1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Single-precision atan(x) function. 3*f3087befSAndrew Turner * 4*f3087befSAndrew Turner * Copyright (c) 2022-2024, Arm Limited. 5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6*f3087befSAndrew Turner */ 7*f3087befSAndrew Turner 8*f3087befSAndrew Turner #include "atanf_common.h" 9*f3087befSAndrew Turner #include "test_sig.h" 10*f3087befSAndrew Turner #include "test_defs.h" 11*f3087befSAndrew Turner 12*f3087befSAndrew Turner #define PiOver2 0x1.921fb6p+0f 13*f3087befSAndrew Turner #define AbsMask 0x7fffffff 14*f3087befSAndrew Turner #define TinyBound 0x30800000 /* asuint(0x1p-30). */ 15*f3087befSAndrew Turner #define BigBound 0x4e800000 /* asuint(0x1p30). */ 16*f3087befSAndrew Turner #define One 0x3f800000 17*f3087befSAndrew Turner 18*f3087befSAndrew Turner /* Approximation of single-precision atan(x) based on 19*f3087befSAndrew Turner atan(x) ~ shift + z + z^3 * P(z^2) with reduction to [0,1] 20*f3087befSAndrew Turner using z=-1/x and shift = pi/2. 21*f3087befSAndrew Turner Maximum error is 2.88 ulps: 22*f3087befSAndrew Turner atanf(0x1.0565ccp+0) got 0x1.97771p-1 23*f3087befSAndrew Turner want 0x1.97770ap-1. */ 24*f3087befSAndrew Turner float 25*f3087befSAndrew Turner atanf (float x) 26*f3087befSAndrew Turner { 27*f3087befSAndrew Turner uint32_t ix = asuint (x); 28*f3087befSAndrew Turner uint32_t sign = ix & ~AbsMask; 29*f3087befSAndrew Turner uint32_t ia = ix & AbsMask; 30*f3087befSAndrew Turner 31*f3087befSAndrew Turner if (unlikely (ia < TinyBound)) 32*f3087befSAndrew Turner /* Avoid underflow by returning x. */ 33*f3087befSAndrew Turner return x; 34*f3087befSAndrew Turner 35*f3087befSAndrew Turner if (unlikely (ia > BigBound)) 36*f3087befSAndrew Turner { 37*f3087befSAndrew Turner if (ia > 0x7f800000) 38*f3087befSAndrew Turner /* Propagate NaN. */ 39*f3087befSAndrew Turner return __math_invalidf (x); 40*f3087befSAndrew Turner /* atan(x) rounds to PiOver2 for large x. */ 41*f3087befSAndrew Turner return asfloat (asuint (PiOver2) ^ sign); 42*f3087befSAndrew Turner } 43*f3087befSAndrew Turner 44*f3087befSAndrew Turner float z, az, shift; 45*f3087befSAndrew Turner if (ia > One) 46*f3087befSAndrew Turner { 47*f3087befSAndrew Turner /* For x > 1, use atan(x) = pi / 2 + atan(-1 / x). */ 48*f3087befSAndrew Turner z = -1.0f / x; 49*f3087befSAndrew Turner shift = PiOver2; 50*f3087befSAndrew Turner /* Use absolute value only when needed (odd powers of z). */ 51*f3087befSAndrew Turner az = -fabsf (z); 52*f3087befSAndrew Turner } 53*f3087befSAndrew Turner else 54*f3087befSAndrew Turner { 55*f3087befSAndrew Turner /* For x < 1, approximate atan(x) directly. */ 56*f3087befSAndrew Turner z = x; 57*f3087befSAndrew Turner az = asfloat (ia); 58*f3087befSAndrew Turner shift = 0; 59*f3087befSAndrew Turner } 60*f3087befSAndrew Turner 61*f3087befSAndrew Turner /* Calculate polynomial, shift + z + z^3 * P(z^2). */ 62*f3087befSAndrew Turner float y = eval_poly (z, az, shift); 63*f3087befSAndrew Turner /* Copy sign. */ 64*f3087befSAndrew Turner return asfloat (asuint (y) ^ sign); 65*f3087befSAndrew Turner } 66*f3087befSAndrew Turner 67*f3087befSAndrew Turner TEST_SIG (S, F, 1, atan, -10.0, 10.0) 68*f3087befSAndrew Turner TEST_ULP (atanf, 2.38) 69*f3087befSAndrew Turner TEST_SYM_INTERVAL (atanf, 0, 0x1p-30, 5000) 70*f3087befSAndrew Turner TEST_SYM_INTERVAL (atanf, 0x1p-30, 1, 40000) 71*f3087befSAndrew Turner TEST_SYM_INTERVAL (atanf, 1, 0x1p30, 40000) 72*f3087befSAndrew Turner TEST_SYM_INTERVAL (atanf, 0x1p30, inf, 1000) 73