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Diffstat (limited to 'pl/math/atan2f_3u.c')
| -rw-r--r-- | pl/math/atan2f_3u.c | 167 |
1 files changed, 167 insertions, 0 deletions
diff --git a/pl/math/atan2f_3u.c b/pl/math/atan2f_3u.c new file mode 100644 index 0000000..38e1df5 --- /dev/null +++ b/pl/math/atan2f_3u.c @@ -0,0 +1,167 @@ +/* + * Single-precision scalar atan2(x) function. + * + * Copyright (c) 2021-2023, Arm Limited. + * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception + */ + +#include <stdbool.h> + +#include "atanf_common.h" +#include "math_config.h" +#include "pl_sig.h" +#include "pl_test.h" + +#define Pi (0x1.921fb6p+1f) +#define PiOver2 (0x1.921fb6p+0f) +#define PiOver4 (0x1.921fb6p-1f) +#define SignMask (0x80000000) + +/* We calculate atan2f by P(n/d), where n and d are similar to the input + arguments, and P is a polynomial. The polynomial may underflow. + POLY_UFLOW_BOUND is the lower bound of the difference in exponents of n and d + for which P underflows, and is used to special-case such inputs. */ +#define POLY_UFLOW_BOUND 24 + +static inline int32_t +biased_exponent (float f) +{ + uint32_t fi = asuint (f); + int32_t ex = (int32_t) ((fi & 0x7f800000) >> 23); + if (unlikely (ex == 0)) + { + /* Subnormal case - we still need to get the exponent right for subnormal + numbers as division may take us back inside the normal range. */ + return ex - __builtin_clz (fi << 9); + } + return ex; +} + +/* Fast implementation of scalar atan2f. Largest observed error is + 2.88ulps in [99.0, 101.0] x [99.0, 101.0]: + atan2f(0x1.9332d8p+6, 0x1.8cb6c4p+6) got 0x1.964646p-1 + want 0x1.964640p-1. */ +float +atan2f (float y, float x) +{ + uint32_t ix = asuint (x); + uint32_t iy = asuint (y); + + uint32_t sign_x = ix & SignMask; + uint32_t sign_y = iy & SignMask; + + uint32_t iax = ix & ~SignMask; + uint32_t iay = iy & ~SignMask; + + /* x or y is NaN. */ + if ((iax > 0x7f800000) || (iay > 0x7f800000)) + return x + y; + + /* m = 2 * sign(x) + sign(y). */ + uint32_t m = ((iy >> 31) & 1) | ((ix >> 30) & 2); + + /* The following follows glibc ieee754 implementation, except + that we do not use +-tiny shifts (non-nearest rounding mode). */ + + int32_t exp_diff = biased_exponent (x) - biased_exponent (y); + + /* Special case for (x, y) either on or very close to the x axis. Either y = + 0, or y is tiny and x is huge (difference in exponents >= + POLY_UFLOW_BOUND). In the second case, we only want to use this special + case when x is negative (i.e. quadrants 2 or 3). */ + if (unlikely (iay == 0 || (exp_diff >= POLY_UFLOW_BOUND && m >= 2))) + { + switch (m) + { + case 0: + case 1: + return y; /* atan(+-0,+anything)=+-0. */ + case 2: + return Pi; /* atan(+0,-anything) = pi. */ + case 3: + return -Pi; /* atan(-0,-anything) =-pi. */ + } + } + /* Special case for (x, y) either on or very close to the y axis. Either x = + 0, or x is tiny and y is huge (difference in exponents >= + POLY_UFLOW_BOUND). */ + if (unlikely (iax == 0 || exp_diff <= -POLY_UFLOW_BOUND)) + return sign_y ? -PiOver2 : PiOver2; + + /* x is INF. */ + if (iax == 0x7f800000) + { + if (iay == 0x7f800000) + { + switch (m) + { + case 0: + return PiOver4; /* atan(+INF,+INF). */ + case 1: + return -PiOver4; /* atan(-INF,+INF). */ + case 2: + return 3.0f * PiOver4; /* atan(+INF,-INF). */ + case 3: + return -3.0f * PiOver4; /* atan(-INF,-INF). */ + } + } + else + { + switch (m) + { + case 0: + return 0.0f; /* atan(+...,+INF). */ + case 1: + return -0.0f; /* atan(-...,+INF). */ + case 2: + return Pi; /* atan(+...,-INF). */ + case 3: + return -Pi; /* atan(-...,-INF). */ + } + } + } + /* y is INF. */ + if (iay == 0x7f800000) + return sign_y ? -PiOver2 : PiOver2; + + uint32_t sign_xy = sign_x ^ sign_y; + + float ax = asfloat (iax); + float ay = asfloat (iay); + + bool pred_aygtax = (ay > ax); + + /* Set up z for call to atanf. */ + float n = pred_aygtax ? -ax : ay; + float d = pred_aygtax ? ay : ax; + float z = n / d; + + float ret; + if (unlikely (m < 2 && exp_diff >= POLY_UFLOW_BOUND)) + { + /* If (x, y) is very close to x axis and x is positive, the polynomial + will underflow and evaluate to z. */ + ret = z; + } + else + { + /* Work out the correct shift. */ + float shift = sign_x ? -2.0f : 0.0f; + shift = pred_aygtax ? shift + 1.0f : shift; + shift *= PiOver2; + + ret = eval_poly (z, z, shift); + } + + /* Account for the sign of x and y. */ + return asfloat (asuint (ret) ^ sign_xy); +} + +/* Arity of 2 means no mathbench entry emitted. See test/mathbench_funcs.h. */ +PL_SIG (S, F, 2, atan2) +PL_TEST_ULP (atan2f, 2.4) +PL_TEST_INTERVAL (atan2f, -10.0, 10.0, 50000) +PL_TEST_INTERVAL (atan2f, -1.0, 1.0, 40000) +PL_TEST_INTERVAL (atan2f, 0.0, 1.0, 40000) +PL_TEST_INTERVAL (atan2f, 1.0, 100.0, 40000) +PL_TEST_INTERVAL (atan2f, 1e6, 1e32, 40000) |