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-rw-r--r--libk/src/math/abs.c14
-rw-r--r--libk/src/math/ceil.c59
-rw-r--r--libk/src/math/copysign.c20
-rw-r--r--libk/src/math/fact.c29
-rw-r--r--libk/src/math/fclamp.c13
-rw-r--r--libk/src/math/floor.c55
-rw-r--r--libk/src/math/fma.c38
-rw-r--r--libk/src/math/fmod.c129
-rw-r--r--libk/src/math/frexp.c19
-rw-r--r--libk/src/math/pow.c152
-rw-r--r--libk/src/math/sqrt.c36
-rw-r--r--libk/src/math/trig.c62
12 files changed, 626 insertions, 0 deletions
diff --git a/libk/src/math/abs.c b/libk/src/math/abs.c
new file mode 100644
index 0000000..1757272
--- /dev/null
+++ b/libk/src/math/abs.c
@@ -0,0 +1,14 @@
+#include <math.h>
+#include <stdint.h>
+
+float fabsf(float num) {
+ union {float f; uint32_t i;} u = {num};
+ u.i &= 0x7fffffff;
+ return u.f;
+}
+
+double fabs(double num) {
+ union {double f; uint64_t i;} u = {num};
+ u.i &= -1ULL/2;
+ return u.f;
+}
diff --git a/libk/src/math/ceil.c b/libk/src/math/ceil.c
new file mode 100644
index 0000000..17b667f
--- /dev/null
+++ b/libk/src/math/ceil.c
@@ -0,0 +1,59 @@
+#include <stdint.h>
+#include <float.h>
+#include <math.h>
+
+#include "internal/libm.h"
+
+#define EPS DBL_EPSILON
+
+static const double toint = 1/EPS;
+
+double ceil(double x)
+{
+ union {double f; uint64_t i;} u = {x};
+ int e = u.i >> 52 & 0x7ff;
+ double y;
+
+ if (e >= 0x3ff+52 || x == 0)
+ return x;
+
+ if (u.i >> 63) {
+ y = x - toint + toint - x;
+ } else {
+ y = x + toint - toint - x;
+ }
+
+ if (e <= 0x3ff-1) {
+ FORCE_EVAL(y);
+ return u.i >> 63 ? -0.0 : 1;
+ }
+
+ if (y < 0)
+ return x + y + 1;
+ return x + y;
+}
+
+float ceilf(float x) {
+ union {float f; uint32_t i;} u = {x};
+ int e = (int)(u.i >> 23 & 0xff) - 0x7f;
+ uint32_t m;
+
+ if (e >= 23)
+ return x;
+ if (e >= 0) {
+ m = 0x007fffff >> e;
+ if ((u.i & m) == 0)
+ return x;
+ FORCE_EVAL(x + 0x1p120f);
+ if (u.i >> 31 == 0)
+ u.i += m;
+ u.i &= ~m;
+ } else {
+ FORCE_EVAL(x + 0x1p120f);
+ if (u.i >> 31)
+ u.f = -0.0;
+ else if (u.i << 1)
+ u.f = 1.0;
+ }
+ return u.f;
+}
diff --git a/libk/src/math/copysign.c b/libk/src/math/copysign.c
new file mode 100644
index 0000000..fd5fd4f
--- /dev/null
+++ b/libk/src/math/copysign.c
@@ -0,0 +1,20 @@
+#include <math.h>
+#include <stdint.h>
+
+#define DMASK 0x8000000000000000
+
+double copysign(double n, double s) {
+ union {double f; uint64_t i;} sb = {s};
+ union {double f; uint64_t i;} nb = {n};
+ nb.i = (nb.i & ~DMASK) | (sb.i & DMASK);
+ return nb.f;
+}
+
+#define FMASK 0x80000000
+
+float copysignf(float n, float s) {
+ union {float f; uint32_t i;} sb = {s};
+ union {float f; uint32_t i;} nb = {n};
+ nb.i = (nb.i & ~FMASK) | (sb.i & FMASK);
+ return nb.f;
+}
diff --git a/libk/src/math/fact.c b/libk/src/math/fact.c
new file mode 100644
index 0000000..a146e4d
--- /dev/null
+++ b/libk/src/math/fact.c
@@ -0,0 +1,29 @@
+#include <math.h>
+
