// luma.gl
// SPDX-License-Identifier: MIT
// Copyright (c) vis.gl contributors
import { glsl } from "../../../lib/glsl-utils/highlight.js";
export const fp64functionShader = `\
const vec2 E_FP64 = vec2(2.7182817459106445e+00, 8.254840366817007e-08);
const vec2 LOG2_FP64 = vec2(0.6931471824645996e+00, -1.9046542121259336e-09);
const vec2 PI_FP64 = vec2(3.1415927410125732, -8.742278012618954e-8);
const vec2 TWO_PI_FP64 = vec2(6.2831854820251465, -1.7484556025237907e-7);
const vec2 PI_2_FP64 = vec2(1.5707963705062866, -4.371139006309477e-8);
const vec2 PI_4_FP64 = vec2(0.7853981852531433, -2.1855695031547384e-8);
const vec2 PI_16_FP64 = vec2(0.19634954631328583, -5.463923757886846e-9);
const vec2 PI_16_2_FP64 = vec2(0.39269909262657166, -1.0927847515773692e-8);
const vec2 PI_16_3_FP64 = vec2(0.5890486240386963, -1.4906100798128818e-9);
const vec2 PI_180_FP64 = vec2(0.01745329238474369, 1.3519960498364902e-10);
const vec2 SIN_TABLE_0_FP64 = vec2(0.19509032368659973, -1.6704714833615242e-9);
const vec2 SIN_TABLE_1_FP64 = vec2(0.3826834261417389, 6.22335089017767e-9);
const vec2 SIN_TABLE_2_FP64 = vec2(0.5555702447891235, -1.1769521357507529e-8);
const vec2 SIN_TABLE_3_FP64 = vec2(0.7071067690849304, 1.2101617041793133e-8);
const vec2 COS_TABLE_0_FP64 = vec2(0.9807852506637573, 2.9739473106360492e-8);
const vec2 COS_TABLE_1_FP64 = vec2(0.9238795042037964, 2.8307490351764386e-8);
const vec2 COS_TABLE_2_FP64 = vec2(0.8314695954322815, 1.6870263741530778e-8);
const vec2 COS_TABLE_3_FP64 = vec2(0.7071067690849304, 1.2101617152815436e-8);
const vec2 INVERSE_FACTORIAL_3_FP64 = vec2(1.666666716337204e-01, -4.967053879312289e-09);
const vec2 INVERSE_FACTORIAL_4_FP64 = vec2(4.16666679084301e-02, -1.2417634698280722e-09);
const vec2 INVERSE_FACTORIAL_5_FP64 = vec2(8.333333767950535e-03, -4.34617203337595e-10);
const vec2 INVERSE_FACTORIAL_6_FP64 = vec2(1.3888889225199819e-03, -3.3631094437103215e-11);
const vec2 INVERSE_FACTORIAL_7_FP64 = vec2(1.9841270113829523e-04,  -2.725596874933456e-12);
const vec2 INVERSE_FACTORIAL_8_FP64 = vec2(2.4801587642286904e-05, -3.406996025904184e-13);
const vec2 INVERSE_FACTORIAL_9_FP64 = vec2(2.75573188446287533e-06, 3.7935713937038186e-14);
const vec2 INVERSE_FACTORIAL_10_FP64 = vec2(2.755731998149713e-07, -7.575112367869873e-15);
float nint(float d) {
if (d == floor(d)) return d;
return floor(d + 0.5);
}
