From 3fdf94ec5101fab63d0e8196d3e557641a0e19e2 Mon Sep 17 00:00:00 2001 From: Szabolcs Nagy Date: Sun, 24 Nov 2013 01:06:38 +0000 Subject: math: clean up __rem_pio2 - remove the HAVE_EFFICIENT_IRINT case: fn is an exact integer, so it can be converted to int32_t a bit more efficiently than with a cast (the rounding mode change can be avoided), but musl does not support this case on any arch. - __rem_pio2: use double_t where possible - __rem_pio2f: use less assignments to avoid stores on i386 - use unsigned int bit manipulation (and union instead of macros) - use hexfloat literals instead of named constants --- src/math/__rem_pio2.c | 72 +++++++++++++++++++++------------------------ src/math/__rem_pio2_large.c | 18 +++++------- src/math/__rem_pio2f.c | 34 ++++++++------------- 3 files changed, 53 insertions(+), 71 deletions(-) (limited to 'src') diff --git a/src/math/__rem_pio2.c b/src/math/__rem_pio2.c index 9305be5f..5fafc4a8 100644 --- a/src/math/__rem_pio2.c +++ b/src/math/__rem_pio2.c @@ -29,7 +29,6 @@ * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) */ static const double -two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ @@ -41,18 +40,19 @@ 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) { - double z,w,t,r,fn; - double tx[3],ty[2]; - int32_t e0,i,j,nx,n,ix,hx; - uint32_t low; + union {double f; uint64_t i;} u = {x}; + double_t z,w,t,r; + double tx[3],ty[2],fn; + uint32_t ix; + int sign, n, ex, ey, i; - GET_HIGH_WORD(hx,x); - ix = hx & 0x7fffffff; + 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 (hx > 0) { + if (!sign) { z = x - pio2_1; /* one round good to 85 bits */ y[0] = z - pio2_1t; y[1] = (z-y[0]) - pio2_1t; @@ -64,7 +64,7 @@ int __rem_pio2(double x, double *y) return -1; } } else { - if (hx > 0) { + if (!sign) { z = x - 2*pio2_1; y[0] = z - 2*pio2_1t; y[1] = (z-y[0]) - 2*pio2_1t; @@ -81,7 +81,7 @@ int __rem_pio2(double x, double *y) if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ goto medium; - if (hx > 0) { + if (!sign) { z = x - 3*pio2_1; y[0] = z - 3*pio2_1t; y[1] = (z-y[0]) - 3*pio2_1t; @@ -95,7 +95,7 @@ int __rem_pio2(double x, double *y) } else { if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ goto medium; - if (hx > 0) { + if (!sign) { z = x - 4*pio2_1; y[0] = z - 4*pio2_1t; y[1] = (z-y[0]) - 4*pio2_1t; @@ -109,32 +109,26 @@ int __rem_pio2(double x, double *y) } } if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ - uint32_t high; medium: - /* Use a specialized rint() to get fn. Assume round-to-nearest. */ + /* rint(x/(pi/2)), Assume round-to-nearest. */ fn = x*invpio2 + 0x1.8p52; fn = fn - 0x1.8p52; -// FIXME -#ifdef HAVE_EFFICIENT_IRINT - n = irint(fn); -#else n = (int32_t)fn; -#endif r = x - fn*pio2_1; w = fn*pio2_1t; /* 1st round, good to 85 bits */ - j = ix>>20; y[0] = r - w; - GET_HIGH_WORD(high,y[0]); - i = j - ((high>>20)&0x7ff); - if (i > 16) { /* 2nd round, good to 118 bits */ + 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; - GET_HIGH_WORD(high,y[0]); - i = j - ((high>>20)&0x7ff); - if (i > 49) { /* 3rd round, good to 151 bits, covers all cases */ + 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; @@ -142,7 +136,7 @@ medium: y[0] = r - w; } } - y[1] = (r-y[0]) - w; + y[1] = (r - y[0]) - w; return n; } /* @@ -152,19 +146,21 @@ medium: y[0] = y[1] = x - x; return 0; } - /* set z = scalbn(|x|,ilogb(x)-23) */ - GET_LOW_WORD(low,x); - e0 = (ix>>20) - 1046; /* e0 = ilogb(z)-23; */ - INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low); - for (i=0; i<2; i++) { - tx[i] = (double)((int32_t)(z)); - z = (z-tx[i])*two24; + /* 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[2] = z; - nx = 3; - while (tx[nx-1] == 0.0) nx--; /* skip zero term */ - n = __rem_pio2_large(tx,ty,e0,nx,1); - if (hx < 0) { + 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; diff --git a/src/math/__rem_pio2_large.c b/src/math/__rem_pio2_large.c index bb2dc43f..958f28c2 100644 --- a/src/math/__rem_pio2_large.c +++ b/src/math/__rem_pio2_large.c @@ -270,10 +270,6 @@ static const double PIo2[] = { 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ }; -static const double -two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ -twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ - int __rem_pio2_large(double *x, double *y, int e0, int nx, int prec) { int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; @@ -304,8 +300,8 @@ int __rem_pio2_large(double *x, double *y, int e0, int nx, int prec) recompute: /* distill q[] into iq[] reversingly */ for (i=0,j=jz,z=q[jz]; j>0; i++,j--) { - fw = (double)((int32_t)(twon24* z)); - iq[i] = (int32_t)(z-two24*fw); + fw = (double)(int32_t)(0x1p-24*z); + iq[i] = (int32_t)(z - 0x1p24*fw); z = q[j-1]+fw; } @@ -330,7 +326,7 @@ recompute: if (carry == 0) { if (j != 0) { carry = 1; - iq[i] = 0x1000000- j; + iq[i] = 0x1000000 - j; } } else iq[i] = 0xffffff - j; @@ -378,9 +374,9 @@ recompute: } } else { /* break z into 24-bit if necessary */ z = scalbn(z,-q0); - if (z >= two24) { - fw = (double)((int32_t)(twon24*z)); - iq[jz] = (int32_t)(z-two24*fw); + if (z >= 0x1p24) { + fw = (double)(int32_t)(0x1p-24*z); + iq[jz] = (int32_t)(z - 0x1p24*fw); jz += 1; q0 += 24; iq[jz] = (int32_t)fw; @@ -392,7 +388,7 @@ recompute: fw = scalbn(1.0,q0); for (i=jz; i>=0; i--) { q[i] = fw*(double)iq[i]; - fw *= twon24; + fw *= 0x1p-24; } /* compute PIo2[0,...,jp]*q[jz,...,0] */ diff --git a/src/math/__rem_pio2f.c b/src/math/__rem_pio2f.c index 5bdeb529..838e1fca 100644 --- a/src/math/__rem_pio2f.c +++ b/src/math/__rem_pio2f.c @@ -34,42 +34,32 @@ pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */ int __rem_pio2f(float x, double *y) { - double w,r,fn; - double tx[1],ty[1]; - float z; - int32_t e0,n,ix,hx; + union {float f; uint32_t i;} u = {x}; + double tx[1],ty[1],fn; + uint32_t ix; + int n, sign, e0; - GET_FLOAT_WORD(hx, x); - ix = hx & 0x7fffffff; + ix = u.i & 0x7fffffff; /* 25+53 bit pi is good enough for medium size */ if (ix < 0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */ /* Use a specialized rint() to get fn. Assume round-to-nearest. */ fn = x*invpio2 + 0x1.8p52; fn = fn - 0x1.8p52; -// FIXME -#ifdef HAVE_EFFICIENT_IRINT - n = irint(fn); -#else n = (int32_t)fn; -#endif - r = x - fn*pio2_1; - w = fn*pio2_1t; - *y = r - w; + *y = x - fn*pio2_1 - fn*pio2_1t; return n; } - /* - * all other (large) arguments - */ if(ix>=0x7f800000) { /* x is inf or NaN */ *y = x-x; return 0; } - /* set z = scalbn(|x|,ilogb(|x|)-23) */ - e0 = (ix>>23) - 150; /* e0 = ilogb(|x|)-23; */ - SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23))); - tx[0] = z; + /* scale x into [2^23, 2^24-1] */ + sign = u.i>>31; + e0 = (ix>>23) - (0x7f+23); /* e0 = ilogb(|x|)-23, positive */ + u.i = ix - (e0<<23); + tx[0] = u.f; n = __rem_pio2_large(tx,ty,e0,1,0); - if (hx < 0) { + if (sign) { *y = -ty[0]; return -n; } -- cgit v1.2.1