| Index: fusl/src/math/__rem_pio2l.c
|
| diff --git a/fusl/src/math/__rem_pio2l.c b/fusl/src/math/__rem_pio2l.c
|
| index 77255bd80ae480004dfe51490a2091f746d9a00f..4b8693d9c398c07b23c42c79c45a8e1ea632882b 100644
|
| --- a/fusl/src/math/__rem_pio2l.c
|
| +++ b/fusl/src/math/__rem_pio2l.c
|
| @@ -20,11 +20,13 @@
|
| * use __rem_pio2_large() for large x
|
| */
|
|
|
| -static const long double toint = 1.5/LDBL_EPSILON;
|
| +static const long double toint = 1.5 / LDBL_EPSILON;
|
|
|
| #if LDBL_MANT_DIG == 64
|
| /* u ~< 0x1p25*pi/2 */
|
| -#define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.m>>48) < ((0x3fff + 25)<<16 | 0x921f>>1 | 0x8000))
|
| +#define SMALL(u) \
|
| + (((u.i.se & 0x7fffU) << 16 | u.i.m >> 48) < \
|
| + ((0x3fff + 25) << 16 | 0x921f >> 1 | 0x8000))
|
| #define QUOBITS(x) ((uint32_t)(int32_t)x & 0x7fffffff)
|
| #define ROUND1 22
|
| #define ROUND2 61
|
| @@ -39,103 +41,118 @@ static const long double toint = 1.5/LDBL_EPSILON;
|
| * pio2_3: third 39 bits of pi/2
|
| * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
|
| */
|
| -static const double
|
| -pio2_1 = 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */
|
| -pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */
|
| -pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */
|
| +static const double pio2_1 =
|
| + 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */
|
| + pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */
|
| + pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */
|
| static const long double
|
| -invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */
|
| -pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
|
| -pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */
|
| -pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
|
| + invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */
|
| + pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
|
| + pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */
|
| + pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
|
| #elif LDBL_MANT_DIG == 113
|
| /* u ~< 0x1p45*pi/2 */
|
| -#define SMALL(u) (((u.i.se & 0x7fffU)<<16 | u.i.top) < ((0x3fff + 45)<<16 | 0x921f))
|
| +#define SMALL(u) \
|
| + (((u.i.se & 0x7fffU) << 16 | u.i.top) < ((0x3fff + 45) << 16 | 0x921f))
|
| #define QUOBITS(x) ((uint32_t)(int64_t)x & 0x7fffffff)
|
| #define ROUND1 51
|
| #define ROUND2 119
|
| #define NX 5
|
| #define NY 3
|
| static const long double
|
| -invpio2 = 6.3661977236758134307553505349005747e-01L, /* 0x145f306dc9c882a53f84eafa3ea6a.0p-113 */
|
| -pio2_1 = 1.5707963267948966192292994253909555e+00L, /* 0x1921fb54442d18469800000000000.0p-112 */
|
| -pio2_1t = 2.0222662487959507323996846200947577e-21L, /* 0x13198a2e03707344a4093822299f3.0p-181 */
|
| -pio2_2 = 2.0222662487959507323994779168837751e-21L, /* 0x13198a2e03707344a400000000000.0p-181 */
|
| -pio2_2t = 2.0670321098263988236496903051604844e-43L, /* 0x127044533e63a0105df531d89cd91.0p-254 */
|
| -pio2_3 = 2.0670321098263988236499468110329591e-43L, /* 0x127044533e63a0105e00000000000.0p-254 */
|
| -pio2_3t = -2.5650587247459238361625433492959285e-65L; /* -0x159c4ec64ddaeb5f78671cbfb2210.0p-327 */
|
| + invpio2 =
|
| + 6.3661977236758134307553505349005747e-01L, /* 0x145f306dc9c882a53f84eafa3ea6a.0p-113
|
| + */
|
| + pio2_1 =
|
| + 1.5707963267948966192292994253909555e+00L, /* 0x1921fb54442d18469800000000000.0p-112
|
| + */
|
| + pio2_1t =
|
| + 2.0222662487959507323996846200947577e-21L, /* 0x13198a2e03707344a4093822299f3.0p-181
|
| + */
|
| + pio2_2 =
|
| + 2.0222662487959507323994779168837751e-21L, /* 0x13198a2e03707344a400000000000.0p-181
|
| + */
|
| + pio2_2t =
|
| + 2.0670321098263988236496903051604844e-43L, /* 0x127044533e63a0105df531d89cd91.0p-254
|
| + */
|
| + pio2_3 =
|
| + 2.0670321098263988236499468110329591e-43L, /* 0x127044533e63a0105e00000000000.0p-254
|
| + */
|
| + pio2_3t =
|
| + -2.5650587247459238361625433492959285e-65L; /* -0x159c4ec64ddaeb5f78671cbfb2210.0p-327
