = ULAB_ZERO;
if (mode == 1) { // Exp-Sinh
x = c + d/r;
if (x == c) // if x hit the finite endpoint then break
Expand All @@ -210,8 +210,8 @@ mp_float_t tanhsinh(mp_float_t (*fun)(mp_float_t), mp_float_t a, mp_float_t b, u
q += y/w;
}
else { // Sinh-Sinh
r = (r - ONE / r) / TWO; // = sinh(sinh(j*h))
w = (w + ONE / w) / TWO; // = cosh(sinh(j*h))
r = (r - ULAB_ONE / r) / ULAB_TWO; // = sinh(sinh(j*h))
w = (w + ULAB_ONE / w) / ULAB_TWO; // = cosh(sinh(j*h))
x = c - d*r;
y = integrate_python_call(type, fun, x, fargs, 0);
if (isfinite(y)) // if f(x) is finite, add to local sum
Expand All @@ -221,7 +221,7 @@ mp_float_t tanhsinh(mp_float_t (*fun)(mp_float_t), mp_float_t a, mp_float_t b, u
y = integrate_python_call(type, fun, x, fargs, 0);
if (isfinite(y)) // if f(x) is finite, add to local sum
q += y*w;
q *= t + POINT_TWO_FIVE / t; // q *= cosh(j*h)
q *= t + ULAB_POINT_TWO_FIVE / t; // q *= cosh(j*h)
p += q;
t *= eh;
} while (MICROPY_FLOAT_C_FUN(fabs)(q) > eps*MICROPY_FLOAT_C_FUN(fabs)(p));
Expand Down Expand Up @@ -319,12 +319,12 @@ mp_float_t qromb(mp_float_t (*fun)(mp_float_t), mp_float_t a, mp_float_t b, uint
for (i = 1; i < n; ++i) {
unsigned long long k = 1UL << i;
unsigned long long s = 1;
mp_float_t sum = ZERO;
mp_float_t sum = ULAB_ZERO;
mp_float_t *Rt;
h /= TWO;
h /= ULAB_TWO;
for (j = 1; j < k; j += 2)
sum += integrate_python_call(type, fun, a+j*h, fargs, 0);
Ru[0] = h*sum + Ro[0] / TWO;
Ru[0] = h*sum + Ro[0] / ULAB_TWO;
for (j = 1; j <= i; ++j) {
s <<= 2;
Ru[j] = (s*Ru[j-1] - Ro[j-1])/(s-1);
Expand Down Expand Up @@ -408,17 +408,17 @@ mp_float_t as(mp_float_t (*fun)(mp_float_t), mp_float_t a, mp_float_t b, mp_floa
mp_float_t fb, mp_float_t v, mp_float_t eps, int n, mp_float_t t) {
const mp_obj_type_t *type = mp_obj_get_type(fun);
mp_obj_t fargs[1];
mp_float_t h = (b-a) / TWO;
mp_float_t f1 = integrate_python_call(type, fun, a + h / TWO, fargs, 0);
mp_float_t f2 = integrate_python_call(type, fun, b - h / TWO, fargs, 0);
mp_float_t sl = h*(fa + FOUR * f1 + fm) / SIX;
mp_float_t sr = h*(fm + FOUR * f2 + fb) / SIX;
mp_float_t h = (b-a) / ULAB_TWO;
mp_float_t f1 = integrate_python_call(type, fun, a + h / ULAB_TWO, fargs, 0);
mp_float_t f2 = integrate_python_call(type, fun, b - h / ULAB_TWO, fargs, 0);
mp_float_t sl = h*(fa + ULAB_FOUR * f1 + fm) / ULAB_SIX;
mp_float_t sr = h*(fm + ULAB_FOUR * f2 + fb) / ULAB_SIX;
mp_float_t s = sl+sr;
mp_float_t d = (s-v) / FIFTEEN;
mp_float_t d = (s-v) / ULAB_FIFTEEN;
mp_float_t m = a+h;
if (n <= 0 || MICROPY_FLOAT_C_FUN(fabs)(d) < eps)
return t + s + d; // note: fabs(d) can be used as error estimate
eps /= TWO;
eps /= ULAB_TWO;
--n;
t = as(fun, a, m, fa, f1, fm, sl, eps, n, t);
return as(fun, m, b, fm, f2, fb, sr, eps, n, t);
Expand All @@ -430,7 +430,7 @@ mp_float_t qasi(mp_float_t (*fun)(mp_float_t), mp_float_t a, mp_float_t b, int n
mp_float_t fa = integrate_python_call(type, fun, a, fargs, 0);
mp_float_t fm = integrate_python_call(type, fun, (a+b)/2, fargs, 0);
mp_float_t fb = integrate_python_call(type, fun, b, fargs, 0);
mp_float_t v = (fa + FOUR * fm + fb) * (b-a) / SIX;
mp_float_t v = (fa + ULAB_FOUR * fm + fb) * (b-a) / ULAB_SIX;
return as(fun, a, b, fa, fm, fb, v, eps, n, 0);
}