vec2 nint_fp64(vec2 a) {
float hi = nint(a.x);
float lo;
vec2 tmp;
if (hi == a.x) {
lo = nint(a.y);
tmp = quickTwoSum(hi, lo);
} else {
lo = 0.0;
if (abs(hi - a.x) == 0.5 && a.y < 0.0) {
hi -= 1.0;
}
tmp = vec2(hi, lo);
}
return tmp;
}
vec2 exp_fp64(vec2 a) {
const int k_power = 4;
const float k = 16.0;
const float inv_k = 1.0 / k;
if (a.x <= -88.0) return vec2(0.0, 0.0);
if (a.x >= 88.0) return vec2(1.0 / 0.0, 1.0 / 0.0);
if (a.x == 0.0 && a.y == 0.0) return vec2(1.0, 0.0);
if (a.x == 1.0 && a.y == 0.0) return E_FP64;
float m = floor(a.x / LOG2_FP64.x + 0.5);
vec2 r = sub_fp64(a, mul_fp64(LOG2_FP64, vec2(m, 0.0))) * inv_k;
vec2 s, t, p;
p = mul_fp64(r, r);
s = sum_fp64(r, p * 0.5);
p = mul_fp64(p, r);
t = mul_fp64(p, INVERSE_FACTORIAL_3_FP64);
s = sum_fp64(s, t);
p = mul_fp64(p, r);
t = mul_fp64(p, INVERSE_FACTORIAL_4_FP64);
s = sum_fp64(s, t);
p = mul_fp64(p, r);
t = mul_fp64(p, INVERSE_FACTORIAL_5_FP64);
s = sum_fp64(s, t);
for (int i = 0; i < k_power; i++) {
s = sum_fp64(s * 2.0, mul_fp64(s, s));
}
#if defined(NVIDIA_FP64_WORKAROUND) || defined(INTEL_FP64_WORKAROUND)
s = sum_fp64(s, vec2(ONE, 0.0));
#else
s = sum_fp64(s, vec2(1.0, 0.0));
#endif
return s * pow(2.0, m);
}
vec2 log_fp64(vec2 a)
{
if (a.x == 1.0 && a.y == 0.0) return vec2(0.0, 0.0);
if (a.x <= 0.0) return vec2(0.0 / 0.0, 0.0 / 0.0);
vec2 x = vec2(log(a.x), 0.0);
vec2 s;
#if defined(NVIDIA_FP64_WORKAROUND) || defined(INTEL_FP64_WORKAROUND)
s = vec2(ONE, 0.0);
#else
s = vec2(1.0, 0.0);
#endif
x = sub_fp64(sum_fp64(x, mul_fp64(a, exp_fp64(-x))), s);
return x;
}
vec2 sin_taylor_fp64(vec2 a) {
vec2 r, s, t, x;
if (a.x == 0.0 && a.y == 0.0) {
return vec2(0.0, 0.0);
}
x = -mul_fp64(a, a);
s = a;
r = a;
r = mul_fp64(r, x);
t = mul_fp64(r, INVERSE_FACTORIAL_3_FP64);
s = sum_fp64(s, t);
r = mul_fp64(r, x);
t = mul_fp64(r, INVERSE_FACTORIAL_5_FP64);
s = sum_fp64(s, t);
return s;
}
vec2 cos_taylor_fp64(vec2 a) {
vec2 r, s, t, x;
if (a.x == 0.0 && a.y == 0.0) {
return vec2(1.0, 0.0);
}
x = -mul_fp64(a, a);
r = x;
s = sum_fp64(vec2(1.0, 0.0), r * 0.5);
r = mul_fp64(r, x);
t = mul_fp64(r, INVERSE_FACTORIAL_4_FP64);
s = sum_fp64(s, t);
r = mul_fp64(r, x);
t = mul_fp64(r, INVERSE_FACTORIAL_6_FP64);
s = sum_fp64(s, t);
return s;
}
void sincos_taylor_fp64(vec2 a, out vec2 sin_t, out vec2 cos_t) {
if (a.x == 0.0 && a.y == 0.0) {
sin_t = vec2(0.0, 0.0);
cos_t = vec2(1.0, 0.0);
}
sin_t = sin_taylor_fp64(a);
