diff options
Diffstat (limited to 'sysdeps/ieee754/dbl-64/s_sin.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/s_sin.c | 392 |
1 files changed, 112 insertions, 280 deletions
diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c index 3b26a61c8e..9c57321bd2 100644 --- a/sysdeps/ieee754/dbl-64/s_sin.c +++ b/sysdeps/ieee754/dbl-64/s_sin.c @@ -32,9 +32,6 @@ /* bsloww1 */ /* bsloww2 */ /* cslow2 */ -/* csloww */ -/* csloww1 */ -/* csloww2 */ /* FILES NEEDED: dla.h endian.h mpa.h mydefs.h usncs.h */ /* branred.c sincos32.c dosincos.c mpa.c */ /* sincos.tbl */ @@ -135,17 +132,14 @@ double __mpcos (double x, double dx, bool reduce_range); static double slow (double x); static double slow1 (double x); static double slow2 (double x); -static double sloww (double x, double dx, double orig); -static double sloww1 (double x, double dx, double orig, int m); +static double sloww (double x, double dx, double orig, int n); +static double sloww1 (double x, double dx, double orig, int m, int n); static double sloww2 (double x, double dx, double orig, int n); static double bsloww (double x, double dx, double orig, int n); static double bsloww1 (double x, double dx, double orig, int n); static double bsloww2 (double x, double dx, double orig, int n); int __branred (double x, double *a, double *aa); static double cslow2 (double x); -static double csloww (double x, double dx, double orig); -static double csloww1 (double x, double dx, double orig, int m); -static double csloww2 (double x, double dx, double orig, int n); /* Given a number partitioned into U and X such that U is an index into the sin/cos table, this macro computes the cosine of the number by combining @@ -278,6 +272,91 @@ reduce_and_compute (double x, unsigned int k) static inline int4 __always_inline +reduce_sincos_1 (double x, double *a, double *da) +{ + mynumber v; + + double t = (x * hpinv + toint); + double xn = t - toint; + v.x = t; + double y = (x - xn * mp1) - xn * mp2; + int4 n = v.i[LOW_HALF] & 3; + double db = xn * mp3; + double b = y - db; + db = (y - b) - db; + + *a = b; + *da = db; + + return n; +} + +/* Compute sin (A + DA). cos can be computed by shifting the quadrant N + clockwise. */ +static double +__always_inline +do_sincos_1 (double a, double da, double x, int4 n, int4 k) +{ + double xx, retval, res, cor, y; + mynumber u; + int m; + double eps = fabs (x) * 1.2e-30; + + int k1 = (n + k) & 3; + switch (k1) + { /* quarter of unit circle */ + case 2: + a = -a; + da = -da; + case 0: + xx = a * a; + if (xx < 0.01588) + { + /* Taylor series. */ + res = TAYLOR_SIN (xx, a, da, cor); + cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps; + retval = (res == res + cor) ? res : sloww (a, da, x, k); + } + else + { + if (a > 0) + m = 1; + else + { + m = 0; + a = -a; + da = -da; + } + u.x = big + a; + y = a - (u.x - big); + res = do_sin (u, y, da, &cor); + cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps; + retval = ((res == res + cor) ? ((m) ? res : -res) + : sloww1 (a, da, x, m, k)); + } + break; + + case 1: + case 3: + if (a < 0) + { + a = -a; + da = -da; + } + u.x = big + a; + y = a - (u.x - big) + da; + res = do_cos (u, y, &cor); + cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps; + retval = ((res == res + cor) ? ((k1 & 2) ? -res : res) + : sloww2 (a, da, x, n)); + break; + } + + return retval; +} + +static inline int4 +__always_inline reduce_sincos_2 (double x, double *a, double *da) { mynumber v; @@ -386,9 +465,9 @@ SECTION #endif __sin (double x) { - double xx, res, t, cor, y, s, c, sn, ssn, cs, ccs, xn, a, da, eps; - mynumber u, v; - int4 k, m, n; + double xx, res, t, cor, y, s, c, sn, ssn, cs, ccs; + mynumber u; + int4 k, m; double retval = 0; #ifndef IN_SINCOS @@ -452,73 +531,15 @@ __sin (double x) retval = (res == res + 1.020 * cor) ? ((m > 0) ? res : -res) : slow2 (x); } /* else if (k < 0x400368fd) */ +#ifndef IN_SINCOS /*-------------------------- 2.426265<|x|< 105414350 ----------------------*/ else if (k < 0x419921FB) { - t = (x * hpinv + toint); - xn = t - toint; - v.x = t; - y = (x - xn * mp1) - xn * mp2; - n = v.i[LOW_HALF] & 3; - da = xn * mp3; - a = y - da; - da = (y - a) - da; - eps = fabs (x) * 1.2e-30; - - switch (n) - { /* quarter of unit circle */ - case 0: - case 2: - xx = a * a; - if (n) - { - a = -a; - da = -da; - } - if (xx < 0.01588) - { - /* Taylor series. */ - res = TAYLOR_SIN (xx, a, da, cor); - cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps; - retval = (res == res + cor) ? res : sloww (a, da, x); - } - else - { - if (a > 0) - m = 1; - else - { - m = 0; - a = -a; - da = -da; - } - u.x = big + a; - y = a - (u.x - big); - res = do_sin (u, y, da, &cor); - cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps; - retval = ((res == res + cor) ? ((m) ? res : -res) - : sloww1 (a, da, x, m)); - } - break; - - case 1: - case 3: - if (a < 0) - { - a = -a; - da = -da; - } - u.x = big + a; - y = a - (u.x - big) + da; - res = do_cos (u, y, &cor); - cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps; - retval = ((res == res + cor) ? ((n & 2) ? -res : res) - : sloww2 (a, da, x, n)); - break; - } + double a, da; + int4 n = reduce_sincos_1 (x, &a, &da); + retval = do_sincos_1 (a, da, x, n, 0); } /* else if (k < 0x419921FB ) */ -#ifndef IN_SINCOS /*---------------------105414350 <|x|< 281474976710656 --------------------*/ else if (k < 0x42F00000) { @@ -558,9 +579,9 @@ SECTION #endif __cos (double x) { - double y, xx, res, t, cor, xn, a, da, eps; - mynumber u, v; - int4 k, m, n; + double y, xx, res, cor, a, da; + mynumber u; + int4 k, m; double retval = 0; @@ -595,7 +616,7 @@ __cos (double x) { res = TAYLOR_SIN (xx, a, da, cor); cor = (cor > 0) ? 1.02 * cor + 1.0e-31 : 1.02 * cor - 1.0e-31; - retval = (res == res + cor) ? res : csloww (a, da, x); + retval = (res == res + cor) ? res : sloww (a, da, x, 1); } else { @@ -614,79 +635,20 @@ __cos (double x) res = do_sin (u, y, da, &cor); cor = (cor > 0) ? 1.035 * cor + 1.0e-31 : 1.035 * cor - 1.0e-31; retval = ((res == res + cor) ? ((m) ? res : -res) - : csloww1 (a, da, x, m)); + : sloww1 (a, da, x, m, 1)); } } /* else if (k < 0x400368fd) */ +#ifndef IN_SINCOS else if (k < 0x419921FB) { /* 2.426265<|x|< 105414350 */ - t = (x * hpinv + toint); - xn = t - toint; - v.x = t; - y = (x - xn * mp1) - xn * mp2; - n = v.i[LOW_HALF] & 3; - da = xn * mp3; - a = y - da; - da = (y - a) - da; - eps = fabs (x) * 1.2e-30; - - switch (n) - { - case 1: - case 3: - xx = a * a; - if (n == 1) - { - a = -a; - da = -da; - } - if (xx < 0.01588) - { - res = TAYLOR_SIN (xx, a, da, cor); - cor = (cor > 0) ? 