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Unified Diff: fusl/src/math/__rem_pio2.c

Issue 1714623002: [fusl] clang-format fusl (Closed) Base URL: git@github.com:domokit/mojo.git@master
Patch Set: headers too Created 4 years, 10 months ago
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« fusl/arch/aarch64/atomic_arch.h ('K') | « fusl/src/math/__polevll.c ('k') | fusl/src/math/__rem_pio2_large.c » ('j') | no next file with comments »
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Index: fusl/src/math/__rem_pio2.c
diff --git a/fusl/src/math/__rem_pio2.c b/fusl/src/math/__rem_pio2.c
index d403f81c792217a195d9680d9356eec17f734f41..025ce4e3799be149bfc917c15aa9973aef83c2f7 100644
--- a/fusl/src/math/__rem_pio2.c
+++ b/fusl/src/math/__rem_pio2.c
@@ -19,9 +19,9 @@
#include "libm.h"
-#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
+#if FLT_EVAL_METHOD == 0 || FLT_EVAL_METHOD == 1
#define EPS DBL_EPSILON
-#elif FLT_EVAL_METHOD==2
+#elif FLT_EVAL_METHOD == 2
#define EPS LDBL_EPSILON
#endif
@@ -34,144 +34,146 @@
* pio2_3: third 33 bit of pi/2
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
*/
-static const double
-toint = 1.5/EPS,
-invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
-pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
-pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
-pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
-pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
-pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
-pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
+static const double toint = 1.5 / EPS,
+ invpio2 =
+ 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
+ pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
+ pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
+ pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
+ pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
+ pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
+ pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
/* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
-int __rem_pio2(double x, double *y)
-{
- union {double f; uint64_t i;} u = {x};
- double_t z,w,t,r,fn;
- double tx[3],ty[2];
- uint32_t ix;
- int sign, n, ex, ey, i;
+int __rem_pio2(double x, double* y) {
+ union {
+ double f;
+ uint64_t i;
+ } u = {x};
+ double_t z, w, t, r, fn;
+ double tx[3], ty[2];
+ uint32_t ix;
+ int sign, n, ex, ey, i;
- sign = u.i>>63;
- ix = u.i>>32 & 0x7fffffff;
- if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */
- if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */
- goto medium; /* cancellation -- use medium case */
- if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */
- if (!sign) {
- z = x - pio2_1; /* one round good to 85 bits */
- y[0] = z - pio2_1t;
- y[1] = (z-y[0]) - pio2_1t;
- return 1;
- } else {
- z = x + pio2_1;
- y[0] = z + pio2_1t;
- y[1] = (z-y[0]) + pio2_1t;
- return -1;
- }
- } else {
- if (!sign) {
- z = x - 2*pio2_1;
- y[0] = z - 2*pio2_1t;
- y[1] = (z-y[0]) - 2*pio2_1t;
- return 2;
- } else {
- z = x + 2*pio2_1;
- y[0] = z + 2*pio2_1t;
- y[1] = (z-y[0]) + 2*pio2_1t;
- return -2;
- }
- }
- }
- if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */
- if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */
- if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */
- goto medium;
- if (!sign) {
- z = x - 3*pio2_1;
- y[0] = z - 3*pio2_1t;
- y[1] = (z-y[0]) - 3*pio2_1t;
- return 3;
- } else {
- z = x + 3*pio2_1;
- y[0] = z + 3*pio2_1t;
- y[1] = (z-y[0]) + 3*pio2_1t;
- return -3;
- }
- } else {
- if (ix == 0x401921fb) /* |x| ~= 4pi/2 */
- goto medium;
- if (!sign) {
- z = x - 4*pio2_1;
- y[0] = z - 4*pio2_1t;
- y[1] = (z-y[0]) - 4*pio2_1t;
- return 4;
- } else {
- z = x + 4*pio2_1;
- y[0] = z + 4*pio2_1t;
- y[1] = (z-y[0]) + 4*pio2_1t;
- return -4;
- }
- }
- }