cos_t = sqrt_fp64(sub_fp64(vec2(1.0, 0.0), mul_fp64(sin_t, sin_t)));
}
vec2 sin_fp64(vec2 a) {
if (a.x == 0.0 && a.y == 0.0) {
return vec2(0.0, 0.0);
}
vec2 z = nint_fp64(div_fp64(a, TWO_PI_FP64));
vec2 r = sub_fp64(a, mul_fp64(TWO_PI_FP64, z));
vec2 t;
float q = floor(r.x / PI_2_FP64.x + 0.5);
int j = int(q);
if (j < -2 || j > 2) {
return vec2(0.0 / 0.0, 0.0 / 0.0);
}
t = sub_fp64(r, mul_fp64(PI_2_FP64, vec2(q, 0.0)));
q = floor(t.x / PI_16_FP64.x + 0.5);
int k = int(q);
if (k == 0) {
if (j == 0) {
return sin_taylor_fp64(t);
} else if (j == 1) {
return cos_taylor_fp64(t);
} else if (j == -1) {
return -cos_taylor_fp64(t);
} else {
return -sin_taylor_fp64(t);
}
}
int abs_k = int(abs(float(k)));
if (abs_k > 4) {
return vec2(0.0 / 0.0, 0.0 / 0.0);
} else {
t = sub_fp64(t, mul_fp64(PI_16_FP64, vec2(q, 0.0)));
}
vec2 u = vec2(0.0, 0.0);
vec2 v = vec2(0.0, 0.0);
#if defined(NVIDIA_FP64_WORKAROUND) || defined(INTEL_FP64_WORKAROUND)
if (abs(float(abs_k) - 1.0) < 0.5) {
u = COS_TABLE_0_FP64;
v = SIN_TABLE_0_FP64;
} else if (abs(float(abs_k) - 2.0) < 0.5) {
u = COS_TABLE_1_FP64;
v = SIN_TABLE_1_FP64;
} else if (abs(float(abs_k) - 3.0) < 0.5) {
u = COS_TABLE_2_FP64;
v = SIN_TABLE_2_FP64;
} else if (abs(float(abs_k) - 4.0) < 0.5) {
u = COS_TABLE_3_FP64;
v = SIN_TABLE_3_FP64;
}
#else
if (abs_k == 1) {
u = COS_TABLE_0_FP64;
v = SIN_TABLE_0_FP64;
} else if (abs_k == 2) {
u = COS_TABLE_1_FP64;
v = SIN_TABLE_1_FP64;
} else if (abs_k == 3) {
u = COS_TABLE_2_FP64;
v = SIN_TABLE_2_FP64;
} else if (abs_k == 4) {
u = COS_TABLE_3_FP64;
v = SIN_TABLE_3_FP64;
}
#endif
vec2 sin_t, cos_t;
sincos_taylor_fp64(t, sin_t, cos_t);
vec2 result = vec2(0.0, 0.0);
if (j == 0) {
if (k > 0) {
result = sum_fp64(mul_fp64(u, sin_t), mul_fp64(v, cos_t));
} else {
result = sub_fp64(mul_fp64(u, sin_t), mul_fp64(v, cos_t));
}
} else if (j == 1) {
if (k > 0) {
result = sub_fp64(mul_fp64(u, cos_t), mul_fp64(v, sin_t));
} else {
result = sum_fp64(mul_fp64(u, cos_t), mul_fp64(v, sin_t));
}
} else if (j == -1) {
if (k > 0) {
result = sub_fp64(mul_fp64(v, sin_t), mul_fp64(u, cos_t));
} else {
result = -sum_fp64(mul_fp64(v, sin_t), mul_fp64(u, cos_t));
}
} else {
if (k > 0) {
result = -sum_fp64(mul_fp64(u, sin_t), mul_fp64(v, cos_t));
} else {
result = sub_fp64(mul_fp64(v, cos_t), mul_fp64(u, sin_t));
}
}
return result;
}
vec2 cos_fp64(vec2 a) {
if (a.x == 0.0 && a.y == 0.0) {
