diff options
Diffstat (limited to 'lib')
| -rw-r--r-- | lib/msun/src/e_rem_pio2f.c | 95 |
1 files changed, 53 insertions, 42 deletions
diff --git a/lib/msun/src/e_rem_pio2f.c b/lib/msun/src/e_rem_pio2f.c index 3d17158..a1d741c 100644 --- a/lib/msun/src/e_rem_pio2f.c +++ b/lib/msun/src/e_rem_pio2f.c @@ -1,6 +1,6 @@ /* e_rem_pio2f.c -- float version of e_rem_pio2.c * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. - * Conversion to not use float except for the arg by Bruce Evans. + * Debugged and optimized by Bruce D. Evans. */ /* @@ -21,7 +21,8 @@ static char rcsid[] = "$FreeBSD$"; /* __ieee754_rem_pio2f(x,y) * * return the remainder of x rem pi/2 in y[0]+y[1] - * use __kernel_rem_pio2f() + * use double precision internally + * use __kernel_rem_pio2() for large x */ #include "math.h" @@ -46,6 +47,10 @@ static const int32_t two_over_pi[] = { /* * invpio2: 53 bits of 2/pi + * e1pio2: 1*pi/2 rounded to 53 bits + * e2pio2: 2*pi/2 rounded to 53 bits + * e3pio2: 3*pi/2 rounded to 53 bits + * e4pio2: 4*pi/2 rounded to 53 bits * pio2_1: first 33 bit of pi/2 * pio2_1t: pi/2 - pio2_1 */ @@ -55,7 +60,10 @@ zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ -pio2 = 1.57079632679489655700e+00, /* 0x3FF921FB, 0x54442d18 */ +e1pio2 = 1*M_PI_2, /* 0x3FF921FB, 0x54442D18 */ +e2pio2 = 2*M_PI_2, /* 0x400921FB, 0x54442D18 */ +e3pio2 = 3*M_PI_2, /* 0x4012D97C, 0x7F3321D2 */ +e4pio2 = 4*M_PI_2, /* 0x401921FB, 0x54442D18 */ pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ pio2_1t = 6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */ @@ -67,52 +75,55 @@ pio2_1t = 6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */ GET_FLOAT_WORD(hx,x); ix = hx&0x7fffffff; - if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ + if(ix<=0x3f490fda) /* |x| ~<= pi/4, reduction is null */ {y[0] = x; y[1] = 0; return 0;} - /* 33+53 bit pi is good enough for special and medium size cases */ - if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ - if(hx>0) { - z = x - pio2; - n = 1; + /* 53 bit pi is good enough for special cases */ + if(ix<=0x407b53d1) { /* |x| ~<= 5*pi/4 */ + if(ix<=0x4016cbe3) { /* |x| ~<= 3*pi/4 */ + if(hx>0) { + z = x - e1pio2; + n = 1; + } else { + z = x + e1pio2; + n = 3; + } + y[0] = z; + y[1] = z - y[0]; + return n; } else { - z = x + pio2; - n = 3; + if(hx>0) + z = x - e2pio2; + else + z = x + e2pio2; + y[0] = z; + y[1] = z - y[0]; + return 2; } - y[0] = z; - y[1] = z - y[0]; - return n; } - if(ix<0x407b53d1) { /* |x| < 5*pi/4, special case with n=+-2 */ - if(hx>0) - z = x - 2*pio2; - else - z = x + 2*pio2; - y[0] = z; - y[1] = z - y[0]; - return 2; - } - if(ix<0x40afeddf) { /* |x| < 7*pi/4, special case with n=+-3 */ - if(hx>0) { - z = x - 3*pio2; - n = 3; + if(ix<=0x40e231d5) { /* |x| ~<= 9*pi/4*/ + if(ix<=0x40afeddf) { /* |x| ~<= 7*pi/4 */ + if(hx>0) { + z = x - e3pio2; + n = 3; + } else { + z = x + e3pio2; + n = 1; + } + y[0] = z; + y[1] = z - y[0]; + return n; } else { - z = x + 3*pio2; - n = 1; + if(hx>0) + z = x - e4pio2; + else + z = x + e4pio2; + y[0] = z; + y[1] = z - y[0]; + return 0; } - y[0] = z; - y[1] = z - y[0]; - return n; - } - if(ix<0x40e231d6) { /* |x| < 9*pi/4, special case with n=+-4 */ - if(hx>0) - z = x - 4*pio2; - else - z = x + 4*pio2; - y[0] = z; - y[1] = z - y[0]; - return 0; } - if(ix<=0x49490f80) { /* |x| ~<= 2^19*(pi/2), medium size */ + /* 33+53 bit pi is good enough for medium size */ + if(ix<=0x49490f80) { /* |x| ~<= 2^19*(pi/2), medium size */ t = fabsf(x); n = (int32_t) (t*invpio2+half); fn = (double)n; |