|
| + */
|
| #endif
|
|
|
| -int __rem_pio2l(long double x, long double *y)
|
| -{
|
| - union ldshape u,uz;
|
| - long double z,w,t,r,fn;
|
| - double tx[NX],ty[NY];
|
| - int ex,ey,n,i;
|
| +int __rem_pio2l(long double x, long double* y) {
|
| + union ldshape u, uz;
|
| + long double z, w, t, r, fn;
|
| + double tx[NX], ty[NY];
|
| + int ex, ey, n, i;
|
|
|
| - u.f = x;
|
| - ex = u.i.se & 0x7fff;
|
| - if (SMALL(u)) {
|
| - /* rint(x/(pi/2)), Assume round-to-nearest. */
|
| - fn = x*invpio2 + toint - toint;
|
| - n = QUOBITS(fn);
|
| - r = x-fn*pio2_1;
|
| - w = fn*pio2_1t; /* 1st round good to 102/180 bits (ld80/ld128) */
|
| - y[0] = r-w;
|
| - u.f = y[0];
|
| - ey = u.i.se & 0x7fff;
|
| - if (ex - ey > ROUND1) { /* 2nd iteration needed, good to 141/248 (ld80/ld128) */
|
| - t = r;
|
| - w = fn*pio2_2;
|
| - r = t-w;
|
| - w = fn*pio2_2t-((t-r)-w);
|
| - y[0] = r-w;
|
| - u.f = y[0];
|
| - ey = u.i.se & 0x7fff;
|
| - if (ex - ey > ROUND2) { /* 3rd iteration, good to 180/316 bits */
|
| - t = r; /* will cover all possible cases (not verified for ld128) */
|
| - w = fn*pio2_3;
|
| - r = t-w;
|
| - w = fn*pio2_3t-((t-r)-w);
|
| - y[0] = r-w;
|
| - }
|
| - }
|
| - y[1] = (r - y[0]) - w;
|
| - return n;
|
| - }
|
| - /*
|
| - * all other (large) arguments
|
| - */
|
| - if (ex == 0x7fff) { /* x is inf or NaN */
|
| - y[0] = y[1] = x - x;
|
| - return 0;
|
| - }
|
| - /* set z = scalbn(|x|,-ilogb(x)+23) */
|
| - uz.f = x;
|
| - uz.i.se = 0x3fff + 23;
|
| - z = uz.f;
|
| - for (i=0; i < NX - 1; i++) {
|
| - tx[i] = (double)(int32_t)z;
|
| - z = (z-tx[i])*0x1p24;
|
| - }
|
| - tx[i] = z;
|
| - while (tx[i] == 0)
|
| - i--;
|
| - n = __rem_pio2_large(tx, ty, ex-0x3fff-23, i+1, NY);
|
| - w = ty[1];
|
| - if (NY == 3)
|
| - w += ty[2];
|
| - r = ty[0] + w;
|
| - /* TODO: for ld128 this does not follow the recommendation of the
|
| - comments of __rem_pio2_large which seem wrong if |ty[0]| > |ty[1]+ty[2]| */
|
| - w -= r - ty[0];
|
| - if (u.i.se >> 15) {
|
| - y[0] = -r;
|
| - y[1] = -w;
|
| - return -n;
|
| - }
|
| - y[0] = r;
|
| - y[1] = w;
|
| - return n;
|
| + u.f = x;
|
| + ex = u.i.se & 0x7fff;
|
| + if (SMALL(u)) {
|
| + /* rint(x/(pi/2)), Assume round-to-nearest. */
|
| + fn = x * invpio2 + toint - toint;
|
| + n = QUOBITS(fn);
|
| + r = x - fn * pio2_1;
|
| + w = fn * pio2_1t; /* 1st round good to 102/180 bits (ld80/ld128) */
|
| + y[0] = r - w;
|
| + u.f = y[0];
|
| + ey = u.i.se & 0x7fff;
|
| + if (ex - ey >
|
| + ROUND1) { /* 2nd iteration needed, good to 141/248 (ld80/ld128) */
|
| + t = r;
|
| + w = fn * pio2_2;
|
| + r = t - w;
|
| + w = fn * pio2_2t - ((t - r) - w);
|
| + y[0] = r - w;
|
| + u.f = y[0];
|
| + ey = u.i.se & 0x7fff;
|
| + if (ex - ey > ROUND2) { /* 3rd iteration, good to 180/316 bits */
|
| + t = r; /* will cover all possible cases (not verified for ld128) */
|
| + w = fn * pio2_3;
|
| + r = t - w;
|
| + w = fn * pio2_3t - ((t - r) - w);
|
| + y[0] = r - w;
|
| + }
|
| + }
|
| + y[1] = (r - y[0]) - w;
|
| + return n;
|
| + }
|
| + /*
|
| + * all other (large) arguments
|
| + */
|
| + if (ex == 0x7fff) { /* x is inf or NaN */
|
| + y[0] = y[1] = x - x;
|
| + return 0;
|
| + }
|
| + /* set z = scalbn(|x|,-ilogb(x)+23) */
|
| + uz.f = x;
|
| + uz.i.se = 0x3fff + 23;
|
| + z = uz.f;
|
| + for (i = 0; i < NX - 1; i++) {
|
| + tx[i] = (double)(int32_t)z;
|
| + z = (z - tx[i]) * 0x1p24;
|
| + }
|
| + tx[i] = z;
|
| + while (tx[i] == 0)
|
| + i--;
|
| + n = __rem_pio2_large(tx, ty, ex - 0x3fff - 23, i + 1, NY);
|
| + w = ty[1];
|
| + if (NY == 3)
|
| + w += ty[2];
|
| + r = ty[0] + w;
|
| + /* TODO: for ld128 this does not follow the recommendation of the
|
| + comments of __rem_pio2_large which seem wrong if |ty[0]| > |ty[1]+ty[2]| */
|
| + w -= r - ty[0];
|
| + if (u.i.se >> 15) {
|
| + y[0] = -r;
|
| + y[1] = -w;
|
| + return -n;
|
| + }
|
| + y[0] = r;
|
| + y[1] = w;
|
| + return n;
|
| }
|
| #endif
|
|
|