return vec2(1.0, 0.0);
}
vec2 z = nint_fp64(div_fp64(a, TWO_PI_FP64));
vec2 r = sub_fp64(a, mul_fp64(TWO_PI_FP64, z));
vec2 t;
float q = floor(r.x / PI_2_FP64.x + 0.5);
int j = int(q);
if (j < -2 || j > 2) {
return vec2(0.0 / 0.0, 0.0 / 0.0);
}
t = sub_fp64(r, mul_fp64(PI_2_FP64, vec2(q, 0.0)));
q = floor(t.x / PI_16_FP64.x + 0.5);
int k = int(q);
if (k == 0) {
if (j == 0) {
return cos_taylor_fp64(t);
} else if (j == 1) {
return -sin_taylor_fp64(t);
} else if (j == -1) {
return sin_taylor_fp64(t);
} else {
return -cos_taylor_fp64(t);
}
}
int abs_k = int(abs(float(k)));
if (abs_k > 4) {
return vec2(0.0 / 0.0, 0.0 / 0.0);
} else {
t = sub_fp64(t, mul_fp64(PI_16_FP64, vec2(q, 0.0)));
}
vec2 u = vec2(0.0, 0.0);
vec2 v = vec2(0.0, 0.0);
#if defined(NVIDIA_FP64_WORKAROUND) || defined(INTEL_FP64_WORKAROUND)
if (abs(float(abs_k) - 1.0) < 0.5) {
u = COS_TABLE_0_FP64;
v = SIN_TABLE_0_FP64;
} else if (abs(float(abs_k) - 2.0) < 0.5) {
u = COS_TABLE_1_FP64;
v = SIN_TABLE_1_FP64;
} else if (abs(float(abs_k) - 3.0) < 0.5) {
u = COS_TABLE_2_FP64;
v = SIN_TABLE_2_FP64;
} else if (abs(float(abs_k) - 4.0) < 0.5) {
u = COS_TABLE_3_FP64;
v = SIN_TABLE_3_FP64;
}
#else
if (abs_k == 1) {
u = COS_TABLE_0_FP64;
v = SIN_TABLE_0_FP64;
} else if (abs_k == 2) {
u = COS_TABLE_1_FP64;
v = SIN_TABLE_1_FP64;
} else if (abs_k == 3) {
u = COS_TABLE_2_FP64;
v = SIN_TABLE_2_FP64;
} else if (abs_k == 4) {
u = COS_TABLE_3_FP64;
v = SIN_TABLE_3_FP64;
}
#endif
vec2 sin_t, cos_t;
sincos_taylor_fp64(t, sin_t, cos_t);
vec2 result = vec2(0.0, 0.0);
if (j == 0) {
if (k > 0) {
result = sub_fp64(mul_fp64(u, cos_t), mul_fp64(v, sin_t));
} else {
result = sum_fp64(mul_fp64(u, cos_t), mul_fp64(v, sin_t));
}
} else if (j == 1) {
if (k > 0) {
result = -sum_fp64(mul_fp64(u, sin_t), mul_fp64(v, cos_t));
} else {
result = sub_fp64(mul_fp64(v, cos_t), mul_fp64(u, sin_t));
}
} else if (j == -1) {
if (k > 0) {
result = sum_fp64(mul_fp64(u, sin_t), mul_fp64(v, cos_t));
} else {
result = sub_fp64(mul_fp64(u, sin_t), mul_fp64(v, cos_t));
}
} else {
if (k > 0) {
result = sub_fp64(mul_fp64(v, sin_t), mul_fp64(u, cos_t));
} else {
result = -sum_fp64(mul_fp64(u, cos_t), mul_fp64(v, sin_t));
}
}
return result;
}
vec2 tan_fp64(vec2 a) {
vec2 sin_a;
vec2 cos_a;
if (a.x == 0.0 && a.y == 0.0) {
return vec2(0.0, 0.0);
}
vec2 z = nint_fp64(div_fp64(a, TWO_PI_FP64));
vec2 r = sub_fp64(a, mul_fp64(TWO_PI_FP64, z));
