/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│ │vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│ ╚──────────────────────────────────────────────────────────────────────────────╝ │ │ │ Musl Libc │ │ Copyright © 2005-2014 Rich Felker, et al. │ │ │ │ Permission is hereby granted, free of charge, to any person obtaining │ │ a copy of this software and associated documentation files (the │ │ "Software"), to deal in the Software without restriction, including │ │ without limitation the rights to use, copy, modify, merge, publish, │ │ distribute, sublicense, and/or sell copies of the Software, and to │ │ permit persons to whom the Software is furnished to do so, subject to │ │ the following conditions: │ │ │ │ The above copyright notice and this permission notice shall be │ │ included in all copies or substantial portions of the Software. │ │ │ │ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ │ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ │ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ │ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ │ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ │ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ │ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ │ │ ╚─────────────────────────────────────────────────────────────────────────────*/ #include "libc/intrin/likely.h" #include "libc/math.h" #include "libc/tinymath/kernel.internal.h" asm(".ident\t\"\\n\\n\ fdlibm (fdlibm license)\\n\ Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\""); asm(".ident\t\"\\n\\n\ Musl libc (MIT License)\\n\ Copyright 2005-2014 Rich Felker, et. al.\""); asm(".include \"libc/disclaimer.inc\""); /* clang-format off */ /* 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 */ #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) */ #define toint (1.5/EPS) #define pio4 0x1.921fb54442d18p-1 #define invpio2 6.36619772367581382433e-01 #define pio2_1 1.57079632673412561417e+00 #define pio2_1t 6.07710050650619224932e-11 #define pio2_2 6.07710050630396597660e-11 #define pio2_2t 2.02226624879595063154e-21 #define pio2_3 2.02226624871116645580e-21 #define pio2_3t 8.47842766036889956997e-32 /* 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 */ /* Matters with directed rounding. */ if (UNLIKELY(r - w < -pio4)) { n--; fn--; r = x - fn*pio2_1; w = fn*pio2_1t; } else if (UNLIKELY(r - w > pio4)) { n++; fn++; r = x - fn*pio2_1; w = fn*pio2_1t; } 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; }