Expand Down Expand Up @@ -562,8 +562,8 @@ mp_float_t gk(mp_float_t (*fun)(mp_float_t), mp_float_t c, mp_float_t d, mp_floa
};
const mp_obj_type_t *type = mp_obj_get_type(fun);
mp_obj_t fargs[1];
mp_float_t p = ZERO; // kronrod quadrature sum
mp_float_t q = ZERO; // gauss quadrature sum
mp_float_t p = ULAB_ZERO; // kronrod quadrature sum
mp_float_t q = ULAB_ZERO; // gauss quadrature sum
mp_float_t fp, fm;
mp_float_t e;
int i;
Expand All @@ -581,24 +581,24 @@ mp_float_t gk(mp_float_t (*fun)(mp_float_t), mp_float_t c, mp_float_t d, mp_floa
p += (fp + fm) * weights[i];
}
*err = MICROPY_FLOAT_C_FUN(fabs)(p - q);
e = MICROPY_FLOAT_C_FUN(fabs)(2 * p * MACHEPS); // optional, to take 1e-17 MachEps prec. into account
e = MICROPY_FLOAT_C_FUN(fabs)(2 * p * ULAB_MACHEPS); // optional, to take 1e-17 MachEps prec. into account
if (*err < e)
*err = e;
return p;
}

mp_float_t qakro(mp_float_t (*fun)(mp_float_t), mp_float_t a, mp_float_t b, int n, mp_float_t tol, mp_float_t eps, mp_float_t *err) {
mp_float_t c = (a+b) / TWO;
mp_float_t d = (b-a) / TWO;
mp_float_t c = (a+b) / ULAB_TWO;
mp_float_t d = (b-a) / ULAB_TWO;
mp_float_t e;
mp_float_t r = gk(fun, c, d, &e);
mp_float_t s = d*r;
mp_float_t t = MICROPY_FLOAT_C_FUN(fabs)(s*tol);
if (tol == ZERO)
if (tol == ULAB_ZERO)
tol = t;
if (n > 0 && t < e && tol < e) {
s = qakro(fun, a, c, n-1, t / TWO, eps, err);
s += qakro(fun, c, b, n-1, t / TWO, eps, &e);
s = qakro(fun, a, c, n-1, t / ULAB_TWO, eps, err);
s += qakro(fun, c, b, n-1, t / ULAB_TWO, eps, &e);
*err += e;
return s;
}
Expand Down
2 changes: 1 addition & 1 deletion code/ulab.c
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Expand Up @@ -33,7 +33,7 @@
#include "user/user.h"
#include "utils/utils.h"

#define ULAB_VERSION 6.7.3
#define ULAB_VERSION 6.7.4
#define xstr(s) str(s)
#define str(s) #s

Expand Down
6 changes: 6 additions & 0 deletions docs/ulab-change-log.md
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@@ -1,3 +1,9 @@
Sun, 16 Mar 2025

version 6.7.4

re-name integration constants to avoid name clash with EPS ports

Sun, 26 Jan 2025

version 6.7.3
Expand Down
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