vec2 t;
float q = floor(r.x / PI_2_FP64.x + 0.5);
int j = int(q);
if (j < -2 || j > 2) {
return vec2(0.0 / 0.0, 0.0 / 0.0);
}
t = sub_fp64(r, mul_fp64(PI_2_FP64, vec2(q, 0.0)));
q = floor(t.x / PI_16_FP64.x + 0.5);
int k = int(q);
int abs_k = int(abs(float(k)));
if (abs_k > 4) {
return vec2(0.0 / 0.0, 0.0 / 0.0);
} else {
t = sub_fp64(t, mul_fp64(PI_16_FP64, vec2(q, 0.0)));
}
vec2 u = vec2(0.0, 0.0);
vec2 v = vec2(0.0, 0.0);
vec2 sin_t, cos_t;
vec2 s, c;
sincos_taylor_fp64(t, sin_t, cos_t);
if (k == 0) {
s = sin_t;
c = cos_t;
} else {
#if defined(NVIDIA_FP64_WORKAROUND) || defined(INTEL_FP64_WORKAROUND)
if (abs(float(abs_k) - 1.0) < 0.5) {
u = COS_TABLE_0_FP64;
v = SIN_TABLE_0_FP64;
} else if (abs(float(abs_k) - 2.0) < 0.5) {
u = COS_TABLE_1_FP64;
v = SIN_TABLE_1_FP64;
} else if (abs(float(abs_k) - 3.0) < 0.5) {
u = COS_TABLE_2_FP64;
v = SIN_TABLE_2_FP64;
} else if (abs(float(abs_k) - 4.0) < 0.5) {
u = COS_TABLE_3_FP64;
v = SIN_TABLE_3_FP64;
}
#else
if (abs_k == 1) {
u = COS_TABLE_0_FP64;
v = SIN_TABLE_0_FP64;
} else if (abs_k == 2) {
u = COS_TABLE_1_FP64;
v = SIN_TABLE_1_FP64;
} else if (abs_k == 3) {
u = COS_TABLE_2_FP64;
v = SIN_TABLE_2_FP64;
} else if (abs_k == 4) {
u = COS_TABLE_3_FP64;
v = SIN_TABLE_3_FP64;
}
#endif
if (k > 0) {
s = sum_fp64(mul_fp64(u, sin_t), mul_fp64(v, cos_t));
c = sub_fp64(mul_fp64(u, cos_t), mul_fp64(v, sin_t));
} else {
s = sub_fp64(mul_fp64(u, sin_t), mul_fp64(v, cos_t));
c = sum_fp64(mul_fp64(u, cos_t), mul_fp64(v, sin_t));
}
}
if (j == 0) {
sin_a = s;
cos_a = c;
} else if (j == 1) {
sin_a = c;
cos_a = -s;
} else if (j == -1) {
sin_a = -c;
cos_a = s;
} else {
sin_a = -s;
cos_a = -c;
}
return div_fp64(sin_a, cos_a);
}
vec2 radians_fp64(vec2 degree) {
return mul_fp64(degree, PI_180_FP64);
}
vec2 mix_fp64(vec2 a, vec2 b, float x) {
vec2 range = sub_fp64(b, a);
return sum_fp64(a, mul_fp64(range, vec2(x, 0.0)));
}
void vec2_sum_fp64(vec2 a[2], vec2 b[2], out vec2 out_val[2]) {
out_val[0] = sum_fp64(a[0], b[0]);
out_val[1] = sum_fp64(a[1], b[1]);
}
void vec2_sub_fp64(vec2 a[2], vec2 b[2], out vec2 out_val[2]) {
out_val[0] = sub_fp64(a[0], b[0]);
out_val[1] = sub_fp64(a[1], b[1]);
}
void vec2_mul_fp64(vec2 a[2], vec2 b[2], out vec2 out_val[2]) {
out_val[0] = mul_fp64(a[0], b[0]);
out_val[1] = mul_fp64(a[1], b[1]);
}
void vec2_div_fp64(vec2 a[2], vec2 b[2], out vec2 out_val[2]) {
out_val[0] = div_fp64(a[0], b[0]);