+static unsigned int FACT_TABLE[] = {
+ 1, // 0
+ 1, // 1
+ 2, // 2
+ 6, // 3
+ 24, // 4
+ 120, // 5
+ 720, // 6
+ 5040, // 7
+ 40320, // 8
+ 362880, // 9
+ 3628800, // 10
+ 39916800, // 11
+ 479001600, // 12
+};
+
+unsigned long long fact(unsigned int num) {
+ if (num < 13) {
+ return FACT_TABLE[num];
+ }
+ unsigned long long l = FACT_TABLE[12];
+ for (unsigned int i = 12; i < num;) {
+ i++;
+ l *= i;
+ }
+ return l;
+}
diff --git a/libk/src/math/fclamp.c b/libk/src/math/fclamp.c
new file mode 100644
index 0000000..f757b48
--- /dev/null
+++ b/libk/src/math/fclamp.c
@@ -0,0 +1,13 @@
+#include <math.h>
+
+double fclamp(double x, double l, double h) {
+ if (x < l) return l;
+ if (x > h) return h;
+ return x;
+}
+
+float fclampf(float x, float l, float h) {
+ if (x < l) return l;
+ if (x > h) return h;
+ return x;
+}
diff --git a/libk/src/math/floor.c b/libk/src/math/floor.c
new file mode 100644
index 0000000..ce8e07e
--- /dev/null
+++ b/libk/src/math/floor.c
@@ -0,0 +1,55 @@
+#include <stdint.h>
+#include <float.h>
+#include <math.h>
+
+#include "internal/libm.h"
+
+#define EPS DBL_EPSILON
+
+static const double toint = 1/EPS;
+
+double floor(double x) {
+ union {double f; uint64_t i;} u = {x};
+ int e = u.i >> 52 & 0x7ff;
+ double y;
+
+ if (e >= 0x3ff+52 || x == 0)
+ return x;
+ if (u.i >> 63)
+ y = x - toint + toint - x;
+ else
+ y = x + toint - toint - x;
+ if (e <= 0x3ff-1) {
+ return u.i >> 63 ? -1 : 0;
+ }
+ if (y > 0) {
+ FORCE_EVAL(y);
+ return x + y - 1;
+ }
+ return x + y;
+}
+
+float floorf(float x) {
+ union {float f; uint32_t i;} u = {x};
+ int e = (int)(u.i >> 23 & 0xff) - 0x7f;
+ uint32_t m;
+
+ if (e >= 23)
+ return x;
+ if (e >= 0) {
+ m = 0x007fffff >> e;
+ if ((u.i & m) == 0)
+ return x;
+ FORCE_EVAL(x + 0x1p120f);
+ if (u.i >> 31)
+ u.i += m;
+ u.i &= ~m;
+ } else {
+ FORCE_EVAL(x + 0x1p120f);
+ if (u.i >> 31 == 0)
+ u.i = 0;
+ else if (u.i << 1)
+ u.f = -1.0;
+ }
+ return u.f;
+}
diff --git a/libk/src/math/fma.c b/libk/src/math/fma.c
new file mode 100644
index 0000000..b26229e
--- /dev/null
+++ b/libk/src/math/fma.c
@@ -0,0 +1,38 @@
+#include <stdint.h>
+#include <math.h>
+
+double fma(double x, double y, double z) {
+ double xy, result;
+ union {double f; uint64_t i;} u;
+ int e;
+
+ xy = (double)x * y;
+ result = xy + z;
+ u.f = result;
+ e = u.i>>52 & 0x7ff;
+ if (
+ (u.i & 0x1fffffff) != 0x10000000 ||
+ e == 0x7ff ||
+ (result - xy == z && result - z == xy)
+ ) {
+ z = result;
+ return z;
+ }
+
+ double err;
+ int neg = u.i >> 63;
+ if (neg == (z > xy))
+ err = xy - result + z;
+ else
+ err = z - result + xy;
+ if (neg == (err < 0))
+ u.i++;
+ else
+ u.i--;
+ z = u.f;
+ return z;
+}
+
+float fmaf(float x, float y, float z) {
+ return fma(x, y, z);
+}
diff --git a/libk/src/math/fmod.c b/libk/src/math/fmod.c
new file mode 100644
index 0000000..996f78b
--- /dev/null
+++ b/libk/src/math/fmod.c
@@ -0,0 +1,129 @@
