diff options
Diffstat (limited to 'libc-top-half/musl/src/math/__rem_pio2.c')
| -rw-r--r-- | libc-top-half/musl/src/math/__rem_pio2.c | 194 |
1 files changed, 194 insertions, 0 deletions
diff --git a/libc-top-half/musl/src/math/__rem_pio2.c b/libc-top-half/musl/src/math/__rem_pio2.c new file mode 100644 index 0000000..326cda7 --- /dev/null +++ b/libc-top-half/musl/src/math/__rem_pio2.c @@ -0,0 +1,194 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * Optimized by Bruce D. Evans. + */ +/* __rem_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __rem_pio2_large() for large x + */ + +#include "libm.h" + +#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1 +#define EPS DBL_EPSILON +#elif FLT_EVAL_METHOD==2 +#define EPS LDBL_EPSILON +#endif + +/* + * invpio2: 53 bits of 2/pi + * pio2_1: first 33 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 33 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * 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, +#ifdef __wasilibc_unmodified_upstream // Wasm doesn't have alternate rounding modes +pio4 = 0x1.921fb54442d18p-1, +#endif +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; + + 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)) */ + 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 */ +#ifdef __wasilibc_unmodified_upstream // Wasm doesn't have alternate rounding modes + /* Matters with directed rounding. */ + if (predict_false(r - w < -pio4)) { + n--; + fn--; + r = x - fn*pio2_1; + w = fn*pio2_1t; + } else if (predict_false(r - w > pio4)) { + n++; + fn++; + r = x - fn*pio2_1; + w = fn*pio2_1t; + } +#endif + 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; +} |