From 6f9bacf36b20b1a87fa4ec24c9d67c47985fbc8b Mon Sep 17 00:00:00 2001 From: Adhemerval Zanella Date: Mon, 18 Nov 2024 17:57:31 -0300 Subject: [PATCH] math: Use atan2f from CORE-MATH The CORE-MATH implementation is correctly rounded (for any rounding mode) and shows slight better performance to the generic atan2f. The code was adapted to glibc style and to use the definition of math_config.h (to handle errno, overflow, and underflow). Benchtest on x64_64 (Ryzen 9 5900X, gcc 14.2.1), aarch64 (Neoverse-N1, gcc 13.3.1), and powerpc (POWER10, gcc 13.2.1): Latency master patched improvement x86_64 68.1175 69.2014 -1.59% x86_64v2 66.9884 66.0081 1.46% x86_64v3 57.7034 61.6407 -6.82% i686 189.8690 152.7560 19.55% aarch64 (Neoverse) 32.6151 24.5382 24.76% power10 21.7282 17.1896 20.89% reciprocal-throughput master patched improvement x86_64 34.5202 31.6155 8.41% x86_64v2 32.6379 30.3372 7.05% x86_64v3 34.3677 23.6455 31.20% i686 157.7290 75.8308 51.92% aarch64 (Neoverse) 27.7788 16.2671 41.44% power10 15.5715 8.1588 47.60% Signed-off-by: Alexei Sibidanov Signed-off-by: Paul Zimmermann Signed-off-by: Adhemerval Zanella Reviewed-by: DJ Delorie --- SHARED-FILES | 4 + sysdeps/aarch64/libm-test-ulps | 8 - sysdeps/alpha/fpu/libm-test-ulps | 8 - sysdeps/arc/fpu/libm-test-ulps | 8 - sysdeps/arc/nofpu/libm-test-ulps | 2 - sysdeps/arm/libm-test-ulps | 8 - sysdeps/csky/fpu/libm-test-ulps | 8 - sysdeps/csky/nofpu/libm-test-ulps | 8 - sysdeps/hppa/fpu/libm-test-ulps | 8 - sysdeps/i386/fpu/e_atan2f.S | 30 -- sysdeps/i386/fpu/libm-test-ulps | 12 +- .../i386/i686/fpu/multiarch/libm-test-ulps | 12 +- sysdeps/ieee754/flt-32/e_atan2f.c | 340 +++++++++++++----- sysdeps/loongarch/lp64/libm-test-ulps | 8 - sysdeps/m68k/coldfire/fpu/libm-test-ulps | 1 - sysdeps/m68k/m680x0/fpu/libm-test-ulps | 8 - sysdeps/microblaze/libm-test-ulps | 2 - sysdeps/mips/mips32/libm-test-ulps | 8 - sysdeps/mips/mips64/libm-test-ulps | 8 - sysdeps/or1k/fpu/libm-test-ulps | 8 - sysdeps/or1k/nofpu/libm-test-ulps | 8 - sysdeps/powerpc/fpu/libm-test-ulps | 8 - sysdeps/powerpc/nofpu/libm-test-ulps | 8 - sysdeps/riscv/nofpu/libm-test-ulps | 8 - sysdeps/riscv/rvd/libm-test-ulps | 8 - sysdeps/s390/fpu/libm-test-ulps | 8 - sysdeps/sh/libm-test-ulps | 4 - sysdeps/sparc/fpu/libm-test-ulps | 8 - sysdeps/x86_64/fpu/libm-test-ulps | 8 - 29 files changed, 270 insertions(+), 297 deletions(-) delete mode 100644 sysdeps/i386/fpu/e_atan2f.S diff --git a/SHARED-FILES b/SHARED-FILES index b9627afdfe..99f8554393 100644 --- a/SHARED-FILES +++ b/SHARED-FILES @@ -314,3 +314,7 @@ sysdeps/ieee754/flt-32/s_atanf.c: (src/binary32/atan/atanf.c in CORE-MATH) - The code was adapted to use glibc code style and internal functions to handle errno, overflow, and underflow. +sysdeps/ieee754/flt-32/e_atan2f.c: + (src/binary32/atan2/atan2f.c in CORE-MATH) + - The code was adapted to use glibc code style and internal + functions to handle errno, overflow, and underflow. diff --git a/sysdeps/aarch64/libm-test-ulps b/sysdeps/aarch64/libm-test-ulps index 33d282231a..931fac6bb0 100644 --- a/sysdeps/aarch64/libm-test-ulps +++ b/sysdeps/aarch64/libm-test-ulps @@ -142,7 +142,6 @@ double: 1 ldouble: 1 Function: "atan2": -float: 1 ldouble: 2 Function: "atan2_advsimd": @@ -151,7 +150,6 @@ float: 2 Function: "atan2_downward": double: 1 -float: 2 ldouble: 2 Function: "atan2_sve": @@ -160,12 +158,10 @@ float: 2 Function: "atan2_towardzero": double: 1 -float: 2 ldouble: 3 Function: "atan2_upward": double: 1 -float: 1 ldouble: 2 Function: "atan2pi": @@ -354,22 +350,18 @@ ldouble: 4 Function: "carg": double: 1 -float: 1 ldouble: 2 Function: "carg_downward": double: 1 -float: 2 ldouble: 2 Function: "carg_towardzero": double: 1 -float: 2 ldouble: 3 Function: "carg_upward": double: 1 -float: 1 ldouble: 2 Function: Real part of "casin": diff --git a/sysdeps/alpha/fpu/libm-test-ulps b/sysdeps/alpha/fpu/libm-test-ulps index f9c1cf7cf5..d098eaf820 100644 --- a/sysdeps/alpha/fpu/libm-test-ulps +++ b/sysdeps/alpha/fpu/libm-test-ulps @@ -70,22 +70,18 @@ double: 1 ldouble: 1 Function: "atan2": -float: 2 ldouble: 2 Function: "atan2_downward": double: 1 -float: 2 ldouble: 2 Function: "atan2_towardzero": double: 1 -float: 2 ldouble: 3 Function: "atan2_upward": double: 1 -float: 2 ldouble: 2 Function: "atan_downward": @@ -217,22 +213,18 @@ float: 2 ldouble: 4 Function: "carg": -float: 1 ldouble: 2 Function: "carg_downward": double: 1 -float: 2 ldouble: 2 Function: "carg_towardzero": double: 1 -float: 2 ldouble: 3 Function: "carg_upward": double: 1 -float: 2 ldouble: 2 Function: Real part of "casin": diff --git a/sysdeps/arc/fpu/libm-test-ulps b/sysdeps/arc/fpu/libm-test-ulps index 37b0efae66..5b89ee2696 100644 --- a/sysdeps/arc/fpu/libm-test-ulps +++ b/sysdeps/arc/fpu/libm-test-ulps @@ -54,19 +54,15 @@ double: 1 Function: "atan2": double: 7 -float: 2 Function: "atan2_downward": double: 5 -float: 2 Function: "atan2_towardzero": double: 5 -float: 2 Function: "atan2_upward": double: 8 -float: 2 Function: "atan_downward": double: 1 @@ -173,19 +169,15 @@ float: 3 Function: "carg": double: 7 -float: 2 Function: "carg_downward": double: 5 -float: 2 Function: "carg_towardzero": double: 5 -float: 2 Function: "carg_upward": double: 8 -float: 2 Function: Real part of "casin": double: 3 diff --git a/sysdeps/arc/nofpu/libm-test-ulps b/sysdeps/arc/nofpu/libm-test-ulps index 8d283f0627..ac43ab8dcc 100644 --- a/sysdeps/arc/nofpu/libm-test-ulps +++ b/sysdeps/arc/nofpu/libm-test-ulps @@ -17,7 +17,6 @@ Function: "atan": double: 1 Function: "atan2": -float: 2 Function: "atanh": double: 2 @@ -43,7 +42,6 @@ double: 1 float: 2 Function: "carg": -float: 1 Function: Real part of "casin": double: 1 diff --git a/sysdeps/arm/libm-test-ulps b/sysdeps/arm/libm-test-ulps index 7b1a541378..234609cae5 100644 --- a/sysdeps/arm/libm-test-ulps +++ b/sysdeps/arm/libm-test-ulps @@ -85,19 +85,15 @@ Function: "atan": double: 1 Function: "atan2": -float: 2 Function: "atan2_downward": double: 1 -float: 2 Function: "atan2_towardzero": double: 1 -float: 2 Function: "atan2_upward": double: 1 -float: 2 Function: "atan2pi": double: 1 @@ -233,19 +229,15 @@ double: 3 float: 2 Function: "carg": -float: 1 Function: "carg_downward": double: 1 -float: 2 Function: "carg_towardzero": double: 1 -float: 2 Function: "carg_upward": double: 1 -float: 2 Function: Real part of "casin": double: 1 diff --git a/sysdeps/csky/fpu/libm-test-ulps b/sysdeps/csky/fpu/libm-test-ulps index 9d3fcf693d..b8de7af6b9 100644 --- a/sysdeps/csky/fpu/libm-test-ulps +++ b/sysdeps/csky/fpu/libm-test-ulps @@ -50,19 +50,15 @@ double: 3 Function: "atan": Function: "atan2": -float: 1 Function: "atan2_downward": double: 1 -float: 2 Function: "atan2_towardzero": double: 1 -float: 2 Function: "atan2_upward": double: 1 -float: 2 Function: "atan_downward": double: 1 @@ -166,19 +162,15 @@ double: 3 float: 2 Function: "carg": -float: 1 Function: "carg_downward": double: 1 -float: 2 Function: "carg_towardzero": double: 1 -float: 2 Function: "carg_upward": double: 1 -float: 2 Function: Real part of "casin": double: 1 diff --git a/sysdeps/csky/nofpu/libm-test-ulps b/sysdeps/csky/nofpu/libm-test-ulps index 1bab8effc7..a7594b6b1c 100644 --- a/sysdeps/csky/nofpu/libm-test-ulps +++ b/sysdeps/csky/nofpu/libm-test-ulps @@ -50,19 +50,15 @@ double: 3 Function: "atan": Function: "atan2": -float: 1 Function: "atan2_downward": double: 1 -float: 2 Function: "atan2_towardzero": double: 1 -float: 2 Function: "atan2_upward": double: 1 -float: 2 Function: "atan_downward": double: 1 @@ -166,19 +162,15 @@ double: 2 float: 2 Function: "carg": -float: 1 Function: "carg_downward": double: 1 -float: 2 Function: "carg_towardzero": double: 1 -float: 2 Function: "carg_upward": double: 1 -float: 2 Function: Real part of "casin": double: 1 diff --git a/sysdeps/hppa/fpu/libm-test-ulps b/sysdeps/hppa/fpu/libm-test-ulps index 74936184b5..5d2074b098 100644 --- a/sysdeps/hppa/fpu/libm-test-ulps +++ b/sysdeps/hppa/fpu/libm-test-ulps @@ -85,19 +85,15 @@ Function: "atan": double: 1 Function: "atan2": -float: 2 Function: "atan2_downward": double: 1 -float: 2 Function: "atan2_towardzero": double: 1 -float: 2 Function: "atan2_upward": double: 1 -float: 2 Function: "atan2pi": double: 1 @@ -233,19 +229,15 @@ double: 3 float: 2 Function: "carg": -float: 1 Function: "carg_downward": double: 1 -float: 2 Function: "carg_towardzero": double: 1 -float: 2 Function: "carg_upward": double: 1 -float: 2 Function: Real part of "casin": double: 1 diff --git a/sysdeps/i386/fpu/e_atan2f.S b/sysdeps/i386/fpu/e_atan2f.S deleted file mode 100644 index 606d4a6f2d..0000000000 --- a/sysdeps/i386/fpu/e_atan2f.S +++ /dev/null @@ -1,30 +0,0 @@ -/* - * Public domain. - */ - -#include -#include -#include - -RCSID("$NetBSD: e_atan2f.S,v 1.1 1995/05/08 23:35:10 jtc Exp $") - -DEFINE_FLT_MIN - -#ifdef PIC -# define MO(op) op##@GOTOFF(%ecx) -#else -# define MO(op) op -#endif - - .text -ENTRY(__ieee754_atan2f) -#ifdef PIC - LOAD_PIC_REG (cx) -#endif - flds 4(%esp) - flds 8(%esp) - fpatan - FLT_CHECK_FORCE_UFLOW_NARROW - ret -END (__ieee754_atan2f) -libm_alias_finite (__ieee754_atan2f, __atan2f) diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps index 1ff3b5cf3a..3c16d8887b 100644 --- a/sysdeps/i386/fpu/libm-test-ulps +++ b/sysdeps/i386/fpu/libm-test-ulps @@ -139,19 +139,16 @@ ldouble: 1 Function: "atan2_downward": double: 1 -float: 1 float128: 2 ldouble: 1 Function: "atan2_towardzero": double: 1 -float: 1 float128: 3 ldouble: 1 Function: "atan2_upward": double: 1 -float: 1 float128: 2 ldouble: 1 @@ -163,19 +160,19 @@ ldouble: 1 Function: "atan2pi_downward": double: 1 -float: 1 +float: 2 float128: 2 ldouble: 2 Function: "atan2pi_towardzero": double: 1 -float: 1 +float: 2 float128: 2 ldouble: 2 Function: "atan2pi_upward": double: 1 -float: 1 +float: 2 float128: 2 ldouble: 2 @@ -364,19 +361,16 @@ ldouble: 1 Function: "carg_downward": double: 1 -float: 1 float128: 2 ldouble: 1 Function: "carg_towardzero": double: 1 -float: 1 float128: 3 ldouble: 1 Function: "carg_upward": double: 1 -float: 1 float128: 2 ldouble: 1 diff --git a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps index c296fefd0f..302d5c63c8 100644 --- a/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps +++ b/sysdeps/i386/i686/fpu/multiarch/libm-test-ulps @@ -139,19 +139,16 @@ ldouble: 1 Function: "atan2_downward": double: 1 -float: 1 float128: 2 ldouble: 1 Function: "atan2_towardzero": double: 1 -float: 1 float128: 3 ldouble: 1 Function: "atan2_upward": double: 1 -float: 1 float128: 2 ldouble: 1 @@ -163,19 +160,19 @@ ldouble: 1 Function: "atan2pi_downward": double: 1 -float: 1 +float: 2 float128: 2 ldouble: 2 Function: "atan2pi_towardzero": double: 1 -float: 1 +float: 2 float128: 2 ldouble: 2 Function: "atan2pi_upward": double: 1 -float: 1 +float: 2 float128: 2 ldouble: 2 @@ -364,19 +361,16 @@ ldouble: 1 Function: "carg_downward": double: 1 -float: 1 float128: 2 ldouble: 1 Function: "carg_towardzero": double: 1 -float: 1 float128: 3 ldouble: 1 Function: "carg_upward": double: 1 -float: 1 float128: 2 ldouble: 1 diff --git a/sysdeps/ieee754/flt-32/e_atan2f.c b/sysdeps/ieee754/flt-32/e_atan2f.c index 75174062e8..6c7bebc24b 100644 --- a/sysdeps/ieee754/flt-32/e_atan2f.c +++ b/sysdeps/ieee754/flt-32/e_atan2f.c @@ -1,94 +1,274 @@ -/* e_atan2f.c -- float version of e_atan2.c. - */ +/* Correctly-rounded arctangent function of two binary32 values. -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ +Copyright (c) 2022-2024 Alexei Sibidanov and Paul Zimmermann. + +The original version of this file was copied from the CORE-MATH +project (file src/binary32/atan2/atan2f.c, revision 7835c5d). + +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 -#include +#include #include +#include "math_config.h" -static const float -tiny = 1.0e-30, -zero = 0.0, -pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */ -pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */ -pi = 