+#include <math.h>
+#include <stdint.h>
+
+double fmod(double x, double y) {
+ union {double f; uint64_t i;} ux = {x}, uy = {y};
+ int ex = ux.i>>52 & 0x7ff;
+ int ey = uy.i>>52 & 0x7ff;
+ int sx = ux.i>>63;
+ uint64_t i;
+
+ /* in the followings uxi should be ux.i, but then gcc wrongly adds */
+ /* float load/store to inner loops ruining performance and code size */
+ uint64_t uxi = ux.i;
+
+ if (uy.i<<1 == 0 || isnan(y) || ex == 0x7ff)
+ return (x*y)/(x*y);
+ if (uxi<<1 <= uy.i<<1) {
+ if (uxi<<1 == uy.i<<1)
+ return 0*x;
+ return x;
+ }
+
+ /* normalize x and y */
+ if (!ex) {
+ for (i = uxi<<12; i>>63 == 0; ex--, i <<= 1);
+ uxi <<= -ex + 1;
+ } else {
+ uxi &= -1ULL >> 12;
+ uxi |= 1ULL << 52;
+ }
+ if (!ey) {
+ for (i = uy.i<<12; i>>63 == 0; ey--, i <<= 1);
+ uy.i <<= -ey + 1;
+ } else {
+ uy.i &= -1ULL >> 12;
+ uy.i |= 1ULL << 52;
+ }
+
+ /* x mod y */
+ for (; ex > ey; ex--) {
+ i = uxi - uy.i;
+ if (i >> 63 == 0) {
+ if (i == 0)
+ return 0*x;
+ uxi = i;
+ }
+ uxi <<= 1;
+ }
+ i = uxi - uy.i;
+ if (i >> 63 == 0) {
+ if (i == 0)
+ return 0*x;
+ uxi = i;
+ }
+ for (; uxi>>52 == 0; uxi <<= 1, ex--);
+
+ /* scale result */
+ if (ex > 0) {
+ uxi -= 1ULL << 52;
+ uxi |= (uint64_t)ex << 52;
+ } else {
+ uxi >>= -ex + 1;
+ }
+ uxi |= (uint64_t)sx << 63;
+ ux.i = uxi;
+ return ux.f;
+}
+
+float fmodf(float x, float y) {
+ union {float f; uint32_t i;} ux = {x}, uy = {y};
+ int ex = ux.i>>23 & 0xff;
+ int ey = uy.i>>23 & 0xff;
+ uint32_t sx = ux.i & 0x80000000;
+ uint32_t i;
+ uint32_t uxi = ux.i;
+
+ if (uy.i<<1 == 0 || isnan(y) || ex == 0xff)
+ return (x*y)/(x*y);
+ if (uxi<<1 <= uy.i<<1) {
+ if (uxi<<1 == uy.i<<1)
+ return 0*x;
+ return x;
+ }
+
+ /* normalize x and y */
+ if (!ex) {
+ for (i = uxi<<9; i>>31 == 0; ex--, i <<= 1);
+ uxi <<= -ex + 1;
+ } else {
+ uxi &= -1U >> 9;
+ uxi |= 1U << 23;
+ }
+ if (!ey) {
+ for (i = uy.i<<9; i>>31 == 0; ey--, i <<= 1);
+ uy.i <<= -ey + 1;
+ } else {
+ uy.i &= -1U >> 9;
+ uy.i |= 1U << 23;
+ }
+
+ /* x mod y */
+ for (; ex > ey; ex--) {
+ i = uxi - uy.i;
+ if (i >> 31 == 0) {
+ if (i == 0)
+ return 0*x;
+ uxi = i;
+ }
+ uxi <<= 1;
+ }
+ i = uxi - uy.i;
+ if (i >> 31 == 0) {
+ if (i == 0)
+ return 0*x;
+ uxi = i;
+ }
+ for (; uxi>>23 == 0; uxi <<= 1, ex--);
+
+ /* scale result up */
+ if (ex > 0) {
+ uxi -= 1U << 23;
+ uxi |= (uint32_t)ex << 23;
+ } else {
+ uxi >>= -ex + 1;
+ }
+ uxi |= sx;
+ ux.i = uxi;
+ return ux.f;
+}
diff --git a/libk/src/math/frexp.c b/libk/src/math/frexp.c
new file mode 100644
index 0000000..16b8dd3
--- /dev/null
+++ b/libk/src/math/frexp.c
@@ -0,0 +1,19 @@
+#include <math.h>
+
+double frexp(double arg, int* exp) {
+ *exp = 0;
+ while (arg > 1) {
+ arg /= 2;;
+ (*exp)++;
+ }
+ return arg;
+}
+
+float frexpf(float arg, int* exp) {
+ *exp = 0;
+ while (arg > 1) {
+ arg /= 2;
+ (*exp)++;
+ }
+ return arg;
+}
diff --git a/libk/src/math/pow.c b/libk/src/math/pow.c
