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| 1 | +/** |
| 2 | +* @license Apache-2.0 |
| 3 | +* |
| 4 | +* Copyright (c) 2024 The Stdlib Authors. |
| 5 | +* |
| 6 | +* Licensed under the Apache License, Version 2.0 (the "License"); |
| 7 | +* you may not use this file except in compliance with the License. |
| 8 | +* You may obtain a copy of the License at |
| 9 | +* |
| 10 | +* http://www.apache.org/licenses/LICENSE-2.0 |
| 11 | +* |
| 12 | +* Unless required by applicable law or agreed to in writing, software |
| 13 | +* distributed under the License is distributed on an "AS IS" BASIS, |
| 14 | +* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 15 | +* See the License for the specific language governing permissions and |
| 16 | +* limitations under the License. |
| 17 | +* |
| 18 | +* |
| 19 | +* ## Notice |
| 20 | +* |
| 21 | +* The original C code, long comment, copyright, license, and constants are from [Cephes]{@link http://www.netlib.org/cephes}. The implementation follows the original, but has been modified according to project conventions. |
| 22 | +* |
| 23 | +* ```text |
| 24 | +* Copyright 1984, 1995, 2000 by Stephen L. Moshier |
| 25 | +* |
| 26 | +* Some software in this archive may be from the book _Methods and Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster International, 1989) or from the Cephes Mathematical Library, a commercial product. In either event, it is copyrighted by the author. What you see here may be used freely but it comes with no support or guarantee. |
| 27 | +* |
| 28 | +* Stephen L. Moshier |
| 29 | + |
| 30 | +* ``` |
| 31 | +*/ |
| 32 | + |
| 33 | +#include "stdlib/math/base/assert/is_infinite.h" |
| 34 | +#include "stdlib/math/base/special/copysign.h" |
| 35 | +#include "stdlib/number/float64/base/signbit.h" |
| 36 | +#include "stdlib/math/base/assert/is_nanf.h" |
| 37 | +#include "stdlib/math/base/special/atan2.h" |
| 38 | +#include "stdlib/constants/float64/pinf.h" |
| 39 | +#include "stdlib/constants/float64/pi.h" |
| 40 | +#include <stdint.h> |
| 41 | + |
| 42 | +// MAIN // |
| 43 | + |
| 44 | +/** |
| 45 | +* Computes the angle in the plane (in radians) between the positive x-axis and the ray from `(0,0)` to the point `(x,y)`. |
| 46 | +* |
| 47 | +* @param y `y` coordinate |
| 48 | +* @param x `x` coordinate |
| 49 | +* @return angle (in radians) |
| 50 | +* |
| 51 | +* @example |
| 52 | +* float v = stdlib_base_atan2f( 2.0, 2.0 ); // => stdlib_base_atanf(1.0f) |
| 53 | +* // returns ~0.785f |
| 54 | +* |
| 55 | +* @example |
| 56 | +* float v = stdlib_base_atan2f( 6.0, 2.0 ); // => stdlib_base_atanf(3.0f) |
| 57 | +* // returns ~1.249f |
| 58 | +* |
| 59 | +* @example |
| 60 | +* float v = stdlib_base_atan2f( -1.0, -1.0f ); // => stdlib_base_atanf(1.0f) - π |
| 61 | +* // returns ~-2.356f |
| 62 | +* |
| 63 | +* @example |
| 64 | +* float v = stdlib_base_atan2f( 3.0f, 0.0f ); // => π/2 |
| 65 | +* // returns ~1.571ff |
| 66 | +* @example |
| 67 | +* float v = stdlib_base_atan2f( -2.0f, 0.0f ); // => -π/2 |
| 68 | +* // returns ~-1.571f |
| 69 | +* |
| 70 | +* @example |
| 71 | +* float v = stdlib_base_atan2f( 0.0f, 0.0f ); |
| 72 | +* // returns 0.0f |
| 73 | +* |
| 74 | +* @example |
| 75 | +* float v = stdlib_base_atan2f( 3.0f, NaN ); |
| 76 | +* // returns NaN |
| 77 | +* |
| 78 | +* @example |
| 79 | +* float v = stdlib_base_atan2f( NaN, 2.0f ); |
| 80 | +* // returns NaN |
| 81 | +*/ |
| 82 | +float stdlib_base_atan2f( const float y, const float x ) { |
| 83 | + float q; |
| 84 | + if ( stdlib_base_is_nanf( x ) || stdlib_base_is_nanf( y ) ) { |
| 85 | + return 0.0f / 0.0f; // float |
| 86 | + } |
| 87 | + if ( stdlib_base_is_infinite( x ) ) { |
| 88 | + if ( x == STDLIB_CONSTANT_FLOAT64_PINF ) { |
| 89 | + if ( stdlib_base_is_infinite( y ) ) { |
| 90 | + return stdlib_base_copysign( STDLIB_CONSTANT_FLOAT64_PI / 4.0f, y ); |
| 91 | + } |
| 92 | + return stdlib_base_copysign( 0.0f, y ); |
| 93 | + } |
| 94 | + // Case: x is -Infinity |
| 95 | + if ( stdlib_base_is_infinite( y ) ) { |
| 96 | + return stdlib_base_copysign( 3.0f * STDLIB_CONSTANT_FLOAT64_PI / 4.0f, y ); |
| 97 | + } |
| 98 | + return stdlib_base_copysign( STDLIB_CONSTANT_FLOAT64_PI, y ); |
| 99 | + } |
| 100 | + if ( stdlib_base_is_infinite( y ) ) { |
| 101 | + return stdlib_base_copysign( STDLIB_CONSTANT_FLOAT64_PI / 2.0f, y ); |
| 102 | + } |
| 103 | + if ( y == 0.0f ) { |
| 104 | + if ( x >= 0.0f && !stdlib_base_float64_signbit( x ) ) { |
| 105 | + return stdlib_base_copysign( 0.0, y ); |
| 106 | + } |
| 107 | + return stdlib_base_copysign( STDLIB_CONSTANT_FLOAT64_PI, y ); |
| 108 | + } |
| 109 | + if ( x == 0.0f ) { |
| 110 | + return stdlib_base_copysign( STDLIB_CONSTANT_FLOAT64_PI / 2.0f, y ); |
| 111 | + } |
| 112 | + q = stdlib_base_atan2( y / x ); |
| 113 | + if ( x < 0.0f ) { |
| 114 | + if ( q <= 0.0f ) { |
| 115 | + return q + STDLIB_CONSTANT_FLOAT64_PI; |
| 116 | + } |
| 117 | + return q - STDLIB_CONSTANT_FLOAT64_PI; |
| 118 | + } |
| 119 | + return q; |
| 120 | +} |
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