1.02 * cor + eps : 1.02 * cor - eps; - retval = (res == res + cor) ? res : csloww (a, da, x); - } - else - { - if (a > 0) - { - m = 1; - } - else - { - m = 0; - a = -a; - da = -da; - } - u.x = big + a; - y = a - (u.x - big); - res = do_sin (u, y, da, &cor); - cor = (cor > 0) ? 1.035 * cor + eps : 1.035 * cor - eps; - retval = ((res == res + cor) ? ((m) ? res : -res) - : csloww1 (a, da, x, m)); - } - break; - - case 0: - case 2: - if (a < 0) - { - a = -a; - da = -da; - } - u.x = big + a; - y = a - (u.x - big) + da; - res = do_cos (u, y, &cor); - cor = (cor > 0) ? 1.025 * cor + eps : 1.025 * cor - eps; - retval = ((res == res + cor) ? ((n) ? -res : res) - : csloww2 (a, da, x, n)); - break; - } + double a, da; + int4 n = reduce_sincos_1 (x, &a, &da); + retval = do_sincos_1 (a, da, x, n, 1); } /* else if (k < 0x419921FB ) */ -#ifndef IN_SINCOS else if (k < 0x42F00000) { double a, da; @@ -805,12 +767,13 @@ slow2 (double x) static double SECTION -sloww (double x, double dx, double orig) +sloww (double x, double dx, double orig, int k) { double y, t, res, cor, w[2], a, da, xn; mynumber v; int4 n; res = TAYLOR_SLOW (x, dx, cor); + if (cor > 0) cor = 1.0005 * cor + fabs (orig) * 3.1e-30; else @@ -832,14 +795,15 @@ sloww (double x, double dx, double orig) xn = t - toint; v.x = t; y = (orig - xn * mp1) - xn * mp2; - n = v.i[LOW_HALF] & 3; + n = (v.i[LOW_HALF] + k) & 3; da = xn * pp3; t = y - da; da = (y - t) - da; y = xn * pp4; a = t - y; da = ((t - a) - y) + da; - if (n & 2) + + if (n == 2 || n == 1) { a = -a; da = -da; @@ -853,7 +817,7 @@ sloww (double x, double dx, double orig) if (w[0] == w[0] + cor) return (a > 0) ? w[0] : -w[0]; - return __mpsin (orig, 0, true); + return (n & 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); } /***************************************************************************/ @@ -865,7 +829,7 @@ sloww (double x, double dx, double orig) static double SECTION -sloww1 (double x, double dx, double orig, int m) +sloww1 (double x, double dx, double orig, int m, int k) { mynumber u; double w[2], y, cor, res; @@ -887,7 +851,7 @@ sloww1 (double x, double dx, double orig, int m) if (w[0] == w[0] + cor) return (m > 0) ? w[0] : -w[0]; - return __mpsin (orig, 0, true); + return (k == 1) ? __mpcos (orig, 0, true) : __mpsin (orig, 0, true); } /***************************************************************************/ @@ -921,7 +885,7 @@ sloww2 (double x, double dx, double orig, int n) if (w[0] == w[0] + cor) return (n & 2) ? -w[0] : w[0]; - return __mpsin (orig, 0, true); + return (n & 1) ? __mpsin (orig, 0, true) : __mpcos (orig, 0, true); } /***************************************************************************/ @@ -1052,138 +1016,6 @@ cslow2 (double x) return __mpcos (x, 0, false); } -/***************************************************************************/ -/* Routine compute cos(x+dx) (Double-Length number) where x is small enough*/ -/* to use Taylor series around zero and (x+dx) .Routine receive also */ -/* (right argument) the original value of x for computing error of */ -/* result.And if result not accurate enough routine calls other routines */ -/***************************************************************************/ - - -static double -SECTION -csloww (double x, double dx, double orig) -{ - double y, t, res, cor, w[2], a, da, xn; - mynumber v; - int4 n; - - /* Taylor series */ - res = TAYLOR_SLOW (x, dx, cor); - - if (cor > 0) - cor = 1.0005 * cor + fabs (orig) * 3.1e-30; - else - cor = 1.0005 * cor - fabs (orig) * 3.1e-30; - - if (res == res + cor) - return res; - - (x > 0) ? __dubsin (x, dx, w) : __dubsin (-x, -dx, w); - - if (w[1] > 0) - cor = 1.000000001 * w[1] + fabs (orig) * 1.1e-30; - else - cor = 1.000000001 * w[1] - fabs (orig) * 1.1e-30; - - if (w[0] == w[0] + cor) - return (x > 0) ? w[0] : -w[0]; - - t = (orig * hpinv + toint); - xn = t - toint; - v.x = t; - y = (orig - xn * mp1) - xn * mp2; - n = v.i[LOW_HALF] & 3; - da = xn * pp3; - t = y - da; - da = (y - t) - da; - y = xn * pp4; - a = t - y; - da = ((t - a) - y) + da; - if (n == 1) - { - a = -a; - da = -da; - } - (a > 0) ? __dubsin (a, da, w) : __dubsin (-a, -da, w); - - if (w[1] > 0) - cor = 1.000000001 * w[1] + fabs (orig) * 1.1e-40; - else - cor = 1.000000001 * w[1] - fabs (orig) * 1.1e-40; - - if (w[0] == w[0] + cor) - return (a > 0) ? w[0] : -w[0]; - - return __mpcos (orig, 0, true); -} - -/***************************************************************************/ -/* Routine compute sin(x+dx) (Double-Length number) where x in first or */ -/* third quarter of unit circle.Routine receive also (right argument) the */ -/* original value of x for computing error of result.And if result not */ -/* accurate enough routine calls other routines */ -/***************************************************************************/ - -static double -SECTION -csloww1 (double x, double dx, double orig, int m) -{ - mynumber u; - double w[2], y, cor, res; - - u.x = big + x; - y = x - (u.x - big); - res = do_sin_slow (u, y, dx, 3.1e-30 * fabs (orig), &cor); - - if (res == res + cor) - return (m > 0) ? res : -res; - - __dubsin (x, dx, w); - if (w[1] > 0) - cor = 1.000000005 * w[1] + 1.1e-30 * fabs (orig); - else - cor = 1.000000005 * w[1] - 1.1e-30 * fabs (orig); - - if (w[0] == w[0] + cor) - return (m > 0) ? w[0] : -w[0]; - - return __mpcos (orig, 0, true); -} - - -/***************************************************************************/ -/* Routine compute sin(x+dx) (Double-Length number) where x in second or */ -/* fourth quarter of unit circle.Routine receive also the original value */ -/* and quarter(n= 1or 3)of x for computing error of result.And if result not*/ -/* accurate enough routine calls other routines */ -/***************************************************************************/ - -static double -SECTION -csloww2 (double x, double dx, double orig, int n) -{ - mynumber u; - double w[2], y, cor, res; - - u.x = big + x; - y = x - (u.x - big); - res = do_cos_slow (u, y, dx, 3.1e-30 * fabs (orig), &cor); - - if (res == res + cor) - return (n) ? -res : res; - - __docos (x, dx, w); - if (w[1] > 0) - cor = 1.000000005 * w[1] + 1.1e-30 * fabs (orig); - else - cor = 1.000000005 * w[1] - 1.1e-30 * fabs (orig); - if (w[0] == w[0] + cor) - return (n) ? -w[0] : w[0]; - - return __mpcos (orig, 0, true); -} - #ifndef __cos weak_alias (__cos, cos) # ifdef NO_LONG_DOUBLE |