new file mode 100644
index 0000000..c850db7
--- /dev/null
+++ b/libk/src/math/pow.c
@@ -0,0 +1,152 @@
+#include <stdint.h>
+#include <string.h>
+#include <math.h>
+
+uint32_t float_as_uint32 (float a) {
+ uint32_t r;
+ memcpy (&r, &a, sizeof r);
+ return r;
+}
+
+float uint32_as_float (uint32_t a) {
+ float r;
+ memcpy (&r, &a, sizeof r);
+ return r;
+}
+
+void logf_ext (float a, float *loghi, float *loglo) {
+ const float LOG2_HI = 6.93147182e-1f;
+ const float LOG2_LO = -1.90465421e-9f;
+ const float SQRT_HALF = 0.70710678f;
+ float m, r, i, s, t, p, qhi, qlo;
+ int e;
+
+ const float POW_TWO_M23 = 1.19209290e-7f;
+ const float POW_TWO_P23 = 8388608.0f;
+ const float FP32_MIN_NORM = 1.175494351e-38f;
+ i = 0.0f;
+
+ if (a < FP32_MIN_NORM) {
+ a = a * POW_TWO_P23;
+ i = -23.0f;
+ }
+
+ e = (float_as_uint32 (a) - float_as_uint32 (SQRT_HALF)) & 0xff800000;
+ m = uint32_as_float (float_as_uint32 (a) - e);
+ i = fmaf ((float)e, POW_TWO_M23, i);
+
+ p = m + 1.0f;
+ m = m - 1.0f;
+ r = 1.0f / p;
+ qhi = r * m;
+ qlo = r * fmaf (qhi, -m, fmaf (qhi, -2.0f, m));
+
+ s = qhi * qhi;
+ r = 0.1293334961f;
+ r = fmaf (r, s, 0.1419928074f);
+ r = fmaf (r, s, 0.2000148296f);
+ r = fmaf (r, s, 0.3333332539f);
+ t = fmaf (qhi, qlo + qlo, fmaf (qhi, qhi, -s));
+ p = s * qhi;
+ t = fmaf (s, qlo, fmaf (t, qhi, fmaf (s, qhi, -p)));
+ s = fmaf (r, p, fmaf (r, t, qlo));
+ r = 2 * qhi;
+
+ t = fmaf ( LOG2_HI, i, r);
+ p = fmaf (-LOG2_HI, i, t);
+ s = fmaf ( LOG2_LO, i, fmaf (2.f, s, r - p));
+ *loghi = p = t + s;
+ *loglo = (t - p) + s;
+}
+
+float expf_unchecked (float a) {
+ float f, j, r;
+ int i;
+
+ j = fmaf (1.442695f, a, 12582912.f) - 12582912.f;
+ f = fmaf (j, -6.93145752e-1f, a);
+ f = fmaf (j, -1.42860677e-6f, f);
+ i = (int)j;
+
+ r = 1.37805939e-3f;
+ r = fmaf (r, f, 8.37312452e-3f);
+ r = fmaf (r, f, 4.16695364e-2f);
+ r = fmaf (r, f, 1.66664720e-1f);
+ r = fmaf (r, f, 4.99999851e-1f);
+ r = fmaf (r, f, 1.00000000e+0f);
+ r = fmaf (r, f, 1.00000000e+0f);
+
+ float s, t;
+ uint32_t ia = (i > 0) ? 0u : 0x83000000u;
+ s = uint32_as_float (0x7f000000u + ia);
+ t = uint32_as_float (((uint32_t)i << 23) - ia);
+ r = r * s;
+ r = r * t;
+
+ return r;
+}
+
+float powf_core (float a, float b) {
+ const float MAX_IEEE754_FLT = uint32_as_float (0x7f7fffff);
+ const float EXP_OVFL_BOUND = 88.7228394f; // 0x1.62e430p+6f;
+ const float EXP_OVFL_UNFL_F = 104.0f;
+ const float MY_INF_F = uint32_as_float (0x7f800000);
+ float lhi, llo, thi, tlo, phi, plo, r;
+
+ logf_ext (a, &lhi, &llo);
+
+ thi = lhi * b;
+
+ if (fabsf (thi) > EXP_OVFL_UNFL_F) {
+ r = (thi < 0.0f) ? 0.0f : MY_INF_F;
+ } else {
+ tlo = fmaf (lhi, b, -thi);
+ tlo = fmaf (llo, b, +tlo);
+ phi = thi + tlo;
+
+ if (phi == EXP_OVFL_BOUND)
+ phi = uint32_as_float (float_as_uint32 (phi) - 1);
+
+ plo = (thi - phi) + tlo;
+ r = expf_unchecked (phi);