3.1415927410e+00, /* 0x40490fdb */ -pi_lo = -8.7422776573e-08; /* 0xb3bbbd2e */ +static inline double +muldd (double xh, double xl, double ch, double cl, double *l) +{ + double ahlh = ch * xl; + double alhh = cl * xh; + double ahhh = ch * xh; + double ahhl = fma (ch, xh, -ahhh); + ahhl += alhh + ahlh; + ch = ahhh + ahhl; + *l = (ahhh - ch) + ahhl; + return ch; +} + +static double +polydd (double xh, double xl, int n, const double c[][2], double *l) +{ + int i = n - 1; + double ch = c[i][0]; + double cl = c[i][1]; + while (--i >= 0) + { + ch = muldd (xh, xl, ch, cl, &cl); + double th = ch + c[i][0]; + double tl = (c[i][0] - th) + ch; + ch = th; + cl += tl + c[i][1]; + } + *l = cl; + return ch; +} + +/* for y/x tiny, use Taylor approximation z - z^3/3 where z=y/x */ +static float +cr_atan2f_tiny (float y, float x) +{ + double dy = y; + double dx = x; + double z = dy / dx; + double e = fma (-z, x, y); + /* z * x + e = y thus y/x = z + e/x */ + static const double c = -0x1.5555555555555p-2; /* -1/3 rounded to nearest */ + double zz = z * z; + double cz = c * z; + e = e / x + cz * zz; + uint64_t t = asuint64 (z); + if ((t & UINT64_C(0xfffffff)) == 0) /* boundary case */ + { + /* If z and e are of same sign (resp. of different signs), we increase + (resp. decrease) the significant of t by 1 to avoid a double-rounding + issue when rounding t to binary32. */ + if (z * e > 0) + t += 1; + else + t -= 1; + } + return asdouble (t); +} float __ieee754_atan2f (float y, float x) { - float z; - int32_t k,m,hx,hy,ix,iy; - - GET_FLOAT_WORD(hx,x); - ix = hx&0x7fffffff; - GET_FLOAT_WORD(hy,y); - iy = hy&0x7fffffff; - if((ix>0x7f800000)|| - (iy>0x7f800000)) /* x or y is NaN */ - return x+y; - if(hx==0x3f800000) return __atanf(y); /* x=1.0 */ - m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ - - /* when y = 0 */ - if(iy==0) { - switch(m) { - case 0: - case 1: return y; /* atan(+-0,+anything)=+-0 */ - case 2: return pi+tiny;/* atan(+0,-anything) = pi */ - case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ - } + static const double cn[] = + { + 0x1p+0, 0x1.40e0698f94c35p+1, 0x1.248c5da347f0dp+1, + 0x1.d873386572976p-1, 0x1.46fa40b20f1dp-3, 0x1.33f5e041eed0fp-7, + 0x1.546bbf28667c5p-14 + }; + static const double cd[] = + { + 0x1p+0, 0x1.6b8b143a3f6dap+1, 0x1.8421201d18ed5p+1, + 0x1.8221d086914ebp+0, 0x1.670657e3a07bap-2, 0x1.0f4951fd1e72dp-5, + 0x1.b3874b8798286p-11 + }; + static const double m[] = { 0, 1 }; +#define pi 0x1.921fb54442d18p+1 +#define pi2 0x1.921fb54442d18p+0 +#define pi2l 0x1.1a62633145c07p-54 + static const double off[] = { 0.0f, pi2, pi, pi2, -0.0f, -pi2, -pi, -pi2 }; + static const double offl[] = + { + 0.0f, pi2l, 2 * pi2l, pi2l, -0.0f, -pi2l, -2 * pi2l, -pi2l + }; + static const double sgn[] = { 1, -1 }; + uint32_t ux = asuint (x); + uint32_t uy = asuint (y); + uint32_t ax = ux & (~0u >> 1); + uint32_t ay = uy & (~0u >> 1); + if (__glibc_unlikely (ay >= (0xff << 23) || ax >= (0xff << 23))) + { + /* we use x+y below so that the invalid exception is set + for (x,y) = (qnan,snan) or (snan,qnan) */ + if (ay > (0xff << 23)) + return x + y; /* nan */ + if (ax > (0xff << 23)) + return x + y; /* nan */ + bool yinf = ay == (0xff << 23); + bool xinf = ax == (0xff << 23); + if (yinf & xinf) + { + if (ux >> 31) + return 0x1.2d97c7f3321d2p+1 * sgn[uy >> 31]; + else + return 0x1.921fb54442d18p-1 * sgn[uy >> 31]; } - /* when x = 0 */ - if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; - - /* when x is INF */ - if(ix==0x7f800000) { - if(iy==0x7f800000) { - switch(m) { - case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ - case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ - case 2: return (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ - case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ - } - } else { - switch(m) { - case 0: return zero ; /* atan(+...,+INF) */ - case 1: return -zero ; /* atan(-...,+INF) */ - case 2: return pi+tiny ; /* atan(+...,-INF) */ - case 3: return -pi-tiny ; /* atan(-...,-INF) */ - } - } + if (xinf) + { + if (ux >> 31) + return pi * sgn[uy >> 31]; + else + return 0.0f * sgn[uy >> 31]; } - /* when y is INF */ - if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; - - /* compute y/x */ - k = (iy-ix)>>23; - if(k > 60) z=pi_o_2+(float)0.5*pi_lo; /* |y/x| > 2**60 */ - else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ - else z=__atanf(fabsf(y/x)); /* safe to do y/x */ - switch (m) { - case 0: return z ; /* atan(+,+) */ - case 1: { - uint32_t zh; - GET_FLOAT_WORD(zh,z); - SET_FLOAT_WORD(z,zh ^ 0x80000000); - } - return z ; /* atan(-,+) */ - case 2: return pi-(z-pi_lo);/* atan(+,-) */ - default: /* case 3 */ - return (z-pi_lo)-pi;/* atan(-,-) */ + if (yinf) + return pi2 * sgn[uy >> 31]; + } + if (__glibc_unlikely (ay == 0)) + { + if (__glibc_unlikely (!(ay | ax))) + { + uint32_t i = (uy >> 31) * 4 + (ux >> 31) * 2; + if (ux >> 31) + return off[i] + offl[i]; + else + return off[i]; } + if (!(ux >> 31)) + return 0.0f * sgn[uy >> 31]; + } + uint32_t gt = ay > ax; + uint32_t i = (uy >> 31) * 4 + (ux >> 31) * 2 + gt; + + double zx = x; + double zy = y; + double z = (m[gt] * zx + m[1 - gt] * zy) / (m[gt] * zy + m[1 - gt] * zx); + /* z = x/y if |y| > |x|, and z = y/x otherwise */ + double r; + int d = (int) ax - (int) ay; + if (__glibc_likely (d < (27 << 23) && d > (-(27 << 23)))) + { + double z2 = z * z, z4 = z2 * z2, z8 = z4 * z4; + /* z2 cannot underflow, since for |y|=0x1p-149 and |x|=0x1.fffffep+127 + we get |z| > 2^-277 thus z2 > 2^-554, but z4 and z8 might underflow, + which might give spurious underflow exceptions. */ + double cn0 = cn[0] + z2 * cn[1]; + double cn2 = cn[2] + z2 * cn[3]; + double cn4 = cn[4] + z2 * cn[5]; + double cn6 = cn[6]; + cn0 += z4 * cn2; + cn4 += z4 * cn6; + cn0 += z8 * cn4; + double cd0 = cd[0] + z2 * cd[1]; + double cd2 = cd[2] + z2 * cd[3]; + double cd4 = cd[4] + z2 * cd[5]; + double cd6 = cd[6]; + cd0 += z4 * cd2; + cd4 += z4 * cd6; + cd0 += z8 * cd4; + r = cn0 / cd0; + } + else + r = 1; + z *= sgn[gt]; + r = z * r + off[i]; + if (__glibc_unlikely (((asuint64 (r) + 8) & 0xfffffff) <= 16)) + { + /* check tiny y/x */ + if (ay < ax && ((ax - ay) >> 23 >= 25)) + return cr_atan2f_tiny (y, x); + double zh; + double zl; + if (gt == 0) + { + zh = zy / zx; + zl = fma (zh, -zx, zy) / zx; + } + else + { + zh = zx / zy; + zl = fma (zh, -zy, zx) / zy; + } + double z2l; + double z2h = muldd (zh, zl, zh, zl, &z2l); + static const double c[32][2] = + { + { 0x1p+0, -0x1.8c1dac5492248p-87 }, + { -0x1.5555555555555p-2, -0x1.55553bf3a2abep-56 }, + { 0x1.999999999999ap-3, -0x1.99deed1ec9071p-57 }, + { -0x1.2492492492492p-3, -0x1.fd99c8d18269ap-58 }, + { 0x1.c71c71c71c717p-4, -0x1.651eee4c4d9dp-61 }, + { -0x1.745d1745d1649p-4, -0x1.632683d6c44a6p-58 }, + { 0x1.3b13b13b11c63p-4, 0x1.bf69c1f8af41dp-58 }, + { -0x1.11111110e6338p-4, 0x1.3c3e431e8bb68p-61 }, + { 0x1.e1e1e1dc45c4ap-5, -0x1.be2db05c77bbfp-59 }, + { -0x1.af286b8164b4fp-5, 0x1.a4673491f0942p-61 }, + { 0x1.86185e9ad4846p-5, 0x1.e12e32d79fceep-59 }, + { -0x1.642c6d5161faep-5, 0x1.3ce76c1ca03fp-59 }, + { 0x1.47ad6f277e5bfp-5, -0x1.abd8d85bdb714p-60 }, + { -0x1.2f64a2ee8896dp-5, 0x1.ef87d4b615323p-61 }, + { 0x1.1a6a2b31741b5p-5, 0x1.a5d9d973547eep-62 }, + { -0x1.07fbdad65e0a6p-5, -0x1.65ac07f5d35f4p-61 }, + { 0x1.ee9932a9a5f8bp-6, 0x1.f8b9623f6f55ap-61 }, + { -0x1.ce8b5b9584dc6p-6, 0x1.fe5af96e8ea2dp-61 }, + { 0x1.ac9cb288087b7p-6, -0x1.450cdfceaf5cap-60 }, + { -0x1.84b025351f3e6p-6, 0x1.579561b0d73dap-61 }, + { 0x1.52f5b8ecdd52bp-6, 0x1.036bd2c6fba47p-60 }, + { -0x1.163a8c44909dcp-6, 0x1.18f735ffb9f16p-60 }, + { 0x1.a400dce3eea6fp-7, -0x1.c90569c0c1b5cp-61 }, + { -0x1.1caa78ae6db3ap-7, -0x1.4c60f8161ea09p-61 }, + { 0x1.52672453c0731p-8, 0x1.834efb598c338p-62 }, + { -0x1.5850c5be137cfp-9, -0x1.445fc150ca7f5p-63 }, + { 0x1.23eb98d22e1cap-10, -0x1.388fbaf1d783p-64 }, + { -0x1.8f4e974a40741p-12, 0x1.271198a97da34p-66 }, + { 0x1.a5cf2e9cf76e5p-14, -0x1.887eb4a63b665p-68 }, + { -0x1.420c270719e32p-16, 0x1.efd595b27888bp-71 }, + { 0x1.3ba2d69b51677p-19, -0x1.4fb06829cdfc7p-73 }, + { -0x1.29b7e6f676385p-23, -0x1.a783b6de718fbp-77 } + }; + double pl; + double ph = polydd (z2h, z2l, 32, c, &pl); + zh *= sgn[gt]; + zl *= sgn[gt]; + ph = muldd (zh, zl, ph, pl, &pl); + double sh = ph + off[i]; + double sl = ((off[i] - sh) + ph) + pl + offl[i]; + float rf = sh; + double th = rf; + double dh = sh - th; + double tm = dh + sl; + uint64_t tth = asuint64 (th); + if (th + th * 0x1p-60 == th - th * 0x1p-60) + { + tth &= UINT64_C(0x7ff) << 52; + tth -= UINT64_C(24) << 52; + if (fabs (tm) > asdouble (tth)) + tm *= 1.25; + else + tm *= 0.75; + } + r = th + tm; + } + return r; } libm_alias_finite (__ieee754_atan2f, __atan2f) diff --git a/sysdeps/loongarch/lp64/libm-test-ulps b/sysdeps/loongarch/lp64/libm-test-ulps index ff1cf6b2e4..a34539753c 100644 --- a/sysdeps/loongarch/lp64/libm-test-ulps +++ b/sysdeps/loongarch/lp64/libm-test-ulps @@ -70,22 +70,18 @@ double: 1 ldouble: 1 Function: "atan2": -float: 2 ldouble: 2 Function: "atan2_downward": double: 1 -float: 2 ldouble: 2 Function: "atan2_towardzero": double: 1 -float: 2 ldouble: 3 Function: "atan2_upward": double: 1 -float: 2 ldouble: 2 Function: "atan_downward": @@ -217,22 +213,18 @@ float: 2 ldouble: 4 Function: "carg": -float: 1 ldouble: 2 Function: "carg_downward": double: 1 -float: 2 ldouble: 2 Function: "carg_towardzero": double: 1 -float: 2 ldouble: 3 Function: "carg_upward": double: 1 -float: 2 ldouble: 2 Function: Real part of "casin": diff --git a/sysdeps/m68k/coldfire/fpu/libm-test-ulps b/sysdeps/m68k/coldfire/fpu/libm-test-ulps index 7e49468421..989015ff9a 100644 --- a/sysdeps/m68k/coldfire/fpu/libm-test-ulps +++ b/sysdeps/m68k/coldfire/fpu/libm-test-ulps @@ -2,7 +2,6 @@ # Maximal error of functions: Function: "atan2": -float: 1 Function: "atanh": float: 1 diff --git a/sysdeps/m68k/m680x0/fpu/libm-test-ulps b/sysdeps/m68k/m680x0/fpu/libm-test-ulps index 7b3e67efaf..1ef5e0e5a3 100644 --- a/sysdeps/m68k/m680x0/fpu/libm-test-ulps +++ b/sysdeps/m68k/m680x0/fpu/libm-test-ulps @@ -50,22 +50,18 @@ ldouble: 3 Function: "atan2": double: 1 -float: 1 ldouble: 1 Function: "atan2_downward": double: 1 -float: 1 ldouble: 2 Function: "atan2_towardzero": double: 1 -float: 1 ldouble: 2 Function: "atan2_upward": double: 1 -float: 1 ldouble: 2 Function: "atan_downward": @@ -191,22 +187,18 @@ float: 2 ldouble: 3 Function: "carg": -float: 1 ldouble: 1 Function: "carg_downward": double: 1 -float: 1 ldouble: 1 Function: "carg_towardzero": double: 1 -float: 1 ldouble: 1 Function: "carg_upward": double: 1 -float: 1 ldouble: 1 Function: Real part of "casin": diff --git a/sysdeps/microblaze/libm-test-ulps b/sysdeps/microblaze/libm-test-ulps index 5dce4c8f89..4fa242daca 100644 --- a/sysdeps/microblaze/libm-test-ulps +++ b/sysdeps/microblaze/libm-test-ulps @@ -14,7 +14,6 @@ double: 1 Function: "atan": Function: "atan2": -float: 1 Function: "atanh": double: 2 @@ -40,7 +39,6 @@ double: 1 float: 2 Function: "carg": -float: 1 Function: Real part of "casin": double: 1 diff --git a/sysdeps/mips/mips32/libm-test-ulps b/sysdeps/mips/mips32/libm-test-ulps index 9046a17170..2f6f7fff23 100644 --- a/sysdeps/mips/mips32/libm-test-ulps +++ b/sysdeps/mips/mips32/libm-test-ulps @@ -53,19 +53,15 @@ Function: "atan": double: 1 Function: "atan2": -float: 2 Function: "atan2_downward": double: 1 -float: 2 Function: "atan2_towardzero": double: 1 -float: 2 Function: "atan2_upward": double: 1 -float: 2 Function: "atan_downward": double: 1 @@ -169,19 +165,15 @@ double: 3 float: 2 Function: "carg": -float: 1 Function: "carg_downward": double: 1 -float: 2 Function: "carg_towardzero": double: 1 -float: 2 Function: "carg_upward": double: 1 -float: 2 Function: Real part of "casin": double: 1 diff --git a/sysdeps/mips/mips64/libm-test-ulps b/sysdeps/mips/mips64/libm-test-ulps index 1525e55eb5..037fb885ed 100644 --- a/sysdeps/mips/mips64/libm-test-ulps +++ b/sysdeps/mips/mips64/libm-test-ulps @@ -70,22 +70,18 @@ double: 1 ldouble: 1 Function: "atan2": -float: 2 ldouble: 2 Function: "atan2_downward": double: 1 -float: 2 ldouble: 2 Function: "atan2_towardzero": double: 1 -float: 2 ldouble: 3 Function: "atan2_upward": double: 1 -float: 2 ldouble: 2 Function: "atan_downward": @@ -217,22 +213,18 @@ float: 2 ldouble: 4 Function: "carg": -float: 1 ldouble: 2 Function: "carg_downward": double: 1 -float: 2 ldouble: 2 Function: "carg_towardzero": double: 1 -float: 2 ldouble: 3 Function: "carg_upward": double: 1 -float: 2 ldouble: 2 Function: Real part of "casin": diff --git a/sysdeps/or1k/fpu/libm-test-ulps b/sysdeps/or1k/fpu/libm-test-ulps index 6edadaed89..3fee2b50cc 100644 --- a/sysdeps/or1k/fpu/libm-test-ulps +++ b/sysdeps/or1k/fpu/libm-test-ulps @@ -53,19 +53,15 @@ Function: "atan": double: 1 Function: "atan2": -float: 2 Function: "atan2_downward": double: 5 -float: 2 Function: "atan2_towardzero": double: 5 -float: 2 Function: "atan2_upward": double: 8 -float: 2 Function: "atan_downward": double: 1 @@ -169,19 +165,15 @@ double: 3 float: 2 Function: "carg": -float: 1 Function: "carg_downward": double: 5 -float: 2 Function: "carg_towardzero": double: 5 -float: 2 Function: "carg_upward": double: 8 -float: 2 Function: Real part of "casin": double: 1 diff --git a/sysdeps/or1k/nofpu/libm-test-ulps b/sysdeps/or1k/nofpu/libm-test-ulps index 318f29aacf..a380709e30 100644 --- a/sysdeps/or1k/nofpu/libm-test-ulps +++ b/sysdeps/or1k/nofpu/libm-test-ulps @@ -61,19 +61,15 @@ Function: "atan": double: 1 Function: "atan2": -float: 2 Function: "atan2_downward": double: 5 -float: 2 Function: "atan2_towardzero": double: 5 -float: 2 Function: "atan2_upward": double: 8 -float: 2 Function: "atan2pi": double: 1 @@ -185,19 +181,15 @@ double: 3 float: 2 Function: "carg": -float: 1 Function: "carg_downward": double: 5 -float: 2 Function: "carg_towardzero": double: 5 -float: 2 Function: "carg_upward": double: 8 -float: 2 Function: Real part of "casin": double: 1 diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps index 0e7996d682..dd166aa532 100644 --- a/sysdeps/powerpc/fpu/libm-test-ulps +++ b/sysdeps/powerpc/fpu/libm-test-ulps @@ -139,25 +139,21 @@ float128: 1 ldouble: 1 Function: "atan2": -float: 1 float128: 2 ldouble: 2 Function: "atan2_downward": double: 1 -float: 2 float128: 2 ldouble: 5 Function: "atan2_towardzero": double: 1 -float: 2 float128: 3 ldouble: 6 Function: "atan2_upward": double: 1 -float: 1 float128: 2 ldouble: 3 @@ -366,25 +362,21 @@ ldouble: 8 Function: "carg": double: 1 -float: 1 float128: 2 ldouble: 2 Function: "carg_downward": double: 1 -float: 2 float128: 2 ldouble: 5 Function: "carg_towardzero": double: 1 -float: 2 float128: 3 ldouble: 6 Function: "carg_upward": double: 1 -float: 1 float128: 2 ldouble: 3 diff --git a/sysdeps/powerpc/nofpu/libm-test-ulps b/sysdeps/powerpc/nofpu/libm-test-ulps index c7242e5fec..8b7ed72386 100644 --- a/sysdeps/powerpc/nofpu/libm-test-ulps +++ b/sysdeps/powerpc/nofpu/libm-test-ulps @@ -74,22 +74,18 @@ double: 1 ldouble: 1 Function: "atan2": -float: 2 ldouble: 2 Function: "atan2_downward": double: 1 -float: 2 ldouble: 5 Function: "atan2_towardzero": double: 1 -float: 2 ldouble: 6 Function: "atan2_upward": double: 1 -float: 2 ldouble: 3 Function: "atan_downward": @@ -221,22 +217,18 @@ float: 2 ldouble: 5 Function: "carg": -float: 1 ldouble: 2 Function: "carg_downward": double: 1 -float: 2 ldouble: 5 Function: "carg_towardzero": double: 1 -float: 2 ldouble: 6 Function: "carg_upward": double: 1 -float: 2 ldouble: 3 Function: Real part of "casin": diff --git a/sysdeps/riscv/nofpu/libm-test-ulps b/sysdeps/riscv/nofpu/libm-test-ulps index 4fa17a3da2..19e36742aa 100644 --- a/sysdeps/riscv/nofpu/libm-test-ulps +++ b/sysdeps/riscv/nofpu/libm-test-ulps @@ -70,22 +70,18 @@ double: 1 ldouble: 1 Function: "atan2": -float: 2 ldouble: 2 Function: "atan2_downward": double: 1 -float: 2 ldouble: 2 Function: "atan2_towardzero": double: 1 -float: 