out_val[1] = div_fp64(a[1], b[1]);
}
void vec2_mix_fp64(vec2 x[2], vec2 y[2], float a, out vec2 out_val[2]) {
vec2 range[2];
vec2_sub_fp64(y, x, range);
vec2 portion[2];
portion[0] = range[0] * a;
portion[1] = range[1] * a;
vec2_sum_fp64(x, portion, out_val);
}
vec2 vec2_length_fp64(vec2 x[2]) {
return sqrt_fp64(sum_fp64(mul_fp64(x[0], x[0]), mul_fp64(x[1], x[1])));
}
void vec2_normalize_fp64(vec2 x[2], out vec2 out_val[2]) {
vec2 length = vec2_length_fp64(x);
vec2 length_vec2[2];
length_vec2[0] = length;
length_vec2[1] = length;
vec2_div_fp64(x, length_vec2, out_val);
}
vec2 vec2_distance_fp64(vec2 x[2], vec2 y[2]) {
vec2 diff[2];
vec2_sub_fp64(x, y, diff);
return vec2_length_fp64(diff);
}
vec2 vec2_dot_fp64(vec2 a[2], vec2 b[2]) {
vec2 v[2];
v[0] = mul_fp64(a[0], b[0]);
v[1] = mul_fp64(a[1], b[1]);
return sum_fp64(v[0], v[1]);
}
void vec3_sub_fp64(vec2 a[3], vec2 b[3], out vec2 out_val[3]) {
for (int i = 0; i < 3; i++) {
out_val[i] = sum_fp64(a[i], b[i]);
}
}
void vec3_sum_fp64(vec2 a[3], vec2 b[3], out vec2 out_val[3]) {
for (int i = 0; i < 3; i++) {
out_val[i] = sum_fp64(a[i], b[i]);
}
}
vec2 vec3_length_fp64(vec2 x[3]) {
return sqrt_fp64(sum_fp64(sum_fp64(mul_fp64(x[0], x[0]), mul_fp64(x[1], x[1])),
mul_fp64(x[2], x[2])));
}
vec2 vec3_distance_fp64(vec2 x[3], vec2 y[3]) {
vec2 diff[3];
vec3_sub_fp64(x, y, diff);
return vec3_length_fp64(diff);
}
void vec4_fp64(vec4 a, out vec2 out_val[4]) {
out_val[0].x = a[0];
out_val[0].y = 0.0;
out_val[1].x = a[1];
out_val[1].y = 0.0;
out_val[2].x = a[2];
out_val[2].y = 0.0;
out_val[3].x = a[3];
out_val[3].y = 0.0;
}
void vec4_scalar_mul_fp64(vec2 a[4], vec2 b, out vec2 out_val[4]) {
out_val[0] = mul_fp64(a[0], b);
out_val[1] = mul_fp64(a[1], b);
out_val[2] = mul_fp64(a[2], b);
out_val[3] = mul_fp64(a[3], b);
}
void vec4_sum_fp64(vec2 a[4], vec2 b[4], out vec2 out_val[4]) {
for (int i = 0; i < 4; i++) {
out_val[i] = sum_fp64(a[i], b[i]);
}
}
void vec4_dot_fp64(vec2 a[4], vec2 b[4], out vec2 out_val) {
vec2 v[4];
v[0] = mul_fp64(a[0], b[0]);
v[1] = mul_fp64(a[1], b[1]);
v[2] = mul_fp64(a[2], b[2]);
v[3] = mul_fp64(a[3], b[3]);
out_val = sum_fp64(sum_fp64(v[0], v[1]), sum_fp64(v[2], v[3]));
}
void mat4_vec4_mul_fp64(vec2 b[16], vec2 a[4], out vec2 out_val[4]) {
vec2 tmp[4];
for (int i = 0; i < 4; i++)
{
for (int j = 0; j < 4; j++)
{
tmp[j] = b[j + i * 4];
}
vec4_dot_fp64(a, tmp, out_val[i]);
}
}
`;