- if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */
-medium:
- /* rint(x/(pi/2)), Assume round-to-nearest. */
- fn = (double_t)x*invpio2 + toint - toint;
- n = (int32_t)fn;
- r = x - fn*pio2_1;
- w = fn*pio2_1t; /* 1st round, good to 85 bits */
- y[0] = r - w;
- u.f = y[0];
- ey = u.i>>52 & 0x7ff;
- ex = ix>>20;
- if (ex - ey > 16) { /* 2nd round, good to 118 bits */
- 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>>52 & 0x7ff;
- if (ex - ey > 49) { /* 3rd round, good to 151 bits, covers all cases */
- t = r;
- 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 (ix >= 0x7ff00000) { /* x is inf or NaN */
- y[0] = y[1] = x - x;
- return 0;
- }
- /* set z = scalbn(|x|,-ilogb(x)+23) */
- u.f = x;
- u.i &= (uint64_t)-1>>12;
- u.i |= (uint64_t)(0x3ff + 23)<<52;
- z = u.f;
- for (i=0; i < 2; i++) {
- tx[i] = (double)(int32_t)z;
- z = (z-tx[i])*0x1p24;
- }
- tx[i] = z;
- /* skip zero terms, first term is non-zero */
- while (tx[i] == 0.0)
- i--;
- n = __rem_pio2_large(tx,ty,(int)(ix>>20)-(0x3ff+23),i+1,1);
- if (sign) {
- y[0] = -ty[0];
- y[1] = -ty[1];
- return -n;
- }
- y[0] = ty[0];
- y[1] = ty[1];
- return n;
+ sign = u.i >> 63;
+ ix = u.i >> 32 & 0x7fffffff;
+ if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */
+ if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */
+ goto medium; /* cancellation -- use medium case */
+ if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */
+ if (!sign) {
+ z = x - pio2_1; /* one round good to 85 bits */
+ y[0] = z - pio2_1t;
+ y[1] = (z - y[0]) - pio2_1t;
+ return 1;
+ } else {
+ z = x + pio2_1;
+ y[0] = z + pio2_1t;
+ y[1] = (z - y[0]) + pio2_1t;
+ return -1;
+ }
+ } else {
+ if (!sign) {
+ z = x - 2 * pio2_1;
+ y[0] = z - 2 * pio2_1t;
+ y[1] = (z - y[0]) - 2 * pio2_1t;
+ return 2;
+ } else {
+ z = x + 2 * pio2_1;
+ y[0] = z + 2 * pio2_1t;
+ y[1] = (z - y[0]) + 2 * pio2_1t;
+ return -2;
+ }
+ }
+ }
+ if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */
+ if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */
+ if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */
+ goto medium;
+ if (!sign) {
+ z = x - 3 * pio2_1;
+ y[0] = z - 3 * pio2_1t;
+ y[1] = (z - y[0]) - 3 * pio2_1t;
+ return 3;
+ } else {
+ z = x + 3 * pio2_1;
+ y[0] = z + 3 * pio2_1t;
+ y[1] = (z - y[0]) + 3 * pio2_1t;
+ return -3;
+ }
+ } else {
+ if (ix == 0x401921fb) /* |x| ~= 4pi/2 */
+ goto medium;
+ if (!sign) {
+ z = x - 4 * pio2_1;
+ y[0] = z - 4 * pio2_1t;
+ y[1] = (z - y[0]) - 4 * pio2_1t;
+ return 4;
+ } else {
+ z = x + 4 * pio2_1;
+ y[0] = z + 4 * pio2_1t;
+ y[1] = (z - y[0]) + 4 * pio2_1t;
+ return -4;
+ }
+ }
+ }
+ if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */
+ medium:
+ /* rint(x/(pi/2)), Assume round-to-nearest. */
+ fn = (double_t)x * invpio2 + toint - toint;
+ n = (int32_t)fn;
+ r = x - fn * pio2_1;
+ w = fn * pio2_1t; /* 1st round, good to 85 bits */
+ y[0] = r - w;
+ u.f = y[0];
+ ey = u.i >> 52 & 0x7ff;
+ ex = ix >> 20;
+ if (ex - ey > 16) { /* 2nd round, good to 118 bits */
+ 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 >> 52 & 0x7ff;
+ if (ex - ey > 49) { /* 3rd round, good to 151 bits, covers all cases */
+ t = r;
+ 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 (ix >= 0x7ff00000) { /* x is inf or NaN */
+ y[0] = y[1] = x - x;
+ return 0;
+ }
+ /* set z = scalbn(|x|,-ilogb(x)+23) */
+ u.f = x;
+ u.i &= (uint64_t)-1 >> 12;
+ u.i |= (uint64_t)(0x3ff + 23) << 52;
+ z = u.f;
+ for (i = 0; i < 2; i++) {
+ tx[i] = (double)(int32_t)z;
+ z = (z - tx[i]) * 0x1p24;
+ }
+ tx[i] = z;
+ /* skip zero terms, first term is non-zero */
+ while (tx[i] == 0.0)
+ i--;
+ n = __rem_pio2_large(tx, ty, (int)(ix >> 20) - (0x3ff + 23), i + 1, 1);
+ if (sign) {
+ y[0] = -ty[0];
+ y[1] = -ty[1];
+ return -n;
+ }
+ y[0] = ty[0];
+ y[1] = ty[1];
+ return n;
}
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