2 ldouble: 3 Function: "atan2_upward": double: 1 -float: 1 ldouble: 2 Function: "atan_downward": @@ -217,22 +213,18 @@ float: 2 ldouble: 4 Function: "carg": -float: 1 ldouble: 2 Function: "carg_downward": double: 1 -float: 2 ldouble: 2 Function: "carg_towardzero": double: 1 -float: 2 ldouble: 3 Function: "carg_upward": double: 1 -float: 1 ldouble: 2 Function: Real part of "casin": diff --git a/sysdeps/riscv/rvd/libm-test-ulps b/sysdeps/riscv/rvd/libm-test-ulps index 0e3fb96ee5..ad3242fefd 100644 --- a/sysdeps/riscv/rvd/libm-test-ulps +++ b/sysdeps/riscv/rvd/libm-test-ulps @@ -70,22 +70,18 @@ double: 1 ldouble: 1 Function: "atan2": -float: 1 ldouble: 2 Function: "atan2_downward": double: 1 -float: 2 ldouble: 2 Function: "atan2_towardzero": double: 1 -float: 2 ldouble: 3 Function: "atan2_upward": double: 1 -float: 1 ldouble: 2 Function: "atan_downward": @@ -217,22 +213,18 @@ float: 2 ldouble: 4 Function: "carg": -float: 1 ldouble: 2 Function: "carg_downward": double: 1 -float: 2 ldouble: 2 Function: "carg_towardzero": double: 1 -float: 2 ldouble: 3 Function: "carg_upward": double: 1 -float: 1 ldouble: 2 Function: Real part of "casin": diff --git a/sysdeps/s390/fpu/libm-test-ulps b/sysdeps/s390/fpu/libm-test-ulps index 1f6d040eb8..7b43058603 100644 --- a/sysdeps/s390/fpu/libm-test-ulps +++ b/sysdeps/s390/fpu/libm-test-ulps @@ -70,22 +70,18 @@ double: 1 ldouble: 1 Function: "atan2": -float: 1 ldouble: 2 Function: "atan2_downward": double: 1 -float: 2 ldouble: 2 Function: "atan2_towardzero": double: 1 -float: 2 ldouble: 3 Function: "atan2_upward": double: 1 -float: 1 ldouble: 2 Function: "atan_downward": @@ -217,22 +213,18 @@ float: 2 ldouble: 4 Function: "carg": -float: 1 ldouble: 2 Function: "carg_downward": double: 1 -float: 2 ldouble: 2 Function: "carg_towardzero": double: 1 -float: 2 ldouble: 3 Function: "carg_upward": double: 1 -float: 1 ldouble: 2 Function: Real part of "casin": diff --git a/sysdeps/sh/libm-test-ulps b/sysdeps/sh/libm-test-ulps index b429f42d89..15655ad3a8 100644 --- a/sysdeps/sh/libm-test-ulps +++ b/sysdeps/sh/libm-test-ulps @@ -26,11 +26,9 @@ double: 2 Function: "atan": Function: "atan2": -float: 1 Function: "atan2_towardzero": double: 1 -float: 2 Function: "atan_towardzero": double: 1 @@ -82,11 +80,9 @@ double: 3 float: 2 Function: "carg": -float: 1 Function: "carg_towardzero": double: 1 -float: 2 Function: Real part of "casin": double: 1 diff --git a/sysdeps/sparc/fpu/libm-test-ulps b/sysdeps/sparc/fpu/libm-test-ulps index 66564e0ab1..0d867464c0 100644 --- a/sysdeps/sparc/fpu/libm-test-ulps +++ b/sysdeps/sparc/fpu/libm-test-ulps @@ -70,22 +70,18 @@ double: 1 ldouble: 1 Function: "atan2": -float: 2 ldouble: 2 Function: "atan2_downward": double: 1 -float: 2 ldouble: 2 Function: "atan2_towardzero": double: 1 -float: 2 ldouble: 3 Function: "atan2_upward": double: 1 -float: 2 ldouble: 2 Function: "atan_downward": @@ -217,22 +213,18 @@ float: 2 ldouble: 4 Function: "carg": -float: 1 ldouble: 2 Function: "carg_downward": double: 1 -float: 2 ldouble: 2 Function: "carg_towardzero": double: 1 -float: 2 ldouble: 3 Function: "carg_upward": double: 1 -float: 2 ldouble: 2 Function: Real part of "casin": diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps index f054d8307a..f09e1288be 100644 --- a/sysdeps/x86_64/fpu/libm-test-ulps +++ b/sysdeps/x86_64/fpu/libm-test-ulps @@ -212,25 +212,21 @@ float128: 1 ldouble: 1 Function: "atan2": -float: 2 float128: 2 ldouble: 1 Function: "atan2_downward": double: 1 -float: 2 float128: 2 ldouble: 1 Function: "atan2_towardzero": double: 1 -float: 2 float128: 3 ldouble: 1 Function: "atan2_upward": double: 1 -float: 2 float128: 2 ldouble: 1 @@ -498,25 +494,21 @@ float128: 4 ldouble: 3 Function: "carg": -float: 1 float128: 2 ldouble: 1 Function: "carg_downward": double: 1 -float: 2 float128: 2 ldouble: 1 Function: "carg_towardzero": double: 1 -float: 2 float128: 3 ldouble: 1 Function: "carg_upward": double: 1 -float: 2 float128: 2 ldouble: 1