+ if (fabsf (r) <= MAX_IEEE754_FLT) {
+ r = fmaf (plo, r, r);
+ }
+ }
+ return r;
+}
+
+float powf (float a, float b) {
+ const float MY_INF_F = uint32_as_float (0x7f800000);
+ const float MY_NAN_F = uint32_as_float (0xffc00000);
+ int expo_odd_int;
+ float r;
+
+ expo_odd_int = fmaf (-2.0f, floorf (0.5f * b), b) == 1.0f;
+ if ((a == 1.0f) || (b == 0.0f)) {
+ r = 1.0f;
+ } else if (isnan (a) || isnan (b)) {
+ r = a + b;
+ } else if (isinf (b)) {
+ r = ((fabsf (a) < 1.0f) != (b < 0.0f)) ? 0.0f : MY_INF_F;
+ if (a == -1.0f) r = 1.0f;
+ } else if (isinf (a)) {
+ r = (b < 0.0f) ? 0.0f : MY_INF_F;
+ if ((a < 0.0f) && expo_odd_int) r = -r;
+ } else if (a == 0.0f) {
+ r = (expo_odd_int) ? (a + a) : 0.0f;
+ if (b < 0.0f) r = copysignf (MY_INF_F, r);
+ } else if ((a < 0.0f) && (b != floorf (b))) {
+ r = MY_NAN_F;
+ } else {
+ r = powf_core (fabsf (a), b);
+ if ((a < 0.0f) && expo_odd_int) {
+ r = -r;
+ }
+ }
+ return r;
+}
+
+double pow (double a, double b) {
+ return powf(a, b); // who cares about precision in a kernel :3
+}
diff --git a/libk/src/math/sqrt.c b/libk/src/math/sqrt.c
new file mode 100644
index 0000000..b875079
--- /dev/null
+++ b/libk/src/math/sqrt.c
@@ -0,0 +1,36 @@
+#include <math.h>
+
+float sqrtf(float num) {
+ if (num < 0)
+ return NAN;
+
+ if (num < 2)
+ return num;
+
+ float y = num;
+ float z = (y + (num / y)) / 2;
+
+ while (fabsf(y - z) >= 0.00001) {
+ y = z;
+ z = (y + (num / y)) / 2;
+ }
+ return z;
+}
+
+double sqrt(double num) {
+ if (num < 0)
+ return NAN;
+
+ if (num < 2)
+ return num;
+
+ double y = num;
+ double z = (y + (num / y)) / 2;
+
+ while (fabs(y - z) >= 0.00001) {
+ y = z;
+ z = (y + (num / y)) / 2;
+ }
+ return z;
+}
+
diff --git a/libk/src/math/trig.c b/libk/src/math/trig.c
new file mode 100644
index 0000000..f234d69
--- /dev/null
+++ b/libk/src/math/trig.c
@@ -0,0 +1,62 @@
+#include <math.h>
+
+double sin(double r) {
+ r = fmod(r + PI, PI * 2) - PI;
+ double d = r;
+ float mult = -1;
+ for (int i = 3; i < 11; i+= 2, mult = -mult) {
+ d += (pow(r, i)/fact(i)) * mult;
+ }
+ return d;
+}
+
+double cos(double r) {
+ r = fmod(r + PI, PI * 2) - PI;
+ double d = 1;
+ float mult = -1;
+ for (int i = 2; i < 10; i+= 2, mult = -mult) {
+ d += (pow(r, i)/fact(i)) * mult;
+ }
+ return d;
+}
+
+double tan(double r) {
+ return sin(r) / cos(r);
+}
+
+double csc(double r) {
+ return 1 / sin(r);
+}
+
+double sec(double r) {
+ return 1 / cos(r);
+}
+
+double cot(double r) {
+ return cos(r) / sin(r);
+}
+
+double sinh(double r) {
+ return (pow(E, r) - pow(E, -r)) / 2;
+}
+
+double cosh(double r) {
+ return (pow(E, r) + pow(E, -r)) / 2;
+}
+
+double tanh(double r) {
+ return sinh(r) / cosh(r);
+}
+
+double csch(double r) {
+ return 1 / sinh(r);
+}
+
+double sech(double r) {
+ return 1 / cosh(r);
+}
+
+double coth(double r) {
+ return cosh(r) / sinh(r);
+}
+
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